uČn i naČrt p redmeta course syllabus - um.si progami... · d. b. west, introduction to graph...
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Predme
Course
ŠtudijStudy
Ma
Mat
Vrsta pr
Univerz
PredavLectu
60
Nosilec
Jeziki / Languag
Pogoji zštudijsk
Poznava
Vsebina
Algebra
uporabe
število
indeks;
diskretn
neenako
prostor
lastnih v
et:
title:
jski programy programm
atematika, 2
thematics, 2
redmeta / C
zitetna koda
vanja ures
SeSe
0
predmeta
ges:
za vključitevkih obvezno
anje teorije
a:
aična komb
e rodovnih
particij n
teorija P
ni matema
ost; pokritj
i ciklov, kr
vrednosti).
UČN
Diskretna m
Discrete Ma
m in stopnjme and leve
2. stopnja
2nd degree
Course type
a predmeta
eminar eminar
15
/ Lecturer:
Pred
Vaje /
v v delo oz.osti:
grafov.
inatorika: r
funkcij (Ca
naravnega
Polya; line
atiki (načr
ja s polnim
roženja in
NI NAČRT P
matematika
athematics
a el
e
a / Universi
Vaje Tutorial
30
Boštjan
davanja / Lectures:
S
Tutorial: S
za opravlja
rodovne fu
atalanova š
števila); c
earna alge
ti in Fish
mi dvodelni
prerezi; up
PREDMETA /
2
2
ŠtudijskaStudy
ty course c
Kliničnewor
n Brešar
SLOVENSKO
SLOVENSKO
anje Pr
Kn
Co
unkcije;
števila,
ciklični
bra v
herjeva
i grafi;
porabe
Al
ap
nu
in
m
co
sp
ei
/ COURSE S
a smer field
ode:
e vajek
Drugšt
O/SLOVENE
O/SLOVENE
rerequisits:
nowledge o
ontent (Syll
lgebraic co
pplications
umbers, pa
ndex; Polya
mathematics
overings wit
pace, circu
genvalues)
SYLLABUS
LAc
ge oblike tudija
S
of graph the
labus outlin
mbinatorics
of genera
rtitions of a
theory; lin
s (designs
th complet
lations and
.
Letnik cademic year
1.
1.
Samost. deloIndivid. work
195
eory.
ne):
s; generati
ating functi
a positive in
near algebr
and Fisher
e bipartite
d cuts; ap
SemesterSemester
2.
2.
o ECTS
10
ng function
ions (Catal
nteger); cyc
ra in discre
r's inequalit
graphs; cyc
pplications
r r
ns;
an
clic
ete
ty;
cle
of
Kode za popravljanje napak: osnovni pojmi;
linearne kode; konstrukcije linearnih kod;
popravljanje napak; ciklične kode; klasifikacija
cikličnih kod.
Teorija grafov: dodatna poglavja iz barvanja
grafov (dokaz Brooksovega izreka, kritični grafi,
krožna barvanja); k‐povezani grafi (dokaz
Mengerjevega izreka); omrežja in pretoki v
omrežjih; dokaz izreka Kuratowskega;
neodvisne in dominirajoče množice.
Kombinatorika delno urejenih množic: linearne
razširitve; dimenzija delne urejenosti;
Dilworthov izrek; Spernerjev izrek. Schnyderjev
izrek.
Ramseyeva teorija: število monokromatičnih trikotnikov; Ramseyev izrek; Ramseyeva števila; uporabe izreka, grafovska Ramseyeva števila.
Error‐correcting codes: basic concepts; linear
codes; constructions of linear codes; correcting
errors; cyclic codes; classification of cyclic
codes.
Graph theory: additional graph coloring topics
(proof of Brooks theorem, critical graphs,
circular colorings); k‐connected graphs (proof of
Menger's theorem); networks and flows in
networks; proof of Kuratowski theorem;
independent and dominating sets.
Combinatorics of partially ordered sets: linear
extensions; dimension of a partial order;
Dilworth's theorem; Sperner's theorem.
Schnyder's theorem.
Ramsey theory: number of monochromatic triangles; Ramsey theorem; Ramsey numbers; applications of the theorem, graph Ramsey numbers.
Temeljni literatura in viri / Readings:
N. L. Biggs, Discrete Mathematics. Second Edition. The Clarendon Press, Oxford University Press,
New York, 1989.
M. Aigner, Discrete Mathematics, American Mathematical Society, Providence RI, 2007.
R. Diestel, Graph Theory, Springer‐Verlag, Berlin Heidelberg, 2005.
M. Juvan, P. Potočnik, Teorija grafov in kombinatorika, DMFA, Ljubljana, 2000.
J. H. van Lint, R. M. Wilson, A Course in Combinatorics, Cambridge University Press, Cambridge,
2001.
D. B. West, Introduction to Graph Theory, Second Edition. Prentice Hall, Inc., Upper Saddle River, NJ, 2001.
Cilji in kompetence:
Objectives and competences:
Poglobiti zahtevnejša področja sodobne
diskretne matematike in njene uporabe:
algebraično kombinatoriko, kode za
popravljanje napak, dodatna poglavja iz teorije
grafov, kombinatoriko delno urejenih množic,
metode linearne algebre v diskretni
matematiki in Ramseyevo teorijo.
To deepen the knowledge of more demanding areas of temporary discrete mathematics and its applications: algebraic combinatorics, error‐correcting codes, additional topics from graph theory, combinatorics of partially ordered sets, tools from linear algebra in discrete mathematics, and Ramsey theory.
Predvideni študijski rezultati: Intended learning outcomes:
Znanje in razumevanje:
Razumevanje zahtevnejših principov diskretne matematike.
Poglobiti netrivialne uporabe diskretne matematike.
Povezati diskretno matematiko z drugimi matematičnimi področji.
Prenosljive/ključne spretnosti in drugi atributi:Prenos zahtevnejšega znanja metod diskretne matematike na druga področja (računalništvo, kemija, biologija, optimizacija, ...)
Knowledge and Understanding:
Be able to understand more demanding principals of discrete mathematics.
To deepen the knowledge of nontrivial applications of discrete mathematics.
To connect discrete mathematics with other fields of mathematics.
Transferable/Key Skills and other attributes: Knowledge transfer of more demanding methods of discrete mathematics into other fields (computer science, chemistry, biology, optimization, …)
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje, naloge, projekt)
‐ Seminarska naloga ‐ Pisni testi ‐ Ustni izpit
Vsaka izmed naštetih obveznosti mora biti opravljena s pozitivno oceno. Pozitivna ocena pri seminarski nalogi in pisnih testih sta pogoja za pristop k ustnemu izpitu.
Delež (v %) / Weight (in %)
25% 25% 50%
Type (examination, oral, coursework, project):
‐ Seminar exercise ‐ Written tests ‐ Oral exam
Each of the mentioned commitments must be assessed with a passing grade. Passing grade of the seminar and of written tests are required for taking the oral exam.
Reference nosilca / Lecturer's references: 1. BREŠAR, Boštjan, KRANER ŠUMENJAK, Tadeja. The hypergraph of [Theta]-classes and
[Theta]-graphs of partial cubes. Ars combinatoria, ISSN 0381-7032, 2014, vol. 113, str. 225-239. [COBISS.SI-ID 16824153]
2. BREŠAR, Boštjan, CHALOPIN, Jérémie, CHEPOI, Victor, GOLOGRANC, Tanja, OSAJDA, Damian. Bucolic complexes. Advances in mathematics, ISSN 0001-8708, 2013, vol. 243, str. 127-167. http://dx.doi.org/10.1016/j.aim.2013.04.009. [COBISS.SI-ID 16633177]
3. BREŠAR, Boštjan, KLAVŽAR, Sandi, KOŠMRLJ, Gašper, RALL, Douglas F. Domination game: extremal families of graphs for 3/5-conjectures. Discrete Applied Mathematics, ISSN 0166-218X. [Print ed.], 2013, vol. 161, iss. 10-11, str. 1308-1316. http://dx.doi.org/10.1016/j.dam.2013.01.025. [COBISS.SI-ID 16614745]
4. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel, TARANENKO, Andrej. On the vertex k-path cover. Discrete Applied Mathematics, ISSN 0166-218X. [Print ed.], 2013, vol. 161, iss. 13/14, str. 1943-1949. http://dx.doi.org/10.1016/j.dam.2013.02.024. [COBISS.SI-ID 19859464]
5. BREŠAR, Boštjan, KLAVŽAR, Sandi, RALL, Douglas F. Domination game played on trees and spanning subgraphs. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2013, vol. 313, iss. 8, str. 915-923. http://dx.doi.org/10.1016/j.disc.2013.01.014. [COBISS.SI-ID 16564313]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Fraktali in dinamični sistemi
Course title: Fractals and dynamic systems
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 15 15 135 7
Nosilec predmeta / Lecturer: Dušan PAGON
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Linearna algebra, Algebra, Analiza 2 Linear algebra, Algebra, Analysis 2
Vsebina:
Content (Syllabus outline):
Metričen prostor, različne vrste
podprostorov, prostor fraktalov.
Afine transformacije, skrčitve, sistemi
iterirajočih funkcij.
Osnove dinamičnih sistemov, dinamika
fraktalnih množic.
Teoretično in eksperimentalno
določanje dimenzije fraktala,
Hausdorff-Bezikovičeva dimenzija.
Juliajeve množice, primeri njihove
uporabe.
A metric space, different types of
subspaces, the space of fractals.
Affine transformations, contraction
mappings, systems of iterating functions.
Introduction to dynamical systems,
dynamics on fractal sets.
The theoretical and experimental
determination of the fractal dimension,
Hausdorff-Besicovitch dimension.
Julia sets, examples of their application.
Temeljni literatura in viri / Readings:
Barnsley, M. F.: Fractals Everywhere. Academic Press, Boston (1988); Second edition (1993)
Barnsley, M. F.: Superfractals. Cambridge University Press, Cambridge (2006)
Devaney, Robert: An Introduction To Chaotic Dynamical Systems, 2nd ed., Westview Press (2003)
Devaney. R. L.: Chaos, Fractals and Dynamics - Computer Experiments in Dynamics, Addison-
Wesley (1990)
Edgar, G: Classics on Fractals. Westview Press, Boulder (1992)
Falconer, K. J.: The Geometry of Fractal Sets. Cambridge University Press,
Cambridge (1985)
Lapidus, M. L., Frankenjuijsen, M. v.: Fractal Geometry, Complex Dimensions
and Zeta Functions. Springer, New York (2006)
Edgar, Gerald: Measure, Topology, and Fractal Geometry, 2nd ed., Springer, New York (2008)
Cilji in kompetence:
Objectives and competences:
Študenti se seznanijo s strukturo podprostora
fraktalov v metričnem prostoru in z osnovnimi
načini generiranja fraktalov (družine
iterirajočih preslikav). Spoznajo tudi različne
pristope k določanju dimenzije fraktala ter
dinamiko fraktalnih množic.
Students get familiar with the structure of the
subset of fractals in a metric space and with the
main ways of generating fractals (iterated
functions systems). They also study different
approaches to the fractal dimension and the
dynamics of fractal sets.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
- aktivno obvladanje strukture metričnega
prostora in prepoznavanje fraktalnih
podmnožic
- teoretično in eksperimentalno določanje
dimenzije fraktalov
- analiza dinamičnih sistemov in njihova
uporaba
Prenesljive/ključne spretnosti in drugi atributi:
- sposobnost generiranja fraktalov
- izračun dimenzije fraktalne množice
- modeliranje z dinamičnimi sistemi
-
Knowledge and Understanding:
- active knowledge of metric space structure
and the ability to recognize its fractal subsets
- theoretical and experimental ways for
finding the dimension of a fractal
- the analysis of dynamical systems and their
application
Transferable/Key Skills and other attributes:
- the abbility to generate fractals
- the calculation of fractal dimension
- modeling with dynamical systems
-
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Individualno delo
Lectures
Tutorial
Individual work
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Seminarska naloga
Pisni izpit– praktični del
Ustni izpit – teoretični del
Delež (v %) /
Weight (in %)
20%
40%
40%
Type (examination, oral, coursework,
project):
Seminar work
Written exam – practical part
Oral exam – theoretical part
Reference nosilca / Lecturer's
references:
1. PAGON, Dušan, REPOVŠ, Dušan, ZAICEV, Mikhail. On the codimension growth of simple
color Lie superalgebras. J. Lie theory, 2012, vol. 22, no. 2, str. 465-479.
http://www.heldermann.de/JLT/JLT22/JLT222/jlt22017.htm. [COBISS.SI-ID 16070233]
2. PAGON, Dušan. Simplified square equation in the quaternion algebra. International journal of
pure and applied mathematics, 2010, vol. 61, no. 2, str. 231-240. [COBISS.SI-ID 17718024]
3. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. On chains in H-closed topological pospaces.
Order (Dordr.), 2010, vol. 27, no. 1, str. 69-81. http://dx.doi.org/10.1007/s11083-010-9140-x.
[COBISS.SI-ID 15502169]
4. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. The continuity of the inversion and the
structure of maximal subgroups in countably compact topological semigroups. Acta math. Hung.,
2009, vol. 124, no. 3, str. 201-214. http://dx.doi.org/10.1007/s10474-009-8144-8, doi:
10.1007/s10474-009-8144-8. [COBISS.SI-ID 15212121]
5. PAGON, Dušan. The dynamics of selfsimilar sets generated by multibranching trees.
International journal of computational and numerical analysis and applications, 2004, vol. 6, no.
1, str. 65-76. [COBISS.SI-ID 14037081]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Integralske transformacije
Course title: Integral Transforms
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
30 15 30
135 7
Nosilec predmeta / Lecturer: Marko JAKOVAC
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje matematične analize. Knowledge of mathematical analysis.
Vsebina: Content (Syllabus outline):
Klasične Fouriereve vrste. Hilbertov prostor.
Ortonormiran sistem.
Fouriereva in Laplaceova tansformacija.
Osnovne lastnosti. Inverzna formula.
Uporaba Fouriereve in Laplaceove
transformacije.
Primeri drugih integralskih transformacij:
Dvostranska Laplaceova transformacija.
Hartleyjeva transformacija. Mellinova
Classical Fourier series. Hilbert space.
Orthonormal system.
Fourier and Laplace transform. Basic properties.
Inversion formula.
Applications of Fourier and Laplace transform.
Examples of other integral transforms: Two
sided Laplace transform. Hartley transform,
Mellin transform. Weierstrass transform. Abel
transform. Hilbert transform.
transformacija. Weierstrassova transformacija.
Abelova transformacija. Hilbertova
transformacija.
Temeljni literatura in viri / Readings:
E. Zakrajšek: Analiza III, DMFA Slovenije, Ljubljana, 1998
E. Zakrajšek: Analiza IV, DMFA Slovenije, Ljubljana, 1999
A. Suhadolc: Integralske transformacije, Integralske enačbe, DMFA Ljubljana, 1994.
A. Suhadolc: Metrični prostor, Hilbertov prostor, Fouriereva analiza, Laplaceova transformacija,
DMFA-založništvo, Ljubljana, 1998.
B. Zmazek: Diferencialna analiza, skripta, Maribor, 2006.
Gabrijel Tomšič, Tomaž Slivnik: Matematika IV, Založba FE in FRI, Ljubljana, 1998.
Cilji in kompetence:
Objectives and competences:
Temeljito spoznati integralske transformacije.
Poznati uporabo Fouriereve in Laplaceove
transformacije.
To know thoroughly integral transforms.
To know thoroughly about applications of
Fourier and Laplace transform.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
- Razumevanje in uporaba integralskih
transformacij.
Prenesljive/ključne spretnosti in drugi atributi:
- Identifikacija, formulacija in reševanje
matematičnih in nematematičnih problemov
s pomočjo integralskih transformacij.
- Prenos znanja v zvezi z integralskimi
transformacijami na druga področja
(strojništvo, astronomija, fizika in druge)
Knowledge and Understanding:
- Be able to understand and implement
integral transforms.
Transferable/Key Skills and other attributes:
- Identification, formulation and solving
mathematical and non mathematical
problems with integral transforms.
- Knowledge transfer of the concepts,
connected with integral transforms into
other fields (mechanical engineering,
astronomy, physics and others).
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Individualno delo
Seminarska naloga
Lectures
Tutorial
Individual work
Seminar
Načini ocenjevanja:
Assessment:
Sprotno preverjanje:
Seminarska naloga
Izpit:
Pisni izpit – problemi
Ustni izpit – teorija
Delež (v %) /
Weight (in %)
20%
40%
40%
Mid-term testing:
Seminary work
Exams:
Written exam – problems
Oral exam – theory
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljene sprotne obveznosti so pogoj
za pristop k pisnemu izpitu – problemi.
Opravljen pisni izpit – problemi je
pogoj za pristop k ustnemu izpitu –
teorija.
Each of the mentioned assessments must
be assessed with a passing grade.
Passing grades of all mid-term testings
are required for taking the written exam –
problems. Passing grade of written exam
– problems is required to take the oral
exam – theory.
Reference nosilca / Lecturer's
references:
1. JAKOVAC, Marko, TARANENKO, Andrej. On the k-path vertex cover of some graph
products. Discrete math.. [Print ed.], 2013, vol. 313, iss. 1, str. 94-
100. http://dx.doi.org/10.1016/j.disc.2012.09.010, doi:10.1016/j.disc.2012.09.010. [COBISS.SI-
ID 19464968]
2. JAKOVAC, Marko, PETERIN, Iztok. The b-chromatic index of a graph. Preprint series, 2012,
vol. 50, no. 1183, str. 1-20. http://www.imfm.si/preprinti/PDF/01183.pdf. [COBISS.SI-
ID 16517977]
3. JAKOVAC, Marko, PETERIN, Iztok. On the b-chromatic number of some graph products. Stud.
sci. math. Hung. (Print), 2012, vol. 49, no. 2, str. 156-
169. http://dx.doi.org/10.1556/SScMath.49.2012.2.1194. [COBISS.SI-ID 16321113]
4. CABELLO, Sergio, JAKOVAC, Marko. On the b-chromatic number of regular graphs. Discrete
appl. math.. [Print ed.], 2011, vol. 159, iss. 13, str. 1303-
1310. http://dx.doi.org/10.1016/j.dam.2011.04.028, doi:10.1016/j.dam.2011.04.028. [COBISS.SI-
ID 15914329]
5. JAKOVAC, Marko, KLAVŽAR, Sandi. The b-chromatic number of cubic graphs. Graphs
comb., 2010, vol. 26, no. 1, str. 107-118. http://dx.doi.org/10.1007/s00373-010-0898-9.
[COBISS.SI-ID 15522905]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Izbrana poglavja iz topologije
Course title: Selected topics from Topology
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30
135 7
Nosilec predmeta / Lecturer: Iztok BANIČ
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje splošne topologije. Knowledge of general topology.
Vsebina: Content (Syllabus outline):
Vsebina predmeta se prilagaja aktualnim
potrebam in razvoju.
1. Poglavja iz splošne topologije:
- Evklidski prostor. Evklidska topologija.
- Uryshnonova lema. Tietzejev
razširitveni izrek.
- Mnogoterost. Notranja točka. Robna
točka. Notranjost. Rob mnogoterosti.
Sklenjena mnogoterost.
- Kompaktne mnogoterosti. Povezane
The contents of this subject is adjusted to the
current needs and development.
1. Topics from general topology:
- Euclidean space. Euclidean topology.
- Urysohn lemma. Tietze extension
theorem.
- Manifold. Internal point. Boundary
point. Interior. Boundary of a manifold.
Closed manifold.
- Compact manifold. Connected manifold.
mnogoterosti.
- Osnovne lastnosti mnogoterosti.
Konstrukcije.
- Klasifikacija sklenjenih 2-mnogoterosti.
2. Poglavja iz teorije kontinuumov
- Kontinuumi. Zgledi kontinuumov.
Vgnezdeni preseki. Verige.
- Osnovne lastnosti.
- Kompozanti.
- Posebni primeri kontinuumov.
Knasterjev kontinuum, psevdolok,
pahljače, grafi.
- Hiperprostori. Konvergenca množic.
- Inverzna zaporedja. Inverzne limite.
- Basic properties of manifolds.
Constructons.
- Classification of closed 2-manifolds.
2. Topics from continuum theory
- Continua. Examples of continua. Nested
intersections. Chains.
- Basic properties
- Composants.
- Special examples. Knaster continuum,
pseudoarc, fans, graphs.
- Hyperspaces. Convergence of sets.
- Inverse sequences. Inverse limits.
Temeljni literatura in viri / Readings:
J.R.Munkres: Topology: a first course,Englewood Cliffs, NJ, Prentice-Hall, 1975
E.H.Spanier: Algebraic topology, New York (etc.), McGraw-Hill, 1966
S.Lipschutz: Schaum's outline of theory and problems of general topology, New York (etc.),
McGraw-Hill,
1965
P.Pavešić, A.Vavpetič: Rešene naloge iz topologije, Ljubljana, Društvo matematikov, fizikov in
astronomov
Slovenije, 1997
M.Cencelj, D.Repovš: Topologija, Ljubljana, Pedagoška fakulteta, 2001
J. Mrčun: Topologija. Izbrana poglavja iz matematike in računalništva 44, Društvo matematikov,
fizikov in astronomov - založništvo, Ljubljana, 2008
S .B. Nadler: Continuum theory: an introduction, Marcel Dekker, New York, 1992
A. Illanes, S. B. Nadler: Hyperspaces. Fundamentals and recent advances, Marcel Dekker, Inc.,
New York, 1999
J. Vrabec: Metrični prostori. Ljubljana: DMFA, 1993.
Cilji in kompetence:
Objectives and competences:
Temeljito spoznati klasične izreke evklidskih
prostorov.
Temeljito spoznati topološke mnogoterosti,
njihove lastnosti in konstrukcije.
To know thoroughly classical theorems of
Euclidean spaces.
To know thoroughly topological manifolds, their
properties and constructions.
Temeljito spoznati kontinuume in njihove
lastnosti.
Temeljito spoznati inverzna zaporedja in
inverzne limite kontinuumov.
To know thoroughly about continua and their
properties.
To know thoroughly about inverse sequences
and inverse limits of continua.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Študent razume in zna uporabiti klasične izreke
evklidskih prostorov.
Študent obvlada osnovne koncepte topoloških
mnogoterosti. Zaveda se pomena odprtih
množic v mnogoterosti in njihovih lastnosti.
Razumevanje in uporaba osnovnih lastnosti
kontinuumov.
Razumevanje in uporaba konstrukcijskih metod
za konstrukcijo novih primerov kontinuumov.
Prenesljive/ključne spretnosti in drugi atributi:
Prenos znanja obravnavanih metod na
druga področja, predvsem na področja
analize, kompleksne analize, teorije grafov,
geometrije in topologije.
Knowledge and Understanding:
To understand basic concepts of classical
theorems of Euclidean spaces and know their
applications.
To understand basic concepts of topological
manifolds. To be aware of the importance of
open sets in manifolds and their properties.
Be able to understand and implement basic
properties of continua.
Be able to understand and implement
construction methods for constructions of new
examples of continua.
Transferable/Key Skills and other attributes:
Knowledge transfer of treated methods into
other fields, to analysis, complex analysis,
graph theory, geometry and topology.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Individualno delo
Lectures
Tutorial
Individual work
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Izpit:
Pisni izpit – problemi
Ustni izpit – teorija
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
50% 50%
Type (examination, oral, coursework,
project):
Exam:
Written exam – problems
Oral exam – theory
Each of the mentioned assessments
must be assessed with a passing grade.
Opravljen pisni izpit – problemi je pogoj
za pristop k ustnemu izpitu – teorija.
Pisni izpit – problemi se lahko nadomesti z enim testom (sprotne obveznosti).
Passing grade of written exam –
problems is required to take the oral
exam – theory.
Written exam – problems can be repalced with one mid-term test.
Reference nosilca / Lecturer's
references:
1. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš, SOVIČ, Tina.
Ważewski's universal dendrite as an inverse limit with one set-valued bonding function. Preprint
series, 2012, vol. 50, št. 1169, str. 1-33. http://www.imfm.si/preprinti/PDF/01169.pdf.
[COBISS.SI-ID 16194137]
2. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Paths through
inverse limits. Topol. appl.. [Print ed.], 2011, vol. 158, iss. 9, str. 1099-1112.
http://dx.doi.org/10.1016/j.topol.2011.03.001. [COBISS.SI-ID 18474504]
3. BANIČ, Iztok, ŽEROVNIK, Janez. Wide diameter of Cartesian graph bundles. Discrete math..
[Print ed.], str. 1697-1701. http://dx.doi.org/10.1016/j.disc.2009.11.024, doi:
10.1016/j.disc.2009.11.024. [COBISS.SI-ID 17543176]
tipologija 1.08 -> 1.01
4. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Limits of
inverse limits. Topol. appl.. [Print ed.], 2010, vol. 157, iss. 2, str. 439-450.
http://dx.doi.org/10.1016/j.topol.2009.10.002. [COBISS.SI-ID 15310169]
5. BANIČ, Iztok, ERVEŠ, Rija, ŽEROVNIK, Janez. Edge, vertex and mixed fault diameters. Adv.
appl. math., 2009, vol. 43, iss. 3, str. 231-238. http://dx.doi.org/10.1016/j.aam.2009.01.005, doi:
10.1016/j.aam.2009.01.005. [COBISS.SI-ID 13396502]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Aktuarska matematika
Course title: Actuarial mathematics
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja
1. ali 2. 2. ali 4.
Mathematics, 2nd
degree
1. or 2. 2. ali 4.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
60
45
195 10
Nosilec predmeta / Lecturer: Marko JAKOVAC
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
1. Matematične podlage
2.Verjetnostni modeli življenja
3.Kapitalska zavarovanja
4.Rekurzijske formule
5.Neto premije, komutacijske funkcije
6.Neto premijske rezerve
7.Tehnični dobiček
8.Stroški in bruto premije
9.Matematična bruto rezerva
10. Modeli izločanja
11. Zavarovanje na več življenj
12. Analiza portfelja
1. Mathematical basis
2. Probability models
3. General life insurance
4. Recursion formulae
5. Net premiums, commutational functions
6. Net premium reserves
7. Technical gain
8. Expense loadings
9. Premium reserves
10. Multiple decrements
11. Multiple life insurance
12. Portfolio analysis
13. Pozavarovanje
14. Specifična zavarovanja
13. Reinsurance
14. Specific insurances
Temeljni literatura in viri / Readings:
1. Gerber H.U..1996. Matematika življenskih zavarovanj. DMFA Ljubljana, Zavarovalnica
Triglav.
2. Bowers N.L., Gerber H.U., Hickman J.C., Jones D.A., Nesbitt C.J:. 1986. Actuarial
Mathematics. Itasca, USA..
3. Gerber H.U..1996. Life Insurance Mathematics. Springer. Berlin, New York.
Cilji in kompetence:
Objectives and competences:
Namen predmeta je posredovati temeljna
teoretična in praktična znanja potrebna pri
kvantitativnem in kvalitativnem obravnavanju
nalog in procesov s področja aktuarske
matematike in zavarovalniškega poslovanja.
Prav tako je namen predmeta dati osnovo za
spremljanje sodobne literature in nadaljnje
strokovno izpopolnjevanje.
The objective is to provide fundamental
theoretical knowledge and practical skills
of actuarial mathematics and insurance
business.
The objective is also to enable the students
for additional learning and individual study of
new methods.
Predvideni študijski rezultati:
Intended learning outcomes:
Poglobljeno znanje in razumevanje temeljnih
vsebin in orodij potrebnih za strokovno
korektno vodenje poslov s področja
aktuarskega dela.
Prenesljive/ključne spretnosti in drugi atributi:
Sposobnost samostojnega praktičnega in
teoretičnega dela. Zmožnost nadaljnega študija.
Knowledge and Understanding:
Fundamental theoretical knowledge and
practical skills of actuarial work.
Transferable/Key Skills and other attributes:
Capabilitiy of understanding and application of
knowledge in praxis. Ability of additional
learning and individual study of new methods.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja, tehnične demonstracije,
aktivne vaje, seminarske vaje
Lectures, technical demonstration,
active work, tutorial
Načini ocenjevanja:
Assessment:
Sprotno preverjanje:
Seminarska naloga
Izpit:
Pisni izpit – problemi
Pisni izpit – teorija
Delež (v %) /
Weight (in %)
20%
40%
40%
Mid-term testing:
Seminary work
Exams:
Written exam – problems
Written exam – theory
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljene sprotne obveznosti so pogoj
za pristop k pisnemu izpitu – problemi.
Opravljen pisni izpit – problemi je
pogoj za pristop k pisnemu izpitu –
teorija.
Pisni izpit – problemi se lahko
nadomesti z dvema delnima testoma
(sprotne obveznosti).
Each of the mentioned assessments must
be assessed with a passing grade.
Passing grades of all mid-term testings
are required for taking the written exam –
problems. Passing grade of written exam
– problems is required to take the written
exam – theory.
Written exam – problems can be replaced
with two mid-term tests.
Reference nosilca / Lecturer's
references:
1. JAKOVAC, Marko. The k-path vertex cover of rooted product graphs. Discrete applied
mathematics, ISSN 0166-218X. [Print ed.], 2015, vol. 187, str. 111-119, doi:
10.1016/j.dam.2015.02.018. [COBISS.SI-ID 21355272]
2. JAKOVAC, Marko. A 2-parametric generalization of Sierpiński gasket graphs. Ars
combinatoria, ISSN 0381-7032, 2014, vol. 116, str. 395-405. [COBISS.SI-ID 17053529]
3. YERO, Ismael G., JAKOVAC, Marko, KUZIAK, Dorota, TARANENKO, Andrej. The partition
dimension of strong product graphs and Cartesian product graphs. Discrete Mathematics, ISSN
0012-365X. [Print ed.], 2014, vol. 331, str. 43-52. http://dx.doi.org/10.1016/j.disc.2014.04.026.
[COBISS.SI-ID 20548104]
4. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel,
TARANENKO, Andrej. On the vertex k-path cover. Discrete applied mathematics, ISSN 0166-
218X. [Print ed.], 2013, vol. 161, iss. 13/14, str. 1943-1949.
http://dx.doi.org/10.1016/j.dam.2013.02.024. [COBISS.SI-ID 19859464]
5. JAKOVAC, Marko, TARANENKO, Andrej. On the k-path vertex cover of some graph
products. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2013, vol. 313, iss. 1, str. 94-100.
http://dx.doi.org/10.1016/j.disc.2012.09.010, doi: 10.1016/j.disc.2012.09.010. [COBISS.SI-ID
19464968]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Numerična analiza
Course title: Numerical Analysis
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja
1. ali 2. 2. ali 4.
Mathematics, 2nd
degree
1. or 2. 2. ali 4.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
60
30 15 195 10
Nosilec predmeta / Lecturer: Valerij ROMANOVSKIJ
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje matematične analize. Knowledge of mathematical analysis.
Vsebina: Content (Syllabus outline):
1. Analize numeričnega računanja.
2. Reševanje nelinearnih enačb: Reševanje
sistemov nelinearnih enačb.
3. Diferenčne operatorji in diferenčne enačbe.
4. Sistemi linearnih enačb. Iterativne metode.
5. Problem lastnih vrednosti: Schurov in
Gershgorinov izrek. Simetrični in
nesimetrični problem lastnih vrednosti.
6. Navadne diferencialne enačbe: Lastnosti
rešitev in stabilnost rešitev. Picardova
1. Analysis of numerical computing.
2. Nonlinear equations solving: Systems of
nonlinear equations.
3. Difference equations and difference
operators.
4. Systems of linear equations. Iterative
methods.
5. Eigenvalues computation problem: Schur's
and Gershgorin's theorems. Symmetric and
non-symmetric eigenvalue problem.
metoda. Metode Runge-Kutta. Večkoračne
metode. Robni problem. Sistemi
diferencialnih enačb.
7. Numerično odvajanje:Richardsonova
ekstrapolacija.
8. Polinomske sistemi: Groebnerjeva baza.
Raznoterost polinomskega ideala in njene
lastnosti. Razcep raznoterosti.
