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FACULTY OF ARTS AND SCIENCES
Course Title Real and Complex Analysis IDepartment MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT501 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Real and Complex analysis including abstract integration, positive Borel measures, -spaces, elementary Hilbert theory, examples of Banach spaces techniques, complex measures, differentiation and integration on product spaces.
Textbook and Supplementary readings1 Real and Complex Analysis, by Walter Rudin, 1987.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Abstract integration
2 Abstract integration
3 Positive Borel measures
4 Positive Borel measures
5 -spaces
6 -spaces
7 Elementary Hilbert theory
8 Elementary Hilbert theory
9 Examples of Banach spaces techniques
10 Examples of Banach spaces techniques
11 Complex measures
12 Complex measures
13 Differentiation and integration on product spaces
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Algebra I Department Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT503 Fall MS Obligatory Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
This course gives the fundamental concepts of groups
Textbook and Supplementary readings1 Algebra,T.W.Hungerfort
2 Contemporary Abstract Algebra, J.A.Gallian 3 Basic Algebra I-II, N. Jacobson4 Basic Abstract Algebra, P.B. Bhattacharya, S.K.Jain, S.R. Nagpaul, Cambridge University Pres5 Fundamentals of Abstract Algebra, D.S.Malik, John M.Mordeson, M.K.Sen, , The McGraw-Hill Companies
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Semigroups, Monoids and Groups
2 Homorphisms and Subgroups
3 Cyclic Groups, Coset and Counting
4 Normal altgruplar , Quotient Groups
5 Isomorphism theorems
6 Symmetric,
7 Alternating and Dihedral Groups
8 Categories
9 Product, Coproduct and Free Objects-EXAM
10 Direct Products and Direct Sums
11 Free Abelian Group
12 Finitely Generated Abelian Groups
13 The Action of Group on a set
14 The Sylow Theorems
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title TopologyDepartment MathematicsDivision in the Dept. Topology
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS creditMAT 505 Fall MS Obligatory Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Adnan MELEKOĞLU
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]
Course Objective and Brief Description
The aim of this course is to provide basic knowledge on General Topology.
Textbook and Supplementary Readings1 Gemignani, M., (1990) Elementary Topology, Dover Publications2 Munkres, J.R. (1999) Topology, Prentice Hall
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Metric spaces
2 Topological spaces
3 Bases and sub bases
4 Continuous functions
5 Subspaces
6 Product spaces
7 Quotient spaces
8 Midterm Exam
9 Sequences
10 Nets
11 Filters
12 Separation axioms
13 Compactness
14 ConnectednessCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Commutative Rings
Department Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT507 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist Prof. Dr. Selma Altınok, Assist Prof. Dr. Erdal Özyurt, Assist Prof. Dr. Semra Doğruöz, Assist Prof. Dr. Hülya İnceboz
Instructor Information
[email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
In order to study open problems in Algebraic Geometry, commutative rings must be studied. This course’s aim is to introduce the fundmental concepts of Commutative Rings.
Textbook and Supplementary readings1 Commutative ring theory, H. Matsumura, Cambridge Unv. Press, 1997
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Rings and ıdeals
2 Localization of rings
3 Modules
4 Exact sequences
5 Prime and Primary ideals
6 Primary decomposition
7 Noetherian rings and modules
8 Noetherian rings and modules
9 Artinian rings and modules Ara sınav
10 Extension of rings
11 Hilbert Nullstellensats
12 Hilbert Nullstellensats
13 Dimension theory
14 Dimension theoryCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Field Extensions
Department MathematicsDivision in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT511 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Prof. Dr. Hatice Kandamar, Yrd. Doç. Dr. Selma Altınok
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 [email protected], [email protected]
Course Objective and Brief Description
This course gives the fundamental concepts of field extensions.
Textbook and Supplementary Readings1 Algebraic Extension of Fields, Paul J. McCarty2
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Algebraic Extensions: Seperability of extensions, normal extensions, Finite Fields2 Algebraically Closed Fields, Norm and Traces3 Galois Theory: Automorphisms of extensions, the Fundamental Theorem of Galois theory4 Cyclotomic Fields, Cyclic Extensions
5 Multiplicative Kummer Theory, Additive Kummer Theory, Solution of Polynomial Equations by Radicals
6 Infinite Galois Extensions, Introduction to Valuation Theory7 Value Groups and Residue Class Fields8 Midterm Exam
9 Relatively Complete Fields10 Extension of Valued Fields11 Ramification and Residue Class Degree, Unramified and Tamely Ramified Extensions12 The Different, Extension with Seperable, Ramification Groups13 Dedekind Fields: The Fundamental Theorem of Dedekind Fields14 Extension of Dedekind Fields, Factoring of Ideals in Extensions.
Course assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Number TheoryDepartment Mathematics
Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT513 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist Prof. Dr. Selma Altınok, Assist Prof. Dr. Erdal Özyurt, Assist Prof. Dr. Semra Doğruöz, Asist. Prof. Hülya İnceboz
Instructor Information
[email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
Number Theory is a branch of science which investigate intigers and things related to them. Its aim is to teach students fundamental concepts of Number Theory
Textbook and Supplementary readings1 Number Theory, Z. I. Borevich and I.R. Shafarevich, Academic Press, 1967
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Congruencies and P-adic numbers
2 Quadratic forms and Rational quadratic forms
3 Decomposition of forms and representations of numbers
4 Classification of modules
5 Representation of numbers by binary quadratic forms
6 Divisors
7 Değerler
8 Dedekind halkalar
9 Dedekind halkalarAra sınav
10 Quadratic fields
11 Extension of fields by valuations
12 Extension of fields by valuations
13 Numbers of divisor class and their Formula
14 Numbers of divisor class and their FormulaCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Differentiable ManifoldsDepartment MathematicDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT515 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Leyla Onat
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü 09010-AdınTel:02562128498 [email protected]
Course Objective and brief Description
The main goal is this course to provide a working knowledge of manifolds, tensors and differential forms.