9. Parcialne diferencialne enačbe.
6. Ordinary differential equations: Properties
of solutions and stability of solutions.
Runge-Kutta methods. Multi-step methods.
Boundary-value problems. Systems of
differential equations.
7. Numeric derivation: Richardson's
extrapolation.
8. Polynomial systems: Groebner basis, Variety
of polynomial ideal and its properties.
Decomposition of varieties. Modular
methods.
9. Partial differential equations.
Temeljni literatura in viri / Readings:
Z. Bohte, Numerično reševanje nelinearnih enačb, DMFA Slovenije, Ljubljana, 1993.
Z. Bohte, Numerično reševanje sistemov linearnih enačb, DMFA Slovenije, Ljubljana, 1994.
D. Kincaid, W. Cheney: Numerical Analysis, Brooks/Cole, Pacific Grove, 1996.
E. Zakrajšek, Uvod v numerične metode, druga izdaja, DMFA Slovenije, Ljubljana, 2000.
V. G. Romanovski and Douglas S. Shafer, The Center and Cyclicity Problems. A Computational
Algebra Approach, Boston-Basel-Berlin: Birkhauser, 2009.
G. Teschl, Ordinary Differential Equations and Dynamical Systems. Providence: American
Mathematical Society, 2012.
Cilji in kompetence:
Objectives and competences:
Poglobiti znanje iz zahtevnejših konceptov in
rezultatov s področja numerične analize –
simbolnega računanja in numeričnih metod.
To deepen the knowledge of more demanding
concepts and results from numerical analysis –
symbolic mathematics and numerical methods.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Poglobiti znanje iz zahtevnejših
numeričnih metode in njihovih
uporabnih vrednosti.
Prepoznati praktične probleme in
njihovo modeliranje z orodji numerične
matematike.
Prenesljive/ključne spretnosti in drugi atributi:
Prenos znanja numeričnih metod na
druga področja (računalništvo,
statistika, optimizacija, ...)
Knowledge and Understanding:
To deepen the knowledge of more
demanding numerical methods and their
applications.
To recognize practical problems and
their modeling with numerical
mathematics tools.
Transferable/Key Skills and other attributes:
Knowledge transfer of numerical
methods into other fields (computer
science, statistics, optimization, …)
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja Lectures
Seminarske vaje
Izdelava seminarske naloge
Tutorial
Seminar (project) work
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Opravljena seminarska naloga
Pisni izpit – problemi
Pisni izpit – teoretija
Pisni izpit - problemi se lahko
nadomesti z dvema delnima testoma
(sprotni obveznosti)
Pisni izpit - teorja se lahko nadomesti z
dvema delnima testoma (sprotni
obveznosti)
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Delež (v %) /
Weight (in %)
10%
50%
40%
Type (examination, oral, coursework,
project):
Completed seminar (project)
work
Written exam – problems
Written exam – theory
Written exam – problems can be replaced
by two parital tests (mid-term testing)
Written exam – theory can be replaced
by two parital tests (mid-term testing)
Each of the mentioned commitments
must be assessed with a passing grade.
Reference nosilca / Lecturer's
references:
1. ROMANOVSKI, Valery, SHAFER, Douglas. The center and cyclicity problems : a
computational algebra approach. Basel: Birkhäuser, 2009. XV; 330 str. ISBN 978-0-8176-4726-1.
[COBISS.SI-ID 62709761]
2. ROMANOVSKI, Valery, PREŠERN, Mateja. An approach to solving systems of polynomials
via modular arithmetics with applications. Journal of Computational and Applied Mathematics,
ISSN 0377-0427. [Print ed.], 2011, vol. 236, iss. 2, str. 196-208. doi: 10.1016/j.cam.2011.06.018.
[COBISS.SI-ID 18552584]
3. PAUSCH, Marina, GROSSMANN, Florian, ECKHARDT, Bruno, ROMANOVSKI, Valery.
Groebner basis methods for stationary solutions of a low-dimensional model for a shear flow.
Journal of nonlinear science, ISSN 0938-8974. [Print ed.], 2014, vol. 24, iss. 5, str. 935-948, doi:
10.1007/s00332-014-9208-7. [COBISS.SI-ID 20920584]
4. MAHDI, Adam, ROMANOVSKI, Valery, SHAFER, Douglas. Stability and periodic
oscillations in the Moon-Rand systems. Nonlinear analysis: real world applications, ISSN 1468-
1218, 2013, vol. 14, iss. 1, str. 294-313. [COBISS.SI-ID 19482120]
5. BOULIER, F., HAN, M., LEMAIRE, F., ROMANOVSKI,V. Qualitative investigation of a gene
model using computer algebra algorithms. Programming and computer software, ISSN 0361-7688,
2015, vol. 41, no. 2, str. 105-111, doi: 10.1134/S0361768815020048. [COBISS.SI-ID 21355784]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Teorija mere
Course title: Measure theory
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul F1 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module F1 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
60
45
165 9
Nosilec predmeta / Lecturer: Valerij Romanovskij
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Osnovni pojmi teorije mere: Algebra, σ-
algebra, Borelova σ-algebra na Rn. Mere in
osnovne lastnosti mer. Merljivi prostori.
Pozitivne mere. Zunanje mere.
Lebesqueova mera na Rn.
Funkcije in integrali: Merljive funkcije.
Stopničaste funkcije. Integral stopničaste
funkcije. Integral merljive funkcije. Izrek o
monotoni konvergenci. Fatoujeva lema in
Lebesqueov izrek o dominantni
konvergenci. Povezanost Riemannovega in
Lebesqueovega integrala.
Basic concepts of measure theory: Algebra,
σ-algebra, Borel σ-algebra on Rn. Measure
and its basic properties. Measurable spaces.
Positive measures. Outer measures.
Lebesque measure on Rn.
Functions and integrals: Measurable
functions. Simple measurable functions. The
integral of a simple measurable function.
The integral of a measurable function. The
monotone convergence theorem. Fatou’s
lemma and Lebesque’s dominated
convergence theorem. Relationships between
Konvergenca: Zaporedja merljivih funkcij
in konvergenca. Konvergenca skoraj
povsod. Norma in normirani Lp-prostori.
Neenakosti (Hölder, Minkowski). Dualni
prostori.
Predznačne in kompleksne mere:
Predznačne mere in Hahnov razcepni izrek.
Kompleksne mere in Radon-Nikodymov
izrek. Funkcije z omejeno varianco.
Produktne mere: Merjenje in integriranje po
produktnih prostorih (Fubinijev izrek).
Odvajanje: Odvodi mer. Odvodi funkcij.
Rieszov izrek o reprezentaciji pozitivnih
linearnih funkcionalov na C(X).
Lebesgue-Stieltjesov integral.
Riemann’s and Lebesque’s integral.
Convergence: Sequences of measurable
functions and convergence. Convergence
almost everywhere. Norm and normed Lp-
spaces. Inequalities (Hölder, Minkowski).
Dual spaces.
Signed and complex measures: Signed
measures and the Hahn decomposition
theorem. Complex measures and the Radon-
Nikodym theorem. Functions of bounded
variation.
Product measures: Measures and integrals on
product spaces (Fubini’s theorem).
Differentiation: Differentiation of measures.
Differentiation of functions.
The Riesz representation theorem on
positive linear functionals on C(X).
Lebesgue-Stieltjes integral
Temeljni literatura in viri / Readings:
1. M. Capinski, E. Kopp: Measure, integral and probability, Springer-Verlag London, 2004.
2. D. L. Cohn: Measure theory, Birkhäuser, 1994.
3. R. Drnovšek: Rešene naloge iz teorije mere, DMFA, 2001.
4. M. Hladnik: Naloge in primeri iz funkcionalne analize in teorije mere, DMFA, 1985.
5. W. Rudin: Real and complex analysis, 3th edition, Mc-Graw-Hill, 1986.
6. H. Sohrab, Basic real analysis, Birkhauser Boston, 2003.
7. I. Vidav, Višja matematika II, DZS, Ljubljana, 1975.
Cilji in kompetence:
Objectives and competences:
Glavni cilj predmeta je proučiti temeljne
koncepte in rezultate teorije mere. The main goal of the course is to study the
fundamental concepts and results of measure
theory.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
merljivi prostori, merljive funkcije,
abstraktno integriranje, izreki o
konvergenci, Lp-prostori, produktne mere,
odvodi mer.
Prenesljive/ključne spretnosti in drugi atributi:
Poznavanje osnov teorije mere je
podlaga za študij različnih matematičnih
področij (funkcionalne analize,
verjetnosti, parcialnih diferencialnih
enačb itd.).
Knowledge and Understanding:
Measurable spaces, measurable functions,
abstract integration, convergence theorems,
Lp-spaces, product measures, differentiation
of measures.
Transferable/Key Skills and other attributes:
Knowing the fundamentals of measure
theory is a prerequisite for studying various
mathematical areas (functional analysis,
probability, partial differential equations
etc.).
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Teoretične vaje
Lectures
Theoretical exercises
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit – problemi
Pisni izpit – teoretija
Pisni izpit - problemi se lahko
nadomesti z dvema delnima testoma
(sprotni obveznosti)
Pisni izpit - teorja se lahko nadomesti z
dvema delnima testoma (sprotni
obveznosti)
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
Written exam – problems
Written exam – theory
Written exam – problems can be replaced
by two parital tests (mid-term testing)
Written exam – theory can be replaced
by two parital tests (mid-term testing)
Each of the mentioned commitments
must be assessed with a passing grade.
Reference nosilca / Lecturer's
references:
1. CHEN, Xingwu, GINÉ, Jaume, ROMANOVSKI, Valery, SHAFER, Douglas. The 1: -q resonant
center problem for certain cubic Lotka-Volterra systems. Appl. math. comput.. [Print ed.], Aug.
2012, vol. 218, iss. 32, str. 11620-11633. http://dx.doi.org/10.1016/j.amc.2012.05.045, doi:
10.1016/j.amc.2012.05.045. [COBISS.SI-ID 19321352]
2. BASOV, Vladimir V., ROMANOVSKI, Valery. Linearization of two-dimensional systems of
ODEs without conditions on small denominators. Appl. math. lett.. [Print ed.], 2012, vol. 25, iss. 2,
str. 99-103. http://dx.doi.org/10.1016/j.aml.2011.06.029, doi: 10.1016/j.aml.2011.06.029.
[COBISS.SI-ID 18675208]
3. LEVANDOVSKYY, Viktor, PFISTER, Gerhard, ROMANOVSKI, Valery. Evaluating cyclicity
of cubic systems with algorithms of computational algebra. Commun. pure appl. anal., 2012, vol.
11, no. 5, str. 2023-2035, doi: 10.3934/cpaa.2012.11.2023. [COBISS.SI-ID 19075080]
4. WENTAO, Huang, CHEN, Xingwu, ROMANOVSKI, Valery. Linear centers with perturbations
of degree 2d + 5. Int. j. bifurc. chaos appl. sci. eng., 2012, vol. 22, no. 1, str. [1250007-1 -
1250007-12]. http://www.ejournals.wspc.com.sg/ijbc/22/2201/S0218127412500071.html, doi:
10.1142/S0218127412500071. [COBISS.SI-ID 69213185]
5. HAN, Maoan, ROMANOVSKI, Valery. Isochronicity and normal forms of polynomial systems
of ODEs. J. symb. comput., Oct. 2012, vol. 47, iss. 10, str. 1163-1174.
http://dx.doi.org/10.1016/j.jsc.2011.12.039, doi: 10.1016/j.jsc.2011.12.039. [COBISS.SI-ID
19324168]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Kompleksna analiza
Course title: Complex Analysis
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul F2 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module F2 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30
135 7
Nosilec predmeta / Lecturer: Marko JAKOVAC
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje analize in kompleksnih števil. Knowledge of analysis and complex numbers.
Vsebina: Content (Syllabus outline):
Funkcije kompleksne spremenljivke.
Elementarne funkcije v kompleksnem: linearne
funkcije, ulomljene linearne funkcije. Potenčne
vrste v kompleksnem. Elementarne funkcije,
definirane s potenčnimi vrstami. Logaritem in
ciklometrične funkcije.
Holomorfne funkcije. Cauchy – Riemannov
izrek. Konformnost holomorfnih funkcij.
Integral funkcije kompleksne spremenljivke.
Cauchyjev izrek in Cauchyjeve formule.
Functions of complex variable. Elementary
functions: linear function, Möbius functions.
Power series. Elementary functions defined by
power series. Logarithm and cyclometric
functions.
Holomorphic functions. Cauchy – Riemann
theorem. Conformality of holomorphic
mappings.
Complex line integrals. Cauchy integral theorem
and Cauchy formula. Liouville theorem. Power
Liouvilleov izrek. Taylorjeva vrsta.
Laurentova vrsta. Klasifikacija izoliranih
singularnih točk. Mali Piccardov izrek. Izrek o
residuih. Uporaba pri računanju realnih
integralov.
Laplaceova in Fourierova transformacija.
Uporaba.
series representation.
Laurent series. Classification of isolated
singularity. Behaviour of holomorphic function
near isolated singularity. Little Piccard
Theorem. Residui theorem. Applications to the
calculations of definite integrals and sums.
Laplace and Fourier transforms. Applications.
Temeljni literatura in viri / Readings:
S. G. Krantz: Handbook of Complex Variables, Birkhäuser, Boston, 1999.
J.B.Conway: Functions of One Complex Variable I, 2nd edition, Springer, New York, 1995.
L. Ahlfors: Complex Analysis, 3rd edition, McGraw-Hill, New york, 1979.
Cilji in kompetence:
Objectives and competences:
Študent poglobi znanje iz osnov teorije funkcij
kompleksne spremenljivke ter poglobi znanje
iz uporabnih aspektov te teorije, predvsem v
povezavi s preslikovanji območij, pri računanju
določenih integralov, seštevanju vrst ter
reševanju diferencialnih enačb.
Deepening the knowledge of concepts from the
theory of functions of one complex variable. To
deepen the knowledge of possible applications
of this theory, specialy in connection with
transformations of the regions, calculating
definite integrals and sums and solving
differential equations.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Študent razume pojem holomorfne funkcije
pozna osnovne s tem povezane rezultate,
posebej tiste, ki se nanašajo na integracijo
in na integralsko reprezentacijo ter
reprezentacijo s potenčno vrsto.
Študent razume koncept preslikovanja
območij z uporabo ulomljenih linearnih in
drugih preprostejših elementarnih funkcij v
kompleksnem.
Študent razume pojem izolirane singularne
funkcije in pozna uporabno vrednost izreka
o residuumih.
Študent razume koncepta Laplaceove in
Fourierove transformacije in pozna njune
možnosti uporabe.
Prenesljive/ključne spretnosti in drugi atributi:
Ilustracija dejstva, da nam teorija, navidez
oddaljene od realnosti, lahko ponudi mnoge
praktično uporabne rezultate.
Dojemanje transformacij kot opcije za
pretvorbo matematične situacije v drugo
Knowledge and Understanding:
To understand the concept of holomorphic
function and to know the basic results,
specialy those about line integrals and about
the integral and the power series
representation of holomorphic functions.
To understend the concept of transforming
plane regions using Möbius transformations
and other basic elementary functions.
To understand the concept of isolated
singularity and to be aware of the
importance of the residui theorem.
To understand the concepts of Laplace and
Fourier tranformations and to be aware of
their possible applications.
Transferable/Key Skills and other attributes:
An illustration of the fact, that a more
abstract theory can give us many nice results
with useful practical applications.
Understanding the concept of
transformations as tools to convert a certain
situacijo, ki je udobnejša za obravnavo. mathematical situation into a more
convenient one.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Izpit:
Pisni izpit – problemi
Ustni izpit – teorija
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljen pisni izpit – problemi je
pogoj za pristop k ustnemu izpitu –
teorija.
Pisni izpit – problemi se lahko
nadomesti z dvema delnima testoma
(sprotne obveznosti).
Delež (v %) /
Weight (in %)
50%
50%
Exams:
Written exam – problems
Oral exam – theory
Each of the mentioned assessments must
be assessed with a passing grade.
Passing grade of written exam –
problems is required to take the oral
exam – theory.
Written exam – problems can be replaced
with two mid-term tests.
Reference nosilca / Lecturer's
references:
1. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel,
TARANENKO, Andrej. On the vertex k-path cover. Discrete Applied Mathematics, ISSN 0166-
218X. [Print ed.], 2013, vol. 161, iss. 13/14, str. 1943-1949.
http://dx.doi.org/10.1016/j.dam.2013.02.024. [COBISS.SI-ID 19859464]
2. JAKOVAC, Marko, TARANENKO, Andrej. On the k-path vertex cover of some graph
products. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2013, vol. 313, iss. 1, str. 94-100.
http://dx.doi.org/10.1016/j.disc.2012.09.010, doi: 10.1016/j.disc.2012.09.010. [COBISS.SI-ID
19464968]
3. JAKOVAC, Marko, PETERIN, Iztok. On the b-chromatic number of some graph products.
Studia scientiarum mathematicarum Hungarica, ISSN 0081-6906, 2012, vol. 49, no. 2, str. 156-
169. http://dx.doi.org/10.1556/SScMath.49.2012.2.1194. [COBISS.SI-ID 16321113]
4. CABELLO, Sergio, JAKOVAC, Marko. On the b-chromatic number of regular graphs. Discrete
Applied Mathematics, ISSN 0166-218X. [Print ed.], 2011, vol. 159, iss. 13, str. 1303-1310.
http://dx.doi.org/10.1016/j.dam.2011.04.028, doi: 10.1016/j.dam.2011.04.028. [COBISS.SI-ID
15914329]
5. JAKOVAC, Marko, KLAVŽAR, Sandi. The b-chromatic number of cubic graphs. Graphs and
combinatorics, ISSN 0911-0119, 2010, vol. 26, no. 1, str. 107-118.
http://dx.doi.org/10.1007/s00373-010-0898-9. [COBISS.SI-ID 15522905]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Algebrska topologija
Course title: Algebraic Topology
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Uroš MILUTINOVIĆ
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje algeberskih struktur in topologije. Knowledge of algebraic structures and
topology..
Vsebina: Content (Syllabus outline):
Kategorije in funktorji. Izomorfizmi.
Homotopija, homotopska kategorija topoloških
prostorov.
Funktor fundamentalne grupe. Krovni prostori.
Primeri uporabe.
Simplicialni kompleksi in poliedri. Funktor
simplicialne homologije. Eulerjeva
karakteristika, Bettijeva števila. Osnove
homološke algebre. Druge homološke teorije.
Categories and functors. Isomorphisms.
Homotopy, homotopy theory of topological
spaces.
The fundamental group functor. Covering
spaces. Examples.
Simplical complexes and polyhedra. The
simplical homology functor. Euler characteristic,
Betti numbers. Fundamentals of homological
algebra. Other homology theories.
Temeljni literatura in viri / Readings:
J.R.Munkres: Topology: a first course,Englewood Cliffs, NJ, Prentice-Hall, 1975
E.H.Spanier: Algebraic topology, New York (etc.), McGraw-Hill, 1966
M.Cencelj: Simplicialni kompleksi in simplicialna homologija, Ljubljana, Pedagoška fakulteta,
1996
Cilji in kompetence:
Objectives and competences:
Obvladati osnovne tehnike dela s funktorji
algebrske topologije. Students learn how to use the basic techniques
of work with algebraic topology functors.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Uporaba kategorij in funktorjev.
Sposobnost uporabe osnovnih tehnik
dela s konkretnimi funktorji algebrske
topologije.
Prenesljive/ključne spretnosti in drugi atributi:
Algebrska topologija je področje, ki
povezuje algebro in topologijo. Je
močan aparat, ki se ga da uporabiti pri
reševanju zelo različnih problemov.
Knowledge and Understanding:
The use of categories and functors.
Be able to use the basic techniques of
work with specific algebraic topology
functors.
Transferable/Key Skills and other attributes:
Algebraic topology connects algebra and
topology. It is a powerful apparatus that
can be used in solving of many different
problems
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja: Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Izpit:
Pisni izpit – problemi
Ustni izpit – teorija
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Pozitivna ocena pri pisnem izpitu -
problemi je pogoj za pristop k ustnemu
izpitu – teorija.
Pisni izpit – problemi se lahko
nadomesti z dvema delnima testoma (ki
sta sprotni obveznosti).
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
Exams:
Written exam – problems
Oral exam – theory
Each of the mentioned assessments must
be assessed with a passing grade.
Passing grade of the written exam –
problems is required for taking the oral
exam – theory.
Written exam – problems can be replaced
by two mid-term tests.
Reference nosilca / Lecturer's
references:
1. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš, SOVIČ, Tina.
Ważewski's universal dendrite as an inverse limit with one set-valued bonding function. Preprint
series, 2012, vol. 50, št. 1169, str. 1-33. http://www.imfm.si/preprinti/PDF/01169.pdf. [COBISS.SI-
ID 16194137]
2. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Paths through
inverse limits. Topol. appl.. [Print ed.], 2011, vol. 158, iss. 9, str. 1099-1112.
http://dx.doi.org/10.1016/j.topol.2011.03.001. [COBISS.SI-ID 18474504]
3. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Limits of
inverse limits. Topol. appl.. [Print ed.], 2010, vol. 157, iss. 2, str. 439-450.
http://dx.doi.org/10.1016/j.topol.2009.10.002. [COBISS.SI-ID 15310169]
4. KLAVŽAR, Sandi, MILUTINOVIĆ, Uroš, PETR, Ciril. Stern polynomials. Adv. appl. math.,
2007, vol. 39, iss. 1, str. 86-95. http://dx.doi.org/10.1016/j.aam.2006.01.003. [COBISS.SI-ID
14276441]
5. IVANŠIĆ, Ivan, MILUTINOVIĆ, Uroš. Closed embeddings into Lipscomb's universal space.
Glas. mat., 2007, vol. 42, no. 1, str. 95-108. [COBISS.SI-ID 14338393]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Analitični pristopi v geometriji
Course title: Analytical approaches in geometry
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja
1. ali 2. 1. ali 3.
Mathematics, 2nd
degree
1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30
135 7
Nosilec predmeta / Lecturer: Bojan HVALA
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Analitična geometrija v kartezičnih
koordinatah. Premice, stožnice. Uporaba v
konkretnih primerih v geometriji. Eulerjeve
stožnice.
Analitična geometrija v trilinearnih
koordinatah. Premice, stožnice. Projektivna
ravnina. Uporaba v konkretnih primerih v
geometriji. Eulerjeva premica, Kiepertova
hiperbola. Kubične krivulje trikotnika.
Kompleksna števila v geometriji. Potrebni
in zadostni pogoji za podobnost trikotnikov
z danimi oglišči. Pogoji za to, da so tri
Analytic geometry in Cartesian coordinates.
Lines, conics. Examples of use in geometry.
Euler's conics.
Analytical geometry in trilinear coordinates.
Lines, conics. Projective plane. Examples of
use in geometry. Euler line, Kieper
hyperbola. Cubics associated with a triangle.
Complex numbers in geometry. Necessary
and sufficient conditions for similarity of
triangles with given vertices. Conditions that
three given points are the vertices of an
equilateral triangle. Napoleon and
točke oglišča enakostraničnega trikotnika.
Napoleonov, Thebaultov izrek, Napoleon –
Barlottijev izrek. Kolinearnost in
koncikličnost. Ptolomejev izrek. Cliffordovi
izreki.
Thebaultov theorem. Napoleon – Barlotti
theorem. Colinearity and concyclity.
Ptolemey theorem. Clifford theorems.
Temeljni literatura in viri / Readings:
B. Spain: Analytical conics, Dover Publications, Mineola, New York, 2007.
O. Botema, R. Erne, R. Hartshorne: Topics in elementary geometry, Springer, New York, 2008
Liang-shin Hahn: Complex numbers & geometry, MAA, Washington, 1994
Cilji in kompetence:
Objectives and competences:
Cilj predmeta je na konkretnih primerih
ravninske geometrije ponoviti in utrditi
analitično geometrijo v kartezičnih
koordinatah.
Predstavitev alternativnih trilinearnih koordinat
ima dvojen namen:
predstaviti sredstvo, ki je včasih bistveno
udobnejše, včasih pa celo zapletenejše od
znanih sredstev;
prestaviti teorijo, ki bo za študente podobno
nova, kot bo klasična analitična geometrija
nova za njihove bodoče dijake.
Cilj zaključnega poglavja je seznaniti študente
s kompleksnimi števili kot močnim orodjem v
ravninski geometriji.
The aim of this course is (through the work on
concrete cases of planar geometry) to
repeat and consolidate the students knowledge
on analytic geometry in Cartesian coordinates.
We introduce an alternative trilinear coordinates
in order to present a new mean, sometimes
substantially more comfortable and sometimes
even more complex than the known ones. This
chapter also brings a completely new method for
work with circles and lines to the future
teachers, which will make them understand
better the situation of their future students being
for the first time acquainted with the usual
methods.
The objective of this course is also to acquaint
students with complex numbers as a powerful
tool in the planar geometry.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Po zaključku tega predmeta bo študent utrdil
znanje klasične analitične geometrije in
pridobil občutek za prednosti alternativnih
metod, kot sta uporaba trilinearnih koordinat in
kompleksnih števil v ravninski geometriji.
Prenesljive/ključne spretnosti in drugi atributi:
Zavest o dejstvu, da investicija v izgradnjo
močnejšega matematičnega orodja prinaša
prednosti v fazi uporabe.
Knowledge and Understanding:
On completion of this course the student will
consolidate his knowledge on classical analitic
geometry and get an insight in the advantages of
the use of trilinear coordinates and complex
numbers in the plane geometry.
Transferable/Key Skills and other attributes:
Awareness of the fact that investment in
building a more powerful mathematical tools
brings advantages during the application.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja Lectures
Teoretične vaje
Individualno delo
Theoretical excersises
Individual work
Načini ocenjevanja:
Assessment:
Izpit:
Pisni izpit – problemi
Ustni izpit
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljen pisni izpit – problemi je
pogoj za pristop k ustnemu izpitu.
Delež (v %) /
Weight (in %)
50%
50%
Exams:
Written exam – problems
Oral exam
Each of the mentioned assessments must
be assessed with a passing grade.
Passing grade of written exam –
problems is required to take the oral
exam.
Reference nosilca / Lecturer's
references:
1. HVALA, Bojan. Diophantine Steiner triples. Math. Gaz., March 2011, vol. 95, no. 532, str. 31-
39. [COBISS.SI-ID 18256648]
2. HVALA, Bojan. Diophantine Steiner triples and Pythagorean-type triangles. Forum geom.,
2010, vol. 10, str. 93-97. http://forumgeom.fau.edu/FG2010volume10/FG201010.pdf. [COBISS.SI-
ID 15669337]
3. HVALA, Bojan. Modernizing mathematics education in Slovenia : a teacher friendly approach.
V: LAMANAUSKAS, Vincentas (ur.). Challenges of science, mathematics and technology teacher
education in Slovenia, (Problems of education in the 21st century, vol. 14). Siauliai: Scientific
Methodological Center Scientia Educologica, 2009, str. 34-43. [COBISS.SI-ID 17351944]
4. HVALA, Bojan. Generalized Lie derivations in prime rings. Taiwan. j. math., dec. 2007, vol. 11,
iss. 5, str. 1425-1430. [COBISS.SI-ID 15969288]
5. BREŠAR, Matej, HVALA, Bojan. On additive maps of prime rings. II. Publ. math. (Debr.),
1999, letn. 54, št. 1/2, str. 39-54. [COBISS.SI-ID 8598617]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Osnove teorije mere
Course title: Basic measure theory
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30
135 7
Nosilec predmeta / Lecturer: Valerij Romanovskij
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Osnovni pojmi teorije mere: Algebra, σ-
algebra, Borelova σ-algebra na Rn. Mere in
osnovne lastnosti mer. Merljivi prostori.
Pozitivne mere. Zunanje mere.
Lebesgueova mera na Rn.
Funkcije in integrali: Merljive funkcije.
Stopničaste funkcije. Integral stopničaste
funkcije. Integral merljive funkcije. Izrek o
monotoni konvergenci. Fatoujeva lema in
Lebesgueov izrek o dominantni
konvergenci. Povezanost Riemannovega in
Lebesgueovega integrala.
Basic concepts of measure theory: Algebra,
σ-algebra, Borel σ-algebra on Rn. Measure
and its basic properties. Measurable spaces.
Positive measures. Outer measures.
Lebesgue measure on Rn.
Functions and integrals: Measurable
functions. Simple measurable functions. The
integral of a simple measurable function.
The integral of a measurable function. The
monotone convergence theorem. Fatou’s
lemma and Lebesgue’s dominated
convergence theorem. Relationships between
Konvergenca: Zaporedja merljivih funkcij
in konvergenca. Konvergenca skoraj
povsod. Norma in normirani Lp-prostori.
Neenakosti (Hölder, Minkowski). Dualni
prostori.
Predznačne in kompleksne mere:
Predznačne mere in Hahnov razcepni izrek.
Kompleksne mere in Radon-Nikodymov
izrek. Funkcije z omejeno varianco.
Lebesgue-Stieltjesov integral.
Riemann’s and Lebesgue’s integral.
Convergence: Sequences of measurable
functions and convergence. Convergence
almost everywhere. Norm and normed Lp-
spaces. Inequalities (Hölder, Minkowski).
Dual spaces.
Signed and complex measures: Signed
measures and the Hahn decomposition
theorem. Complex measures and the Radon-
Nikodym theorem. Functions of bounded
variation.
Lebesgue-Stieltjes integral
Temeljni literatura in viri / Readings:
1. M. Capinski, E. Kopp: Measure, integral and probability, Springer-Verlag London, 2004.
2. D. L. Cohn: Measure theory, Birkhäuser, 1994.
3. R. Drnovšek: Rešene naloge iz teorije mere, DMFA, 2001.
4. M. Hladnik: Naloge in primeri iz funkcionalne analize in teorije mere, DMFA, 1985.
5. W. Rudin: Real and complex analysis, 3th edition, Mc-Graw-Hill, 1986.
6. H. Sohrab, Basic real analysis, Birkhauser Boston, 2003.
7. I. Vidav, Višja matematika II, DZS, Ljubljana, 1975.
Cilji in kompetence:
Objectives and competences:
Glavni cilj predmeta je proučiti temeljne
koncepte in rezultate teorije mere. The main goal of the course is to study the
fundamental concepts and results of measure
theory.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
merljivi prostori, merljive funkcije,
abstraktno integriranje, izreki o
konvergenci, Lp-prostori, produktne mere,
odvodi mer.
Prenesljive/ključne spretnosti in drugi atributi:
Poznavanje osnov teorije mere je podlaga za
študij različnih matematičnih področij
(funkcionalne analize, verjetnosti, parcialnih
diferencialnih enačb itd.).
Knowledge and Understanding:
Measurable spaces, measurable functions,
abstract integration, convergence theorems,
Lp-spaces, product measures, differentiation
of measures.
Transferable/Key Skills and other attributes:
Knowing the fundamentals of measure theory is
a prerequisite for studying various mathematical
areas (functional analysis, probability, partial
differential equations etc.).
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Teoretične vaje
Lectures
Theoretical exercises
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje, Delež (v %) / Type (examination, oral, coursework,
naloge, projekt)
Pisni izpit – problemi
Pisni izpit – teoretija
Pisni izpit - problemi se lahko
nadomesti z dvema delnima testoma
(sprotni obveznosti)
Pisni izpit - teorja se lahko nadomesti z
dvema delnima testoma (sprotni
obveznosti)
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Weight (in %)
50%
50%
project):
Written exam – problems
Written exam – theory
Written exam – problems can be replaced
by two parital tests (mid-term testing)
Written exam – theory can be replaced
by two parital tests (mid-term testing)
Each of the mentioned commitments
must be assessed with a passing grade.
Reference nosilca / Lecturer's
references:
1. CHEN, Xingwu, GINÉ, Jaume, ROMANOVSKI, Valery, SHAFER, Douglas. The 1: -q resonant
center problem for certain cubic Lotka-Volterra systems. Appl. math. comput.. [Print ed.], Aug.
2012, vol. 218, iss. 32, str. 11620-11633. http://dx.doi.org/10.1016/j.amc.2012.05.045, doi:
10.1016/j.amc.2012.05.045. [COBISS.SI-ID 19321352]
2. BASOV, Vladimir V., ROMANOVSKI, Valery. Linearization of two-dimensional systems of
ODEs without conditions on small denominators. Appl. math. lett.. [Print ed.], 2012, vol. 25, iss. 2,
str. 99-103. http://dx.doi.org/10.1016/j.aml.2011.06.029, doi: 10.1016/j.aml.2011.06.029.
[COBISS.SI-ID 18675208]
3. LEVANDOVSKYY, Viktor, PFISTER, Gerhard, ROMANOVSKI, Valery. Evaluating cyclicity
of cubic systems with algorithms of computational algebra. Commun. pure appl. anal., 2012, vol.
11, no. 5, str. 2023-2035, doi: 10.3934/cpaa.2012.11.2023. [COBISS.SI-ID 19075080]
4. WENTAO, Huang, CHEN, Xingwu, ROMANOVSKI, Valery. Linear centers with perturbations
of degree 2d + 5. Int. j. bifurc. chaos appl. sci. eng., 2012, vol. 22, no. 1, str. [1250007-1 -
1250007-12]. http://www.ejournals.wspc.com.sg/ijbc/22/2201/S0218127412500071.html, doi:
10.1142/S0218127412500071. [COBISS.SI-ID 69213185]
5. HAN, Maoan, ROMANOVSKI, Valery. Isochronicity and normal forms of polynomial systems
of ODEs. J. symb. comput., Oct. 2012, vol. 47, iss. 10, str. 1163-1174.
http://dx.doi.org/10.1016/j.jsc.2011.12.039, doi: 10.1016/j.jsc.2011.12.039. [COBISS.SI-ID
19324168]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Kompleksna analiza
Course title: Complex Analysis
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30
135 7
Nosilec predmeta / Lecturer: Marko JAKOVAC
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje analize in kompleksnih števil. Knowledge of analysis and complex numbers.
Vsebina: Content (Syllabus outline):
Funkcije kompleksne spremenljivke.
Elementarne funkcije v kompleksnem: linearne
funkcije, ulomljene linearne funkcije. Potenčne
vrste v kompleksnem. Elementarne funkcije,
definirane s potenčnimi vrstami. Logaritem in
ciklometrične funkcije.
Holomorfne funkcije. Cauchy – Riemannov
izrek. Konformnost holomorfnih funkcij.
Integral funkcije kompleksne spremenljivke.
Cauchyjev izrek in Cauchyjeve formule.
Functions of complex variable. Elementary
functions: linear function, Möbius functions.
Power series. Elementary functions defined by
power series. Logarithm and cyclometric
functions.
Holomorphic functions. Cauchy – Riemann
theorem. Conformality of holomorphic
mappings.
Complex line integrals. Cauchy integral theorem
and Cauchy formula. Liouville theorem. Power
Liouvilleov izrek. Taylorjeva vrsta.
Laurentova vrsta. Klasifikacija izoliranih
singularnih točk. Mali Piccardov izrek. Izrek o
residuih. Uporaba pri računanju realnih
integralov.
Laplaceova in Fourierova transformacija.
Uporaba.
series representation.
Laurent series. Classification of isolated
singularity. Behaviour of holomorphic function
near isolated singularity. Little Piccard
Theorem. Residui theorem. Applications to the
calculations of definite integrals and sums.
Laplace and Fourier transforms. Applications.
Temeljni literatura in viri / Readings:
S. G. Krantz: Handbook of Complex Variables, Birkhäuser, Boston, 1999.
J.B.Conway: Functions of One Complex Variable I, 2nd edition, Springer, New York, 1995.
L. Ahlfors: Complex Analysis, 3rd edition, McGraw-Hill, New york, 1979.
Cilji in kompetence:
Objectives and competences:
Študent poglobi znanje iz osnov teorije funkcij
kompleksne spremenljivke ter poglobi znanje
iz uporabnih aspektov te teorije, predvsem v
povezavi s preslikovanji območij, pri računanju
določenih integralov, seštevanju vrst ter
reševanju diferencialnih enačb.
Deepening the knowledge of concepts from the
theory of functions of one complex variable. To
deepen the knowledge of possible applications
of this theory, specialy in connection with
transformations of the regions, calculating
definite integrals and sums and solving
differential equations.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Študent razume pojem holomorfne funkcije
pozna osnovne s tem povezane rezultate,
posebej tiste, ki se nanašajo na integracijo
in na integralsko reprezentacijo ter
reprezentacijo s potenčno vrsto.
Študent razume koncept preslikovanja
območij z uporabo ulomljenih linearnih in
drugih preprostejših elementarnih funkcij v
kompleksnem.
Študent razume pojem izolirane singularne
funkcije in pozna uporabno vrednost izreka
o residuumih.
Študent razume koncepta Laplaceove in
Fourierove transformacije in pozna njune
možnosti uporabe.
Prenesljive/ključne spretnosti in drugi atributi:
Ilustracija dejstva, da nam teorija, navidez
oddaljene od realnosti, lahko ponudi mnoge
praktično uporabne rezultate.
Dojemanje transformacij kot opcije za
pretvorbo matematične situacije v drugo
Knowledge and Understanding:
To understand the concept of holomorphic
function and to know the basic results,
specialy those about line integrals and about
the integral and the power series
representation of holomorphic functions.
To understend the concept of transforming
plane regions using Möbius transformations
and other basic elementary functions.
To understand the concept of isolated
singularity and to be aware of the
importance of the residui theorem.
To understand the concepts of Laplace and
Fourier tranformations and to be aware of
their possible applications.
Transferable/Key Skills and other attributes:
An illustration of the fact, that a more
abstract theory can give us many nice results
with useful practical applications.
Understanding the concept of
transformations as tools to convert a certain
situacijo, ki je udobnejša za obravnavo. mathematical situation into a more
convenient one.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Izpit:
Pisni izpit – problemi
Ustni izpit – teorija
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljen pisni izpit – problemi je
pogoj za pristop k ustnemu izpitu –
teorija.
Pisni izpit – problemi se lahko
nadomesti z dvema delnima testoma
(sprotne obveznosti).
Delež (v %) /
Weight (in %)
50%
50%
Exams:
Written exam – problems
Oral exam – theory
Each of the mentioned assessments must
be assessed with a passing grade.
Passing grade of written exam –
problems is required to take the oral
exam – theory.
Written exam – problems can be replaced
with two mid-term tests.
Reference nosilca / Lecturer's
references:
1. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel,
TARANENKO, Andrej. On the vertex k-path cover. Discrete Applied Mathematics, ISSN 0166-
218X. [Print ed.], 2013, vol. 161, iss. 13/14, str. 1943-1949.
http://dx.doi.org/10.1016/j.dam.2013.02.024. [COBISS.SI-ID 19859464]
2. JAKOVAC, Marko, TARANENKO, Andrej. On the k-path vertex cover of some graph
products. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2013, vol. 313, iss. 1, str. 94-100.
http://dx.doi.org/10.1016/j.disc.2012.09.010, doi: 10.1016/j.disc.2012.09.010. [COBISS.SI-ID
19464968]
3. JAKOVAC, Marko, PETERIN, Iztok. On the b-chromatic number of some graph products.
Studia scientiarum mathematicarum Hungarica, ISSN 0081-6906, 2012, vol. 49, no. 2, str. 156-
169. http://dx.doi.org/10.1556/SScMath.49.2012.2.1194. [COBISS.SI-ID 16321113]
4. CABELLO, Sergio, JAKOVAC, Marko. On the b-chromatic number of regular graphs. Discrete
Applied Mathematics, ISSN 0166-218X. [Print ed.], 2011, vol. 159, iss. 13, str. 1303-1310.
http://dx.doi.org/10.1016/j.dam.2011.04.028, doi: 10.1016/j.dam.2011.04.028. [COBISS.SI-ID
15914329]
5. JAKOVAC, Marko, KLAVŽAR, Sandi. The b-chromatic number of cubic graphs. Graphs and
combinatorics, ISSN 0911-0119, 2010, vol. 26, no. 1, str. 107-118.
http://dx.doi.org/10.1007/s00373-010-0898-9. [COBISS.SI-ID 15522905]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Teorija grup
Course title: Group Theory
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Dušan PAGON
Jeziki /
Languages:
Predavanja / Lectures: SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za
opravljanje študijskih obveznosti:
Prerequisits:
Ne. None.
Vsebina: Content (Syllabus outline):
Simetrične grupe. Konjugirani elementi in
podgrupe. Delovanje grupe na množico.
Linearne grupe: osnovne lastnosti in primeri.
Izreki Sylowa. Podajanje grupe z generatorji
in relacijami. Direktni produkt grup. Abelove
grupe.
Enostavne grupe. Komutant grupe, rešljivost
končnih p-grup in grupe zgornje trikotnih
matrik.
Upodobitve grup: osnovni pojmi in primeri.
Symetric groups. Conjugated elements and
subgroups. The action of a group on a set. Linear
groups: main properties and examples.
Sylow's theorems. Definition of a group by
generators and relations. Direct product of groups.
Abelian groups.
Simple groups. Derived group, solvability of finite
p-groups and the group of upper triangular
matrices.
Representations of groups: concepts and examples.
Temeljni literatura in viri / Readings:
W. Y. Gilbert, W. K. Nicholson, Modern Algebra with Applications, Wiley, Chichester 2004
S. Lang, Undergraduate Algebra, Springer, 2005
J. F. Humphreys, A Course in Group Theory, Oxford University Press, 1997
I. Vidav, Algebra, DMFA, Ljubljana 1980
Cilji in kompetence:
Objectives and competences:
Študentje poglobijo znanje osnove teorije grup
in njihovih upodobitev. Students deepen the knowledge of the concepts
of the theory of groups and their representations.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Razumevanje osnov teorije grup in
njihovih upodobitev.
Poznavanje osnovnih značilnosti in
tipičnih primerov grup.
Prenesljive/ključne spretnosti in drugi atributi:
Pridobljena znanja prispevajo k
razumevanju ostalih predmetov s
področja algebre, geometrije in
topologije.
Knowledge and Understanding:
To understand the main concepts of
groups and their representations.
To recognize the typical properties and
main examples of groups.
Transferable/Key Skills and other attributes:
The obtained knowledge contributes to
better understanding of other subjects in
fields of algebra, geometry and topology.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit – praktični del
Ustni izpit – teoretični del
Pisni izpit – praktični del se lahko
nadomesti z dvema delnima testoma
(sprotni obveznosti).
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
Written exam – practical part
Oral exam – theoretical part
Written exam – practical part can be
replaced by two partial tests (mid-term
testing).
Reference nosilca / Lecturer's
references:
1. PAGON, Dušan, REPOVŠ, Dušan, ZAICEV, Mikhail. On the codimension growth of simple
color Lie superalgebras. J. Lie theory, 2012, vol. 22, no. 2, str. 465-479.
http://www.heldermann.de/JLT/JLT22/JLT222/jlt22017.htm. [COBISS.SI-ID 16070233]
2. PAGON, Dušan. Simplified square equation in the quaternion algebra. International journal of
pure and applied mathematics, 2010, vol. 61, no. 2, str. 231-240. [COBISS.SI-ID 17718024]
3. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. On chains in H-closed topological pospaces.
Order (Dordr.), 2010, vol. 27, no. 1, str. 69-81. http://dx.doi.org/10.1007/s11083-010-9140-x.
[COBISS.SI-ID 15502169]
4. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. The continuity of the inversion and the
structure of maximal subgroups in countably compact topological semigroups. Acta math. Hung.,
2009, vol. 124, no. 3, str. 201-214. http://dx.doi.org/10.1007/s10474-009-8144-8, doi:
10.1007/s10474-009-8144-8. [COBISS.SI-ID 15212121]
5. PAGON, Dušan. The dynamics of selfsimilar sets generated by multibranching trees.
International journal of computational and numerical analysis and applications, 2004, vol. 6, no.
1, str. 65-76. [COBISS.SI-ID 14037081]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Zgodovina matematike
Course title: History of Mathematics
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
75
135 7
Nosilec predmeta / Lecturer: Daniel EREMITA
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Metodologija zgodovine matematike,
zgodovinski viri.
Glavni centri in obdobja razvoja matematike:
mezopotamska matematika, egipčanska
matematika, starogrška in helenistična
matematika, kitajska matematika, indijska
matematika, japonska matematika, matematika
indijanskih civilizacij, arabska matematika,
matematika renesanse, matematika XV., XVI.,
Methodology of the history of mathematics,
historical sources.
The main centers and periods of mathematical
development: Mesopotamian mathematics,
Egyptian mathematics, Ancient Greek and
Hellenistic mathematics, Chinese mathematics,
Hindu mathematics, Japanese mathematics,
mathematics of indigenous cultures of the
Americas, Arabic mathematics, Renaissance
mathematics, mathematics of XV., XVI., XVII.,
XVII., XVIII., XIX. in XX. stoletja.
Razvoj glavnih področij matematike:
geometrije, aritmetike, algebre, teorije števil,
analize, matematične logike, teorije množic,
topologije, teorije grafov, teorije verjetnosti,
statistike, računalništva, metodike matematike,
zgodovine matematike idr. Razvoj osnovnih
matematičnih pojmov.
Pomembni matematiki in njihov prispevek k
razvoju matematike. Slovenski matematiki.
Zgodovina matematike kot del splošne
zgodovine. Filozofski, sociološki, psihološki,
lingvistični in podobni aspekti matematike.
Matematika in druge znanosti.
XVIII., XIX. and XX. centuries.
The development of the major areas of
mathematics: geometry, arithmetic, algebra,
number theory, analysis, mathematical logic, set
theory, topology, graph theory, probability
theory, statistics, computer science,
methodology of mathematics, history of
mathematics, etc. The development of the
fundamental mathematical notions.
Important mathematicians and their contribution
to mathematics. Slovenian mathematicians.
A history of mathematics as a part of a general
history. Philosophical, sociological,
psychological, linguistic and similar aspects of
mathematics. Mathematics and other sciences.
Temeljni literatura in viri / Readings:
A History of Mathematics. New York: J. Wiley & Sons, 1989.
A History of Mathematics, An Introduction. Reading (Mass.) [etc.] : Addison-
Wesley, 1998
A History of Mathematicad Notation. New York: Dover Publications, Inc., 1993.
Geometry and Algebra in Ancient Civilizations. Berlin: Springer Verlag,
1983.
Kratka zgodovina matematike. Ljubljana: Državna založba Slovenije, 1978.
Cilji in kompetence:
Objectives and competences:
Spoznati zgodovinski razvoj matematike,
razvoj njenih osnovnih področij in razvoj
osnovnih matematičnih pojmov. Seznaniti se s
pomembnimi matematiki in njihovimi
prispevki k razvoju matematike.
To obtain knowledge of the historical
development of mathematics, the development
of its major areas, and the development of the
fundamental mathematical notions. To get
acquainted with the important mathematicians
and their contribution to mathematics.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
zgodovinski razvoj matematike, razvoj
njenih osnovnih področij in razvoj osnovnih
matematičnih pojmov
pomembni matematiki in njihovi prispevki
k razvoju matematike
Prenesljive/ključne spretnosti in drugi atributi:
Knowledge and Understanding:
historical development of mathematics,
the development of its major areas, and
the development of the fundamental
mathematical notions
important mathematicians and their
contribution to mathematics
prenos znanja zgodovine matematike na vse
matematične predmete in na nekatera druga
področja (fizika, astronomija, mehanika,
računalništvo, filozofija, zgodovina, …).
Transferable/Key Skills and other attributes:
knowledge transfer of history of
mathematics to all mathematical courses and
also to other areas (physics, astronomy,
mechanics, computer science, philosophy,
history, …).
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Individualno delo
Lectures
Individual work
Načini ocenjevanja:
Assessment:
Seminarska naloga
Ustni izpit
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljena seminarska naloga je pogoj
za pristop k izpitu.
Delež (v %) /
Weight (in %)
20%
80%
Seminar assignment
Oral exam
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grade of the seminar assignment
is required to take the exam.
Reference nosilca / Lecturer's
references:
1. EREMITA, Daniel. Functional identities of degree 2 in triangular rings revisited. Linear and Multilinear Algebra, ISSN 0308-1087, 2015, vol. 63, iss. 3, str. 534-553. http://dx.doi.org/10.1080/03081087.2013.877012. [COBISS.SI-ID 17044057] 2. EREMITA, Daniel, GOGIĆ, Ilja, ILIŠEVIĆ, Dijana. Generalized skew derivations implemented by elementary operators. Algebras and representation theory, ISSN 1386-923X, 2014, vol. 17, iss. 3, str. 983-996. http://dx.doi.org/10.1007/s10468-013-9429-8. [COBISS.SI-ID 17043545] 3. EREMITA, Daniel. Functional identities of degree 2 in triangular rings. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2013, vol. 438, iss 1, str. 584-597. http://dx.doi.org/10.1016/j.laa.2012.07.028. [COBISS.SI-ID 16528217] 4. EREMITA, Daniel, ILIŠEVIĆ, Dijana. On (anti-)multiplicative generalized derivations. Glasnik matematički. Serija 3, ISSN 0017-095X, 2012, vol. 47, no. 1, str. 105-118. http://dx.doi.org/10.3336/gm.47.1.08. [COBISS.SI-ID 16341849] 5. BENKOVIČ, Dominik, EREMITA, Daniel. Multiplicative Lie n-derivations of triangular rings. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2012, vol. 436, iss
11, str. 4223-4240. http://dx.doi.org/10.1016/j.laa.2012.01.022. [COBISS.SI-ID 16278361]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Algebrska topologija
Course title: Algebraic Topology
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul R1 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module R1 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Uroš MILUTINOVIĆ
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje algeberskih struktur in topologije. Knowledge of algebraic structures and
topology..
Vsebina: Content (Syllabus outline):
Kategorije in funktorji. Izomorfizmi.
Homotopija, homotopska kategorija topoloških
prostorov.
Funktor fundamentalne grupe. Krovni prostori.
Primeri uporabe.
Simplicialni kompleksi in poliedri. Funktor
simplicialne homologije. Eulerjeva
karakteristika, Bettijeva števila. Osnove
homološke algebre. Druge homološke teorije.
Categories and functors. Isomorphisms.
Homotopy, homotopy theory of topological
spaces.
The fundamental group functor. Covering
spaces. Examples.
Simplical complexes and polyhedra. The
simplical homology functor. Euler
characteristic, Betti numbers. Fundamentals of
homological algebra. Other homology theories.
Temeljni literatura in viri / Readings:
J.R.Munkres: Topology: a first course,Englewood Cliffs, NJ, Prentice-Hall, 1975
E.H.Spanier: Algebraic topology, New York (etc.), McGraw-Hill, 1966
M.Cencelj: Simplicialni kompleksi in simplicialna homologija, Ljubljana, Pedagoška fakulteta,
1996
Cilji in kompetence:
Objectives and competences:
Obvladati osnovne tehnike dela s funktorji
algebrske topologije. Students learn how to use the basic techniques
of work with algebraic topology functors.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Uporaba kategorij in funktorjev.
Sposobnost uporabe osnovnih tehnik
dela s konkretnimi funktorji algebrske
topologije.
Prenesljive/ključne spretnosti in drugi atributi:
Algebrska topologija je področje, ki
povezuje algebro in topologijo. Je
močan aparat, ki se ga da uporabiti pri
reševanju zelo različnih problemov.
Knowledge and Understanding:
The use of categories and functors.
Be able to use the basic techniques of
work with specific algebraic topology
functors.
Transferable/Key Skills and other attributes:
Algebraic topology connects algebra and
topology. It is a powerful apparatus that
can be used in solving of many different
problems
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja: Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Izpit:
Pisni izpit – problemi
Ustni izpit – teorija
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Pozitivna ocena pri pisnem izpitu -
problemi je pogoj za pristop k ustnemu
izpitu – teorija.
Pisni izpit – problemi se lahko
nadomesti z dvema delnima testoma (ki
sta sprotni obveznosti).
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
Exams:
Written exam – problems
Oral exam – theory
Each of the mentioned assessments must
be assessed with a passing grade.
Passing grade of the written exam –
problems is required for taking the oral
exam – theory.
Written exam – problems can be replaced
by two mid-term tests.
Reference nosilca / Lecturer's
references:
1. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš, SOVIČ, Tina.
Ważewski's universal dendrite as an inverse limit with one set-valued bonding function. Preprint
series, 2012, vol. 50, št. 1169, str. 1-33. http://www.imfm.si/preprinti/PDF/01169.pdf. [COBISS.SI-
ID 16194137]
2. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Paths through
inverse limits. Topol. appl.. [Print ed.], 2011, vol. 158, iss. 9, str. 1099-1112.
http://dx.doi.org/10.1016/j.topol.2011.03.001. [COBISS.SI-ID 18474504]
3. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Limits of
inverse limits. Topol. appl.. [Print ed.], 2010, vol. 157, iss. 2, str. 439-450.
http://dx.doi.org/10.1016/j.topol.2009.10.002. [COBISS.SI-ID 15310169]
4. KLAVŽAR, Sandi, MILUTINOVIĆ, Uroš, PETR, Ciril. Stern polynomials. Adv. appl. math.,
2007, vol. 39, iss. 1, str. 86-95. http://dx.doi.org/10.1016/j.aam.2006.01.003. [COBISS.SI-ID
14276441]
5. IVANŠIĆ, Ivan, MILUTINOVIĆ, Uroš. Closed embeddings into Lipscomb's universal space.
Glas. mat., 2007, vol. 42, no. 1, str. 95-108. [COBISS.SI-ID 14338393]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Teorija grup
Course title: Group Theory
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul R2 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module R2 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Dušan PAGON
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za
opravljanje študijskih obveznosti:
Prerequisits:
Ne. None.
Vsebina:
Content (Syllabus outline):
Simetrične grupe. Konjugirani elementi in
podgrupe. Delovanje grupe na množico.
Linearne grupe: osnovne lastnosti in primeri.
Izreki Sylowa. Podajanje grupe z generatorji
in relacijami. Direktni produkt grup. Abelove
grupe.
Enostavne grupe. Komutant grupe, rešljivost
končnih p-grup in grupe zgornje trikotnih
matrik.
Upodobitve grup: osnovni pojmi in primeri.
Symetric groups. Conjugated elements and
subgroups. The action of a group on a set. Linear
groups: main properties and examples.
Sylow's theorems. Definition of a group by
generators and relations. Direct product of groups.
Abelian groups.
Simple groups. Derived group, solvability of finite
p-groups and the group of upper triangular
matrices.
Representations of groups: concepts and examples.
Temeljni literatura in viri / Readings:
W. Y. Gilbert, W. K. Nicholson, Modern Algebra with Applications, Wiley, Chichester 2004
S. Lang, Undergraduate Algebra, Springer, 2005
J. F. Humphreys, A Course in Group Theory, Oxford University Press, 1997
I. Vidav, Algebra, DMFA, Ljubljana 1980
Cilji in kompetence:
Objectives and competences:
Študentje poglobijo znanje osnove teorije grup
in njihovih upodobitev. Students deepen the knowledge of the basic
concepts of the theory of groups and their
representations.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Razumevanje osnov teorije grup in
njihovih upodobitev.
Poznavanje osnovnih značilnosti in
tipičnih primerov grup.
Prenesljive/ključne spretnosti in drugi atributi:
Pridobljena znanja prispevajo k
razumevanju ostalih predmetov s
področja algebre, geometrije in
topologije.
Knowledge and Understanding:
To understand the main concepts of
groups and their representations.
To recognize the typical properties and
main examples of groups.
Transferable/Key Skills and other attributes:
The obtained knowledge contributes to
better understanding of other subjects in
fields of algebra, geometry and topology.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit – praktični del
Ustni izpit – teoretični del
Pisni izpit – praktični del se lahko
nadomesti z dvema delnima testoma (sprotni
obveznosti).
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
Written exam – practical part
Oral exam – theoretical part
Written exam – practical part can be
replaced by two partial tests (mid-
term testing).
Reference nosilca / Lecturer's references:
1. PAGON, Dušan, REPOVŠ, Dušan, ZAICEV, Mikhail. On the codimension growth of simple
color Lie superalgebras. J. Lie theory, 2012, vol. 22, no. 2, str. 465-479.
http://www.heldermann.de/JLT/JLT22/JLT222/jlt22017.htm. [COBISS.SI-ID 16070233]
2. PAGON, Dušan. Simplified square equation in the quaternion algebra. International journal of
pure and applied mathematics, 2010, vol. 61, no. 2, str. 231-240. [COBISS.SI-ID 17718024]
3. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. On chains in H-closed topological pospaces.
Order (Dordr.), 2010, vol. 27, no. 1, str. 69-81. http://dx.doi.org/10.1007/s11083-010-9140-x.
[COBISS.SI-ID 15502169]
4. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. The continuity of the inversion and the
structure of maximal subgroups in countably compact topological semigroups. Acta math. Hung.,
2009, vol. 124, no. 3, str. 201-214. http://dx.doi.org/10.1007/s10474-009-8144-8, doi:
10.1007/s10474-009-8144-8. [COBISS.SI-ID 15212121]
5. PAGON, Dušan. The dynamics of selfsimilar sets generated by multibranching trees.
International journal of computational and numerical analysis and applications, 2004, vol. 6, no.
1, str. 65-76. [COBISS.SI-ID 14037081]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Algebrska topologija
Course title: Algebraic Topology
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul S1 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module S1 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Uroš MILUTINOVIĆ
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje algeberskih struktur in topologije. Knowledge of algebraic structures and
topology..
Vsebina: Content (Syllabus outline):
Kategorije in funktorji. Izomorfizmi.
Homotopija, homotopska kategorija topoloških
prostorov.
Funktor fundamentalne grupe. Krovni prostori.
Primeri uporabe.
Simplicialni kompleksi in poliedri. Funktor
simplicialne homologije. Eulerjeva
karakteristika, Bettijeva števila. Osnove
homološke algebre. Druge homološke teorije.
Categories and functors. Isomorphisms.
Homotopy, homotopy theory of topological
spaces.
The fundamental group functor. Covering
spaces. Examples.
Simplical complexes and polyhedra. The
simplical homology functor. Euler characteristic,
Betti numbers. Fundamentals of homological
algebra. Other homology theories.
Temeljni literatura in viri / Readings:
J.R.Munkres: Topology: a first course,Englewood Cliffs, NJ, Prentice-Hall, 1975
E.H.Spanier: Algebraic topology, New York (etc.), McGraw-Hill, 1966
M.Cencelj: Simplicialni kompleksi in simplicialna homologija, Ljubljana, Pedagoška fakulteta,
1996
Cilji in kompetence:
Objectives and competences:
Obvladati osnovne tehnike dela s funktorji
algebrske topologije. Students learn how to use the basic techniques
of work with algebraic topology functors.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Uporaba kategorij in funktorjev.
Sposobnost uporabe osnovnih tehnik
dela s konkretnimi funktorji algebrske
topologije.
Prenesljive/ključne spretnosti in drugi atributi:
Algebrska topologija je področje, ki
povezuje algebro in topologijo. Je
močan aparat, ki se ga da uporabiti pri
reševanju zelo različnih problemov.
Knowledge and Understanding:
The use of categories and functors.
Be able to use the basic techniques of
work with specific algebraic topology
functors.
Transferable/Key Skills and other attributes:
Algebraic topology connects algebra and
topology. It is a powerful apparatus that
can be used in solving of many different
problems
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja: Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Izpit:
Pisni izpit – problemi
Ustni izpit – teorija
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Pozitivna ocena pri pisnem izpitu -
problemi je pogoj za pristop k ustnemu
izpitu – teorija.
Pisni izpit – problemi se lahko
nadomesti z dvema delnima testoma (ki
sta sprotni obveznosti).
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
Exams:
Written exam – problems
Oral exam – theory
Each of the mentioned assessments must
be assessed with a passing grade.
Passing grade of the written exam –
problems is required for taking the oral
exam – theory.
Written exam – problems can be replaced
by two mid-term tests.
Reference nosilca / Lecturer's
references:
1. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš, SOVIČ, Tina.
Ważewski's universal dendrite as an inverse limit with one set-valued bonding function. Preprint
series, 2012, vol. 50, št. 1169, str. 1-33. http://www.imfm.si/preprinti/PDF/01169.pdf. [COBISS.SI-
ID 16194137]
2. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Paths through
inverse limits. Topol. appl.. [Print ed.], 2011, vol. 158, iss. 9, str. 1099-1112.
http://dx.doi.org/10.1016/j.topol.2011.03.001. [COBISS.SI-ID 18474504]
3. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Limits of
inverse limits. Topol. appl.. [Print ed.], 2010, vol. 157, iss. 2, str. 439-450.
http://dx.doi.org/10.1016/j.topol.2009.10.002. [COBISS.SI-ID 15310169]
4. KLAVŽAR, Sandi, MILUTINOVIĆ, Uroš, PETR, Ciril. Stern polynomials. Adv. appl. math.,
2007, vol. 39, iss. 1, str. 86-95. http://dx.doi.org/10.1016/j.aam.2006.01.003. [COBISS.SI-ID
14276441]
5. IVANŠIĆ, Ivan, MILUTINOVIĆ, Uroš. Closed embeddings into Lipscomb's universal space.
Glas. mat., 2007, vol. 42, no. 1, str. 95-108. [COBISS.SI-ID 14338393]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Teorija mere
Course title: Measure theory
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul S1 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module S1 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
60
45
165 9
Nosilec predmeta / Lecturer: Valerij Romanovskij
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Osnovni pojmi teorije mere: Algebra, σ-
algebra, Borelova σ-algebra na Rn. Mere in
osnovne lastnosti mer. Merljivi prostori.
Pozitivne mere. Zunanje mere.
Lebesqueova mera na Rn.
Funkcije in integrali: Merljive funkcije.
Stopničaste funkcije. Integral stopničaste
funkcije. Integral merljive funkcije. Izrek o
monotoni konvergenci. Fatoujeva lema in
Lebesqueov izrek o dominantni
konvergenci. Povezanost Riemannovega in
Lebesqueovega integrala.
Basic concepts of measure theory: Algebra,
σ-algebra, Borel σ-algebra on Rn. Measure
and its basic properties. Measurable spaces.
Positive measures. Outer measures.
Lebesque measure on Rn.
Functions and integrals: Measurable
functions. Simple measurable functions. The
integral of a simple measurable function.
The integral of a measurable function. The
monotone convergence theorem. Fatou’s
lemma and Lebesque’s dominated
convergence theorem. Relationships between
Konvergenca: Zaporedja merljivih funkcij
in konvergenca. Konvergenca skoraj
povsod. Norma in normirani Lp-prostori.
Neenakosti (Hölder, Minkowski). Dualni
prostori.
Predznačne in kompleksne mere:
Predznačne mere in Hahnov razcepni izrek.
Kompleksne mere in Radon-Nikodymov
izrek. Funkcije z omejeno varianco.
Produktne mere: Merjenje in integriranje po
produktnih prostorih (Fubinijev izrek).
Odvajanje: Odvodi mer. Odvodi funkcij.
Rieszov izrek o reprezentaciji pozitivnih
linearnih funkcionalov na C(X).
Lebesgue-Stieltjesov integral.
Riemann’s and Lebesque’s integral.
Convergence: Sequences of measurable
functions and convergence. Convergence
almost everywhere. Norm and normed Lp-
spaces. Inequalities (Hölder, Minkowski).
Dual spaces.
Signed and complex measures: Signed
measures and the Hahn decomposition
theorem. Complex measures and the Radon-
Nikodym theorem. Functions of bounded
variation.
Product measures: Measures and integrals on
product spaces (Fubini’s theorem).
Differentiation: Differentiation of measures.
Differentiation of functions.
The Riesz representation theorem on
positive linear functionals on C(X).