Textbook and Supplementary readings1 Boothby, William M. An Introduction to Differentiable Manifolds and Riemannian Geometry Academic
Press, New York,1975COURSE CALANDER / SCHEDULE
Week Lecture topics Practice/Lab/Field1 Define manifold
2 Construct the topology of a manifolds
3 Define the tangent vectors
4 D,ifferentiable maps between manifolds
5 Define the Riemannian metric and Riemannian manifold
6 Define the Lie Bracket
7 Solve the problem about what he has learned
8 Observe the Koszul Formulas
9 Define tensors and tensor fields
10 Take derivative on the tensor field
11 Define spaces of constant curvature
12 Define spaces of constant curvature Define the Ricci tensor and scalar curvature
13 Solve the problem about what he has learned
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Mathematical Statistics IDepartment MathematicsDivision in the Dept. Application Mathematic
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTC Credit
MAT519 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Hüsnü Barutoğlu
Instructor Information
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100 [email protected]
Course Objective and brief Description
This course introduces fundamental probability and mathematical statistical theory
Textbook and Supplementary readings1 İnal C. Olasılıksal ve Matematiksel İstatistik,Hacettepe Üniv. Fen Fak yayınları No: 16, 19822 Kendall,M, Stuart,A.,Ord J.K.-The Advanced theory of Statistics. Charles griffin com. London 1983.3 Alexander, W.H. –Elements of Mathematical Statistics John Wiley and Sons, NewYork,1961.4 Mood,A.M.,Graybill,F.A. Probabilitiy and Statistical Applications McGraw-Hill Book Com.
NewYork,1963COURSE CALANDER / SCHEDULE
Week Lecture topics Practice/Lab/Field1 Permutation, Combination
2 Probability
3 Discrete distribution functions
4 Continuous distribution function
5 Expected value
6 Arithmetic mean, Variance
7 Moment generation function
8 Characteristic function
9 QUIZ
10 Maping of variable
11 Estimations Theory
12 Point Estimation
13 Interval Estimation
14 ExercisesCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Foundation StatisticsDepartment MathematicsDivision in the Dept. Application Mathematic
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT521 Fall MS Elective Turkish 2 2 3 8Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Hüsnü Barutoğlu
Instructor Information
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100 [email protected]
Course Objective and brief Description
This course introduces fundamental probability and mathematical statistical theory
Textbook and Supplementary readings1 Kendall,M, Stuart,A.,Ord J.K.-The Advanced theory of Statistics. Charles griffin com. London 1983.2 Mood,A.M.,Graybill,F.A. Probabilitiy and Statistical Applications McGraw-Hill Book Com.
NewYork,1963.34
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Measures of location
2 Measures of distribution
3 Moments
4 Regression
5 Correlation
6 Normal distribution
7 Standard normal distribution
8 Confidence intervals
9 QUIZ
10 Student-t distribution
11 Chi-square distribution
12 Test of hypothesis.
13 Test of hypothesis.
14 Test of hypothesis.Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Regression AnalysisDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT523 Fall MS Elective Turkish 3 0 3 8Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Hüsnü Barutoğlu
InstuctorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100 [email protected]
Course Objective and brief Description
This course introduces fundamental experiment design and analysis of variance.
Textbook and Supplementary readings1 Mood A.M.,GraybillF.G., An Indroduction to Statistics Theory Çeviri Prof.Dr. Süeda Moralı Özarkadaş
Matbaası İstanbul 1973.2 Kendal M.,Stuart A., Ord J.K., The Advanced Theory of Statistics. Charles griffin com. London 1983.3 Graybill F.A., An Indroduction to Linear Statistical Models, McGraw-Hill Book Com. İnc. NewYork 1961.
COURSE CALANDER/ SCHEDULEWeek Lecture topics Prectice/Lab/Field
1 Point estimation and interval estimation
2 Testing hypothesis
3 The multivariate normal distribution
4 Distribution of quadratic forms
5 Linear models
6 The general linear of full rank
7 Functional relationships
8 Regression models
9 Experimental design models
10 Factorial models
11 Analysis of varians
12 Incomplete block models
13 Latin squares
14 Final ExamCourse assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Mathematical ModellingDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type Language Credit hours/week
Lecture Lab Credit ECTS CreditMAT525 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Ali Filiz, Assist. Prof. Dr. Ali IŞIK
Instructor Information
Adnan Menderes Üniversity, Faculty of arts and science 09100 AydınTel:256 2128498 [email protected], [email protected]
Course Objective and brief Description
This course aims to acquaint students with the basic knowledge of numerical solution of some kinds of integral equations and ODEs. Students will be familiar with classification of equations Volterra and Fredholm method of solutions. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to biology, and other sciences.
Textbook and Supplementary readings1 Paul Davis, (1999), Differential Equations : Modeling with MATLAB, Prentice Hall.2 G. A Turskey, F. Yuan, D. K. Katz, (2004), Tranport Phenomena in Biological Systems3 S. M. Dunn, A. Constantides, P. V. Moghe, (2006) Numerical methods in Biomedical Engineer, Academic
pres. 4
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to mathematical modelling
2 Applications in real life
3 Finite difference methods for ODEs,
4 Finite difference methods for PDEs
5 Numerical solution and stability of differential equations
6 Cauchy- Riemann equations
7 Local truncation errors
8 Midterm exam
9 Linear and non-linear differential equations
10 Population and logistic equations
11 Harvesting and toxicity
12 Time depend phenomena
13 Toxicity term via integral terms
14 Final ExamCourse assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Coerce Title Numerical solution of Differential EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type Language Credit hours/week
Lecture Lab Credit ECTS CreditMat 527 Fall MS Elective Turkish 3 0 3 10
Name of Instructors Assist. Prof. Dr. Ali Filiz, Assist. Prof. Dr. Ali IŞIK
Instructor Information
Adnan Menderes Üniversity, Faculty of arts and science 09100 AydınTel:256 2128498 [email protected], [email protected]
Course Objective and brief Description
This course aims to acquaint students with the basic knowledge of numerical solution of some differential equations. Students will be familiar with classification of equations initial and boundary value problems and relation between Volterra and Fredholm integrals. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to biology, and other sciences.