Lebesgue-Stieltjes integral
Temeljni literatura in viri / Readings:
1. M. Capinski, E. Kopp: Measure, integral and probability, Springer-Verlag London, 2004.
2. D. L. Cohn: Measure theory, Birkhäuser, 1994.
3. R. Drnovšek: Rešene naloge iz teorije mere, DMFA, 2001.
4. M. Hladnik: Naloge in primeri iz funkcionalne analize in teorije mere, DMFA, 1985.
5. W. Rudin: Real and complex analysis, 3th edition, Mc-Graw-Hill, 1986.
6. H. Sohrab, Basic real analysis, Birkhauser Boston, 2003.
7. I. Vidav, Višja matematika II, DZS, Ljubljana, 1975.
Cilji in kompetence:
Objectives and competences:
Glavni cilj predmeta je proučiti temeljne
koncepte in rezultate teorije mere. The main goal of the course is to study the
fundamental concepts and results of measure
theory.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
merljivi prostori, merljive funkcije,
abstraktno integriranje, izreki o
konvergenci, Lp-prostori, produktne mere,
odvodi mer.
Prenesljive/ključne spretnosti in drugi atributi:
Poznavanje osnov teorije mere je
podlaga za študij različnih matematičnih
področij (funkcionalne analize,
verjetnosti, parcialnih diferencialnih
enačb itd.).
Knowledge and Understanding:
Measurable spaces, measurable functions,
abstract integration, convergence theorems,
Lp-spaces, product measures, differentiation
of measures.
Transferable/Key Skills and other attributes:
Knowing the fundamentals of measure
theory is a prerequisite for studying various
mathematical areas (functional analysis,
probability, partial differential equations
etc.).
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Teoretične vaje
Lectures
Theoretical exercises
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit – problemi
Pisni izpit – teoretija
Pisni izpit - problemi se lahko
nadomesti z dvema delnima testoma
(sprotni obveznosti)
Pisni izpit - teorja se lahko nadomesti z
dvema delnima testoma (sprotni
obveznosti)
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
Written exam – problems
Written exam – theory
Written exam – problems can be replaced
by two parital tests (mid-term testing)
Written exam – theory can be replaced
by two parital tests (mid-term testing)
Each of the mentioned commitments
must be assessed with a passing grade.
Reference nosilca / Lecturer's
references:
1. CHEN, Xingwu, GINÉ, Jaume, ROMANOVSKI, Valery, SHAFER, Douglas. The 1: -q resonant
center problem for certain cubic Lotka-Volterra systems. Appl. math. comput.. [Print ed.], Aug.
2012, vol. 218, iss. 32, str. 11620-11633. http://dx.doi.org/10.1016/j.amc.2012.05.045, doi:
10.1016/j.amc.2012.05.045. [COBISS.SI-ID 19321352]
2. BASOV, Vladimir V., ROMANOVSKI, Valery. Linearization of two-dimensional systems of
ODEs without conditions on small denominators. Appl. math. lett.. [Print ed.], 2012, vol. 25, iss. 2,
str. 99-103. http://dx.doi.org/10.1016/j.aml.2011.06.029, doi: 10.1016/j.aml.2011.06.029.
[COBISS.SI-ID 18675208]
3. LEVANDOVSKYY, Viktor, PFISTER, Gerhard, ROMANOVSKI, Valery. Evaluating cyclicity
of cubic systems with algorithms of computational algebra. Commun. pure appl. anal., 2012, vol.
11, no. 5, str. 2023-2035, doi: 10.3934/cpaa.2012.11.2023. [COBISS.SI-ID 19075080]
4. WENTAO, Huang, CHEN, Xingwu, ROMANOVSKI, Valery. Linear centers with perturbations
of degree 2d + 5. Int. j. bifurc. chaos appl. sci. eng., 2012, vol. 22, no. 1, str. [1250007-1 -
1250007-12]. http://www.ejournals.wspc.com.sg/ijbc/22/2201/S0218127412500071.html, doi:
10.1142/S0218127412500071. [COBISS.SI-ID 69213185]
5. HAN, Maoan, ROMANOVSKI, Valery. Isochronicity and normal forms of polynomial systems
of ODEs. J. symb. comput., Oct. 2012, vol. 47, iss. 10, str. 1163-1174.
http://dx.doi.org/10.1016/j.jsc.2011.12.039, doi: 10.1016/j.jsc.2011.12.039. [COBISS.SI-ID
19324168]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Kompleksna analiza
Course title: Complex Analysis
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul S2 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module S2 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30
135 7
Nosilec predmeta / Lecturer: Marko JAKOVAC
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje analize in kompleksnih števil. Knowledge of analysis and complex numbers.
Vsebina: Content (Syllabus outline):
Funkcije kompleksne spremenljivke.
Elementarne funkcije v kompleksnem: linearne
funkcije, ulomljene linearne funkcije. Potenčne
vrste v kompleksnem. Elementarne funkcije,
definirane s potenčnimi vrstami. Logaritem in
ciklometrične funkcije.
Holomorfne funkcije. Cauchy – Riemannov
izrek. Konformnost holomorfnih funkcij.
Integral funkcije kompleksne spremenljivke.
Cauchyjev izrek in Cauchyjeve formule.
Functions of complex variable. Elementary
functions: linear function, Möbius functions.
Power series. Elementary functions defined by
power series. Logarithm and cyclometric
functions.
Holomorphic functions. Cauchy – Riemann
theorem. Conformality of holomorphic
mappings.
Complex line integrals. Cauchy integral theorem
and Cauchy formula. Liouville theorem. Power
Liouvilleov izrek. Taylorjeva vrsta.
Laurentova vrsta. Klasifikacija izoliranih
singularnih točk. Mali Piccardov izrek. Izrek o
residuih. Uporaba pri računanju realnih
integralov.
Laplaceova in Fourierova transformacija.
Uporaba.
series representation.
Laurent series. Classification of isolated
singularity. Behaviour of holomorphic function
near isolated singularity. Little Piccard
Theorem. Residui theorem. Applications to the
calculations of definite integrals and sums.
Laplace and Fourier transforms. Applications.
Temeljni literatura in viri / Readings:
S. G. Krantz: Handbook of Complex Variables, Birkhäuser, Boston, 1999.
J.B.Conway: Functions of One Complex Variable I, 2nd edition, Springer, New York, 1995.
L. Ahlfors: Complex Analysis, 3rd edition, McGraw-Hill, New york, 1979.
Cilji in kompetence:
Objectives and competences:
Študent poglobi znanje iz osnov teorije funkcij
kompleksne spremenljivke ter poglobi znanje
iz uporabnih aspektov te teorije, predvsem v
povezavi s preslikovanji območij, pri računanju
določenih integralov, seštevanju vrst ter
reševanju diferencialnih enačb.
Deepening the knowledge of concepts from the
theory of functions of one complex variable. To
deepen the knowledge of possible applications
of this theory, specialy in connection with
transformations of the regions, calculating
definite integrals and sums and solving
differential equations.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Študent razume pojem holomorfne funkcije
pozna osnovne s tem povezane rezultate,
posebej tiste, ki se nanašajo na integracijo
in na integralsko reprezentacijo ter
reprezentacijo s potenčno vrsto.
Študent razume koncept preslikovanja
območij z uporabo ulomljenih linearnih in
drugih preprostejših elementarnih funkcij v
kompleksnem.
Študent razume pojem izolirane singularne
funkcije in pozna uporabno vrednost izreka
o residuumih.
Študent razume koncepta Laplaceove in
Fourierove transformacije in pozna njune
možnosti uporabe.
Prenesljive/ključne spretnosti in drugi atributi:
Ilustracija dejstva, da nam teorija, navidez
oddaljene od realnosti, lahko ponudi mnoge
praktično uporabne rezultate.
Dojemanje transformacij kot opcije za
pretvorbo matematične situacije v drugo
Knowledge and Understanding:
To understand the concept of holomorphic
function and to know the basic results,
specialy those about line integrals and about
the integral and the power series
representation of holomorphic functions.
To understend the concept of transforming
plane regions using Möbius transformations
and other basic elementary functions.
To understand the concept of isolated
singularity and to be aware of the
importance of the residui theorem.
To understand the concepts of Laplace and
Fourier tranformations and to be aware of
their possible applications.
Transferable/Key Skills and other attributes:
An illustration of the fact, that a more
abstract theory can give us many nice results
with useful practical applications.
Understanding the concept of
transformations as tools to convert a certain
situacijo, ki je udobnejša za obravnavo. mathematical situation into a more
convenient one.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Izpit:
Pisni izpit – problemi
Ustni izpit – teorija
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljen pisni izpit – problemi je
pogoj za pristop k ustnemu izpitu –
teorija.
Pisni izpit – problemi se lahko
nadomesti z dvema delnima testoma
(sprotne obveznosti).
Delež (v %) /
Weight (in %)
50%
50%
Exams:
Written exam – problems
Oral exam – theory
Each of the mentioned assessments must
be assessed with a passing grade.
Passing grade of written exam –
problems is required to take the oral
exam – theory.
Written exam – problems can be replaced
with two mid-term tests.
Reference nosilca / Lecturer's
references:
1. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel,
TARANENKO, Andrej. On the vertex k-path cover. Discrete Applied Mathematics, ISSN 0166-
218X. [Print ed.], 2013, vol. 161, iss. 13/14, str. 1943-1949.
http://dx.doi.org/10.1016/j.dam.2013.02.024. [COBISS.SI-ID 19859464]
2. JAKOVAC, Marko, TARANENKO, Andrej. On the k-path vertex cover of some graph
products. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2013, vol. 313, iss. 1, str. 94-100.
http://dx.doi.org/10.1016/j.disc.2012.09.010, doi: 10.1016/j.disc.2012.09.010. [COBISS.SI-ID
19464968]
3. JAKOVAC, Marko, PETERIN, Iztok. On the b-chromatic number of some graph products.
Studia scientiarum mathematicarum Hungarica, ISSN 0081-6906, 2012, vol. 49, no. 2, str. 156-
169. http://dx.doi.org/10.1556/SScMath.49.2012.2.1194. [COBISS.SI-ID 16321113]
4. CABELLO, Sergio, JAKOVAC, Marko. On the b-chromatic number of regular graphs. Discrete
Applied Mathematics, ISSN 0166-218X. [Print ed.], 2011, vol. 159, iss. 13, str. 1303-1310.
http://dx.doi.org/10.1016/j.dam.2011.04.028, doi: 10.1016/j.dam.2011.04.028. [COBISS.SI-ID
15914329]
5. JAKOVAC, Marko, KLAVŽAR, Sandi. The b-chromatic number of cubic graphs. Graphs and
combinatorics, ISSN 0911-0119, 2010, vol. 26, no. 1, str. 107-118.
http://dx.doi.org/10.1007/s00373-010-0898-9. [COBISS.SI-ID 15522905]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Teorija grup
Course title: Group Theory
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul S2 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module S2 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Dušan PAGON
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za
opravljanje študijskih obveznosti:
Prerequisits:
Ne. None.
Vsebina: Content (Syllabus outline):
Simetrične grupe. Konjugirani elementi in
podgrupe. Delovanje grupe na množico.
Linearne grupe: glavne lastnosti in primeri.
Izreki Sylowa. Podajanje grupe z generatorji
in relacijami. Direktni produkt grup.
Abelove grupe.
Enostavne grupe. Komutant grupe, rešljivost
končnih p-grup in grupe zgornje trikotnih
matrik.
Upodobitve grup: osnovni pojmi in primeri.
Symetric groups. Conjugated elements and
subgroups. The action of a group on a set. Linear
groups: main properties and examples.
Sylow's theorems. Definition of a group by
generators and relations. Direct product of groups.
Abelian groups.
Simple groups. Derived group, solvability of finite
p-groups and the group of upper triangular matrices.
Representations of groups: concepts and examples.
Temeljni literatura in viri / Readings:
W. Y. Gilbert, W. K. Nicholson, Modern Algebra with Applications, Wiley, Chichester 2004
S. Lang, Undergraduate Algebra, Springer, 2005
J. F. Humphreys, A Course in Group Theory, Oxford University Press, 1997
I. Vidav, Algebra, DMFA, Ljubljana 1980
Cilji in kompetence:
Objectives and competences:
Študentje poglobijo znanje osnove teorije grup
in njihovih upodobitev. Students deepen the knowledge of the basic
concepts of the theory of groups and their
representations.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Razumevanje osnov teorije grup in
njihovih upodobitev.
Poznavanje osnovnih značilnosti in
tipičnih primerov grup.
Prenesljive/ključne spretnosti in drugi atributi:
Pridobljena znanja prispevajo k
razumevanju ostalih predmetov s
področja algebre, geometrije in
topologije.
Knowledge and Understanding:
To understand the main concepts of
groups and their representations.
To recognize the typical properties and
main examples of groups.
Transferable/Key Skills and other attributes:
The obtained knowledge contributes to
better understanding of other subjects in
fields of algebra, geometry and topology.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit – praktični del
Ustni izpit – teoretični del
Pisni izpit – praktični del se lahko
nadomesti z dvema delnima testoma (sprotni
obveznosti).
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
Written exam – practical part
Oral exam – theoretical part
Written exam – practical part can be
replaced by two partial tests (mid-
term testing).
Reference nosilca / Lecturer's references:
1. PAGON, Dušan, REPOVŠ, Dušan, ZAICEV, Mikhail. On the codimension growth of simple
color Lie superalgebras. J. Lie theory, 2012, vol. 22, no. 2, str. 465-479.
http://www.heldermann.de/JLT/JLT22/JLT222/jlt22017.htm. [COBISS.SI-ID 16070233]
2. PAGON, Dušan. Simplified square equation in the quaternion algebra. International journal of
pure and applied mathematics, 2010, vol. 61, no. 2, str. 231-240. [COBISS.SI-ID 17718024]
3. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. On chains in H-closed topological pospaces.
Order (Dordr.), 2010, vol. 27, no. 1, str. 69-81. http://dx.doi.org/10.1007/s11083-010-9140-x.
[COBISS.SI-ID 15502169]
4. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. The continuity of the inversion and the
structure of maximal subgroups in countably compact topological semigroups. Acta math. Hung.,
2009, vol. 124, no. 3, str. 201-214. http://dx.doi.org/10.1007/s10474-009-8144-8, doi:
10.1007/s10474-009-8144-8. [COBISS.SI-ID 15212121]
5. PAGON, Dušan. The dynamics of selfsimilar sets generated by multibranching trees.
International journal of computational and numerical analysis and applications, 2004, vol. 6, no.
1, str. 65-76. [COBISS.SI-ID 14037081]
Predme
Course
ŠtudijStudy
Ma
Mat
Vrsta pr
Univerz
PredavLectu
45
Nosilec
Jeziki / Languag
Pogoji zštudijsk
Jih ni.
Vsebina
FinančnČasovnaVrednotUvod v Strošek InvesticOcena dStrukturNavadnDolgoroFinancir
et:
title:
jski programy programm
atematika, 2
thematics, 2
redmeta / C
zitetna koda
vanja ures
SeSe
5
predmeta
ges:
za vključitevkih obvezno
a:
na funkcija va vrednost dtenje finančobvladovankapitala
cijske odločidenarnega tra kapitala i lastniški kočni dolžnišranje z zaku
UČN
Uvod v pos
Introductio
m in stopnjme and leve
2. stopnja
2nd degree
Course type
a predmeta
eminar eminar
/ Lecturer:
Pred
Vaje /
v v delo oz.osti:
v podjetju denarja čnih instrumnje tveganj
itve toka
apital in poki instrumeupom
NI NAČRT P
lovne finan
n to corpor
a el
e
a / Universi
Vaje Tutorial
30
Prof. d
davanja / Lectures:
P
Tutorial: D
za opravlja
mentov
litika dividenti
PREDMETA /
ce za matem
rate finance
ŠtudijskaStudy
ty course c
Kliničnewor
dr. Timotej
Prof. ddr. Ti
Doc. dr. Fra
anje Pr
Th
Co
end
FiTiVaInCoInFoCaEqLoLe
/ COURSE S
matike
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Drugšt
Jagrič, CRM
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rerequisits:
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nancial funme value oaluation of ntroduction ost of capitanvestment dorecasting capital structquity financong‐term deeasing
SYLLABUS
maticians
LAc
1
1
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S
M
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ne.
labus outlin
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Letnik cademic year
1. ali 2.
1. or 2.
Samost. deloIndivid. work
135
ne):
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vidend polic
SemesterSemester
1. ali 3.
1. or 3.
o ECTS
7
y
r r
Upravljanje obratnega kapitala Upravljanje s terjatvami do kupcev in zalogami
Working capital management Accounts receivable and inventory management
Temeljni literatura in viri / Readings:
Berk, A., Lončarski, I., Zajc, P. in drugi, (2007). Poslovne finance, Ljubljana: Ekonomska fakulteta.ZRFRS. 2003. Slovenski poslovnofinančni standardi – Kodeks poslovnofinančnih načel. Ljubljana. (dostopno na www.si‐revizija.si). ZFPPIPP‐NUPB št. 14.(uvodni členi finančne vsebine). Tuji vir: Keown, A.J., Martin, J.D, Petty, J.W. 2014. Foundations of Finance. (primerna tudi starejša izdaja).
Cilji in kompetence:
Objectives and competences:
Študenti pri tem predmetu: Spoznajo teoretično ogrodje poslovnih financ in njihovo vlogo v procesu vodenja podjetja ter prepoznavajo ključne notranje in zunanje vire informacij za sprejemanje finančnih odločitev. in osvojijo osnove dobre prakse za apliciranje teh znanj. Pridobijo sposobnost uporabe teoretičnega znanja za reševanje praktičnih izzivov s pomočjo dela na raznolikih in razumljivih primerih v realističnih okoliščinah. Osvojijo standard dobre prakse in teorije, ki jim omogoča preudarno sprejemanje poslovno‐finančnih odločitev.
In this course students: recognize the theoretical framework of corporate finance and its role in a company management process and they are capable to recognize key internal and external information sources for financial decision making; earn the capability to use theoretical knowledgefor solving practical issues by working on various examples in understandable but realistic circumstances; acquire a standard of best practice and theory which enables them to find a solid ground for prudent financial decisions.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje: Študenti: pridobijo znanje na področju osnov poslovnih financ; se naučijo strukturirati in razložiti fenomene na poslovno‐finančnem področju; pridobi praktične izkušnje na področju finančnega upravljanja in vodenja podjetij.
Knowledge and understanding: Students: acquire knowledge in the area of corporate finance fundamentals; are able to structure and explain phenomena in the field of finance in a company; receive practical experience in the field of corporate financial management.
Metode poučevanja in učenja:
Learning and teaching methods:
klasična predavanja AV predstavitve obravnava primerov
common lectures AV presentations case studies
Načini ocenjevanja:
Delež (v %) / Weight (in %)
Assessment:
Način (pisni izpit, ustno izpraševanje, naloge, projekt) Pisni izpit ali 2 kolokvija. 100%
Type (examination, oral, coursework, project): Written examtion or 2 colloquiums.
Reference nosilca / Lecturer's references:
ZDOLŠEK, Daniel, JAGRIČ, Timotej, ODAR, Marjan. Identification of auditor´s report qualifications : an empirical analysis for Slovenia. Ekonomska istraživanja, ISSN 1331‐677X, 2015, vol. 28, no. 1, str. 994‐1005. http://www.tandfonline.com/doi/pdf/10.1080/1331677X.2015.1101960, doi: 10.1080/1331677X.2015.1101960. [COBISS.SI‐ID 12136476], [JCR, SNIP, WoS do 8. 2. 2016: št. citatov (TC): 0, čistih citatov (CI): 0, Scopus do 5. 9. 2016: št. citatov (TC): 0, čistih citatov (CI): 0] BRICELJ, Bor, STRAŠEK, Sebastjan, JAGRIČ, Timotej. Financial crisis and the liquidity effect on market risk. The business review, Cambridge, ISSN 1553‐5827, 2014, vol. 22, no. 1, str. 127‐133. [COBISS.SI‐ID 11727900] TREFALT, Polona, JAGRIČ, Timotej. Kreditno tveganje in finančne omejitve slovenskih podjetij. IB revija, ISSN 1318‐2803. [Slovenska tiskana izd.], 2014, letn. 48, št. 1, str. 29‐42, ilustr. http://www.umar.gov.si/fileadmin/user_upload/publikacije/ib/2014/IB01‐14splet.pdf#page=31. [COBISS.SI‐ID 11715356] LEŠNIK, Tomaž, KRAČUN, Davorin, JAGRIČ, Timotej. Tax compliance and corporate income tax ‐ the case of Slovenia. Lex localis, ISSN 1581‐5374, Oct. 2014, vol. 12, no. 4, str. 793‐811, doi: 10.4335/12.4.793‐811(2014). [COBISS.SI‐ID 11815964], [JCR, SNIP, WoS do 2. 9. 2015: št. citatov (TC): 1, čistih citatov (CI): 1, Scopus do 2. 9. 2015: št. citatov (TC): 1, čistih citatov (CI): 1] ZDOLŠEK, Daniel, JAGRIČ, Timotej. Audit opinion identification using accounting ratios : experience of United Kingdom and Ireland. Aktual´ni problemi ekonomìki, ISSN 1993‐6788, 2011, no. 1 (115), str. 285‐310, graf. prikazi, tabele. [COBISS.SI‐ID 10625564], [JCR, SNIP, WoS do 5. 6. 2015: št. citatov (TC): 1, čistih citatov (CI): 1, Scopus do 14. 10. 2015: št. citatov (TC): 2, čistih citatov (CI): 2]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Borzni trendi in strategije
Course title: Stock Market Trends and Strategies
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30
135 7
Nosilec predmeta / Lecturer: Sebastjan STRAŠEK
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Poslovni ciklus
Investicijski trgi in transakcije
Pozicioniranje sektorjev v borznem trendu
Splošni indikatorji trgov in strategije
Psihološki tržni indikatorji
Mednarodne povezave borznih trendov
Fundamentalna analiza
Tehnična analiza
Borzne krize in modeli reševanja
Business cycle
Investment markets and transactions
Positioning of sectors in market trend
General market indicators and strategies
Psychological market indicators
International links between market trends
Fundamental analysis
Stock market crises and models of resolving
Temeljni literatura in viri / Readings:
Strašek, S. in Jagrič, T. Borzni trendi in strategije (načrtovana izdaja v letu 2007).
Gitman L., Joehnk, M. 1996. Fundamentals of Investing. Harper&Collins Publishers.
Teweles, R., Bradley, E. 2003. The Stock Market. John Wiley&Sons, Co.
Cilji in kompetence:
Objectives and competences:
Predmet omogoča poglabljanje znanj s
področja delovanja kapitalskih trgov.
Predmet obravnava povezavo med
poslovnim ciklusom in borznimi trendi,
makroekonomske in mikroekonomske
implikacije sprememb fundamentalnih
spremenljivk, osnove tehnične in
fundamentalne analize, značilnosti
potencialnih borznih strategij ter
obnašanje akterjev v različnih fazah
borznega in poslovnega ciklusa.
The aim of the course is to deepen the
knowledge on the stock market
functioning. The course researches the
links between business cycle and the
stock trends, macroeconomic and
microeconomic implications of the
changes in fundamentals, the basics of
technical and fundamental analysis, the
characteristics of potential stock market
strategies and behavior of players in
different phases of stock market and
business cycle.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
- znanje o merodajnih informacijah za
poslovno odločanje in tržne strategij;
- zmožnost analiziranja borznih trendov
in individualnih delnic;
- razumevanje gospodarskih posledic
sprememb v makro in mikro okolju na
pozicioniranje delnic.
Prenesljive/ključne spretnosti in drugi atributi:
- sposobnost analize in sinteze;
- sposobnost uporabe znanja v praksi;
- samostojno delo;
- ustna in pisna komunikacija;
- reševanje problemov;
- sposobnost prilagajanja novim
razmeram.
Knowledge and Understanding:
- knowledge about relevant information
- for business decisions and market
strategies;
- capability to analyze stock market trends
and individual stocks;
- comprehension of economic
consequences of changes in macro and
micro environment on stocks
positioning.
Transferable/Key Skills and other attributes:
- capability for analysis and synthesis;
- capacity for applying knowledge in
practice;
- autonomous work;
- oral and written communication;
- problem solving;
- capacity to adapt to new situations.
Metode poučevanja in učenja:
Learning and teaching methods:
Pri predmetu so uporabljene sledeče metode
poučevanja in učenja:
predavanja (predavatelj bo podal študentom
vsebino ključnih teorij in tehnik);
vodene vaje v računalniški učilnici (primeri
modeliranja in razprava o domačih nalogah);
individualne konzultacije s predavateljem;
samostojno delo v računalniški učilnici, s
posebnim poudarkom na uporabi interneta
The following methods and forms of study are
used in the course:
lectures (lecturer will provide students with
knowledge of the fundamental theories and
techniques);
guided classes in computer room (sample
modeling is done and the main problems of
home assignments are discussed);
teachers' consultations;
(izdelava domačih nalog z uporabo Excela,
delo z ekonomskimi bazami podatkov, učna
gradiva na internetu, spletne predstavitve);
samostojni študij gradiva.
self study in computer room, in particular with
the Internet (making home assignments using
Excel, work with economic data bases, study
guides on the Internet, looking through sets of
lecture slides);
self study with literature.
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit
Seminarska naloga
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Delež (v %) /
Weight (in %)
80%
20%
Type (examination, oral, coursework,
project):
Written exam
Seminar paper
Each of the mentioned commitments
must be assessed with a passing grade.
Reference nosilca / Lecturer's
references:
1. STRAŠEK, Sebastjan, MUNDA, Gal. Beating the market in less developed financial
exchange. Aktual. probl. ekon., 2012, no. 1 (127), str. 425-433. [COBISS.SI-
ID 10971420]
2. MUNDA, Gal, STRAŠEK, Sebastjan. Use of the TRP ratio in selected countries =
Uporaba TRP indikatorjev v izbranih državah. Naše gospod., 2011, letn. 57, št. 1/2, str.
55-60. [COBISS.SI-ID 10578716]
3. JAGRIČ, Timotej, MARKOVIČ-HRIBERNIK, Tanja, STRAŠEK, Sebastjan,
JAGRIČ, Vita. The power of market mood - Evidence from an emerging market. Econ.
model.. [Print ed.], 2010, vol. 27, iss. 5, str. [959]-967,
doi: 10.1016/j.econmod.2010.05.005. [COBISS.SI-ID 10310428]
4. STRAŠEK, Sebastjan, ŠPES, Nataša. Pojasnjevalna moč modelov finančnih
kriz. Organizacija (Kranj), jul./avg. 2010, letn. 43, št. 4, str. A 119-A 128. [COBISS.SI-
ID 10298908]
5. STRAŠEK, Sebastjan, JAGRIČ, Timotej. Policy failures and current crisis. Rev.
econ. (Sibiu), 2010, vol. 50, no. 3, str. 456-462. [COBISS.SI-ID 10432284]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Diferencialne enačbe
Course title: Differential equations
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja
1. 2.
Mathematics, 2nd
degree
1. 2.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
60
45
195 10
Nosilec predmeta / Lecturer: Blaž ZMAZEK
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje odvodov in integralov. Knowledge of differentials and integrals.
Vsebina: Content (Syllabus outline):
1. Osnovni pojmi: Konstrukcija NDE,
grafično reševanje, enačbe z ločljivima
spremenljivkama.
2. Navadne diferencialne enačbe: Osnovni tipi
NDE, parametrično reševanje, singularni
integrali, uporaba v geometriji in fiziki.
3. Eksistenčni izreki: Lokalni in globalni
eksistenčni izrek za NDE, odvisnost rešitve
od parametra, splošna enačba prvega reda.
4. Linearne diferencialne enačbe: Sistemi
linearnih diferencialnih enačb, Liouvilleva
1. Basics: Construction of ODE, graphical
solutions, equations with separable variables.
2. Ordinary differential equations: Basic types
of ODE, parametric solving, singular
integrals, applications in geometry and
physics.
3. Existence theorems: Local and global
existence theorems for ODE, solution
dependence of parameter, ODE of first
order.
4. Linear differential equations: Systems of
formula, linearna diferencialna enačba reda
n, LDE z realnimi in konstantnimi
koeficienti, Euler-Cauchyjeva enačba.
5. Variacijski račun: Naloge variacijskega
računa, osnovni izrek variacijskega računa,
Euler-Lagrangeva enačba, posplošitve,
dinamični robni pogoji, izoperimetrični
problem, Lagrangeva naloga.
6. Diferencialne enačbe v kompleksnem:
Rešitev v okolici regularne točke,
homogena linearna enačba, pravilne
singularne točke, Frobeniusova metoda.
7. Trigonometrične vrste in transformacije:
Fourierova vrsta, Fourierova
transformacija, diskretna Fourireova
transformacija.
8. Besselova diferencialna enačba: Rešitve
Besselove DE, integralske representacije.
linear differential equations, Liouvill's
formula, linear differential equation of n-th
order, LDE with real and constant
coefficients, Euler-Cauchy equation.
5. Calculus of variations: Calculus of variations
tasks, fundamental theorem of calculus of
variations, Euler-Lagrange equation,
generalizations, dynamic boundary
conditions, isoperimetric problem, Lagrange
task.
6. Differential equations in complex: Solutions
in regular point surroundings, homogeneous
linear equation, proper singular point,
Frobenius's method.
7. Trigonometric series and transformations:
Fourier series, Fourier transformation,
discrete Fourier transform
8. Bessel differential equation: Solutions of
Bessel DE, integral representations.
Temeljni literatura in viri / Readings:
E. Zakrajšek, Analiza III, DMFA Slovenije, Ljubljana, 1998.
F. Križanič, Navadne diferencialne enačbe in variacijski račun, DZS, Ljubljana 1974.
W. Kaplan, Advanced Calculusi, Fourth Edition. Addisson-Wesley Publishing Company, Redwood
City, California, 1991.
Cilji in kompetence:
Objectives and competences:
Temeljito poglobiti znanje iz navadnih
diferencialnih enačbe, integralske
transformacije in variacijski račun.
To deepen the knowledge of ordinary
differential equations, integral transformations
and calculus of variations.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Poznavanje in razumevanje
diferencialnih enačb in metod za
njihovo reševanje.
Razumevanje in uporaba integralskih
transformacij in variacijskega računa.
Prenesljive/ključne spretnosti in drugi atributi:
Pridobljena znanja so podlaga za mnogo
predmetov v nadaljevanju študija.
Knowledge and Understanding:
Knowledge and understanding of
differential equations and methods of
their solution.
Be able to understand and implement
integral transformations and calculus of
variations.
Transferable/Key Skills and other attributes:
The obtained knowledge is a basis for
many of the later subjects.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje, Delež (v %) / Type (examination, oral, coursework,
naloge, projekt)
Pisni test – praktični del
Izpit (ustni) – teoretični del
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Pozitivna ocena pri pisnem testu je
pogoj za pristop k izpitu.
Weight (in %)
50%
50%
project):
Written test – practical part
Exam (oral) – theoretical part
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grade of the written test is
required for taking the exam.
Reference nosilca / Lecturer's
references:
1. PRNAVER, Katja, ZMAZEK, Blaž. On total chromatic number of direct product graphs. J.
appl. math. comput. (Internet), 2010, issue 1-2, vol. 33, str. 449-457.
http://dx.doi.org/10.1007/s12190-009-0296-8, doi: 10.1007/s12190-009-0296-8. [COBISS.SI-ID
17523720]
2. ZMAZEK, Blaž, ŽEROVNIK, Janez. The Hosoya-Wiener polynomial of weighted trees. Croat.
chem. acta, 2007, vol. 80, 1, str. 75-80. [COBISS.SI-ID 11338518]
3. ZMAZEK, Blaž, ŽEROVNIK, Janez. Weak reconstruction of strong product graphs. Discrete
math.. [Print ed.], 2007, vol. 307, iss. 3-5, str. 641-649.
http://dx.doi.org/10.1016/j.disc.2006.07.013. [COBISS.SI-ID 14184025]
4. ZMAZEK, Blaž, ŽEROVNIK, Janez. On domination numbers of graph bundles. J. Appl. Math.
Comput., Int. J., 2006, vol. 22, no. 1/2, str. 39-48. [COBISS.SI-ID 10636822]
5. ZMAZEK, Blaž, ŽEROVNIK, Janez. On generalization of the Hosoya-Wiener polynomial.
MATCH Commun. Math. Comput. Chem. (Krag.), 2006, vol. 55, no. 2, str. 359-362. [COBISS.SI-
ID 13990745]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Temelji finančnega inženiringa
Course title: Foundations of financial engineering
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul F1 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module F1 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30
135 7
Nosilec predmeta / Lecturer: Miklavž MASTINŠEK
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
1.Matematične osnove
2.Izvedeni finančni instrumenti
3.Tveganje in varnost
4.Opcije
5.Vrednotenje opcij, hedging
6.Binomski model
7.Black-Scholesov
8.Delta, gamma, sigma
9.Monte-Carlo metoda
10.Vodenje portfelja
11.Realne opcije
1.Mathematical tools
2.Financial derivatives
3.Risk and security
5.Option valuation, hedging
6.Binomial model
7.Black-Scholes model
8.The greeks
9.Monte-Carlo method
10.Portfolio management
11.Real options
Temeljni literatura in viri / Readings:
1. Hull J., »Options, Futures and other Derivative Securities«, New Jersey, Prentice Hall Int.,
1996.