Textbook and Supplementary readings1 Clay C. Rose, (2004), Differential Equations, Springer, second edition.2 B. R. Hunt, R. L. Lipsman, J. E. Osborn, J. M. Rosenberg, (2005), Differential Equations with MATLAB34
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction of MATLAB and differential equations
2 Ordinary differential equations., Initial and boundary value problems and solution of methods,
3 Numerical methods and their stabilities
4 Numerical solution of IVP and Volterra integral equations
5 Local truncation errors and order of convergence
6 Linear and non-linear differential equations
7 Single step methods for differential equations
8 Midterm exam
9 Linear and Nonlinear Volterra integral equations of the second kind
10 Numerical stability of Single step methods
11 Taylor series and Runge-Kutta methods
12 Butcher table and Runge-Kutta method And Adams methods
13 Numerical stability of Multi-step methods
14 Final ExamCourse assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Academic Software Department MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type Language Credit hours/week
Lecture Lab Credit ECTS CreditMAT533 Fall MS Elective Turkish 3 0 3 8Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Ali Filiz
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2114 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamentals of academic software. Classes will be held in the computer laboratory and lab computers will be used for practices during whole class hours of lecturing
Textbook and Supplementary readings1 LaTeX: A Document Preparation System, Leslie Lamport, 1992.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Matematiksel yazılımın tarihi The history of academic software
2 İnternet and knowledge source
3 Search in the internet
4 LaTeX and mathematical writing
5 Project with LaTeX’de
6 Project via Ms Word
7 The comparasion LaTeX and Word
8 Project I
9 Article style
10 Book style
11 Thesis style
12 LaTeX’s error Messages
13 Prepare index and reference
14 Proje IICourse assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Mathematical Analysis IDepartment MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT541 Fall MS Obligatory Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of mathematical analysis including the real and complex number systems, basic topology, numerical sequences and series, continuity, differentiation, the Riemann-Stieltjes Integral
Textbook and Supplementary readings1 Principles of Mathematical Analysis, Walter Rudin.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Real and complex number systems
2 Real and complex number systems
3 Basic topology
4 Basic topology
5 Numerical sequences and series
6 Numerical sequences and series
7 Continuity
8 Continuity
9 Differentiation
10 Differentiation
11 Riemann-Stieltjes Integral
12 Riemann-Stieltjes Integral
13 Riemann-Stieltjes Integral
14 Final Exam
Course assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Divegent Series IIDepartment MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT551 Fall MS Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of divergent series including elementary Tauberian theorems, Tauberian theorems, A tauberian theorem for Euler method, Fourier series, Convergence of Fourier series, Convergence tests, Cesaro summability of Fourier series, Abel-Poisson summability of Fourier series, Riemann’s method of summation, Absolute convergence, Fourier transforms, Applications of summability to analytic continuation, the Borel exponential method, the Okada theorem
Textbook and Supplementary readings1 Divergent Series, G. H. Hardy234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Elementary Tauberian theorems
2 Tauberian theorems
3 A tauberian theorem for Euler method
4 Fourier series
5 Convergence of Fourier series
6 Convergence tests
7 Cesaro summability of Fourier series
8 Abel-Poisson summability of Fourier series
9 Riemann’s method of summation
10 Absolute convergence
11 Fourier transforms
12 Applications of summability to analytic continuation
13 the Borel exponential method and the Okada theorem
14 Final Exam
Course assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Riemann surfacesDepartment MathematicsDivision in the Dept. Topology
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS credit
MAT 555 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Adnan MELEKOĞLU
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]
Course Objective and Brief Description
The aim of this course is to provide introductory knowledge for Riemann surfaces regarding them as the quotient spaces of Fuchsian groups.
Textbook and Supplementary Readings1 Jones G.A. and Singerman D. (1987) Complex Functions, Cambridge University Press2 Katok S. (1992) Fuchsian groups, The University of Chicago Press
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Riemann surfaces
2 The methods of obtaining Riemann surfaces
3 Lattices
4 Riemann surfaces of genus one
5 Fuchsian groups
6 Generators and geometric properties of Fuchsian groups
7 Fundamental regions and quotient spaces of Fuchsian groups
8 Midterm Exam
9 Fuchsian groups whose quotient spaces are Riemann surfaces
10 Triangle groups
11 Platonic Riemann surfaces
12 Automorphisms of Riemann surfaces
13 Hyperelliptic Riemann surfaces
14 Symmetric Riemann surfacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Algebraic Geometry IIDepartment MathematicsDivision in the Dept. Topology and Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT557 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Prof. Dr. Hatice Kandamar, Yrd. Doç. Dr. Selma Altınok
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 [email protected], [email protected]
Course Objective and Brief Description
This course is a continuation of Algebraic Geometry I. Its aim is to introduce the advanced subjects of Algebraic Geometry to students.
Textbook and Supplementary Readings1 Algebraic Geometry, R. Hartshorne2
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Sheaves2 Sheaves3 Schemes, affine Schemes, Projective Schemes4 Schemes, affine Schemes, Projective Schemes5 Morphisms6 Sheaves of Modules7 Sheaves of Modules8 Midterm Exam
9 Divisors on Varietes or Schemes10 Divisors on Curves11 Cohomology and Cohomology Sheaves 12 Cohomology of Affine Schemes13 Cech Cohomology14 Cohomology of Projective Spaces
Course assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination
FACULTY OF ARTS AND SCIENCES
Course Title Groups and SymmetryDepartment MathematicsDivision in the Dept. Topology
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS creditMAT 559 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Adnan MELEKOĞLU
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]
Course Objective and Brief Description
The aim of this course is to provide knowledge for the geometric properties of groups by giving concrete examples.
Textbook and Supplementary Readings1 Armstrong, M.A. (1988) Groups and Symmetry, Springer
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Groups, cyclic and dihedral groups
2 Subgroups and generators
3 Symmetry groups of regular polygons
4 Group action
5 The orbit and the stabilizer of a point
6 Permutations
7 Symmetry groups of regular polytopes
8 Midterm Exam
9 Finite rotation groups
10 Isometries in the Euclidean plane
11 Translations and rotations
12 Reflections and glide reflections
13 Euclidean groups and their quotient spaces
14 Euclidean groups with compact quotient spacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Matrix AnalysisDepartment MathematicsDivision in the Dept. Algebra and Number Theory
Code Term Level Type Language Credit hours/WeekLecture Lab. Credit ECTS Credit
MAT561 Fall MS Elective Turkish 3 0 3 10Course None
Prerequisites
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist Prof. Dr. Selma Altınok, Asist Prof. Dr. Erdal Özyurt, Assist Prof. Dr. Semra Doğruöz, Asist. Prof. Hülya İnceboz
InstructorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
This course introduces fundamental concepts of linear algebra which are indispensable in all branches of basic science.
Textbook and Supplementary readings1 Matrix Analysis and Applied Linear Algebra, Roger A. Horn, Charles R. Johnson, 2001.2 Linear Algebra, K. Hoffman and R. Kuntze, Printice Hall 2.Edition, 1971.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Linear equations and matrices
2 Matrix algebra, some specail matrices,row and column operations
3 Echelon form in matrices, LU-decompositions
4 Vector spaces, linear independence,basis and dimensions
5 Homojen equation systems
6 Coordinates, isomorphisms, rank of matrix
7 Linear transformations, kernel, image
8 Matrix representation, of linear transformations
9 Linear functionals, Dual, MIDTERM
10 Determinants and its aplications
11 Eigenvalues and eigenvectors,
12 Diagonalization, similar matrices
13 Inner product spaces, R^2 and R^3 standart inner product spaces
14 Gram-Schmidt method, orthonormal setsCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Visual Programming IDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT563 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Ali FİLİZ
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09100 AydınTelephone Number:0 256 2128498-2114 and 2116 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamentals of visual programming. Classes will be held in the computer laboratory and lab computers will be used for practices during whole class hours of lecturing.