2. Wilmott P.« Paul Wilmott on Quantitative Finance«, John Wiley, (2000).
3. Cuthbertson K., »Financial engineering: derivatives and risk management«, Wiley,
(2001)
Cilji in kompetence:
Objectives and competences:
Namen predmeta je posredovati temeljna
teoretična in praktična znanja potrebna pri
kvantitativnem in kvalitativnem obravnavanju
nalog in procesov s področja finančnega
inženiringa. Prav tako je namen predmeta dati
osnovo za spremljanje sodobne literature in
nadaljnje strokovno izpopolnjevanje.
The objective is to provide fundamental
theoretical knowledge and practical skills
of financial engineering.
The objective is also to enable the students
for additional learning and individual study of
new methods.
Predvideni študijski rezultati:
Intended learning outcomes:
Poglobljeno znanje in razumevanje temeljnih
vsebin in orodij potrebnih za strokovno
korektno vodenje poslov s področja finančnega
inženiringa.
Prenesljive/ključne spretnosti in drugi atributi:
Sposobnost samostojnega praktičnega in
teoretičnega dela. Zmožnost nadaljnega študija
novih kvantitativnih
metod finančnega inženiringa.
Knowledge and Understanding:
Fundamental theoretical knowledge and
practical skills of financial engineering.
Transferable/Key Skills and other attributes:
Capabilitiy of understanding and application of
knowledge in praxis. Ability of additional
learning and individual study of new methods.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja, tehnične demonstracije,
aktivne vaje, seminarske vaje
Written examination
Seminary work
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit
seminarska naloga
Delež (v %) /
Weight (in %)
80%
20%
Type (examination, oral, coursework,
project):
Written exam
Semynar
Reference nosilca / Lecturer's
references:
1. MASTINŠEK, Miklavž. Charm-adjusted delta and delta gamma hedging. J. deriv., 2012, vol.
19, no. 3, str. 69-76, doi: 10.3905/jod.2012.19.3.069. [COBISS.SI-ID 10970908]
2. MASTINŠEK, Miklavž. Financial derivatives trading and delta hedging = Trgovanje z
izvedenimi finančnimi instrumenti ter delta hedging. Naše gospod., 2011, letn. 57, št. 3/4, str. 10-
15. [COBISS.SI-ID 10733084]
3. MASTINŠEK, Miklavž. Descrete-time delta hedging and the Black-Scholes model with
transaction costs. Math. methods oper. res. (Heidelb.). [Print ed.], 2006, vol. 64, iss. 2, str. [227]-
236, doi: 10.1007/s00186-006-0086-0. [COBISS.SI-ID 8939292]
4. MASTINŠEK, Miklavž. Identifiability for a partial functional differential equation. Acta sci.
math. (Szeged), 2003, vol. 69, str. 121-130. [COBISS.SI-ID 7029276]
5. MASTINŠEK, Miklavž. Norm continuity for a functional differential equation with fractional
power. International journal of pure and applied mathematics, 2003, vol. 5, no. 1, str. 49-56.
[COBISS.SI-ID 6783772]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Osnove programiranja v diskretni matematiki
Course title: Basic programming in discrete mathematics
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul F1 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module F1 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30 135 7
Nosilec predmeta / Lecturer: Aleksander VESEL
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Vsebina predmeta se prilagaja aktualnim
potrebam in razvoju. Poglobili bomo znanje iz
uporabe računalnika pri reševanju
matematičnih problemov, predvsem s področja
diskretne matematike.
- Relacije in algoritmi nad relacijami
- Boolova algebra
- Prirejanja v grafih
The contents of this subject is adjusted to the
current needs and development. We will deepen
the knowledge of using a computer to solve
mathematical problems, mainly from discrete
mathematics.
- relations and algorithms on relations
- Bool algebra
- matchings in graphs
Temeljni literatura in viri / Readings:
B. Vilfan, Osnovni algoritmi, ISBN 961-6209-13-2, Založba FER in FRI, 2. izd., 2002.
Kenneth H. Rosen, Discrete Mathematics and Its Applications, ISBN 007-2880-08-2, McGraw-
Hill, 6th ed., 2007.
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Introduction to
Algorithms, ISBN 026-2032-93-7, The MIT Press, 2nd ed., 2001.
Cilji in kompetence:
Objectives and competences:
Z uporabo modernega, predmetno usmerjenega
programskega jezika, poglobiti znanje iz
pristopov, podatkovnih struktur in algoritmov
pri reševanju matematičnih problemov.
With the usage of modern object oriented
programming language, to deepen the
knowledge of the basic approaches, data
structures and algorithms for solving
mathematical problems.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
podatkovne strukture matematičnih
modelov
razumevanje, implementacija in
uporaba pomembnejših algoritmov
Prenesljive/ključne spretnosti in drugi atributi:
uporaba matematičnih pojmov v
programskih aplikacijah
uporaba ustreznih podatkovnih struktur
pri implementaciji matematičnih
algoritmov
pridobljena znanja se prenašajo na
druge z računalništvom povezane
predmete
Knowledge and Understanding:
data structures of mathematical models
understanding, implementation and
usage of important algorithms
Transferable/Key Skills and other attributes:
the usage of mathematical notions in
applications
the usage of appropriate data structures
while implementing mathematical
algorithms
the obtained knowledge is transferable
to the other computer science oriented
subjects
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Računalniške vaje
Lectures
Computer exercises
Načini ocenjevanja:
Assessment:
Sprotno preverjanje:
Projekt
Pisni testi – teorija (3 do 5 pisnih testov
na semester)
Izpit:
Pisni izpit – problemi
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljene sprotne obveznosti so pogoj
za pristop k izpitu.
Delež (v %) /
Weight (in %)
40%
40%
20%
Mid-term testing:
Project
Written tests – theory (from 3 to 5
written tests during the semester)
Exams:
Written exam - problems
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grades of all mid-term testings
are required for taking the exam.
Reference nosilca / Lecturer's
references:
1. VESEL, Aleksander. Fibonacci dimension of the resonance graphs of catacondensed benzenoid
graphs. Discrete appl. math.. [Print ed.], 2013, str. 1-11, doi: 10.1016/j.dam.2013.03.019.
2. SHAO, Zehui, VESEL, Aleksander. A note on the chromatic number of the square of the
Cartesian product of two cycles. Discrete math.. [Print ed.], 2013, vol. 313, iss. 9, str. 999-1001.
3. KORŽE, Danilo, VESEL, Aleksander. A note on the independence number of strong products of
odd cycles. Ars comb., 2012, vol. 106, str. 473-481. [COBISS.SI-ID 16138006]
4. TARANENKO, Andrej, VESEL, Aleksander. 1-factors and characterization of reducible faces
of plane elementary bipartite graphs. Discuss. Math., Graph Theory, 2012, vol. 32, no. 2, str. 289-
297, doi: 10.7151/dmgt.1607. [COBISS.SI-ID 19104264]
5. SALEM, Khaled, KLAVŽAR, Sandi, VESEL, Aleksander, ŽIGERT, Petra. The Clar formulas
of a benzenoid system and the resonance graph. Discrete appl. math.. [Print ed.], 2009, vol. 157,
iss. 11, str. 2565-2569. http://dx.doi.org/10.1016/j.dam.2009.02.016. [COBISS.SI-ID 15142489
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Programiranje v diskretni matematiki
Course title: Programming in discrete mathematics
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul F1 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module F1 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 15 45 165 9
Nosilec predmeta / Lecturer: Andrej Taranenko
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Vsebina predmeta se prilagaja aktualnim
potrebam in razvoju. Poglobili bomo znanje iz
uporabe računalnika pri reševanju
matematičnih problemov, predvsem s področja
diskretne matematike.
- Relacije in algoritmi nad relacijami
- Boolova algebra
- Prirejanja v grafih
The contents of this subject is adjusted to the
current needs and development. We will deepen
the knowledge of using a computer to solve
mathematical problems, mainly from discrete
mathematics.
- relations and algorithms on relations
- Bool algebra
- matchings in graphs
Temeljni literatura in viri / Readings:
B. Vilfan, Osnovni algoritmi, ISBN 961-6209-13-2, Založba FER in FRI, 2. izd., 2002.
Kenneth H. Rosen, Discrete Mathematics and Its Applications, ISBN 007-2880-08-2, McGraw-
Hill, 6th ed., 2007.
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Introduction to
Algorithms, ISBN 026-2032-93-7, The MIT Press, 2nd ed., 2001.
Cilji in kompetence:
Objectives and competences:
Z uporabo modernega, predmetno usmerjenega
programskega jezika, poglobiti znanje iz
pristopov, podatkovnih struktur in algoritmov
pri reševanju matematičnih problemov.
With the usage of modern object oriented
programming language, to deepen the
knowledge of the basic approaches, data
structures and algorithms for solving
mathematical problems.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
podatkovne strukture matematičnih
modelov
razumevanje, implementacija in
uporaba pomembnejših algoritmov
Prenesljive/ključne spretnosti in drugi atributi:
uporaba matematičnih pojmov v
programskih aplikacijah
uporaba ustreznih podatkovnih struktur
pri implementaciji matematičnih
algoritmov
pridobljena znanja se prenašajo na
druge z računalništvom povezane
predmete
Knowledge and Understanding:
data structures of mathematical models
understanding, implementation and
usage of important algorithms
Transferable/Key Skills and other attributes:
the usage of mathematical notions in
applications
the usage of appropriate data structures
while implementing mathematical
algorithms
the obtained knowledge is transferable
to the other computer science oriented
subjects
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja, seminar
Računalniške vaje
Lectures, seminary
Computer exercises
Načini ocenjevanja:
Assessment:
Sprotno preverjanje:
Seminarska naloga
Projekt
Pisni testi – teorija (3 do 5 pisnih testov
na semester)
Delež (v %) /
Weight (in %)
20%
20%
40%
Mid-term testing:
Seminary work
Project
Written tests – theory (from 3 to 5
written tests during the semester)
Izpit:
Pisni izpit – problemi
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljene sprotne obveznosti so pogoj
za pristop k izpitu.
20%
Exams:
Written exam - problems
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grades of all mid-term testings
are required for taking the exam.
Reference nosilca / Lecturer's
references:
1. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel,
TARANENKO, Andrej. On the vertex k-path cover. Discrete appl. math.. [Print ed.], 2013, vol.
161, iss. 13/14, str. 1943-1949, doi: 10.1016/j.dam.2013.02.024. [COBISS.SI-ID19859464]
2. JAKOVAC, Marko, TARANENKO, Andrej. On the k-path vertex cover of some graph
products. Discrete math.. [Print ed.], 2013, vol. 313, iss. 1, str. 94-100.
http://dx.doi.org/10.1016/j.disc.2012.09.010, doi: 10.1016/j.disc.2012.09.010. [COBISS.SI-
ID19464968]
3. TARANENKO, Andrej, VESEL, Aleksander. 1-factors and characterization of reducible faces
of plane elementary bipartite graphs. Discuss. Math., Graph Theory, 2012, vol. 32, no. 2, str. 289-
297, doi: 10.7151/dmgt.1607. [COBISS.SI-ID 19104264]
4. TARANENKO, Andrej, ŽIGERT PLETERŠEK, Petra. Resonant sets of benzenoid graphs and
hypercubes of their resonance graphs. MATCH Commun. Math. Comput. Chem. (Krag.), 2012, vol.
68, no. 1, str. 65-77.http://www.pmf.kg.ac.rs/match/content68n1.htm. [COBISS.SI-ID 16051990]
5. KLAVŽAR, Sandi, SALEM, Khaled, TARANENKO, Andrej. Maximum cardinality resonant
sets and maximal alternating sets of hexagonal systems. Comput. math. appl. (1987). [Print ed.],
2010, vol. 59, no. 1, str. 506-513.http://dx.doi.org/10.1016/j.camwa.2009.06.011. [COBISS.SI-
ID 15383641]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Ekonometrija
Course title: Econometrics
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul F2 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module F2 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
60
45
165 9
Nosilec predmeta / Lecturer: Timotej JAGRIČ
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
- Uvod (Uvod v ekonometrijo, Ponovitev
statistike);
- Multipli regresijski model (Uvod, Ocena
parametrov, Lastnosti, Testiranje hipotez,
Mere primernosti, linearne transformacije,
napovedovanje);
- Neizpolnjevanje predpostavk (Specifikacija
modela, Normalna porazdelitev,
Multikolinearnost, Heteroskedastičnost,
Avtokorelacija);
-Introduction (Introduction to Econometrics,
Statistics Review);
-The Multiple Regression Model (Introduction,
Estimating the Parameters, Properties,
Hypothesis Testing, Goodness of Fit, linear
transformations, forecasting);
-Violations of Assumptions (Model
Specification, Multicollinearity,
Heteroskedasticity, Serial Correlation);
- Dummy variables;
- Slamnate spremenljivke;
- Odložene spremenljivke;
- Simultani sistemi;
LOGIT modeli.
- Lagged variables;
- Simultaneous systems;
- LOGIT models.
Temeljni literatura in viri / Readings:
N. Gujarati (2003). Basic Econometrics – Fourth Edition. McGraw-Hill, New York.
W. H. Green (2003). Econometric Analysis – Fifth Edition. Prentice Hall, New Jersey.
G. S. Maddala (2003). Introduction to Econometrics – Third Edition. John Wiley & Sons, New
York.
Cilji in kompetence:
Objectives and competences:
Študentje naj bi dobili znanja in spretnosti, ki
so potrebna za ekonometrično analizo. V
okviru predmeta se bodo študentje učili
tradicionalne ekonometrične metode. Razumeli
bodo bistvene razlike med časovnimi vrstami in
presečnimi podatki. Študentje bodo dobili
spretnosti, ki so potrebne za oblikovanje in
razvoj enostavnih in multiplih regresijskih
modelov. Obravnavane metode bodo razumeli
do te mere, da jih lahko uporabijo na realnih
ekonomskih bazah podatkov z uporabo
sodobnih ekonometričnih programov.
The students will get the knowledge and skills of
econometric analysis. In the course the students
will learn traditional econometric methods. They
will understand differences between the time
series and cross sections data. The students will
get the skills of construction and development of
simple and multiple regression models. The
students will be able to apply methods on real
economic data bases with modern econometric
software.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
- poznavanje osnovnih matričnih operacij in
njihova aplikacija v linearnih regresijskih
modelih;
- razumevanje predpostavk, na katerih
temeljijo linearni regresijski modeli;
- razumevanje posledic odstopanja modela
od teh predpostavk;
- poznavanje principov statističnega
testiranja;
- poznavanje uporabe računalniških
programov za ocenjevanje in testiranje
ekonometričnih modelov;
- interpretacija in komentiranje rezultatov;
- sposobnost prebiranja literature s področja
kvantitativnih ekonomskih analiz, ki
temeljijo na ekonometriji.
Prenesljive/ključne spretnosti in drugi atributi:
- sposobnost analize in sinteze;
Knowledge and Understanding:
- Use of basic matrix operations and their
application to the linear regression model;
- understand the assumptions of the linear
regression model
- awareness of the implications for the model
departures from assumptions;
- understand statistical testing principles;
- use software in the estimation and testing of
econometric models;
- interpret and discuss results;
- be able to understand quantitative econ.
literature that uses econometric methods.
Transferable/Key Skills and other attributes:
- capability for analysis and synthesis;
- capacity for applying knowledge in practice;
- autonomous work;
- oral and written communication;
- problem solving;
- sposobnost uporabe znanja v praksi;
- samostojno delo;
- ustna in pisna komunikacija;
- reševanje problemov;
- sposobnost prilagajanja novim razmeram;
- raziskovalne sposobnosti;
- sposobnost generiranja novih idej.
- capacity to adapt to new situations;
- research skills;
- capacity for generating new ideas.
Metode poučevanja in učenja:
Learning and teaching methods:
predavanja (predavatelj bo podal študentom
vsebino ključnih teorij in tehnik);
vodene vaje v računalniški učilnici (primeri
modeliranja in razprava o domačih
nalogah);
individualne konzultacije s predavateljem;
samostojno delo v računalniški učilnici, s
posebnim poudarkom na uporabi interneta
(izdelava domačih nalog z uporabo
računalnika, delo z ekonomskimi bazami
podatkov, učna gradiva na internetu, spletne
predstavitve predavanj iz ekonometrije);
samostojni študij gradiva
lectures (lecturer will provide students with
knowledge of the fundamental theories and
techniques);
guided classes in computer room (sample
modeling is done and the main problems of
home assignments are discussed);
teachers' consultations;
self study in computer room, in particular
with the Internet (making home assignments
using PC, work with economic data bases,
study guides on the Internet, looking through
sets of slides in Econometrics);
self study with literature
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
- seminarska naloga
- pisni izpit
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
- seminar work
- written examination
Reference nosilca / Lecturer's
references:
1. ŽUNKO, Matjaž, JAGRIČ, Timotej. Raven razkrivanja z metodo tvegane vrednosti v slovenskih
poslovnih bankah. Banč. vestn., apr. 2012, letn. 61, št. 4, str. 42-46. [COBISS.SI-ID 10994460]
2. ZDOLŠEK, Daniel, JAGRIČ, Timotej. Audit opinion identification using accounting ratios :
experience of United Kingdom and Ireland. Aktual. probl. ekon., 2011, no. 1 (115), str. 285-310,
graf. prikazi, tabele. [COBISS.SI-ID 10625564]
3. BEKŐ, Jani, JAGRIČ, Timotej. Demand models for direct mail and periodicals delivery services
: results for a transition economy. Appl. econ., apr. 2011, vol. 43, no. 9, str. 1125-1138, doi:
10.1080/00036840802600244. [COBISS.SI-ID 10071324]
4. JAGRIČ, Vita, JAGRIČ, Timotej. Primerjalna presoja bančnih bonitetnih modelov za
prebivalstvo = A comparative assessment of credit risk models for bank retail portfolio. Banč.
vestn., jan.-feb. 2011, letn. 60, št. 1/2, str. 48-52. [COBISS.SI-ID 10593052]
5. JAGRIČ, Timotej, JAGRIČ, Vita. A comparison of growing cell structures neural networks and
linear scoring models in the retail credit environment : a case of a small EU and EMU member
country. East. Europ. econ., nov-dec 2011, vol. 49, no. 6, str. 74-96, doi: 10.2753/EEE0012-
8775490605. [COBISS.SI-ID 10975772]
Fakulteta za naravoslovje in matematiko
Oddelek za matematiko in računalništvo
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Kombinatorična optimizacija
Course title: Combinatorial optimization
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika Modul F2 1 ali 2 1 ali 3
Mathematics Module F2 1 or 2 1 or 3
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Janez Žerovnik
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Jih ni. None.
Vsebina:
Content (Syllabus outline):
Obvezna vsebina, ki pri študentih vzpostavi
temeljni nabor znanj s področja kombinatorične
optimizacije:
Večkriterijska linearna optimizacija.
Ciljno programiranje. Celoštevilsko
programiranje.
Problem nahrbtnika in njegove različice.
Pretoki v omrežjih. Ford-Fulkersonov
algoritem.
Problem maksimalnega prirejanja.
Problem maksimalnega prereza.
Mandatory content, that familiarizes the students
with fundamentals of operations research and
mathematical programs:
Multicriteria linear optimization. Goal
programming. Integer programming.
Knapsack problems and its variants.
Network flows. Ford-Fulkerson’s algorithm.
Maximum matching problem.
Maximum cut problem.
Transport problem. Chinese postman
problem.
Transportni problem. Problem kitajskega
poštarja. Problem trgovskega potnika.
Aproksimacijski algoritmi.
Hevristike in metahevristike. Lokalna
optimizacija. Tabu search. Simulirano
ohlajanje. Genetski algoritmi.
Nevronske mreže. Samo-organizirajoče
se mreže.
V okviru vsebine študentje izberejo zahtevnejši
problem, s katerimi se poglobljeno ukvarjajo
pri seminarski nalogi. Problem je povezan z
njihovo bodočo kariero (praktični problemi iz
gospodarstva, teoretični problemi iz teorije
matematičnega programiranja in pripadajočih
numeričnih algoritmov). Preostala predavanja
se prilagodijo problemom, ki so jih izbrali
študentje, in obsegajo vsebine z naslednjega
seznama:
Optimalni portfelj celoštevilskih lotov in
celoštevilsko programiranje.
Problem delovnega razporeda.
Problem urnika.
Problem razporejanja nalog enega in več
strojev.
Problem optimizacije zalog.
Problemi rezanja in pakiranja.
Travelling salesman problem.
Approximation algorithms.
Heuristics and metaheuristics. Local
optimization. Tabu search. Simulated
annealing. Genetic aglorithms. Neural nets.
Self-organized maps.
Within the coursework, the students select
smaller problems whose result are coursework
reports. The problems are related to their future
career (practical problems from industry and
business, theoretical problems from the areas of
optimization, algorithms, modelling). The
content of the remaining lectures is selected
according to these projects from the following
list:
Optimal portfolio of integer lots and integer
programming.
Employee timetabling problem.
School timetabling problems.
Scheduling tasks of one or several
processors.
Stock optimization.
Cutting and packing problems.
Temeljni literatura in viri / Readings:
J.Žerovnik: Osnove teorije grafov in diskretne optimizacije, (druga izdaja), Fakulteta za
strojništvo, Maribor 2005.
R. Wilson, M. Watkins, Uvod v teorijo grafov, DMFA, Ljubljana 1997.
B. Robič: Aproksimacijski algoritmi, Založba FRI, Ljubljana 2002.
E. Zakrajšek: Matematično modeliranje, DMFA, Ljubljana 2004.
B. Korte, J. Vygen: Combinatorial Optimization, Theory and Algorithms, Springer, Berlin 2000.
D. Cvetković, V. Kovačević-Vujčić: Kombinatorna optimizacija, DOPIS Beograd 1996.
S. Zlobec, J. Petrić: Nelinearno programiranje, Naučna knjiga, Beograd 1989.
E. Kreyszig: Advanced Engineering Mathematics, (seventh edition), Wiley, New York 1993.
Cilji in kompetence:
Objectives and competences:
Usvojiti proces matematičnega modeliranja na
diskretnih optimizacijskih problemih.
Razviti kompetenco samostojnega apliciranja
matematičnih metod na probleme iz finančne
optimizacije, ekonomije, ter širše iz
gospodarstva.
Spoznati tehnološka orodja, s katerimi se
srečujemo pri reševanju optimizacijskih
Familiarize the students with the process of
mathematical modelling of continuous
optimization problems.
Develop competent skills of independent
application of mathematical methods to the
problems from financial optimization,
economics, and broader from industry.
Familiarize the students with technological tools
problemov in problemov matematičnega
modeliranja.
that assist solving optimization problems and
problems related to mathematical modelling.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Razumevanje zahtevnejših principov
kombinatorične optimizacije.
Poglobi znanje iz sodobnih metod za
reševanje problemov kombinatorične
optimizacije.
Poglobiti znanje iz diskretnih modelov
in drugih zahtevnih aplikacij
kombinatorične optimizacije v finančni
matematiki, optimiranju virov, in širše
Prenesljive/ključne spretnosti in drugi atributi:
Direktne aplikacije v finančni matematiki,
ekonomiji, poslovnih vedah, inžinirstvu,
fiziki in številnih drugih družboslovnih in
naravoslovnih vedah.
Suvereno obvladovanje procesa
matematičnega modeliranja in uporabe
tehnik kombinatorične optimizacije v
problemih s področja finančne
optimizacije, ekonomije in širše.
Knowledge and Understanding:
To be able to understand advanced principles
of combinatorial optimization.
To deepen the knowledge of modern
methods for solving combinatorial
optimization problems.
To deepen the knowledge of details of
discrete models and other advanced
applications of combinatorial optimization in
financial optimization, resource
optimization, and wider.
Transferable/Key Skills and other attributes:
Direct applications in finacial mathematics,
economy, business, engineering, physics,
and numerous other social and natural
sciences.
Competent mastering of the process of
mathematical modelling and applications of
the techniques of combinatorial optimization
in problems from financial optimization,
economics, and wider.
Metode poučevanja in učenja:
Learning and teaching methods:
Pri predavanjih študentje spoznajo snov
predmeta.
V okviru seminarskih vaj študentje
razumevanje snovi utrjujejo na večjem
projektu, povezanem z njihovo bodočo
kariero. Razporejeni so v večje skupine, ki
po metodah problemskega učenja
obravnavajo izbrani problem od zbiranja
podatkov, preko razvoja modela, izbora in
prilagajanja ustreznih tehnoloških rešitev do
razmisleka o implementaciji rešitve.
Koncept poučevanja je podrobneje
predstavljen kot ciljni aplikativni predmet.
At the lectures, the students are familiarized
with the course content.
At the tutorials, the student deepen their
understanding of the material by working on
an extensive problem related to their future
career. They are organized in larger groups
who research the choosen problem guided by
methodologies of problem-based learning.
Within solving the problem, they experience
all the stages from requirements and data
gathering, model development, selecting and
adapting technological solutions to
discussing various aspects of implementation
of the results.
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Seminarska naloga
Ustni izpit
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Pozitivna ocena pri seminarski nalogi je
pogoj za pristop k izpitu.
Delež (v %) /
Weight (in %)
80%,
20%
Type (examination, oral, coursework,
project):
Coursework report
Oral exam
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grade of the seminar exercise is
required for taking the exam.
Reference nosilca / Lecturer's
references:
1. ŠPARL, Petra, WITKOWSKI, Rafeł, ŽEROVNIK, Janez. 1-local 7/5-competitive algorithm for
multicoloring hexagonal graphs. Algorithmica, in press, doi: 10.1007/s00453-011-9562-x.
[COBISS.SI-ID 7055123]
2. ERVEŠ, Rija, ŽEROVNIK, Janez. Mixed fault diameter of Cartesian graph bundles. Discrete
appl. math.. [Print ed.], Available online 10. December 2011, doi: 10.1016/j.dam.2011.11.020.
[COBISS.SI-ID 15997718]
3. SAU WALLS, Ignasi, ŠPARL, Petra, ŽEROVNIK, Janez. Simpler multicoloring of triangle-free
hexagonal graphs. Discrete math.. [Print ed.], str. 181-187.
http://dx.doi.org/10.1016/j.disc.2011.07.031. [COBISS.SI-ID 6917907]
tipologija 1.08 -> 1.01
4. ŠPARL, Petra, WITKOWSKI, Rafał, ŽEROVNIK, Janez. A linear time algorithm for 7-
[3]coloring triangle-free hexagonal graphs. Inf. process. lett.. [Print ed.], 2012, vol. 112, iss. 14-15,
str. 567-571. http://dx.doi.org/10.1016/j.ipl.2012.02.008. [COBISS.SI-ID 7018003]
5. HRASTNIK LADINEK, Irena, ŽEROVNIK, Janez. Cyclic bundle Hamiltonicity. Int. j. comput.
math., 2012, vol. 89, iss. 2, str. 129-136, doi: 10.1080/00207160.2011.638375. [COBISS.SI-ID
15651862]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Funkcionalna analiza
Course title: Functional analysis
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 2. ali 4.
Mathematics, 2nd
degree 1. or 2. 2. or 4.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
60
45
195 10
Nosilec predmeta / Lecturer: Matej BREŠAR
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje linearne algebre in analize. Knowledge of linear algebra and analysis.
Vsebina: Content (Syllabus outline):
Banachovi prostori: vektorski in normirani
prostori, polnost, primeri; podprostori in
kvocientni prostori; končno-razsežni normirani
prostori, kompaktne množice; Banachove
algebre, spekter.
Linearni operatorji in funkcionali: omejeni in
neomejeni linearni operatorji; kompaktni
operatorji; izreki o enakomerni omejenosti,
odprti preslikavi in zaprtem grafu; dual, Hahn-
Banachov izrek, refleksivni prostori.
Banach spaces: vector spaces and normed
spaces, completness, examples; subspaces and
quotient spaces; finite dimensional normed
spaces, compact sets; Banach algebras,
spectrum.
Linear operators and functionals: bounded and
unbounded linear operators; compact operators;
uniform boundedness principle, open mapping
theorem, closed graph theorem; dual, Hahn-
Banach theorem, reflexive spaces.
Hilbertovi prostori: osnovni pojmi in primeri;
ortogonalnost, Rieszov izrek; ortonormirane
množice; adjungirani operatorji.
Hilbert spaces: basic concepts and examples;
orthogonality, Riesz theorem; orthonormal
bases, adjoint operators.
Temeljni literatura in viri / Readings:
B. Brown, A. Page, Elements of functional analysis, Van Nostrand, 1970.
M. Hladnik, Naloge in primeri iz funkcionalne analize in teorije mere, DMFA, 1985.
B. P. Rynne, M. A. Youngson, Linear functional analysis, Springer, 2000.
J. Vrabec, Metrični prostori, DMFA, 1993.
Cilji in kompetence:
Objectives and competences:
Poglobi znanje temeljnih konceptov in
rezultatov funkcionalne analize.
Deepening the knowledge of fundamental
concepts and results of functional analysis.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Banachovih prostorov
Hilbertovih prostorov
Teorije operatorjev
Prenesljive/ključne spretnosti in drugi atributi:
Pridobljeno znanje je podlaga tako za
teoretično kot uporabno analizo na višji ravni.
Knowledge and Understanding:
Banach spaces
Hilbert spaces
Operator theory
Transferable/Key Skills and other attributes:
The obtained knowledge is a basis for both
theoretical and applied analysis on an advanced
level.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit
Delež (v %) /
Weight (in %)
100%
Type (examination, oral, coursework,
project):
Written exam
Reference nosilca / Lecturer's
references:
1. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, ŠPENKO, Špela. Lie superautomorphisms
on associative algebras, II. Algebr. represent. theory, 2012, vol. 15, no 3, str. 507-525.
http://dx.doi.org/10.1007/s10468-010-9254-2. [COBISS.SI-ID 16299353]
2. BIERWIRTH, Hannes, BREŠAR, Matej, GRAŠIČ, Mateja. On maps determined by zero
products. Commun. Algebra, 2012, vol. 40, no. 6, str. 2081-2090.
http://dx.doi.org/10.1080/00927872.2011.570833. [COBISS.SI-ID 16315481]
3. BREŠAR, Matej, MAGAJNA, Bojan, ŠPENKO, Špela. Identifying derivations through the
spectra of their values. Integr. equ. oper. theory, 2012, vol. 73, no. 3, str. 395-411.
http://dx.doi.org/10.1007/s00020-012-1975-7. [COBISS.SI-ID 16339289]
4. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, KOCHETOV, Mikhail. Group gradings on
finitary simple Lie algebras. Int. j. algebra comput., 2012, vol. 22, no. 5, 1250046 (46 str.).
http://dx.doi.org/10.1142/S0218196712500464. [COBISS.SI-ID 16339545]
5. ALAMINOS, J., BREŠAR, Matej, ŠEMRL, Peter, VILLENA, A. R. A note on spectrum-
preserving maps. J. math. anal. appl., 2012, vol. 387, iss. 2, str. 595-603.
http://dx.doi.org/10.1016/j.jmaa.2011.09.024. [COBISS.SI-ID 16067673]
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Izbrana poglavja iz algebre Course title: Selected topics from algebra
Študijski program in stopnja Study programme and level
Študijska smer Study field
Letnik Academic
year
Semester Semester
Matematika 2. stopnja 1. ali 2. 1. ali 3.
Mathematics 2nd degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type Univerzitetna koda predmeta / University course code:
Predavanja Lectures
Seminar Seminar
Sem. vaje Tutorial
Lab. vaje Laboratory
work
Teren. vaje Field work
Samost. delo Individ.
work ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Matej BREŠAR Jeziki / Languages:
Predavanja / Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:
Prerequisits:
Poznavanje teorije grup. Knowledge of group theory.
Vsebina:
Content (Syllabus outline):
Kategorije: osnovni pojmi in primeri. Kolobarji: osnovni pojmi in primeri; glavni kolobarji, faktorizacija; posebni razredi kolobarjev. Moduli: osnovni pojmi in primeri; posebni razredi modulov. Polja: končne razširitve, algebraične razširitve; razpadna polja, algebraično zaprta polja; konstruktibilna števila; osnove Galoisjeve teorije.
Categories: basic concepts and examples. Rings: basic concepts and examples; principal ideal domains, factorization; special classes of rings. Modules: basic concepts and examples; special classes of modules. Fields: finite extensions, algebraic extensions; splitting fields, algebraically closed fields; constructible numbers; fundamentals of Galois theory.
Temeljni literatura in viri / Readings: W. Y. Gilbert, W. K. Nicholson, Modern algebra with applications, Chichester: Wiley, 2004. I. N. Herstein, Topics in algebra, Xerox, 1975. T. W. Hungerford, Algebra, Springer-Verlag, 1980. S. Lang, Undergraduate algebra, Springer, 2005. I. Vidav, Algebra, DMFA, 1980.
Cilji in kompetence:
Objectives and competences:
Poglobiti znanje nekaterih osnovnih področij abstraktne algebre.
Deepening the knowledge of some fundamental areas of abstract algebra..
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
• Teorije kolobarjev in modulov • Teorije polj
Knowledge and Understanding:
• Ring and module theory • Field theory
Prenesljive/ključne spretnosti in drugi atributi:
• Algebraične strukture so pojavljajo na vseh matematičnih področjih, zato mora biti profesionalni matematik z njimi poglobi znanje.
Transferable/Key Skills and other attributes:
• Algebraic structures appear in all mathematical areas, and therefore their knowledge is necessary for every professional mathematician.
Metode poučevanja in učenja:
Learning and teaching methods:
• Predavanja • Seminarske vaje
• Lectures • Tutorial
Načini ocenjevanja:
Delež (v %) / Weight (in %)
Assessment:
Pisni izpit
100%
Written exam
Reference nosilca / Lecturer's references: 1. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, ŠPENKO, Špela. Lie superautomorphisms on associative algebras, II. Algebr. represent. theory, 2012, vol. 15, no 3, str. 507-525. http://dx.doi.org/10.1007/s10468-010-9254-2. [COBISS.SI-ID 16299353]
2. BIERWIRTH, Hannes, BREŠAR, Matej, GRAŠIČ, Mateja. On maps determined by zero products. Commun. Algebra, 2012, vol. 40, no. 6, str. 2081-2090. http://dx.doi.org/10.1080/00927872.2011.570833. [COBISS.SI-ID 16315481]
3. ALAMINOS, J., BREŠAR, Matej, ŠEMRL, Peter, VILLENA, A. R. A note on spectrum-preserving maps. J. math. anal. appl., 2012, vol. 387, iss. 2, str. 595-603. http://dx.doi.org/10.1016/j.jmaa.2011.09.024. [COBISS.SI-ID 16067673]
4. BREŠAR, Matej, ŠPENKO, Špela. Determining elements in Banach algebras through spectral properties. J. math. anal. appl., 2012, vol. 393, iss. 1, str. 144-150. http://dx.doi.org/10.1016/j.jmaa.2012.03.058. [COBISS.SI-ID 16287833]
5. BREŠAR, Matej. Multiplication algebra and maps determined by zero products. Linear multilinear algebra, str. 763-768. http://dx.doi.org/10.1080/03081087.2011.564580. [COBISS.SI-ID 16310105]
Fakulteta za naravoslovje in matematiko
Oddelek za matematiko in računalništvo
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Kombinatorična optimizacija
Course title: Combinatorial optimization
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika 1 ali 2 1 ali 3
Mathematics 1 or 2 1 or 3
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Janez Žerovnik
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Jih ni. None.
Vsebina:
Content (Syllabus outline):
Obvezna vsebina, ki pri študentih vzpostavi
temeljni nabor znanj s področja kombinatorične
optimizacije:
Večkriterijska linearna optimizacija.
Ciljno programiranje. Celoštevilsko
programiranje.
Problem nahrbtnika in njegove različice.
Pretoki v omrežjih. Ford-Fulkersonov
algoritem.
Problem maksimalnega prirejanja.
Problem maksimalnega prereza.
Mandatory content, that familiarizes the students
with fundamentals of operations research and
mathematical programs:
Multicriteria linear optimization. Goal
programming. Integer programming.
Knapsack problems and its variants.
Network flows. Ford-Fulkerson’s algorithm.
Maximum matching problem.
Maximum cut problem.
Transport problem. Chinese postman
problem.
Transportni problem. Problem kitajskega
poštarja. Problem trgovskega potnika.
Aproksimacijski algoritmi.
Hevristike in metahevristike. Lokalna
optimizacija. Tabu search. Simulirano
ohlajanje. Genetski algoritmi.
Nevronske mreže. Samo-organizirajoče
se mreže.
V okviru vsebine študentje izberejo zahtevnejši
problem, s katerimi se poglobljeno ukvarjajo
pri seminarski nalogi. Problem je povezan z
njihovo bodočo kariero (praktični problemi iz
gospodarstva, teoretični problemi iz teorije
matematičnega programiranja in pripadajočih
numeričnih algoritmov). Preostala predavanja
se prilagodijo problemom, ki so jih izbrali
študentje, in obsegajo vsebine z naslednjega
seznama:
Optimalni portfelj celoštevilskih lotov in
celoštevilsko programiranje.
Problem delovnega razporeda.
Problem urnika.
Problem razporejanja nalog enega in več
strojev.
Problem optimizacije zalog.
Problemi rezanja in pakiranja.
Travelling salesman problem.
Approximation algorithms.
Heuristics and metaheuristics. Local
optimization. Tabu search. Simulated
annealing. Genetic aglorithms. Neural nets.
Self-organized maps.
Within the coursework, the students select
smaller problems whose result are coursework
reports. The problems are related to their future
career (practical problems from industry and
business, theoretical problems from the areas of
optimization, algorithms, modelling). The
content of the remaining lectures is selected
according to these projects from the following
list:
Optimal portfolio of integer lots and integer
programming.
Employee timetabling problem.
School timetabling problems.
Scheduling tasks of one or several
processors.
Stock optimization.
Cutting and packing problems.
Temeljni literatura in viri / Readings:
J.Žerovnik: Osnove teorije grafov in diskretne optimizacije, (druga izdaja), Fakulteta za
strojništvo, Maribor 2005.
R. Wilson, M. Watkins, Uvod v teorijo grafov, DMFA, Ljubljana 1997.
B. Robič: Aproksimacijski algoritmi, Založba FRI, Ljubljana 2002.
E. Zakrajšek: Matematično modeliranje, DMFA, Ljubljana 2004.
B. Korte, J. Vygen: Combinatorial Optimization, Theory and Algorithms, Springer, Berlin 2000.
D. Cvetković, V. Kovačević-Vujčić: Kombinatorna optimizacija, DOPIS Beograd 1996.
S. Zlobec, J. Petrić: Nelinearno programiranje, Naučna knjiga, Beograd 1989.
E. Kreyszig: Advanced Engineering Mathematics, (seventh edition), Wiley, New York 1993.
Cilji in kompetence:
Objectives and competences:
Usvojiti proces matematičnega modeliranja na
diskretnih optimizacijskih problemih.
Razviti kompetenco samostojnega apliciranja
matematičnih metod na probleme iz finančne
optimizacije, ekonomije, ter širše iz
gospodarstva.
Spoznati tehnološka orodja, s katerimi se
srečujemo pri reševanju optimizacijskih
Familiarize the students with the process of
mathematical modelling of continuous
optimization problems.
Develop competent skills of independent
application of mathematical methods to the
problems from financial optimization,
economics, and broader from industry.
Familiarize the students with technological tools
problemov in problemov matematičnega
modeliranja.
that assist solving optimization problems and
problems related to mathematical modelling.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Razumevanje zahtevnejših principov
kombinatorične optimizacije.
Poglobi znanje iz sodobnih metod za
reševanje problemov kombinatorične
optimizacije.
Poglobiti znanje iz diskretnih modelov
in drugih zahtevnih aplikacij
kombinatorične optimizacije v finančni
matematiki, optimiranju virov, in širše
Prenesljive/ključne spretnosti in drugi atributi:
Direktne aplikacije v finančni matematiki,
ekonomiji, poslovnih vedah, inžinirstvu,
fiziki in številnih drugih družboslovnih in
naravoslovnih vedah.
Suvereno obvladovanje procesa
matematičnega modeliranja in uporabe
tehnik kombinatorične optimizacije v
problemih s področja finančne
optimizacije, ekonomije in širše.
Knowledge and Understanding:
To be able to understand advanced principles
of combinatorial optimization.
To deepen the knowledge of modern
methods for solving combinatorial
optimization problems.
To deepen the knowledge of details of
discrete models and other advanced
applications of combinatorial optimization in
financial optimization, resource
optimization, and wider.
Transferable/Key Skills and other attributes:
Direct applications in finacial mathematics,
economy, business, engineering, physics,
and numerous other social and natural
sciences.
Competent mastering of the process of
mathematical modelling and applications of
the techniques of combinatorial optimization
in problems from financial optimization,
economics, and wider.
Metode poučevanja in učenja:
Learning and teaching methods:
Pri predavanjih študentje spoznajo snov
predmeta.
V okviru seminarskih vaj študentje
razumevanje snovi utrjujejo na večjem
projektu, povezanem z njihovo bodočo
kariero. Razporejeni so v večje skupine, ki
po metodah problemskega učenja
obravnavajo izbrani problem od zbiranja
podatkov, preko razvoja modela, izbora in
prilagajanja ustreznih tehnoloških rešitev do
razmisleka o implementaciji rešitve.
Koncept poučevanja je podrobneje
predstavljen kot ciljni aplikativni predmet.
At the lectures, the students are familiarized
with the course content.
At the tutorials, the student deepen their
understanding of the material by working on
an extensive problem related to their future
career. They are organized in larger groups
who research the choosen problem guided by
methodologies of problem-based learning.
Within solving the problem, they experience
all the stages from requirements and data
gathering, model development, selecting and
adapting technological solutions to
discussing various aspects of implementation
of the results.
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Seminarska naloga
Ustni izpit
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Pozitivna ocena pri seminarski nalogi je
pogoj za pristop k izpitu.
Delež (v %) /
Weight (in %)
80%,
20%
Type (examination, oral, coursework,
project):
Coursework report
Oral exam
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grade of the seminar exercise is
required for taking the exam.
Reference nosilca / Lecturer's
references:
1. ŠPARL, Petra, WITKOWSKI, Rafeł, ŽEROVNIK, Janez. 1-local 7/5-competitive algorithm for
multicoloring hexagonal graphs. Algorithmica, in press, doi: 10.1007/s00453-011-9562-x.
[COBISS.SI-ID 7055123]
2. ERVEŠ, Rija, ŽEROVNIK, Janez. Mixed fault diameter of Cartesian graph bundles. Discrete
appl. math.. [Print ed.], Available online 10. December 2011, doi: 10.1016/j.dam.2011.11.020.
[COBISS.SI-ID 15997718]
3. SAU WALLS, Ignasi, ŠPARL, Petra, ŽEROVNIK, Janez. Simpler multicoloring of triangle-free
hexagonal graphs. Discrete math.. [Print ed.], str. 181-187.
http://dx.doi.org/10.1016/j.disc.2011.07.031. [COBISS.SI-ID 6917907]
tipologija 1.08 -> 1.01
4. ŠPARL, Petra, WITKOWSKI, Rafał, ŽEROVNIK, Janez. A linear time algorithm for 7-
[3]coloring triangle-free hexagonal graphs. Inf. process. lett.. [Print ed.], 2012, vol. 112, iss. 14-15,
str. 567-571. http://dx.doi.org/10.1016/j.ipl.2012.02.008. [COBISS.SI-ID 7018003]
5. HRASTNIK LADINEK, Irena, ŽEROVNIK, Janez. Cyclic bundle Hamiltonicity. Int. j. comput.
math., 2012, vol. 89, iss. 2, str. 129-136, doi: 10.1080/00207160.2011.638375. [COBISS.SI-ID
15651862]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Magistrsko delo in magistrski izpit
Course title: Master Work and Master Exam
Študijski program in stopnja Study programme and level
Študijska smer Study field
Letnik Academic
year
Semester Semester
Matematika, 2. stopnja 2. 4.
Mathematics, 2nd
degree 2. 4.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja Lectures
Seminar Seminar
Sem. vaje Tutorial
Lab. vaje Laboratory
work
Teren. vaje Field work
Samost. delo Individ.
work ECTS
600 20
Nosilec predmeta / Lecturer: Izbrani mentor / Chosen Mentor
Jeziki / Languages:
Predavanja / Lectures:
/
Vaje / Tutorial: /
Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:
Prerequisits:
Opravljeni vsi predmeti na drugi stopnji študijskega programa Matematika
All subjects finished on the second degree of the study programme Mathematics
Vsebina:
Content (Syllabus outline):
Študent se nauči osnovna področja matematike
in svoje znanje zagovarja na magistrskem
izpitu.
Študent se nauči snov, ki mu jo poda mentor, in
napiše magistrsko delo ter ga predstavi na
zagovoru magistrskega dela.
Student learns the basic fields of general
mathematics and defends his knowledge in the
master exam.
Student learn a subject given by a mentor and
writes his master work and presents it at the
defence of the master work.
Temeljni literatura in viri / Readings: Študijski vir poda mentor / Textbooks are given by a mentor.
Cilji in kompetence:
Objectives and competences:
Uspešno zagovarjati magistrsko delo in opraviti
magistrski izpit Successfully finish master work and master
exam.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
- pomembnih konceptov matematike: Analiza
in Algebra.
Knowledge and understanding:
- important koncepts of mathematics: Analysis,
Algebra.
Metode poučevanja in učenja:
Learning and teaching methods:
Samostojno delo Individual work
Načini ocenjevanja:
Delež (v %) / Weight (in %)
Assessment:
- magistrski izpit
- magistrsko delo
50%
50%
- master exam
- master work
Reference nosilca / Lecturer's references:
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Matematične osnove računalniških omrežij
Course title: Mathematical Foundations of Computer Networks
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30 135 7
Nosilec predmeta / Lecturer: Andrej TARANENKO
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Matematične osnove in teorija računalniških
omrežij: terija grafov, usmerjevalni postopki,
dodeljevanje frekvenc.
Omrežni račun.
Omrežno upravljanje in varnost.
Kriptografija in varnost v omrežjih: uporaba
teorije števil, klasični kriptografski algoritmi,
kriptografija z javnimi ključi, digitalni podpisi.
Petrijeve mreže in uporaba pri analizi
računalniških omrežij.
Modeliranje omrežnega prometa.
Mathematical principles and theory of computer
networks: graph theory, routing algorithms,
frequency assignment.
Network calculus.
Network menagement and security.
Cryptography and network security: number
theory, clasical encription algorithms, public-
key cryptography, digital signatures.
Application of Petri Nets to
Communication Networks.
Network traffic modeling.
Medomrežno povezovanje in zaščita: varnostni
zid.
Inter-network communications and security:
firewall.
Temeljni literatura in viri / Readings:
T. Vidmar: Računalniška omrežja in storitve, Atlantis, 1997.
A. Kumar, D. Manjunath, and J. Kuri: Communication Networking: An Analytical Approach,
Elsevier, 2004.
James D. McCabe: Practical Computer Network Analysis and Design. Morgan Kaufmann
Publishers, 1998.
William Stallings: Cryptography and Network Security: Princpiles and Practice. Prentice Hall,
2003.
J. Billington, M. Diaz, G. Rozenberg: Application of Petri Nets to Communication Networks.
Springer, 1999.
Thomas G. Robertazzi: Computer Networks and Systems. Springer-Verlag, 2000.
W. Mao: Modern cryptography : theory and practice, Upper Saddle River, Prentice-Hall, 2004.
Cilji in kompetence:
Objectives and competences:
Poglobiti znanje iz matematičnih osnove,
teorije in temeljnih koncepte računalniških
omrežij. Nadgraditi znanja pridobljena pri
drugih predmetih (diskretne matematiki,
algoritmih,...) za potrebe računalniških omrežij.
Deepen the knowledge of mathematical theory
and fundamental concepts of computer
networks. Upgrade the knowledge obtained with
other subjects (algorithms, discrete mathematics,
...) for computer networks.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
• Razumeti matematične principe in
teorijo
• Poglobiti znanje iz algoritmov za
usmerjanje ter algoritmov za dodeljevanje
frekvenc.
• Poglobiti znanje iz osnov varnosti in
zaščite podatkov v računalniških omrežjih
Prenesljive/ključne spretnosti in drugi atributi:
• Pridobljena znanja se prenašajo na
druge z računalništvom povezane predmete.
Knowledge and Understanding:
• To understand mathematical principles
and theory
• To deepen the knowledge of routing
algorithms and frequency assignment
algorithms.
• To deepen the knowledge of basics of
network security
• To understand secure data transmission
methods
Transferable/Key Skills and other attributes:
• The obtained knowledge is transferable
to the other computer science oriented subjects.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Računalniške vaje
Lectures
Computer exercises
Načini ocenjevanja:
Assessment:
Sprotno preverjanje:
Pisni testi – teorija (3 do 5 pisnih testov
na semester)
Izpit:
Pisni izpit – praktični del
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljene sprotne obveznosti so pogoj
za pristop k izpitu.
Delež (v %) /
Weight (in %)
50%
50%
Mid-term testing:
Written tests – theory (from 3 to 5
written tests during the semester)
Exams:
Written exam – practical part
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grades of all mid-term testings
are required for taking the exam.
Reference nosilca / Lecturer's
references:
1. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel,
TARANENKO, Andrej. On the vertex k-path cover. Discrete appl. math.. [Print ed.], 2013, vol.
161, iss. 13/14, str. 1943-1949, doi: 10.1016/j.dam.2013.02.024. [COBISS.SI-ID19859464]
2. JAKOVAC, Marko, TARANENKO, Andrej. On the k-path vertex cover of some graph
products. Discrete math.. [Print ed.], 2013, vol. 313, iss. 1, str. 94-100.
http://dx.doi.org/10.1016/j.disc.2012.09.010, doi: 10.1016/j.disc.2012.09.010. [COBISS.SI-
ID19464968]
3. TARANENKO, Andrej, VESEL, Aleksander. 1-factors and characterization of reducible faces
of plane elementary bipartite graphs. Discuss. Math., Graph Theory, 2012, vol. 32, no. 2, str. 289-
297, doi: 10.7151/dmgt.1607. [COBISS.SI-ID 19104264]
4. TARANENKO, Andrej, ŽIGERT PLETERŠEK, Petra. Resonant sets of benzenoid graphs and
hypercubes of their resonance graphs. MATCH Commun. Math. Comput. Chem. (Krag.), 2012, vol.
68, no. 1, str. 65-77.http://www.pmf.kg.ac.rs/match/content68n1.htm. [COBISS.SI-ID 16051990]
5. KLAVŽAR, Sandi, SALEM, Khaled, TARANENKO, Andrej. Maximum cardinality resonant
sets and maximal alternating sets of hexagonal systems. Comput. math. appl. (1987). [Print ed.],
2010, vol. 59, no. 1, str. 506-513.http://dx.doi.org/10.1016/j.camwa.2009.06.011. [COBISS.SI-
ID 15383641]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Multivariatne statistične metode
Course title: Multivariate statistics methods
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30 135 7
Nosilec predmeta / Lecturer: Dominik BENKOVIČ
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje splošne (osnovne) statistike. Knowledge of general (basic) statistics.
Vsebina: Content (Syllabus outline):
• Uvod v multivariatno analizo: Osnove
statistične analize podatkov. Variančno-
kovariančna matrika in korelacijska matrika.
Standardiziranje podatkov. Grafična
predstavitev multivariatnih podatkov.
• Razvrščanje v skupine: Proces
razvrščanja v skupine. Mera podobnosti in
različnosti. Optimizacija in kriterijske funkcije.
Hierarhične metode (minimalna, maksimalna,
Wardova,...) in nehierarhične metode (metoda
voditeljev). Dendrogram. Določanje števila
• Introduction to multivariate analysis:
Basic statistical data analysis. Variance-
covariance matrix and correlation matrix. Data
standardization. Graphical representation of
multivariate data.
• Clustering: Clustering process. Measure
of similarity and dissimilarity. Optimization and
criteria functions. Hierarchical methods
(minimal, maximal, Ward's) and non-
hierarchical methods (k-means clustering).
Dendrogram. Choosing the number of clusters.
skupin. Grafična predstavitev večrazsežnih
podatkov.
• Metoda glavnih komponent:
Večrazsežnost podatkov. Korelacijska matrika.
Komunalitete in pojasnjena varianca.
Določanje števila glavnih komponent.
• Faktorska analiza: Manifestne in
latentne spremenljivke. Splošni faktorski model
in ocenjevanje. Metode faktorske analize
(metoda glavnih osi, metoda največjega
verjetja). Pravokotne in poševne rotacije.
• Diskriminantna analiza: Predpostavke.
Diskriminantni kriterij. Pravila uvrščanja enot v
skupine. Diskriminantna funkcija in
klasifikacijska tabela. Pomen napovednih
spremenljivk in centroidov.
• Kanonična korelacijska analiza:
Kanonične rešitve. Kanonične in strukturne
uteži.
Graphical representation of high-dimensional
data.).
• Principal component analysis: High-
dimensional data space. Correlation matrix.
Comunalities and explained variance. Choosing
the number of principal components.
• Factor analysis: Manifest and latent
variables. Factor model and estimation. General
factor model and estimation. Factor analysis
methods (principal axis factoring and maximum
likelihood). Orthogonal and oblique rotations.
• Discriminant analysis: Assumptions.
Discriminant kriteria. Classification rules.
Discriminant function and classification table.
Importance of manifest variables and centroids.
• Canonical correlation analysis:
Canonical solutions. Canonical and structure
loadings.
Temeljni literatura in viri / Readings:
1.Dillon W.R. in Goldstein M.: Multivariate Analysis, Wiley, New York, 1984.
2.Mardia K.V., Kent J.T. in Billy J.m.: Multivariate Analysis, Academic Press, London, 1979.
3.Sharman S.: Applied multivariate tecniques, Wiley, New York, 1996.
4.Ferligoj A.: Razvrščanje v skupine, Metodološki zvezki, 4, FSPN, Ljubljana, 1989.
5.Omladič V.: Uporaba linearne algebre v statistiki, Metodološki zvezki, 13, FDV, Ljubljana,
1997.
Cilji in kompetence:
Objectives and competences:
Glavni cilj predmeta je proučiti
najpomembnejše koncepte, metode in rezultate
multivariatne analize.
The main goal of the course is to study the
fundamental concepts, methods and results of
multivariate analysis.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
• Razumevanje in poznavanje osnovnih
pojmov multivariatne analize.
• Razumevanje, izvajanje in interpretacija
različnih metod multivariatne analize.
• Obvladanje ustrezne programske
opreme za namene statističnega raziskovanja.
Prenesljive/ključne spretnosti in drugi atributi:
• Prenos znanja iz statistike na različna
strokovna in znanstvena področja, kjer se
uporabljajo metode multivariatne analize.
Knowledge and Understanding:
• Understanding and knowledge of the
basic concepts of multivariate analysis.
• Understanding, correct application and
interpretation of different methods of
multivariate analysis.
• Knowledge of using an appropriate
software for statistical research.
Transferable/Key Skills and other attributes:
• Knowledge transfer of statistical methods
into different areas dealing with multivariate
analysis methods.
Metode poučevanja in učenja:
Learning and teaching methods:
• Predavanja
• Laboratorijske vaje
• Projekt
• Lectures
• Laboratory exercises
• Project
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
- Pisni test – praktični del
- Izpit (ustni) – teoretični del
- Projekt
- Vsaka izmed naštetih obveznosti
mora biti opravljena s pozitivno
oceno.
- Pozitivna ocena pri pisnem testu je
pogoj za pristop k izpitu.
Delež (v %) /
Weight (in %)
50%
30%
20%
Type (examination, oral, coursework,
project):
- Written test – practical part
- Exam (oral) – theoretical part
- Project
- Each of the mentioned commitments
must be assessed with a passing
grade.
- Passing grade of the written test is
required for taking the exam.
Reference nosilca / Lecturer's
references:
1. BENKOVIČ, Dominik, EREMITA, Daniel. Multiplicative Lie n-derivations of triangular rings.
Linear algebra appl.. [Print ed.], 2012, vol. 436, iss 11, str. 4223-4240.
http://dx.doi.org/10.1016/j.laa.2012.01.022. [COBISS.SI-ID 16278361]
2. BENKOVIČ, Dominik, ŠIROVNIK, Nejc. Jordan derivations of unital algebras with
idempotents. Linear algebra appl.. [Print ed.], 2012, vol. 437, iss. 9, str. 2271-2284.
http://dx.doi.org/10.1016/j.laa.2012.06.009. [COBISS.SI-ID 16410201]
3. BENKOVIČ, Dominik. Lie triple derivations on triangular matrices. Algebra colloq., 2011, vol.
18, spec. iss. 1, str. 819-826. http://www.worldscinet.com/ac/18/preserved-
docs/18spec01/S1005386711000708.pdf. [COBISS.SI-ID 16204377]
4. LI, Yanbo, BENKOVIČ, Dominik. Jordan generalized derivations on triangular algebras.
Linear multilinear algebra, 2011, vol. 59, no. 8, str. 841-849.
http://dx.doi.org/10.1080/03081087.2010.507600. [COBISS.SI-ID 16006233]
5. BENKOVIČ, Dominik. Generalized Lie derivations on triangular algebras. Linear algebra
appl.. [Print ed.], 2011, vol. 434, iss 6, str. 1532-1544. [COBISS.SI-ID 15863897]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Napredni algoritmi
Course title: Advanced algorithms
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30 135 7
Nosilec predmeta / Lecturer: Aleksander Vesel
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Razreda NP in P. Primeri NP-polni polnih
problemov. Problemi kombinatorične
optimizacije.
Algoritmi urejanja in njihova zahtevnost.
Iskanje niza v besedilu. Klasični algoritmi:
Boyer-Mooreov algoritem, Knuth-Morris-
Prattov algoritem. Priponska drevesa:
Ukkonenov algoritem in Weinerjev algoritem.
Neeksaktno iskanje niza.
Aproksimacijski algoritmi. Lokalno iskanje.
Classes NP and P. NP-complete problems.
Combinatorial optimization problems.
Sorting algorithms in their complexity.
String matching. Classical methods: Boyer-
Moore algorithm, Knuth-Morris-Pratt algorithm.
Suffix trees: Ukkonen's algorithm, Weiner's
algoritem. Inexact matching.
Approximation algorithms. Local search.
Fundamentals of heuristics and metaheuristics
methods.
Osnove hevrističnih in metahevrističnih
algoritmov.
Zahtevnejša analiza algoritmov. Metoda
amortiziranih stroškov.
Advanced algorithm analysis. Amortized
analysis.
Temeljni literatura in viri / Readings:
M. A. Weiss, Data Structures and Algorithm Analysis in C++, Addison-Wesley, 2007.
C.H. Papadimitriou, K. Steiglitz, Combinatorial Optimization - Algorithms and Complexity,
Prentice-Hall, 1998.
M. Dorigo, T. Stutzle, Ant colony optimization, MIT Press, 2004.
D. Gusfield, Algorithms on strings, trees and sequences, Cambridge University Press, 1999.
M. Mitchell, An introduction to genetic algorithms, MIT Press, 2002.
Cilji in kompetence:
Objectives and competences:
Poglobiti znanje iz izbranih algoritmov, tehnik
zahtevnejših analiz algoritmov in osnov teorije
NP-polnosti. Poglobiti znanje iz načinov
reševanja težkih (grafovskih) problemov.
Predstaviti algoritme iskanja niza.
To deepen the knowledge of selected
algorithms, techniques for advanced algorithm
analysis and the principles of NP-completeness
theory. To deepen the knowledge of skills for
solving hard (graph) problems. To present string
matching algorithms.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
- Poglobiti znanje iz osnovnih in zahtevnejših
grafovskih algoritmov.
- Prepoznati težke probleme.
- Razumeti pomen aproksimacijskih
algoritmov.
- Poglobiti znanje iz različnih vrst
hevrističnih in metahevrističnih tehnik.
- Razumevanje zahtevnejših postopkov
analize algoritmov.
Prenesljive/ključne spretnosti in drugi atributi:
- Prenos znanja algoritmičnih tehnik na druga
področja (diskretna matematika, biologija,
ekonomija, ...).
Knowledge and Understanding:
To deepen the knowledge of elementary
and advanced graph algorithms
To recognize hard problems.
To understand the importance of
approximation algorithms.
To deepen the knowledge of a variety of
heuristics and metaheuristics techniques.
To understand techniques for advanced
algorithm analysis
Transferable/Key Skills and other attributes:
- Knowledge transfer of algorithmic
techniques into other fields (discrete
mathematics, computer science, biology,
economics, …).
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Računalniške vaje
Lectures
Computer exercises
Načini ocenjevanja:
Assessment:
Sprotno preverjanje:
Projekt
Pisni testi – teorija (3 do 5 pisnih testov
na semester)
Izpit:
Pisni izpit – problemi
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljene sprotne obveznosti so pogoj
za pristop k izpitu.
Delež (v %) /
Weight (in %)
40%
40%
20%
Mid-term testing:
Project
Written tests – theory (from 3 to 5
written tests during the semester)
Exams:
Written exam - problems
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grades of all mid-term testings
are required for taking the exam.
Reference nosilca / Lecturer's
references:
1. VESEL, Aleksander. Fibonacci dimension of the resonance graphs of catacondensed benzenoid
graphs. Discrete appl. math.. [Print ed.], 2013, str. 1-11, doi: 10.1016/j.dam.2013.03.019.
2. SHAO, Zehui, VESEL, Aleksander. A note on the chromatic number of the square of the
Cartesian product of two cycles. Discrete math.. [Print ed.], 2013, vol. 313, iss. 9, str. 999-1001.
3. KORŽE, Danilo, VESEL, Aleksander. A note on the independence number of strong products of
odd cycles. Ars comb., 2012, vol. 106, str. 473-481. [COBISS.SI-ID 16138006]
4. TARANENKO, Andrej, VESEL, Aleksander. 1-factors and characterization of reducible faces
of plane elementary bipartite graphs. Discuss. Math., Graph Theory, 2012, vol. 32, no. 2, str. 289-
297, doi: 10.7151/dmgt.1607. [COBISS.SI-ID 19104264]
5. SALEM, Khaled, KLAVŽAR, Sandi, VESEL, Aleksander, ŽIGERT, Petra. The Clar formulas
of a benzenoid system and the resonance graph. Discrete appl. math.. [Print ed.], 2009, vol. 157,
iss. 11, str. 2565-2569. http://dx.doi.org/10.1016/j.dam.2009.02.016. [COBISS.SI-ID 15142489]
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Operacijske raziskave z matematičnim programiranjem Course title: Operations research with mathematical programming
Študijski program in stopnja Study programme and level
Študijska smer Study field
Letnik Academic
year
Semester Semester
Matematika 2. stopnja 1. ali 2. 1. ali 3. Mathematics 2nd degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type Univerzitetna koda predmeta / University course code:
Predavanja Lectures
Seminar Seminar
Sem. vaje Tutorial
Lab. vaje Laboratory
work
Teren. vaje Field work
Samost. delo Individ.
work ECTS
45 30 135 7 Nosilec predmeta / Lecturer: Drago Bokal Jeziki / Languages:
Predavanja / Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:
Prerequisits:
Poznavanje enostavnih algoritmov. Poznavanje osnov linearne algebre in vektorske analize. Predmet matematično modeliranje.