Textbook and Supplementary readings1 C Dersi Proglamlamaya Giriş, N. Ercil Çağıtay, G.Tokdemir, C. Fügen Selbes, Ç. Turhan, Bizim Büro
Basımevi, 2007.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Visual programming setup
2 Programming languages and user interface
3 Programming languages and user interface
4 Using form
5 Using form
6 Form events
7 Form events
8 Constants
9 Project I
10 Variables
11 Operators
12 Control structures and loop structures
13 Arrays. Menus
14 Project II
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Applications of MATHEMATICA in Mathematics EducationDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT565 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Ali Filiz, Assist. Prof. Dr. Ali IŞIK
Instructor Information
Adnan Menderes Üniversity, Faculty of arts and science 09100 AydınTel:256 2128498 [email protected], [email protected]
Course Objective and brief Description
MATHEMATICA is used by scientists and engineers in disciplines ranging from astronomy to zoology; typical applications include computational number theory, ecosystem modeling, financial derivatives pricing, quantum computation, statistical analysis, and hundreds more.
Textbook and Supplementary readings1 http://www.wolfram.com/2 The Student's Introduction to Mathematica : A Handbook for Precalculus, Calculus, and Linear Algebra
(Paperback), B. F. Torrence, Eve. A. Torrence, Camb. Univ. Press, 1999.3 The Mathematica book, 3rd Edition, S, Wolfram, Camb. Univ. Press, 1999.4
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to MATHEMATICA
2 Common errors and suggestions
3 MATHEMATICA commands
4 Application of MATHEMATICA
5 Simple calculations for different subjects
6 Plotting functions
7 Combining two or more plots,
8 Project I
9 Algebra, Calculus
10 multivariable calculus and linear algebra with mathematica,
11 Derivatives and integrals
12 Special functions with MATHEMATICA
13 Programming with MATHEMATICA
14 Project II
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Normed Spaces and Inner Product Spaces
Department MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT567 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Normed and Inner Product Spaces including Normed linear spaces, linear subspaces, infinite series, convex sets, linear functionals, finite-dimensional spaces, dual space and second dual space, weak convergence, inner product spaces, orthogonal complements, Fourier series, Riesz representation theorem
Textbook and Supplementary readings1 Topology and Normed Spaces, G. J. O. Jameson.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Normed linear spaces
2 Linear subspaces
3 Infinite series
4 Convex sets
5 Linear functionals
6 Finite-dimensional spaces
7 Dual space and second dual space
8 Weak convergence
9 Inner product spaces
10 Orthogonal complements
11 Fourier series
12 Riesz representation theorem
13 Riesz representation theorem
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Natural Language ProcessingDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 569 Fall MS Elective Turkish 3 0 3 8
Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Rıfat Aşlıyan
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected]
Course Objective and brief Description
This course aims to present the basics of Natura Language Processing.
Textbook and Supplementary readings1 D. Jurafsky and J. H. Martin, "Speech and Language Processing" , Prentice Hall, 2000.2 E. Ranchod and N.J. Mamede, "Advances in Natural Languge Processing", Springer-Verlag, 2002.34
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to Natural Language Processing
2 Basics of the linguistics
3 Linguistics and languages
4 Language models
5 Syntax analysis (POS)
6 Corpora, N-gram
7 Probabilistic models of spelling
8 Hidden Markov Model-Viterbi algorithm
9 Document classification
10 Information retrieval, information retrieval systems
11 Machine learning
12 Question replying systems
13 Semantic analysis
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Data MiningDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 571 Fall MS Elective Turkish 3 0 3 8
Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Rıfat Aşlıyan
Instructor Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-
Information 09010 Aydın Tel: 256 21284 98 - 2116 [email protected]
Course Objective and brief Description
Today, a lot of information can be collected via computer based technologies. Interpreting, evaluating the collected information is very important subject for decision systems. Data mining is useful field for many areas. The fundamentals of data mining will be mentioned in this course.
Textbook and Supplementary readings1 Data Mining Concept and Techniques , J.Han and M.Kamber2 Data Preparation for Data Mining, D.Pyle3 Advances in Data Mining, P. Perner4
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to Data Mining
2 Survey of data mining applications, techniques and models
3 Data mining steps: Define goal, data cleaning
4 Data selection and preprocessing
5 Data reduction and data transformation
6 Select data mining algorithm, model assessment, interpretation
7 Exploration of data mining algorithms
8 Decision trees, regression
9 Association rules
10 Memory based methods
11 K-nearest neighbor method
12 Clustering
13 Artificial neural networks
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Mathematical Methods of Physics IDepartment Mathematics Division in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT 573 Fall MS Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors
Assist. Prof. Dr. İnci Ege
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN, [email protected]
Course Objective and brief Description
This course gives the fundamental concepts of generalized functions
Textbook and Supplementary readings1 Generalized Functions, Vol. I, I. M. Gelfand and Shilov, Academic Press, 1964
2 Distributions, Ultradistributions and Other Generalized Functions, R. Hoskins and J.S. Pinto, Ellis
Horward, Chichester, 1994
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Test functions
2 Generalized functions
3 Local properties of generalized functions
4 Translations, rotations andother linear transformations on the independent variables of generalized functions
5 Regularization of divergent integrals
6 Convergence of generalized function sequences
7 Complex test functions and generalized functions
8 EXAM
9 Differentiation and integration of generalized functions
10 Differentiation and integration of generalized functions
11 Delta-convergent sequences
12 The generalized functions , , , ,
13 Canonical regularization
14 The generalized function Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Introduction to Homological Algebra
Department Mathematics
Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ETSC CreditMAT575 Fall MS Elective Turkish 3 0 3 10Course Prerequisites
Name of Instructors Yrd. Doç. Dr. Süleyman GÜLER
Instructor Information [email protected]
Course Objective and brief Description
This course aims to give students the basic concepts of algebraic topology., the concept based on fundamental group and homology groups of topological spaces . Aims to develop the ability to solve problems.and to give students their use in the daily life of homological algebra topics, to develop analytical thinking and to understand abstract concepts. Aims to gain a systematic approach to define problems and to solve the problems by the topics discussed.
Textbook and Supplementary readings1 Rotman, J.J., “An Introduction to Homological Algebra”, Academic Press, 1979.2 Northcott D. G. “An Introduction to Homological Algebra”, Cambridge at the University Press, 196034
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Abel Groups
2 Rings
3 Modules
4 Homomorphisms
5 Free Modules, Exact Sequences
6 5- Lemma ve 3x3 Lemma
7 Hom Functor
8 Projektive ve İnjektive Modules
9 Midterm Exam
10 Essential and Superfluous Submodules, Supplements
11 Category of Complexes
12 Projektive and İnjektive Resolutions
13 Derived Functor
14 Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Real and Complex Analysis IIDepartment MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT502 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Real and Complex analysis including Fourier transforms, elementary properties of Holomorphic functions, Harmonic functions, the maximum modulus principle, approximation by rational functions, conformal mapping, zeros of holomorphic functions.
Textbook and Supplementary readings1 Real and Complex Analysis, by Walter Rudin, 1987.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Fourier transforms
2 Fourier transforms
3 Elementary properties of Holomorphic functions
4 Elementary properties of Holomorphic functions
5 Harmonic functions
6 Harmonic functions
7 The maximum modulus principle
8 The maximum modulus principle
9 Approximation by rational functions
10 Approximation by rational functions
11 Conformal mapping, zeros of holomorphic functions
12 Conformal mapping, zeros of holomorphic functions
13 Conformal mapping, zeros of holomorphic functions
14 Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Algebra IIDepartment Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT504 Spring MS Elective Turkish 3 0 3 10Course Prerequisites Algebra I
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Doç. Dr. Erdal Özyurt, Assist. Doç. Dr. Selma Altınok, Yrd. Doç.Dr. Semra Doğruöz, Yrd. Doç.Dr. Hülya İnceboz Günaydın
Instructor Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-
Information 09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
This course gives the fundamental concepts of groups
Textbook and Supplementary readings1 Algebra, T.W.Hungerford
2 Contemporary Abstract Algebra, J.A.Gallian 3 Basic Algebra I-II, N. Jacobson4 Basic Abstract Algebra, P.B. Bhattacharya, S.K.Jain, S.R. Nagpaul, Cambridge University Pres5 Fundamentals of Abstract Algebra, D.S.Malik, John M.Mordeson, M.K. Sen, , The McGraw-Hill Companies
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Rings
2 Rings and Homomorphisms, Ideals
3 Some Classic Theorems(Isomorphism theorems)
4 Prime and Maximal Ideals
5 Factorization in Commutative Rings
6 Division Rings and Localization
7 Rings of Polinomials and Formal Power Series
8 Factorization in Polynomial Rings
9 Modules- EXAM
10 Homomorphism and Exact Series
11 Free Modules
12 Vector spaces
13 Projective Modules
14 Injective Modules
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Algebraic TopologyDepartment MathematicsDivision in the Dept. Topology
Code Term Level Type LanguageCredit hours/week
Lecture Credit ECTS creditMAT 506 Spring MS Elective Turkish 3 3 10
Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Adnan MELEKOĞLU
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDIN
Tel: 256 2128498 [email protected] Objective and Brief Description
The aim of this course is to provide introductory knowledge for Algebraic Topology.
Textbook and Supplementary Readings1 Massey, W. (1967) Algebraic Topology, Springer-Verlag2 Munkres, J.R. (1999) Topology, Prentice Hall
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Manifolds
2 Surfaces
3 Topology of surfaces
4 Classification of compact orientable surfaces
5 Classification of compact non-orientable surfaces
6 Homotopy
7 Fundamental group
8 Midterm Exam
9 Fundamental group of circle
10 Fundamental group of product spaces
11 Fundamental group of surfaces
12 Van Kampen theorem
13 Covering spaces
14 Covering spacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Noncommutaive Rings
Department Mathematics
Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT508 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Günğöroğlu, Asist. Prof. Dr. Semra DoğruözInstructor Information
ADÜ Faculty of Arts and Science, Department of Mathematics, Aydın, [email protected]
Course Objective and brief Description
This course suggested to students who study noncommutative rings. It gives the fundemantal concepts of noncommutative rings.
Textbook and Supplementary readings1 Noncommutative Rings, I.N.Herstein2 Algebra, Hungerford3 Topics In Ring Theory, I.N.Herstein
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Simple and primitive rings.
2 The radical of a ring, semisimple Artinian Rings.
3 Semisimple rings, The Density Theorem.
4 Semisimple rings.
5 Applications of Wedderburn’s Theorem.
6 Commutativity theorems.
7 Simple algebras.
8 The Brauer’s Groups
9 Exam
10 Maximal subfields.
11 Some classic theorems.
12 Representation of finite groups, polynomial identities.
13 The Goldie’s Theorem, Ultra-products and a theorem of Posner.
14 Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Module TheoryDepartment Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT510 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected],
[email protected], [email protected], [email protected] Objective and brief Description
This course gives the fundamental concepts of groups
Textbook and Supplementary readings1 Rings and Categories of Modules, F.W. Anderson-K.R. Fuller, Springer Verlag 1974
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Review of Rings and Their Homomorphisms
2 Modules and Submodules, Homomorphisms of Modules
3 Categories of Modules, Endomorphism Rings
4 Direct Summands, Direct Sums and Products of Modules
5 Decomposition of Rings
6 Generating and Cogenerating
7 Semisimple Modules-The Socle and the Radical
8 Finitely Generated and Finitely Cogenerated Modules, Chain Condations
9 Modules With Composition Series -EXAM
10 Indecompositions of Modules
11 Classical Ring, Structure Theorems(Semisimple Rings, The Density Theorem, The Radikal of a Ring, Artinian Rings)
12 The Hom Functors and Exactness
13 Projective and Injective Modules
14 The Tensor Functors and Flat Modules
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Rings and RadicalsDepartment Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT512 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Günğöroğlu, Asist. Prof. Dr. Semra Doğruöz
Instructor Information
ADÜ Faculty of Arts and Science, Department of Mathematics, Aydın, [email protected]
Course Objective and brief
The goal of this course finds some properties of rings by using radicals.
DescriptionTextbook and Supplementary readings
1 Rings and Radicals, N.J.DivinskyCOURSE CALANDER / SCHEDULE
Week Lecture topics Practice/Lab/Field1 The general theory of radicals.
2 Rings with the descending chain condition, Nil and Nilpotent, descending chain condition ideals in nil semi-simple rings with D.C.C.