Knowledge of simple algorithms. Knowledge of basic linear algebra and calculus. Predmet matematično modeliranje.
Vsebina:
Content (Syllabus outline):
Obvezna vsebina, ki pri študentih vzpostavi temeljni nabor znanj s področja operacijskih raziskav in matematičnih programov:
• Nevezani ekstrem, Newtonova metoda. • Vezani ekstrem. Lagrangeovi
multiplikatoriji. Potrebni in zadostni pogoji za nastop vezanega lokalnega ekstrema. Wolfe-ov dual konveksnega programa.
• Kvadratično programiranje. Lagrangeovske metode in metoda aktivne množice. Programi z linearnimi vezmi. Cikcakanje.
• Nelinearno programiranje. Kazenska in odbojna funkcija. Langrange-Newtonova methoda (SQP).
• Stožčasto programiranje. Lorentzov in semidefinitni stožec. Stožčasto kvadratično programiranje.
• Semidefinitno programiranje. Aplikacije v kombinatorični optimizaciji.
• Metoda notranje točke za linearno in konveksno programiranje. Dokaz obstoja centralne poti. Primarno-dualna metoda sledenja centralni poti.
V okviru vsebine študentje izberejo zahtevnejši problem, s katerimi se poglobljeno ukvarjajo pri seminarski nalogi. Problem je povezan z njihovo bodočo kariero (praktični problemi iz gospodarstva, teoretični problemi iz teorije matematičnega programiranja in pripadajočih numeričnih algoritmov). Preostala predavanja se prilagodijo problemom, ki so jih izbrali študentje, in obsegajo vsebine z naslednjega seznama:
• Robustna optimizacija po metodi cene robustnosti.
• Imunizacija portfelja in stohastično programiranje.
• Stohastično nelinearno programiranje (diskretna in zvezna slučajna spremenljivka). Dekompozicija.
• Aplikacijie semidefinitnega programiranja: kvadratični problem prirejanja, problem trgovskega potnika, problem maksimalnega prereza grafa.
• Aplikaciji stohastičnega programiranja: Markowitzevi modeli optimizacije portfelja, modeli večfaznega stohastičnega načrtovanja.
• Modeli največjega verjetja, metoda najmanjših kvadratov, umerjanje modelov na znane podatke, inverzni problemi, druge podatkovne analize.
• Optimizacijski matematični modeli s področja kontrolnih sistemov, obdelave signalov.
• Metoda podpornih vektorjev. • Druge vsebine s področja operacijskih
raziskav in matematičnega modeliranja, povezane s študentskimi projekti.
Mandatory content, that familiarizes the students with fundamentals of operations research and mathematical programs:
• Unconstrained optimization. Newton's method.
• Constrained optimization. Lagrange multipliers. Necessery and sufficient conditions for a constrained local optimum. Dual of a convex program.
• Quadratic programming. Lagrange methods and active set methods. Programs with linear constraints. Zigzagging.
• Nonlinear programming. Penalty and barrier functions. Lagrange-Newton method. Sequential Quadratic Programming.
• Conic programming. Lorentz and semidefinite cone. Conic quadratic programming.
• Semidefinite programming. Applications in combinatorial optimization.
• Interior point methods for linear and convex programming. Existence of the central path. Primal-dual methods of following the central path.
Within the coursework, the students select smaller problems whose result are coursework reports. The problems are related to their future career (practical problems from industry and business, theoretical problems from the areas of optimization, algorithms, modelling). The content of the remaining lectures is selected according to these projects from the following list:
• Price of robustness robust optimization method.
• Portfolio immunization using stohastic programming.
• Stohastic nonlinear programming (discrete and continuous stohastic variables). Decomposition.
• Applications of semidefinite programming: quadratic assignment problem, travelling salesman problem, max cut problem.
• Applications of stohastic programming: Markowitz models of portfolio optimization, multiperiod stohastic planning models.
• Maximum likelihood models, least squares method, parameter fitting for given data.
• Optimization mathematical models from control theory and signal processing.
• Support Vector Machine. • Other content from the domain of operations
research and mathematical programming, related to students' problems.
Within their coursework and exercisces, the students familiarize themselves with software for mathematical modelling, either commercial (Excel, Lindo, Matlab) or freely avaliable open source
V okviru seminarskih nalog se študentje srečajo tudi s programsko opremo za matematično modeliranje. komercialno (Excel, Lindo, Matlab) oz. prostodostopno in odprtokodno (SciLab, NEOS, R).
(SciLab, Neos, R).
Temeljni literatura in viri / Readings: R. Rardin. Optimization in Operations Research. Prentice Hall, Inc., Upper Saddle River, New Jersey, 2000. J. Curwin, R. Slater. Quantitive Methods for Business Decisions. Third Edition. Chapman & Hall, London, 1991. S. A. Zenios, Financial Optimization. Cambridge University Press, Cambridge, 1993. R. Fletcher, Practical Methods of Optimization. Second Edition. Wiley, Chichester, 2001. A. Ben-Tal, A. Nemirowski: Lectures on modern convex optimization. H. Milton Stewart School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, 2012. C. Huang, R. H. Litzenberger. Foundations for Finacial Economics. Prentice Hall, Inc., Upper Saddle River, New Jersey, 1988. P. Kall, S. W. Wallace. Stochastic Programming. Wiley, Chichester, 1994. L. Neralić, Uvod u matematičko programiranje 1. Udžbenici Sveučilišta u Zagrebu, Zagreb, 2001. R. Rardin. Optimization in Operations Research. Prentice Hall, Inc., Upper Saddle River, New Jersey, 2000. J. Renegar. A Mathematical View of Interior-Point Methods in Convex Optimization. MPS-SIAM Series on Optimization. SIAM, Philadelphia, 2001. S. A. Zenios, Financial Optimization. Cambridge University Press, Cambridge, 1993. Cilji in kompetence:
Objectives and competences:
Usvojiti proces matematičnega modeliranja na zveznih optimizacijskih problemih. Razviti kompetenco samostojnega apliciranja matematičnih metod na probleme iz finančne optimizacije, ekonomije, ter širše iz gospodarstva. Spoznati tehnološka orodja, s katerimi se srečujemo pri reševanju optimizacijskih problemov in problemov matematičnega modeliranja.
Familiarize the students with the process of mathematical modelling of continuous optimization problems. Develop competent skills of independent application of mathematical methods to the problems from financial optimization, economics, and broader from industry. Familiarize the students with technological tools that assist solving optimization problems and problems related to mathematical modelling.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje: • Razumevanje zahtevnejših principov matematičnega
programiranja. • Poglobi znanje iz sodobnih numeričnih metod za
reševanje matematičnih programov. • Poglobiti znanje iz Markowitzevih modelov in
drugih zahtevnih aplikacij matematičnega programiranja v finančni optimizaciji in širše.
Prenesljive/ključne spretnosti in drugi atributi: • Direktne aplikacije v finančni matematiki,
Knowledge and Understanding: • To be able to understand advanced principles of
mathematical programming. • To deepen the knowledge of modern numerical
methods for solving mathematical programs. • To deepen the knowledge of details of Markowitz
models and other advanced applications of mathematical programming, financial optimization and wider.
Transferable/Key Skills and other attributes:
ekonomiji, poslovnih vedah, inžinirstvu, fiziki in številnih drugih družboslovnih in naravoslovnih vedah.
• Suvereno obvladovanje procesa matematičnega modeliranja in uporabe tehnik matematičnega progamiranja v problemih s področja finančne optimizacije, ekonomije in širše.
• Direct applications in finacial mathematics, economy, business, engineering, physics, and numerous other social and natural sciences.
• Competent mastering of the process of mathematical modelling and applications od its techniques in problems from financial optimization, economics, and wider.
Metode poučevanja in učenja:
Learning and teaching methods:
• Pri predavanjih študentje spoznajo snov predmeta. • V okviru seminarskih vaj študentje razumevanje
snovi utrjujejo na večjem projektu, povezanem z njihovo bodočo kariero. Razporejeni so v večje skupine, ki po metodah problemskega učenja obravnavajo izbrani problem od zbiranja podatkov, preko razvoja modela, izbora in prilagajanja ustreznih tehnoloških rešitev do razmisleka o implementaciji rešitve. Koncept poučevanja je podrobneje predstavljen kot ciljni aplikativni predmet.
• At the lectures, the students are familiarized with the
course content. • At the tutorials, the student deepen their
understanding of the material by working on an extensive problem related to their future career. They are organized in larger groups who research the choosen problem guided by methodologies of problem-based learning. Within solving the problem, they experience all the stages from requirements and data gathering, model development, selecting and adapting technological solutions to discussing various aspects of implementation of the results.
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje, naloge, projekt) Seminarska naloga Ustni izpit Vsaka izmed naštetih obveznosti mora biti opravljena s pozitivno oceno. Pozitivna ocena pri seminarski nalogi je pogoj za pristop k izpitu.
Delež (v %) / Weight (in %) 80% 20%
Type (examination, oral, coursework, project): Coursework report Oral exam Each of the mentioned commitments must be assessed with a passing grade. Passing grade of the seminar exercise is required for taking the exam.
Reference nosilca / Lecturer's references:
1. BOKAL, Drago, BREŠAR, Boštjan, JEREBIC, Janja. A generalization of Hungarian method and Hall's theorem with applications in wireless sensor networks. Discrete appl. math.. [Print ed.], 2012, vol. 160, iss. 4-5, str. 460-470. http://dx.doi.org/10.1016/j.dam.2011.11.007. [COBISS.SI-ID 16191577]
2. BOKAL, Drago, DEVOS, Matt, KLAVŽAR, Sandi, MIMOTO, Aki, MOOERS, Arne Ø.
Computing quadratic entropy in evolutionary trees. Comput. math. appl. (1987). [Print ed.], 2011, vol. 62, no. 10, str. 3821-3828. http://dx.doi.org/10.1016/j.camwa.2011.09.030. [COBISS.SI-ID 16059481]
3. ŽUNKO, Matjaž, BOKAL, Drago, JAGRIČ, Timotej. Testiranje modelov VaR v izjemnih okoliščinah. IB rev. (Ljubl., Tisk. izd.). [Tiskana izd.], 2011, letn. 45, št. 3, str. 57-67, tabele, graf. prikazi. [COBISS.SI-ID 10777884]
4. BOKAL, Drago, CZABARKA, Éva, SZÉKELY, László, VRT'O, Imrich. General lower bounds for the minor crossing number of graphs. Discrete comput. geom., 2010, vol. 44, no. 2, str. 463-483. http://dx.doi.org/10.1007/s00454-010-9245-4. [COBISS.SI-ID 15636057]
5. BEAUDOU, Laurent, BOKAL, Drago. On the sharpness of some results relating cuts and crossing numbers. Electron. j. comb. (On line). [Online ed.], 2010, vol. 17, no. 1, r96 (8 str.). http://www.combinatorics.org/Volume_17/PDF/v17i1r96.pdf. [COBISS.SI-ID 15638361]
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Osnove ekonometrije Course title: Basic econometrics
Študijski program in stopnja Study programme and level
Študijska smer Study field
Letnik Academic
year
Semester Semester
Matematika 2. stopnja 1. ali 2. 1. ali 3.
Mathematics 2nd degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type Univerzitetna koda predmeta / University course code:
Predavanja Lectures
Seminar Seminar
Sem. vaje Tutorial
Lab. vaje Laboratory
work
Teren. vaje Field work
Samost. delo Individ.
work ECTS
45 30 135 7 Nosilec predmeta / Lecturer: Timotej JAGRIČ Jeziki / Languages:
Predavanja / Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:
Prerequisits:
Jih ni. Jih ni.
Vsebina:
Content (Syllabus outline):
- Uvod (Uvod v ekonometrijo, Ponovitev statistike);
- Multipli regresijski model (Uvod, Ocena parametrov, Lastnosti, Testiranje hipotez, Mere primernosti, linearne transformacije, napovedovanje);
- Neizpolnjevanje predpostavk (Specifikacija modela, Normalna porazdelitev, Multikolinearnost, Heteroskedastičnost, Avtokorelacija);
Slamnate spremenljivke.
-Introduction (Introduction to Econometrics, Statistics Review); -The Multiple Regression Model (Introduction, Estimating the Parameters, Properties, Hypothesis Testing, Goodness of Fit, linear transformations, forecasting); -Violations of Assumptions (Model Specification, Multicollinearity, Heteroskedasticity, Serial Correlation); - Dummy variables.
Temeljni literatura in viri / Readings: N. Gujarati (2003). Basic Econometrics – Fourth Edition. McGraw-Hill, New York. W. H. Green (2003). Econometric Analysis – Fifth Edition. Prentice Hall, New Jersey. G. S. Maddala (2003). Introduction to Econometrics – Third Edition. John Wiley & Sons, New York.
Cilji in kompetence:
Objectives and competences:
Študentje naj bi dobili znanja in spretnosti, ki so potrebna za ekonometrično analizo. V okviru predmeta se bodo študentje učili tradicionalne ekonometrične metode. Razumeli bodo bistvene razlike med časovnimi vrstami in presečnimi podatki. Študentje bodo dobili spretnosti, ki so potrebne za oblikovanje in razvoj enostavnih in multiplih regresijskih modelov. Obravnavane metode bodo razumeli do te mere, da jih lahko uporabijo na realnih ekonomskih bazah podatkov z uporabo sodobnih ekonometričnih programov.
The students will get the knowledge and skills of econometric analysis. In the course the students will learn traditional econometric methods. They will understand differences between the time series and cross sections data. The students will get the skills of construction and development of simple and multiple regression models. The students will be able to apply methods on real economic data bases with modern econometric software.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje: - poznavanje osnovnih matričnih operacij in
njihova aplikacija v linearnih regresijskih modelih;
- razumevanje predpostavk, na katerih temeljijo linearni regresijski modeli;
- razumevanje posledic odstopanja modela
Knowledge and understanding: - Use of basic matrix operations and their
application to the linear regression model; - understand the assumptions of the linear
regression model - awareness of the implications for the model
departures from assumptions;
od teh predpostavk; - poznavanje principov statističnega
testiranja; - poznavanje uporabe računalniških
programov za ocenjevanje in testiranje ekonometričnih modelov;
- interpretacija in komentiranje rezultatov; sposobnost prebiranja literature s področja kvantitativnih ekonomskih analiz, ki temeljijo na ekonometriji.
- understand statistical testing principles; - use software in the estimation and testing
of econometric models; - interpret and discuss results; be able to understand quantitative econ. literature that uses econometric methods.
Metode poučevanja in učenja:
Learning and teaching methods:
- predavanja (predavatelj bo podal študentom vsebino ključnih teorij in tehnik);
- vodene vaje v računalniški učilnici (primeri modeliranja in razprava o domačih nalogah);
- individualne konzultacije s predavateljem; - samostojno delo v računalniški učilnici, s
posebnim poudarkom na uporabi interneta (izdelava domačih nalog z uporabo računalnika, delo z ekonomskimi bazami podatkov, učna gradiva na internetu, spletne predstavitve predavanj iz ekonometrije);
- samostojni študij gradiva
- lectures (lecturer will provide students with knowledge of the fundamental theories and techniques);
- guided classes in computer room (sample modeling is done and the main problems of home assignments are discussed);
- teachers' consultations; - self study in computer room, in particular
with the Internet (making home assignments using PC, work with economic data bases, study guides on the Internet, looking through sets of slides in Econometrics);
- self study with literature
Načini ocenjevanja:
Delež (v %) / Weight (in %)
Assessment:
- pisni izpit 100% - written examination
Reference nosilca / Lecturer's references: 1. ŽUNKO, Matjaž, JAGRIČ, Timotej. Raven razkrivanja z metodo tvegane vrednosti v slovenskih poslovnih bankah. Banč. vestn., apr. 2012, letn. 61, št. 4, str. 42-46. [COBISS.SI-ID 10994460]
2. ZDOLŠEK, Daniel, JAGRIČ, Timotej. Audit opinion identification using accounting ratios : experience of United Kingdom and Ireland. Aktual. probl. ekon., 2011, no. 1 (115), str. 285-310, graf. prikazi, tabele. [COBISS.SI-ID 10625564]
3. BEKŐ, Jani, JAGRIČ, Timotej. Demand models for direct mail and periodicals delivery services : results for a transition economy. Appl. econ., apr. 2011, vol. 43, no. 9, str. 1125-1138, doi: 10.1080/00036840802600244. [COBISS.SI-ID 10071324]
4. JAGRIČ, Vita, JAGRIČ, Timotej. Primerjalna presoja bančnih bonitetnih modelov za prebivalstvo. Banč. vestn., 2011, letn. 60, št. 1/2, str. 48-52. [COBISS.SI-ID 10593052]
5. JAGRIČ, Timotej, JAGRIČ, Vita. A comparison of growing cell structures neural networks and linear scoring models in the retail credit environment : a case of a small EU and EMU member country. East. Europ. econ., nov-dec 2011, vol. 49, no. 6, str. 74-96, doi: 10.2753/EEE0012-8775490605. [COBISS.SI-ID 10975772]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Osnove informacijske tehnologije
Course title: Basic of information technology
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30 135 7
Nosilec predmeta / Lecturer: Krista RIZMAN ŽALIK
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Informacijska teorija.
Merilo informacije,
enačba informacije,
entropija informacije.
Algoritmična informacijska teorija.
Uporaba informacijske teorije v strojnem
učenju: Bayesovo učenje, lučenje odločitvenih
dreves.
Uveljavljene in novejše metode in orodja
razvoja informacijskih sistemov in programske
opreme.
Information theory.
Data and information.
Measure of information equation,
entropy of information.
Algorithmic information theory.
The use of information theory in machine
learning:
Bayesian inference, learning decision trees.
Enforced and new methods and tools for
software development of information systems
development.
Arhitekture informacijskih sistemov:
podatkovno usmerjena, pretočna arhitektura,
arhitektura z virtualnim strojem, arhitektura
klica in vrnitve, aktualne komponente
arhitekture.
Arhitektura aplikacij za svetovni splet in
distribuirani objektni sistemi.
Vzporedno programiranje in koncepti
vzporednost, večnitnost, sinhronizacija.
Načrtovalni vzorci.
Architectures: data cantered, dataflow
architecture, virtual machine architecture, call
and return architecture, actual component
architecture.
Architecture of internet applications and
distributed object systems.
Concurrent programming and concept
concurrency, parallelism, multithreading,
synchronization.
Design patterns.
Temeljni literatura in viri / Readings:
U. Mesojedec, Java, programiranje za internet, Pasadena, 1997.
M. Campione, K.Walrath, The Java tutorial : object-oriented programming for the Internet,
Addison-Wesley, 1996.
Stevens, P., Pooley, R., Using UML: software engineering with objects and components, Addison-
Wesley, 2000.
Erich Gamma, Design Patterns: Elements of Reusable Object-Oriented Software (Addison-Wesley,
1995.
Eric Reiss, Practical Information Architecture. Harlow, UK: Pearson Education, 2000.
Cilji in kompetence:
Objectives and competences:
Poglobiti znanje iz pojmov informacij in
elementov teorije informacij in obdelave
informacij.
The main objective is to deepen the knowledge
about information, elements of information
theory and information management.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Znanje temeljnih teoretičnih konceptov
informacij, obdelav informacij in teorije
informacij in obdelave informacij ter različnih
arhitektur.
Knowledge and Understanding:
The knowledge of basic theoretical foundations
of information, manipulation of information and
information theory and different architectures.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Računalniške vaje
Lectures
Computer exercises
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
- Računalniške vaje
- Pisni izpit
- Vsaka izmed naštetih obveznosti
mora biti opravljena s pozitivno
oceno.
- Pozitivna ocena pri vajah je pogoj
za pristop k izpitu.
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
- Computer exercises
- Written exam
- Each of the mentioned commitments
must be assessed with a passing
grade.
- Passing grade of the exercises is
required for taking the exam.
Reference nosilca / Lecturer's
references:
1. RIZMAN ŽALIK, Krista, ŽALIK, Borut. Validity index for clusters of different sizes
and densities. Pattern recogn. lett. (Print). [Print ed.], Jan. 2011, vol. 32, iss. 2, str. 221-
234, doi: 10.1016/j.patrec.2010.08.007. [COBISS.SI-ID 14640150]
2. RIZMAN ŽALIK, Krista. Cluster validity index for estimation of fuzzy clusters of
different sizes and densities. Pattern recogn.. [Print ed.], Oct. 2010, vol. 43, iss. 10, str.
3374-3390, doi:10.1016/j.patcog.2010.04.025. [COBISS.SI-ID 14640406]
3. RIZMAN ŽALIK, Krista, ŽALIK, Borut. A sweep-line algorithm for spatial
clustering. Adv. eng. softw. (1992). [Print ed.], Jun. 2009, vol. 40, iss. 6, str. 445-451,
doi: 10.1016/j.advengsoft.2008.06.003. [COBISS.SI-ID 12450582]
4. RIZMAN ŽALIK, Krista. An efficient k'-means clustering algorithm. Pattern recogn.
lett. (Print). [Print ed.], July 2008, vol. 29, iss. 9, str. 1385-
1391. http://dx.doi.org/10.1016/j.patrec.2008.02.014. [COBISS.SI-ID 12121366]
5. RIZMAN ŽALIK, Krista. Discovering significant biclusters in gene expression
data. WSEAS transactions on information science and applications, Sep. 2005, vol. 2,
iss. 9, str. 1454-1461. [COBISS.SI-ID14906120]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Programiranje v diskretni matematiki
Course title: Programming in discrete mathematics
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul R1 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module R1 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 15 45 165 9
Nosilec predmeta / Lecturer: Andrej Taranenko
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Vsebina predmeta se prilagaja aktualnim
potrebam in razvoju. Poglobili bomo znanje iz
uporabe računalnika pri reševanju
matematičnih problemov, predvsem s področja
diskretne matematike.
- Relacije in algoritmi nad relacijami
- Boolova algebra
- Prirejanja v grafih
The contents of this subject is adjusted to the
current needs and development. We will deepen
the knowledge of using a computer to solve
mathematical problems, mainly from discrete
mathematics.
- relations and algorithms on relations
- Bool algebra
- matchings in graphs
Temeljni literatura in viri / Readings:
B. Vilfan, Osnovni algoritmi, ISBN 961-6209-13-2, Založba FER in FRI, 2. izd., 2002.
Kenneth H. Rosen, Discrete Mathematics and Its Applications, ISBN 007-2880-08-2, McGraw-
Hill, 6th ed., 2007.
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Introduction to
Algorithms, ISBN 026-2032-93-7, The MIT Press, 2nd ed., 2001.
Cilji in kompetence:
Objectives and competences:
Z uporabo modernega, predmetno usmerjenega
programskega jezika, poglobiti znanje iz
pristopov, podatkovnih struktur in algoritmov
pri reševanju matematičnih problemov.
With the usage of modern object oriented
programming language, to deepen the
knowledge of the basic approaches, data
structures and algorithms for solving
mathematical problems.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
podatkovne strukture matematičnih
modelov
razumevanje, implementacija in
uporaba pomembnejših algoritmov
Prenesljive/ključne spretnosti in drugi atributi:
uporaba matematičnih pojmov v
programskih aplikacijah
uporaba ustreznih podatkovnih struktur
pri implementaciji matematičnih
algoritmov
pridobljena znanja se prenašajo na
druge z računalništvom povezane
predmete
Knowledge and Understanding:
data structures of mathematical models
understanding, implementation and
usage of important algorithms
Transferable/Key Skills and other attributes:
the usage of mathematical notions in
applications
the usage of appropriate data structures
while implementing mathematical
algorithms
the obtained knowledge is transferable
to the other computer science oriented
subjects
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja, seminar
Računalniške vaje
Lectures, seminary
Computer exercises
Načini ocenjevanja:
Assessment:
Sprotno preverjanje:
Seminarska naloga
Projekt
Pisni testi – teorija (3 do 5 pisnih testov
na semester)
Delež (v %) /
Weight (in %)
20%
20%
40%
Mid-term testing:
Seminary work
Project
Written tests – theory (from 3 to 5
written tests during the semester)
Izpit:
Pisni izpit – problemi
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljene sprotne obveznosti so pogoj
za pristop k izpitu.
20%
Exams:
Written exam - problems
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grades of all mid-term testings
are required for taking the exam.
Reference nosilca / Lecturer's
references:
1. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel,
TARANENKO, Andrej. On the vertex k-path cover. Discrete appl. math.. [Print ed.], 2013, vol.
161, iss. 13/14, str. 1943-1949, doi: 10.1016/j.dam.2013.02.024. [COBISS.SI-ID19859464]
2. JAKOVAC, Marko, TARANENKO, Andrej. On the k-path vertex cover of some graph
products. Discrete math.. [Print ed.], 2013, vol. 313, iss. 1, str. 94-100.
http://dx.doi.org/10.1016/j.disc.2012.09.010, doi: 10.1016/j.disc.2012.09.010. [COBISS.SI-
ID19464968]
3. TARANENKO, Andrej, VESEL, Aleksander. 1-factors and characterization of reducible faces
of plane elementary bipartite graphs. Discuss. Math., Graph Theory, 2012, vol. 32, no. 2, str. 289-
297, doi: 10.7151/dmgt.1607. [COBISS.SI-ID 19104264]
4. TARANENKO, Andrej, ŽIGERT PLETERŠEK, Petra. Resonant sets of benzenoid graphs and
hypercubes of their resonance graphs. MATCH Commun. Math. Comput. Chem. (Krag.), 2012, vol.
68, no. 1, str. 65-77.http://www.pmf.kg.ac.rs/match/content68n1.htm. [COBISS.SI-ID 16051990]
5. KLAVŽAR, Sandi, SALEM, Khaled, TARANENKO, Andrej. Maximum cardinality resonant
sets and maximal alternating sets of hexagonal systems. Comput. math. appl. (1987). [Print ed.],
2010, vol. 59, no. 1, str. 506-513.http://dx.doi.org/10.1016/j.camwa.2009.06.011. [COBISS.SI-
ID 15383641]
Fakulteta za naravoslovje in matematiko
Oddelek za matematiko in računalništvo
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Kombinatorična optimizacija
Course title: Combinatorial optimization
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika Modul R2 1 ali 2 1 ali 3
Mathematics Module R2 1 or 2 1 or 3
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 30 135 7
Nosilec predmeta / Lecturer: Janez Žerovnik
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Jih ni. None.
Vsebina:
Content (Syllabus outline):
Obvezna vsebina, ki pri študentih vzpostavi
temeljni nabor znanj s področja kombinatorične
optimizacije:
Večkriterijska linearna optimizacija.
Ciljno programiranje. Celoštevilsko
programiranje.
Problem nahrbtnika in njegove različice.
Pretoki v omrežjih. Ford-Fulkersonov
algoritem.
Problem maksimalnega prirejanja.
Problem maksimalnega prereza.
Mandatory content, that familiarizes the students
with fundamentals of operations research and
mathematical programs:
Multicriteria linear optimization. Goal
programming. Integer programming.
Knapsack problems and its variants.
Network flows. Ford-Fulkerson’s algorithm.
Maximum matching problem.
Maximum cut problem.
Transport problem. Chinese postman
problem.
Transportni problem. Problem kitajskega
poštarja. Problem trgovskega potnika.
Aproksimacijski algoritmi.
Hevristike in metahevristike. Lokalna
optimizacija. Tabu search. Simulirano
ohlajanje. Genetski algoritmi.
Nevronske mreže. Samo-organizirajoče
se mreže.
V okviru vsebine študentje izberejo zahtevnejši
problem, s katerimi se poglobljeno ukvarjajo
pri seminarski nalogi. Problem je povezan z
njihovo bodočo kariero (praktični problemi iz
gospodarstva, teoretični problemi iz teorije
matematičnega programiranja in pripadajočih
numeričnih algoritmov). Preostala predavanja
se prilagodijo problemom, ki so jih izbrali
študentje, in obsegajo vsebine z naslednjega
seznama:
Optimalni portfelj celoštevilskih lotov in
celoštevilsko programiranje.
Problem delovnega razporeda.
Problem urnika.
Problem razporejanja nalog enega in več
strojev.
Problem optimizacije zalog.
Problemi rezanja in pakiranja.
Travelling salesman problem.
Approximation algorithms.
Heuristics and metaheuristics. Local
optimization. Tabu search. Simulated
annealing. Genetic aglorithms. Neural nets.
Self-organized maps.
Within the coursework, the students select
smaller problems whose result are coursework
reports. The problems are related to their future
career (practical problems from industry and
business, theoretical problems from the areas of
optimization, algorithms, modelling). The
content of the remaining lectures is selected
according to these projects from the following
list:
Optimal portfolio of integer lots and integer
programming.
Employee timetabling problem.
School timetabling problems.
Scheduling tasks of one or several
processors.
Stock optimization.
Cutting and packing problems.
Temeljni literatura in viri / Readings:
J.Žerovnik: Osnove teorije grafov in diskretne optimizacije, (druga izdaja), Fakulteta za
strojništvo, Maribor 2005.
R. Wilson, M. Watkins, Uvod v teorijo grafov, DMFA, Ljubljana 1997.
B. Robič: Aproksimacijski algoritmi, Založba FRI, Ljubljana 2002.
E. Zakrajšek: Matematično modeliranje, DMFA, Ljubljana 2004.
B. Korte, J. Vygen: Combinatorial Optimization, Theory and Algorithms, Springer, Berlin 2000.
D. Cvetković, V. Kovačević-Vujčić: Kombinatorna optimizacija, DOPIS Beograd 1996.
S. Zlobec, J. Petrić: Nelinearno programiranje, Naučna knjiga, Beograd 1989.
E. Kreyszig: Advanced Engineering Mathematics, (seventh edition), Wiley, New York 1993.
Cilji in kompetence:
Objectives and competences:
Usvojiti proces matematičnega modeliranja na
diskretnih optimizacijskih problemih.
Razviti kompetenco samostojnega apliciranja
matematičnih metod na probleme iz finančne
optimizacije, ekonomije, ter širše iz
gospodarstva.
Spoznati tehnološka orodja, s katerimi se
srečujemo pri reševanju optimizacijskih
Familiarize the students with the process of
mathematical modelling of continuous
optimization problems.
Develop competent skills of independent
application of mathematical methods to the
problems from financial optimization,
economics, and broader from industry.
Familiarize the students with technological tools
problemov in problemov matematičnega
modeliranja.
that assist solving optimization problems and
problems related to mathematical modelling.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Razumevanje zahtevnejših principov
kombinatorične optimizacije.
Poglobi znanje iz sodobnih metod za
reševanje problemov kombinatorične
optimizacije.
Poglobiti znanje iz diskretnih modelov
in drugih zahtevnih aplikacij
kombinatorične optimizacije v finančni
matematiki, optimiranju virov, in širše
Prenesljive/ključne spretnosti in drugi atributi:
Direktne aplikacije v finančni matematiki,
ekonomiji, poslovnih vedah, inžinirstvu,
fiziki in številnih drugih družboslovnih in
naravoslovnih vedah.
Suvereno obvladovanje procesa
matematičnega modeliranja in uporabe
tehnik kombinatorične optimizacije v
problemih s področja finančne
optimizacije, ekonomije in širše.
Knowledge and Understanding:
To be able to understand advanced principles
of combinatorial optimization.
To deepen the knowledge of modern
methods for solving combinatorial
optimization problems.
To deepen the knowledge of details of
discrete models and other advanced
applications of combinatorial optimization in
financial optimization, resource
optimization, and wider.
Transferable/Key Skills and other attributes:
Direct applications in finacial mathematics,
economy, business, engineering, physics,
and numerous other social and natural
sciences.
Competent mastering of the process of
mathematical modelling and applications of
the techniques of combinatorial optimization
in problems from financial optimization,
economics, and wider.