3 Central idempotent elements, I. and II. structure theorems.
4 Simple rings, radical properties, rings with ascending chain condition, relationship between A.C.C. and D.C.C.
5 Nil and Nilpotent, Bear Lower Radical.
6 Prime rings, Zorn Lemma, prime ideals, subdirect sums.
7 Semi-prime rings, prime and semi-prime rings with A.C.C.
8 The Jacobson Radical, quasi-regularity, right primitive rings.
9 Exam
10 The Jacobson Radical and general radical theory.
11 The Brown-MacCoy Radical, G-regularity, G-semi-simple rings.
12 The Brown-MacCoy Radical and general radikal theory.
13 The Levitzki Radical, local nilpotency, the eight radicals and recent results.
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Minimal SubmanifoldsDepartment MathematicDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT516 Spring MS Elective Turkish 3 0 3 10Course Prerequisites Differentiable Manifolds
Name of Instructors Assist. Prof. Dr. Leyla Onat
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematikj Bölümü 19010-AYDIN Tel:0262128498 [email protected]
Course Objective and brief Description
Our aim is to give some related topics in minimalsubmanifold .
Textbook and Supplementary readings1 Xin,Yuanling, Minimal Submanifolds and Related topics, World Scientific
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Define manifold
2 Define topologies of submanifolds
3 Second fundamental form
4 Minimal submanifold s in Euclidean spaces
5 Minimal submanifold s in the sphere
6 Examples
7 Rigidity theorems
8 Solve th problems
9 Gauss map
10 The Weierstrass representation
11 The mean curvature
12 Minimal hypersurfaces
13 Solve the problems
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Non- Euclidean GeometryDepartment MathematicDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT518 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Asist.Prof.Dr. Leyla Onat
Instructor Information
Adnan Menderes Üniversitesi Fen edebiyat Fakültesi Matematik Bölümü –AydınTel:02562128498 [email protected]
Course Objective and brief Description
Our aim is to give some definitions on non Euclidean geometry.
Textbook and Supplementary readings
1 Coxeter, H.S. Non- Euclidean Ceometry Washington. D.C.20036
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Euclid
2 Saccheri, Gauss, Bolyai, Riemann
3 Definitions and axioms
4 Models
5 Elliptic geometry in one one dimension
6 Elliptic geometry in two dimension
7 Elliptic geometry in three dimension
8 Euclidean and hyperbolic geometry
9 Solve the problems
10 Circles and triangles
11 Area
12 Euclidean models
13 Solve the problems
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Mathematical Statistics IIDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type Language Credit hours/Week
Lecture Lab. Credit ECTS Credit
MAT520 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Hüsnü Barutoğlu
InstuctorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100 [email protected]
Course Objective and brief
This course introdues fundamental probablitiy and mathematical statistical theory
DescriptionTextbook and Supplementary readings
1 İnal C. Olasılıksal ve Matematiksel İstatistik,Hacettepe Üniv. Fen Fak yayınları No: 16, 1982.2 Kendall,M, Stuart,A.,Ord J.K.-The Advanced theory of Statistics. Charles griffin com. London 1983.3 Alexander, W.H. –Elements of Mathematical Statistics John Wiley and Sons, NewYork,1961.4 Mood,A.M.,Graybill,F.A. Probabilitiy and Statistical Applications McGraw-Hill Book Com.
NewYork,1963.COURSE CALANDER/ SCHEDULE
Week Lecture Topics Practice/Lab/Field1 Permutation and combination
2 Probability
3 Discrete function of probability and function of distribution
4 Continuous function of probability and function of distribution
5 Expected value ,mean and variance
6 Transform of veriable at function of probability
7 Functions of moment generation and functions of characteristic
8 Estimation theory
9 Property of estimations
10 Least squares method
11 Maximum likelihood method
12 Bayesian estimation method
13 Moments estimation method
14 Final ExamCourse assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Nonparametric StatisticDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type Language Credit hours/Week
Lecture Lab. Credit ECTS Credit
MAT522 Spring MS Elective Turkish 3 0 3 8Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Hüsnü Barutoğlu
InstuctorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100 [email protected]
Course Objective This course introduce various and important test of nonparametic statictical
and brief Description
Textbook and Supplementary readings1 Siegel S. Nonparametric Statistics for the Behavioral Sciences McGraw-Hill Kagakuska Ltd. Tokyo 1956. 2 Gamgam H. Parametrik Olmayanİstatistik Teknikleri Gazi Üniv. Yayınları No: 140 Ankara 198934
COURSE CALANDER/ SCHEDULEWeek Lecture Topics Practice/Lab/Field
1 Binomial test,khi-square test for one example
2 Kolmogorov-Smirnov test for one example
3 McNemar test for meaningfulness in variations
4 Signal test, Wilcoxon testfor degree
5 Fisher complete probability test
6 Mann-Whitney U test
7 Kolmogorov-Smirnov test for pair example
8 Moses test for extreme reactions
9 Test of rondomness
10 Cochran Q test
11 Analysis of variance whit degree . Friedman and Kruskal-Wall test
12 Spearman and Kendall, correlation coefficient of degree
13 Kendall conformity coeficient w.
14 Final Exam
Course assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCİENCES
Course Title Numerical solution of Integral EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT528 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Ali Filiz, Assist. Prof. Dr. Ali IŞIK
Instructor Information
Adnan Menderes Üniversity, Faculty of arts and science 09100 AydınTel:256 2128498 [email protected], [email protected]
Course Objective and brief Description
This course aims to acquaint students with the basic knowledge of numerical solution of some kinds of integral equations. Students will be familiar with classification of equations Volterra and Fredholm method of solutions. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to biology, and other sciences.
Textbook and Supplementary readings1 Ram P. KANWAL (1971) Lineer integral denklemler, Academic Pres, New York and London2 Villiam Vernon LOVITT (1950) Lineer integral denklemler, Dower publications, New York3 Yavuz AKSOY (1983) İntegral Denklemler, Yıldız Üniversitesi yayınları4
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction of MATLAB and integral equations
2 Relation between linear differential equations and integral equations with Fredholm and Volterra integral equations
3 Relation between linear differential equations and integral equations with Fredholm and Volterra integral equations
4 Numerical solution and stability of Volterra integral equations
5 Numerical solution and stability of Volterra integral equations, Linear and non-linear integro-differential equations
6 Linear and non-linear integro-differential equations, Linear and Nonlinear Volterra integral equations of the second kind
7 Volterra integral equations with time lags
8 Midterm exam
9 Lotka-Volterra systems
10 Numerical solution of integro-differential equations with parabolic type.
11 Numerical error analysis
12 Numerical solution of integro-differential equations with parabolic Volterra type.
13 Numerical error analysis
14 Final Exam
Değerlendirme 1 adet ara sınavın %40 ve yarıyılsonu sınavının %60 alınarak yapılır. Sınav şekli öğretim üyesinin tercihine bağlı olarak sözlü ve/veya yazılı sınav, ödev, proje, laboratuvar denemesi, grup sunumu, veya bunların kombinasyonu şeklinde yapılabilir.
FACULTY OF ARTS AND SCIENCES
Course Title Stochastic ProcessesDepartment Matematik Division in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hour/week
Lecture Lab Credit ECTS CreditMAT534 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Hüsnü Barutoğlu
InstuctorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100 [email protected],
Course Objective and brief Description
This course intruduces fundamental stochastic processes
Textbook and Supplementary readings1 İnal C. Olasılıksal Süreçler Hacettepe Üniv. Fen-Ed Fak. Yayınları 1998.
2 Parzen E., Stochastic Processes Holden-day Inc. NewYork 1962.3 Karlin S. Taylor H.M., A first course in Stochastic processes Academic press. NewYork 1975.4 Papoulis A., Probability,Random Variable and Stochastic Processes McGraw Hill Book com. 1965
COURSE CALANDER/ SCHEDULE
Week Lecture topics Practice/Lab/Field
1 Theory of stochastic processes
2 Markov chains
3 Markov processes
4 Poisson processes
5 Birth and death processes
6 Birth and death processes
7 Random walk
8 Renewal processes
9 Renewal processes
10 Brownian motions
11 Brownian motions
12 Branching processes
13 Branching processes
14 Final Exam
Course assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Fourier AnalysisDepartment MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT536 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Fourier Analysis including trigonometric sums, integrability of trigonometric sums, convergence and Cesaro summability of Fourier series, convergence and summability of trigonometric series, multiple Fourier series, Fourier transform and applications, orthogonal systems, bessel functions
Textbook and Supplementary readings1 Theory and Applications of Fourier Series, C. S. Rees, S. M. Shah and C. V. Stanojevic.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Trigonometric sums
2 Integrability of trigonometric sums
3 Convergence and Cesaro summability of Fourier series
4 Convergence and summability of trigonometric series
5 Convergence and summability of trigonometric series
6 Multiple Fourier series
7 Multiple Fourier series
8 Fourier transform and applications
9 Fourier transform and applications
10 Orthogonal systems
11 Orthogonal systems
12 Bessel functions
13 Bessel functions
14 Final Exam
Course assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Partial Differential EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMat 538 Spring MS Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors Assist. Prof. Ali IŞIK, Assist. Prof. Ali FİLİZ
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09100 AydınTel:256 2128498 [email protected], [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental structures of Partial Differential Equations first order and second order equations. Students will be familiar with classification of equations, linear first order equations, method of langrange, Cauchy problem for quasilinear first order equations, linear second order equations, hyperbolic, parabolic and elliptic equations. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to physics, and other sciences.
Textbook and Supplementary readings1 Rene Denemeyer (1968) Introduction to Partial Differential Equations and Boundary Value problems,
McGraw-Hill2 V.S. Vladımırov (1971) Equations of Mathematical Physics, Marcel Dekker, inc, Newyork3 Kerim Koca (2003) Kısmi Türevli Denklemler, Gündüz yayıncılık4 Mehmet Çağlayan, Okay Çelebi (2002) Kısmi Diferensiyel Denklemler Uludağ üniversitesi
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction, Classification of partial differential equations,
2 Linear fist order equations,
3 Linear and Quasilinear equations Method of Langrange
4 Cauchy problem for first order equations
5 Types of nonlinear first order equations, Method of Charpit,
6 Linear second order equations and generalization of linear second order equations, Non-homogeneous equations
7 Classification of linear second order equations and reduction of canonical form,
8 Hyperbolic, Parabolic, and Elliptic equations,
9 Introduction to wave equations,
10 One-dimensional wave equation; Initial-value problem,
11 Two-dimensional wave equation. Initial-value problem,
12 One-dimensional heat equation. Initial-value problem.
13 One-dimensional heat equation. Initial-value problem.
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Theory of Integral EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMat 540 Spring MS Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors Assist. Prof. Ali IŞIK, Assist. Prof. Ali FİLİZ
Instructor Information
Adnan Menderes Üniversity, Faculty of arts and science 09100 AydınTel:256 2128498 [email protected], [email protected]
Course Objective and brief Description
This course aims to acquaint students with the basic knowledge of integral equations. Students will be familiar with classification of equations Volterra and Fredholm method of solutions. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to physics, and other sciences.
Textbook and Supplementary readings1 Ram P. KANWAL (1971) Linear integral equations, Academic Pres, New York and London2 Villiam Vernon LOVITT (1950) Linear integral equations, Dower publications, New York3 Yavuz AKSOY (1983) İntegral Denklemler, Yıldız üniversitesi yayınları
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction, Classification of integral equations
2 Relation between linear differential equations and integral equations,
3 Integral equations with separable kernels,
4 Method of successive approximation,
5 Volterra integral equations,
6 Linear system of Volterra integral equations,
7 Nonlinear Volterra integral equations of the second kind,
8 Fredholm integral equations with degenerate kernel
9 Fredholm theorem for integral equations,
10 Eigenvalues of the kernel of an integral equations
11 Integral equations with continuous kernel
12 Singular Volterra integral equations.
13 Singular Volterra integral equations.
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Mathematical Analysis IIDepartment MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT542 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Mathematical Analysis including sequences and series of functions, some special functions, functions of several variables, integration of differential forms, the Lebesque theory
Textbook and Supplementary readings1 Principles of Mathematical Analysis, W. Rudin.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Sequences and series of functions
2 Sequences and series of functions
3 Some special functions
4 Some special functions
5 Functions of several variables
6 Functions of several variables
7 Functions of several variables
8 Integration of differential forms
9 Integration of differential forms
10 Integration of differential forms
11 Lebesque theory
12 Lebesque theory
13 Lebesque theory
14 Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Functional Analysis
Department MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT544 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Functional Analysis including normed linear spaces, linear maps, Hilbert spaces, the Hahn Banach theorem, weak topolojies, separable spaces, fixed point theorems
Textbook and Supplementary readings1 Elements of Functional Analysis, I. J. Maddox234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Normed linear spaces
2 Normed linear spaces
3 Linear maps
4 Linear maps
5 Hilbert spaces
6 Hilbert spaces
7 Hahn Banach theorem
8 Hahn Banach theorem
9 Weak topolojies
10 Weak topolojies
11 Separable spaces
12 Separable spaces
13 Fixed point theorems
14 Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Divergent Series I
Department MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT552 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of divergent series including Abel convergence, Cesaro convergence, Euler-Maclaurin sum Formula, Abel’s inequality, the Silverman-Toeplitz theorem, Nörlund and Nörlund type transformations, Hölder and Cesaro means, Euler, Taylor and Borel exponential transformations, Hausdorff means
Textbook and Supplementary readings1 Divergent Series, G. H. Hardy234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Abel convergence
2 Cesaro convergence
3 Euler-Maclaurin sum Formula
4 Abel’s inequality
5 the Silverman-Toeplitz theorem
6 the Silverman-Toeplitz theorem
7 Nörlund and Nörlund type transformations
8 Nörlund and Nörlund type transformations
9 Hölder and Cesaro means
10 Hölder and Cesaro means
11 Euler, Taylor and Borel exponential transformations
12 Euler, Taylor and Borel exponential transformations
13 Hausdorff means
14 Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Hyperbolic GeometryDepartment MathematicsDivision in the Dept. Topology
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS credit
MAT 556 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Adnan MELEKOĞLU
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]
Course Objective and Brief Description
The aim of this course is to provide introductory knowledge for Hyperbolic Geometry.