Metode poučevanja in učenja:
Learning and teaching methods:
Pri predavanjih študentje spoznajo snov
predmeta.
V okviru seminarskih vaj študentje
razumevanje snovi utrjujejo na večjem
projektu, povezanem z njihovo bodočo
kariero. Razporejeni so v večje skupine, ki
po metodah problemskega učenja
obravnavajo izbrani problem od zbiranja
podatkov, preko razvoja modela, izbora in
prilagajanja ustreznih tehnoloških rešitev do
razmisleka o implementaciji rešitve.
Koncept poučevanja je podrobneje
predstavljen kot ciljni aplikativni predmet.
At the lectures, the students are familiarized
with the course content.
At the tutorials, the student deepen their
understanding of the material by working on
an extensive problem related to their future
career. They are organized in larger groups
who research the choosen problem guided by
methodologies of problem-based learning.
Within solving the problem, they experience
all the stages from requirements and data
gathering, model development, selecting and
adapting technological solutions to
discussing various aspects of implementation
of the results.
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Seminarska naloga
Ustni izpit
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Pozitivna ocena pri seminarski nalogi je
pogoj za pristop k izpitu.
Delež (v %) /
Weight (in %)
80%,
20%
Type (examination, oral, coursework,
project):
Coursework report
Oral exam
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grade of the seminar exercise is
required for taking the exam.
Reference nosilca / Lecturer's
references:
1. ŠPARL, Petra, WITKOWSKI, Rafeł, ŽEROVNIK, Janez. 1-local 7/5-competitive algorithm for
multicoloring hexagonal graphs. Algorithmica, in press, doi: 10.1007/s00453-011-9562-x.
[COBISS.SI-ID 7055123]
2. ERVEŠ, Rija, ŽEROVNIK, Janez. Mixed fault diameter of Cartesian graph bundles. Discrete
appl. math.. [Print ed.], Available online 10. December 2011, doi: 10.1016/j.dam.2011.11.020.
[COBISS.SI-ID 15997718]
3. SAU WALLS, Ignasi, ŠPARL, Petra, ŽEROVNIK, Janez. Simpler multicoloring of triangle-free
hexagonal graphs. Discrete math.. [Print ed.], str. 181-187.
http://dx.doi.org/10.1016/j.disc.2011.07.031. [COBISS.SI-ID 6917907]
tipologija 1.08 -> 1.01
4. ŠPARL, Petra, WITKOWSKI, Rafał, ŽEROVNIK, Janez. A linear time algorithm for 7-
[3]coloring triangle-free hexagonal graphs. Inf. process. lett.. [Print ed.], 2012, vol. 112, iss. 14-15,
str. 567-571. http://dx.doi.org/10.1016/j.ipl.2012.02.008. [COBISS.SI-ID 7018003]
5. HRASTNIK LADINEK, Irena, ŽEROVNIK, Janez. Cyclic bundle Hamiltonicity. Int. j. comput.
math., 2012, vol. 89, iss. 2, str. 129-136, doi: 10.1080/00207160.2011.638375. [COBISS.SI-ID
15651862]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Izbrani algoritmi
Course title: Selected algorithms
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul R2 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module R2 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45 15 45 165 9
Nosilec predmeta / Lecturer: Aleksander Vesel
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Razreda NP in P. Primeri NP-polni polnih
problemov. Problemi kombinatorične
optimizacije.
Algoritmi urejanja in njihova zahtevnost.
Iskanje niza v besedilu. Klasični algoritmi:
Boyer-Mooreov algoritem, Knuth-Morris-
Prattov algoritem. Priponska drevesa:
Ukkonenov algoritem in Weinerjev algoritem.
Neeksaktno iskanje niza.
Aproksimacijski algoritmi. Lokalno iskanje.
Classes NP and P. NP-complete problems.
Combinatorial optimization problems.
Sorting algorithms in their complexity.
String matching. Classical methods: Boyer-
Moore algorithm, Knuth-Morris-Pratt algorithm.
Suffix trees: Ukkonen's algorithm, Weiner's
algoritem. Inexact matching.
Approximation algorithms. Local search.
Fundamentals of heuristics and metaheuristics
methods.
Osnove hevrističnih in metahevrističnih
algoritmov.
Zahtevnejša analiza algoritmov. Metoda
amortiziranih stroškov.
Advanced algorithm analysis. Amortized
analysis.
Temeljni literatura in viri / Readings:
M. A. Weiss, Data Structures and Algorithm Analysis in C++, Addison-Wesley, 2007.
C.H. Papadimitriou, K. Steiglitz, Combinatorial Optimization - Algorithms and Complexity,
Prentice-Hall, 1998.
M. Dorigo, T. Stutzle, Ant colony optimization, MIT Press, 2004.
D. Gusfield, Algorithms on strings, trees and sequences, Cambridge University Press, 1999.
M. Mitchell, An introduction to genetic algorithms, MIT Press, 2002.
Cilji in kompetence:
Objectives and competences:
Poglobiti znanje iz izbranih algoritmov, tehnik
zahtevnejših analiz algoritmov in osnov teorije
NP-polnosti. Poglobiti znanje iz načinov
reševanja težkih (grafovskih) problemov.
Predstaviti algoritme iskanja niza.
To deepen the knowledge of selected
algorithms, techniques for advanced algorithm
analysis and the principles of NP-completeness
theory. To deepen the knowledge of skills for
solving hard (graph) problems. To present string
matching algorithms.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Poglobiti znanje iz osnovnih in
zahtevnejših grafovskih algoritmov.
Prepoznati težke probleme.
Razumeti pomen aproksimacijskih
algoritmov.
Poglobiti znanje iz različnih vrst
hevrističnih in metahevrističnih tehnik.
Razumevanje zahtevnejših postopkov
analize algoritmov.
Prenesljive/ključne spretnosti in drugi atributi:
Prenos znanja algoritmičnih tehnik na
druga področja (diskretna matematika,
biologija, ekonomija, ...).
Knowledge and Understanding:
To deepen the knowledge of elementary
and advanced graph algorithms
To recognize hard problems.
To understand the importance of
approximation algorithms.
To deepen the knowledge of a variety of
heuristics and metaheuristics techniques.
To understand techniques for advanced
algorithm analysis
Transferable/Key Skills and other attributes:
Knowledge transfer of algorithmic
techniques into other fields (discrete
mathematics, computer science, biology,
economics, …).
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja, seminar
Računalniške vaje
Lectures, seminary
Computer exercises
Načini ocenjevanja:
Assessment:
Sprotno preverjanje:
Seminarska naloga
Projekt
Pisni testi – teorija (3 do 5 pisnih testov
na semester)
Izpit:
Pisni izpit – problemi
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljene sprotne obveznosti so pogoj
za pristop k izpitu.
Delež (v %) /
Weight (in %)
20%
20%
40%
20%
Mid-term testing:
Seminary work
Project
Written tests – theory (from 3 to 5
written tests during the semester)
Exams:
Written exam - problems
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grades of all mid-term testings
are required for taking the exam.
Reference nosilca / Lecturer's
references:
1. VESEL, Aleksander. Fibonacci dimension of the resonance graphs of catacondensed benzenoid
graphs. Discrete appl. math.. [Print ed.], 2013, str. 1-11, doi: 10.1016/j.dam.2013.03.019.
2. SHAO, Zehui, VESEL, Aleksander. A note on the chromatic number of the square of the
Cartesian product of two cycles. Discrete math.. [Print ed.], 2013, vol. 313, iss. 9, str. 999-1001.
3. KORŽE, Danilo, VESEL, Aleksander. A note on the independence number of strong products of
odd cycles. Ars comb., 2012, vol. 106, str. 473-481. [COBISS.SI-ID 16138006]
4. TARANENKO, Andrej, VESEL, Aleksander. 1-factors and characterization of reducible faces
of plane elementary bipartite graphs. Discuss. Math., Graph Theory, 2012, vol. 32, no. 2, str. 289-
297, doi: 10.7151/dmgt.1607. [COBISS.SI-ID 19104264]
5. SALEM, Khaled, KLAVŽAR, Sandi, VESEL, Aleksander, ŽIGERT, Petra. The Clar formulas
of a benzenoid system and the resonance graph. Discrete appl. math.. [Print ed.], 2009, vol. 157,
iss. 11, str. 2565-2569. http://dx.doi.org/10.1016/j.dam.2009.02.016. [COBISS.SI-ID 15142489
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Osnove programiranja v diskretni matematiki
Course title: Basic programming in discrete mathematics
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul S1 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module S1 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30 135 7
Nosilec predmeta / Lecturer: Aleksander VESEL
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Vsebina predmeta se prilagaja aktualnim
potrebam in razvoju. Poglobili bomo znanje iz
uporabe računalnika pri reševanju
matematičnih problemov, predvsem s področja
diskretne matematike.
- Relacije in algoritmi nad relacijami
- Boolova algebra
- Prirejanja v grafih
The contents of this subject is adjusted to the
current needs and development. We will deepen
the knowledge of using a computer to solve
mathematical problems, mainly from discrete
mathematics.
- relations and algorithms on relations
- Bool algebra
- matchings in graphs
Temeljni literatura in viri / Readings:
B. Vilfan, Osnovni algoritmi, ISBN 961-6209-13-2, Založba FER in FRI, 2. izd., 2002.
Kenneth H. Rosen, Discrete Mathematics and Its Applications, ISBN 007-2880-08-2, McGraw-
Hill, 6th ed., 2007.
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Introduction to
Algorithms, ISBN 026-2032-93-7, The MIT Press, 2nd ed., 2001.
Cilji in kompetence:
Objectives and competences:
Z uporabo modernega, predmetno usmerjenega
programskega jezika, poglobiti znanje iz
pristopov, podatkovnih struktur in algoritmov
pri reševanju matematičnih problemov.
With the usage of modern object oriented
programming language, to deepen the
knowledge of the basic approaches, data
structures and algorithms for solving
mathematical problems.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
podatkovne strukture matematičnih
modelov
razumevanje, implementacija in
uporaba pomembnejših algoritmov
Prenesljive/ključne spretnosti in drugi atributi:
uporaba matematičnih pojmov v
programskih aplikacijah
uporaba ustreznih podatkovnih struktur
pri implementaciji matematičnih
algoritmov
pridobljena znanja se prenašajo na
druge z računalništvom povezane
predmete
Knowledge and Understanding:
data structures of mathematical models
understanding, implementation and
usage of important algorithms
Transferable/Key Skills and other attributes:
the usage of mathematical notions in
applications
the usage of appropriate data structures
while implementing mathematical
algorithms
the obtained knowledge is transferable
to the other computer science oriented
subjects
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Računalniške vaje
Lectures
Computer exercises
Načini ocenjevanja:
Assessment:
Sprotno preverjanje:
Projekt
Pisni testi – teorija (3 do 5 pisnih testov
na semester)
Izpit:
Pisni izpit – problemi
Vsaka izmed naštetih obveznosti mora
biti opravljena s pozitivno oceno.
Opravljene sprotne obveznosti so pogoj
za pristop k izpitu.
Delež (v %) /
Weight (in %)
40%
40%
20%
Mid-term testing:
Project
Written tests – theory (from 3 to 5
written tests during the semester)
Exams:
Written exam - problems
Each of the mentioned commitments
must be assessed with a passing grade.
Passing grades of all mid-term testings
are required for taking the exam.
Reference nosilca / Lecturer's
references:
1. VESEL, Aleksander. Fibonacci dimension of the resonance graphs of catacondensed benzenoid
graphs. Discrete appl. math.. [Print ed.], 2013, str. 1-11, doi: 10.1016/j.dam.2013.03.019.
2. SHAO, Zehui, VESEL, Aleksander. A note on the chromatic number of the square of the
Cartesian product of two cycles. Discrete math.. [Print ed.], 2013, vol. 313, iss. 9, str. 999-1001.
3. KORŽE, Danilo, VESEL, Aleksander. A note on the independence number of strong products of
odd cycles. Ars comb., 2012, vol. 106, str. 473-481. [COBISS.SI-ID 16138006]
4. TARANENKO, Andrej, VESEL, Aleksander. 1-factors and characterization of reducible faces
of plane elementary bipartite graphs. Discuss. Math., Graph Theory, 2012, vol. 32, no. 2, str. 289-
297, doi: 10.7151/dmgt.1607. [COBISS.SI-ID 19104264]
5. SALEM, Khaled, KLAVŽAR, Sandi, VESEL, Aleksander, ŽIGERT, Petra. The Clar formulas
of a benzenoid system and the resonance graph. Discrete appl. math.. [Print ed.], 2009, vol. 157,
iss. 11, str. 2565-2569. http://dx.doi.org/10.1016/j.dam.2009.02.016. [COBISS.SI-ID 15142489
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Poglavja iz algebre
Course title: Topics from algebra
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja Modul S2 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree Module S2 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
60
45
165 9
Nosilec predmeta / Lecturer: Matej BREŠAR
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Poznavanje teorije grup. Knowledge of group theory.
Vsebina: Content (Syllabus outline):
Kategorije: osnovni pojmi in primeri.
Kolobarji: osnovni pojmi in primeri; glavni
kolobarji, faktorizacija; posebni razredi
kolobarjev.
Moduli: osnovni pojmi in primeri; posebni
razredi modulov; tenzorski produkt modulov in
algeber.
Categories: basic concepts and examples.
Rings: basic concepts and examples; principal
ideal domains, factorization; special classes of
rings.
Modules: basic concepts and examples; special
classes of modules; tensor products of modules
and algebras.
Fields: finite extensions, algebraic extensions;
Polja: končne razširitve, algebraične razširitve;
razpadna polja, algebraično zaprta polja;
konstruktibilna števila; osnove Galoisjeve
teorije.
splitting fields, algebraically closed fields;
constructible numbers; fundamentals of Galois
theory.
Temeljni literatura in viri / Readings:
W. Y. Gilbert, W. K. Nicholson, Modern algebra with applications, Chichester: Wiley, 2004.
I. N. Herstein, Topics in algebra, Xerox, 1975.
T. W. Hungerford, Algebra, Springer-Verlag, 1980.
S. Lang, Undergraduate algebra, Springer, 2005.
I. Vidav, Algebra, DMFA, 1980.
Cilji in kompetence:
Objectives and competences:
Poglobiti znanje nekaterih osnovnih področij
abstraktne algebre. Deepening the knowledge of some fundamental
areas of abstract algebra..
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
Teorije kolobarjev in modulov
Teorije polj
Prenesljive/ključne spretnosti in drugi atributi:
Algebraične strukture so pojavljajo na vseh
matematičnih področjih, zato mora biti
profesionalni matematik z njimi poglobi znanje.
Knowledge and Understanding:
Ring and module theory
Field theory
Transferable/Key Skills and other attributes:
Algebraic structures appear in all mathematical
areas, and therefore their knowledge is
necessary for every professional mathematician
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja
Seminarske vaje
Lectures
Tutorial
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit
Delež (v %) /
Weight (in %)
100%
Type (examination, oral, coursework,
project):
Written exam
Reference nosilca / Lecturer's
references:
1. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, ŠPENKO, Špela. Lie superautomorphisms
on associative algebras, II. Algebr. represent. theory, 2012, vol. 15, no 3, str. 507-525.
http://dx.doi.org/10.1007/s10468-010-9254-2. [COBISS.SI-ID 16299353]
2. BIERWIRTH, Hannes, BREŠAR, Matej, GRAŠIČ, Mateja. On maps determined by zero
products. Commun. Algebra, 2012, vol. 40, no. 6, str. 2081-2090.
http://dx.doi.org/10.1080/00927872.2011.570833. [COBISS.SI-ID 16315481]
3. BREŠAR, Matej, MAGAJNA, Bojan, ŠPENKO, Špela. Identifying derivations through the
spectra of their values. Integr. equ. oper. theory, 2012, vol. 73, no. 3, str. 395-411.
http://dx.doi.org/10.1007/s00020-012-1975-7. [COBISS.SI-ID 16339289]
4. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, KOCHETOV, Mikhail. Group gradings on
finitary simple Lie algebras. Int. j. algebra comput., 2012, vol. 22, no. 5, 1250046 (46 str.).
http://dx.doi.org/10.1142/S0218196712500464. [COBISS.SI-ID 16339545]
5. ALAMINOS, J., BREŠAR, Matej, ŠEMRL, Peter, VILLENA, A. R. A note on spectrum-
preserving maps. J. math. anal. appl., 2012, vol. 387, iss. 2, str. 595-603.
http://dx.doi.org/10.1016/j.jmaa.2011.09.024. [COBISS.SI-ID 16067673]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Tehnologija znanja
Course title: Knowledge technology
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30 135 7
Nosilec predmeta / Lecturer: Krista RIZMAN ŽALIK
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Uvod: metode odkrivanja znanja, proces
odkrivanja znanja, naloge podatkovnega
rudarjenja, aplikacije podatkovnega rudarjenja,
uporaba odkritega znanja pri inteligentnih,
odločitvenih in ekspertnih sistemih.
Predstavitev znanja in operatorji: izjavni račun,
predikatni račun prvega reda, diskriminante in
regresijske funkcije, verjetnostne porazdelitve.
Osnovne teorije naučljivosti: teorija
Introduction to knowledge discovery methods,
process of knowledge discovery, tasks of data
mining, applications of data mining and the use
of discovered knowledge by intelligent, decision
and expert systems.
Knowledge presentation and operators: first
order predicate calculus, regression functions,
probability distribution.
Basic theory of learn ability, theory of
izračunljivosti in teorija rekurzivnih funkcij,
formalna teorija učenja, naučljivost glede na
lastnosti učnih funkcij, vhodnih podatkov in
konvergence učenja.
Podatki in modeli, vizualizacija podatkov,
jeziki in arhitektura sistemov podatkovnega
rudarjenja.
Metode podatkovnega rudarjenja:
Rudarjenje pogostih vzorcev, asociacij in
korelacij podatkov.
Klasifikacija in napoved: Bayesova
klasifikacija, Bayesove verjetnostne mreže,
odločitvena drevesa, nevronske mreže, metoda
podpornih vektorjev,
genetski algoritmi.
Analiza gruč: delitvene metode, hierarhične
metode, metode gostote, mrežno razvrščanje,
samoorganizirajoče nevronske mreže-
Kohonenova nevronska mreža, ugotavljanje
redkih vrednosti in napak.
Rudarjenje kompleksnih podatkov: prostorskih,
večpredstavnostnih, časovnih vrst in zaporedij,
besedil in vsebin svetovnega spleta.
computability, theory of recursive functions,
formal theory of learning, learn ability regarding
the characteristics of learning functions, input
data and learning convergence.
Data and models, data visualization, languages
and architecture of data mining systems.
Methods of data mining:
Mining of patterns, associations and data
correlations.
Classification and prediction: Bayes classifier,
Bayes probability nets, decision trees, neural
networks, support vector machines, genetical
algorithms.
Cluster analysis: partition methods, hierarchical
methods, grid-based methods , self organizing
neural networks- Kohonen neural networks,
outlier detection.
Data mining of complex data: spatial,
multidimensional, time series and sequences,
documents and contents of internet.
Temeljni literatura in viri / Readings:
Ian H. Witten, Eibe Frank: Data Mining: Practical Machine Learning Tools and Techniques with
Java Implementations, Morgan Kaufmann, 2005.
J.Han, M.Kamber: Data Mining: Concepts and Techniques, Morgan Kaufmann, 2001.
I. Kononenko, Strojno učenje, Založba FE in FRI, 2005.
Cilji in kompetence:
Objectives and competences:
Predstaviti osnovne teorije naučljivosti, tehnike
predstavitve znanja in operatorje.
Predstaviti principe odkrivanja znanja v
ogromnih količinah zbranih podatkov in
uporabo znanja v inteligentnih sistemih.
The main objective is to provide students with a
theory of learnability, techniques of knowledge
presentation and operators.
To provide students with principles of
knowledge discovery in great amount of
collected data and the use of data in the
intelligent systems.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
• Razumevanje temeljnih principov
predstavitve in zajemanja znanja, operatorjev in
osnovne teorije naučljivosti.
• Poznavanje metod za podatkovno
rudarjenje, tako da se lahko uporabijo ali
prilagodijo za reševanje trenutnih problemov.
Knowledge and Understanding:
Understanding of basic principles of data
presentation and comprising of
knowledge, operators and basic theory of
learnability.
Knowing of data mining methods in
such depth, that they can be used and
adapted to solve current problems.
Metode poučevanja in učenja:
Learning and teaching methods:
• Predavanja
• Računalniške vaje
• Computer exercises
• Written exam
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
- Računalniške vaje
- Pisni izpit
- Vsaka izmed naštetih obveznosti
mora biti opravljena s pozitivno
oceno.
- Pozitivna ocena pri vajah je pogoj
za pristop k izpitu.
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
- Computer exercises
- Written exam
- Each of the mentioned commitments
must be assessed with a passing
grade.
- Passing grade of the exercises is
required for taking the exam.
Reference nosilca / Lecturer's
references:
1. RIZMAN ŽALIK, Krista, ŽALIK, Borut. Validity index for clusters of different sizes and
densities. Pattern recogn. lett. (Print). [Print ed.], Jan. 2011, vol. 32, iss. 2, str. 221-234, doi:
10.1016/j.patrec.2010.08.007. [COBISS.SI-ID 14640150]
2. RIZMAN ŽALIK, Krista. Cluster validity index for estimation of fuzzy clusters of different
sizes and densities. Pattern recogn.. [Print ed.], Oct. 2010, vol. 43, iss. 10, str. 3374-3390, doi:
10.1016/j.patcog.2010.04.025. [COBISS.SI-ID 14640406]
3. RIZMAN ŽALIK, Krista, ŽALIK, Borut. A sweep-line algorithm for spatial clustering. Adv.
eng. softw. (1992). [Print ed.], Jun. 2009, vol. 40, iss. 6, str. 445-451, doi:
10.1016/j.advengsoft.2008.06.003. [COBISS.SI-ID 12450582]
4. RIZMAN ŽALIK, Krista. An efficient k'-means clustering algorithm. Pattern recogn. lett.
(Print). [Print ed.], July 2008, vol. 29, iss. 9, str. 1385-1391.
http://dx.doi.org/10.1016/j.patrec.2008.02.014. [COBISS.SI-ID 12121366]
5. RIZMAN ŽALIK, Krista. Discovering significant biclusters in gene expression data. WSEAS
transactions on information science and applications, Sep. 2005, vol. 2, iss. 9, str. 1454-1461.
[COBISS.SI-ID 14906120]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Temelji finančnega inženiringa
Course title: Foundations of financial engineering
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30
135 7
Nosilec predmeta / Lecturer: Miklavž MASTINŠEK
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
1.Matematične osnove
2.Izvedeni finančni instrumenti
3.Tveganje in varnost
4.Opcije
5.Vrednotenje opcij, hedging
6.Binomski model
7.Black-Scholesov
8.Delta, gamma, sigma
9.Monte-Carlo metoda
10.Vodenje portfelja
11.Realne opcije
1.Mathematical tools
2.Financial derivatives
3.Risk and security
5.Option valuation, hedging
6.Binomial model
7.Black-Scholes model
8.The greeks
9.Monte-Carlo method
10.Portfolio management
11.Real options
Temeljni literatura in viri / Readings:
1. Hull J., »Options, Futures and other Derivative Securities«, New Jersey, Prentice Hall Int.,
1996.
2. Wilmott P.« Paul Wilmott on Quantitative Finance«, John Wiley, (2000).
3. Cuthbertson K., »Financial engineering: derivatives and risk management«, Wiley,
(2001)
Cilji in kompetence:
Objectives and competences:
Namen predmeta je posredovati temeljna
teoretična in praktična znanja potrebna pri
kvantitativnem in kvalitativnem obravnavanju
nalog in procesov s področja finančnega
inženiringa. Prav tako je namen predmeta dati
osnovo za spremljanje sodobne literature in
nadaljnje strokovno izpopolnjevanje.
The objective is to provide fundamental
theoretical knowledge and practical skills
of financial engineering.
The objective is also to enable the students
for additional learning and individual study of
new methods.
Predvideni študijski rezultati:
Intended learning outcomes:
Poglobljeno znanje in razumevanje temeljnih
vsebin in orodij potrebnih za strokovno
korektno vodenje poslov s področja finančnega
inženiringa.
Prenesljive/ključne spretnosti in drugi atributi:
Sposobnost samostojnega praktičnega in
teoretičnega dela. Zmožnost nadaljnega študija
novih kvantitativnih
metod finančnega inženiringa.
Knowledge and Understanding:
Fundamental theoretical knowledge and
practical skills of financial engineering.
Transferable/Key Skills and other attributes:
Capabilitiy of understanding and application of
knowledge in praxis. Ability of additional
learning and individual study of new methods.
Metode poučevanja in učenja:
Learning and teaching methods:
Predavanja, tehnične demonstracije,
aktivne vaje, seminarske vaje
Written examination
Seminary work
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
Pisni izpit
seminarska naloga
Delež (v %) /
Weight (in %)
80%
20%
Type (examination, oral, coursework,
project):
Written exam
Semynar
Reference nosilca / Lecturer's
references:
1. MASTINŠEK, Miklavž. Charm-adjusted delta and delta gamma hedging. J. deriv., 2012, vol.
19, no. 3, str. 69-76, doi: 10.3905/jod.2012.19.3.069. [COBISS.SI-ID 10970908]
2. MASTINŠEK, Miklavž. Financial derivatives trading and delta hedging = Trgovanje z
izvedenimi finančnimi instrumenti ter delta hedging. Naše gospod., 2011, letn. 57, št. 3/4, str. 10-
15. [COBISS.SI-ID 10733084]
3. MASTINŠEK, Miklavž. Descrete-time delta hedging and the Black-Scholes model with
transaction costs. Math. methods oper. res. (Heidelb.). [Print ed.], 2006, vol. 64, iss. 2, str. [227]-
236, doi: 10.1007/s00186-006-0086-0. [COBISS.SI-ID 8939292]
4. MASTINŠEK, Miklavž. Identifiability for a partial functional differential equation. Acta sci.
math. (Szeged), 2003, vol. 69, str. 121-130. [COBISS.SI-ID 7029276]
5. MASTINŠEK, Miklavž. Norm continuity for a functional differential equation with fractional
power. International journal of pure and applied mathematics, 2003, vol. 5, no. 1, str. 49-56.
[COBISS.SI-ID 6783772]
UČNI NAČRT PREDMETA / COURSE SYLLABUS
Predmet: Teorija programskih jezikov
Course title: Theory of programming languages
Študijski program in stopnja
Study programme and level
Študijska smer
Study field
Letnik
Academic
year
Semester
Semester
Matematika, 2. stopnja 1. ali 2. 1. ali 3.
Mathematics, 2nd
degree 1. or 2. 1. or 3.
Vrsta predmeta / Course type
Univerzitetna koda predmeta / University course code:
Predavanja
Lectures
Seminar
Seminar
Sem. vaje
Tutorial
Lab. vaje
Laboratory
work
Teren. vaje
Field work
Samost. delo
Individ.
work
ECTS
45
30 135 7
Nosilec predmeta / Lecturer: Krista RIZMAN ŽALIK
Jeziki /
Languages:
Predavanja /
Lectures:
SLOVENSKO/SLOVENE
Vaje / Tutorial: SLOVENSKO/SLOVENE
Pogoji za vključitev v delo oz. za opravljanje
študijskih obveznosti:
Prerequisits:
Vsebina: Content (Syllabus outline):
Formalna logika kot programski jezik,
avtomatsko dokazovanje izrekov kot
interpretiranje nepostopkovnih programov.
Formalna semantika programskih jezikov:
operacijska semantika, denotacijska semantika,
aksiomatska semantika.
Uporaba semantike (dokazovanje pravilnosti in
lastnosti programov, statična analiza
programov).
Formal logic as programming languages,
automatic proof of lemas as interpreting of
nonprocedural programs.
Semantic of programming languages:
operational semantics, denotational semantics,
axiomatic semantics, the use of semantic
(proving of corectnes, characteristics of
programmes,
static analysis of programms).
Koncepti objektno usmerjenih jezikov: meta-
razred, podrazredi in podtipi, kovarianca in
kontravarianca, polimorfizem. Formalni opis
objektno usmerjenih jezikov.
Funkcijski programski jeziki.
Lambda kalkulus: proste in vezane
spremenljivke, redukcije, pretvorbe, rekurzija,
izračunljive funkcije,
typed lambda calculus, second-order lambda
calculus.
Basic concepts of object-oriented programming
languages : meta-class, subclass and subtype,
covariance in contravariance, polimorphism.
Formal description of object-oriented languages.
Functional programing languages. Lambda
calculus: free and bound variables, reduction,
conversions, recursions, computable functions,
typed lambda calculus, second-order lambda
calculus.
Temeljni literatura in viri / Readings:
D. A. Watt: Programming Language Concepts and Paradigms, Prentice-Hall, New York 1990.
H.R. Nielson, F. Nielson. Semantics with Applications: A Formal
Introduction. John Wiley & Sons, Chichester, 1992.
M. Abadi, L. Cardelli. A Theory of Objects. Springer-Verlag, New York, 1996.
K. Bruce. Foundations of Object-Oriented Languages: Types and Semantics.
The MIT Press, 2002.
H. P. Barendregt. The Lambda Calculus: Its Syntax and Semantics. Studies
in Logic and the Foundations of Mathematics, Volume 103, North-Holland, 1984.
H. P. Barendregt. Introduction to Lambda Calculus. Workshop on
Implementation of Functional Languages, 1988.
Cilji in kompetence:
Objectives and competences:
Poglobiti znanje iz teoretičnih osnov
programskih jezikov. The main objective is to provide students with a
theoretical background of programming
languages.
Predvideni študijski rezultati:
Intended learning outcomes:
Znanje in razumevanje:
- Teoretičnih osnov programskih jezikov
Knowledge and Understanding:
- Theoretical background of programming
languages
Metode poučevanja in učenja:
Learning and teaching methods:
• Predavanja
• Računalniške vaje
• Computer exercises
• Written exam
Načini ocenjevanja:
Assessment:
Način (pisni izpit, ustno izpraševanje,
naloge, projekt)
- Računalniške vaje
- Pisni izpit
- Vsaka izmed naštetih obveznosti
mora biti opravljena s pozitivno
oceno.
Delež (v %) /
Weight (in %)
50%
50%
Type (examination, oral, coursework,
project):
- Computer exercises
- Written exam
- Each of the mentioned commitments
must be assessed with a passing
grade.
- Pozitivna ocena pri vajah je pogoj
za pristop k izpitu.
- Passing grade of the exercises is
required for taking the exam.
Reference nosilca / Lecturer's
references:
1. RIZMAN ŽALIK, Krista, ŽALIK, Borut. Validity index for clusters of different sizes and
densities. Pattern recogn. lett. (Print). [Print ed.], Jan. 2011, vol. 32, iss. 2, str. 221-234, doi:
10.1016/j.patrec.2010.08.007. [COBISS.SI-ID 14640150]
2. RIZMAN ŽALIK, Krista. Cluster validity index for estimation of fuzzy clusters of different
sizes and densities. Pattern recogn.. [Print ed.], Oct. 2010, vol. 43, iss. 10, str. 3374-3390, doi:
10.1016/j.patcog.2010.04.025. [COBISS.SI-ID 14640406]
3. RIZMAN ŽALIK, Krista, ŽALIK, Borut. A sweep-line algorithm for spatial clustering. Adv.
eng. softw. (1992). [Print ed.], Jun. 2009, vol. 40, iss. 6, str. 445-451, doi:
10.1016/j.advengsoft.2008.06.003. [COBISS.SI-ID 12450582]
4. RIZMAN ŽALIK, Krista. An efficient k'-means clustering algorithm. Pattern recogn. lett.
(Print). [Print ed.], July 2008, vol. 29, iss. 9, str. 1385-1391.
http://dx.doi.org/10.1016/j.patrec.2008.02.014. [COBISS.SI-ID 12121366]
5. RIZMAN ŽALIK, Krista. Discovering significant biclusters in gene expression data. WSEAS
transactions on information science and applications, Sep. 2005, vol. 2, iss. 9, str. 1454-1461.
[COBISS.SI-ID 14906120]