Textbook and Supplementary Readings1 Anderson J.W. (2005) Hyperbolic Geometry, Springer2 Stillwell J. (1992) Geometry of Surfaces, Springer-Verlag
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Surfaces of negative curvature and psedosphere
2 Hyperbolic metric
3 Hyperbolic length of curves
4 Hyperbolic plane and some models
5 Upper half plane model
6 Unit disc model
7 Geodesics
8 Midterm Exam
9 Reflections and the other isometries in the hyperbolic plane
10 Classification of isometries
11 Möbius transformations
12 PSL(2,R) and its discrete subgroups
13 Hyperbolic area and Gauss-Bonnet Formula
14 Hyperbolic trigonometryCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Algebraic Geometry IDepartment MathematicsDivision in the Dept. Topology and Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT558 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Prof. Dr. Hatice Kandamar, Yrd. Doç. Dr. Selma Altınok
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 [email protected], [email protected]
Course Objective and Brief Description
This course gives the study of Geometry coming from Algebra and Rings
Textbook and Supplementary Readings1 Undergraduate algebraic Geometry, M. Reid2 Algebraic Geometry, R. Hartshorne
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Conics, cubics and group law2 Curves and genus3 Affine varieties4 Functions on Affine varieties, Projective varieties5 Tangent spaces and dimension6 Lines on Cubic spaces7 Regular functions and transformations8 Midterm Exam
9 Parametric spaces10 Rational functions and rational transformations11 Algebraic groups12 Hilbert polynomials13 Gauss transformation, tangent and dual varieties14 Singular points and tangent spaces. Parametric and moduler spaces.
Course assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework
FACULTY OF ARTS AND SCIENCES
Course Title CryptologyDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type Language Credit hours/week
Lecture Lab Credit ECTS CreditMAT560 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Ali FilizInstructor Information
Adnan Menderes University, Faculty of Art and Sciences, 09100 AydınTel: 256 2128498-2116 [email protected]
Course Objective and brief Description
This course aims to acquaint students with Cryptography. Lectures will be given at the class. Students take notes. Some projects are given to students.
Textbook and Supplementary readings1 Applied Cryptography: Protocols, Algorithms and Source Code in C, John Wiley & Sons, 1995, ISBN 978-
04711170942 Şifreleme Matematiği: Kriptografi, Ortadoğu Teknik Üniversitesi, Toplum Bilim Merkesi, Canana Çimen,
Sedat Akleylek, Ersan Akyıldız, 2007, ISBN 978-9944-344-27-23 Lecture notes about this course are going to be given. Any book related with this course can be used for
this lesson.COURSE CALANDER / SCHEDULE
Week Lecture topics Practice/Lab/Field1 Introduction to cryptography
2 History of cryptography
3 Classical methods of cryptography
4 Classical methods of cryptography
5 Symmetric algorithms
6 Data encryption standard (DES)
7 Asymmetcal algorithms
8 Asymmetcal algorithms
9 Rivest, Shamir, Adleman Algorithm (RSA)
10 E1 Gamal algorithm
11 Digital Signs Standards
12 Cryptographic Protocols
13 Cryptographic Protocols
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Visual Programming IIDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type Language Credit hours/week
Lecture Lab Credit ECTS CreditMAT564 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Ali FİLİZ
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09100 AydınTelephone Number:0 256 2128498-2114 and 2116 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamentals of visual programming. Classes will be held in the computer laboratory and lab computers will be used for practices during whole class hours of lecturing.
Textbook and Supplementary readings1 Borland C++ Builder, İ. Karagülle ve Z. Pala, Türkmen Kitabevi, 2002.23
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to Visual Programming
2 Procedures
3 Procedures
4 Functions,
5 Functions,
6 Introduction to Database management systems, SQL
7 Introduction to Database management systems, SQL
8 Introduction to Database management systems, SQL
9 Project I
10 Debugging
11 Debugging
12 Database design and ADO.
13 Database design and ADO.
14 Project II
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Linear AlgebraDepartment MathematicsDivision in the Dept. Algebra and Number Theory
Code Term Level Type Language Credit hour/week
Lecture Lab. Credit ECTS CreditMAT566 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. İnceboz
InstructorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100, [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
This course introduces fundamental concepts of linear algebra which are indispensable in all branches of basic science. Its aim is to teach students fundamental concepts of Number Theory.
Textbook and Supplementary readings1 Linear Algebra, K. Hoffman and R. Kuntze, Printice Hall 2.Edition, 1971.2 Topics in Linear Algebra, Cemal Koç, ODTÜ Matematik Vakfı Yayınları, 2002.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Linear equations
2 Vector spaces
3 Linear independence, base, dimension
4 Linear transformations
5 Determınats
6 Applıcatıon of determınants
7 Characteristic and minimal polynomials
8 Eigenvalue, eigenvectors, diagonalization
9 Rational Forms MIDTERM
10 Jordan forms
11 Diogonalization in complex matrices
12 Inner products, norm, orthogonality
13 Application of iner products
14 Normal, unitary and orthogonal operations Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Group TheoryDepartment MathematicsDivision in the Dept. Algebra and Number Theory
Code Term Level Type Language Credit hours/Week
Lecture Lab. Credit ECTS Credit
MAT568 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma Altınok, Yrd. Doç.Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz
InstuctorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
The goal of the course is to introduce the fundamental concepts of abstract group theory. The group is defined by certain structure. Group theory is the oldest baranch of modern algebra. Its origin comes from the permutation of variable or of the roots of polynomials. All these groups were finite permutation groups. It plays an important part in all science branch, aspecially Physics and Chemstry.
Textbook and Supplementary readings1 A course in the theory of the groups, Derek R. J. Robinson, Springer-Verlag New York, 1996.
2 An introduction to theory of the groups, Rotman, J.J., Springer-Verlag New York, 1995.COURSE CALANDER/ SCHEDULE
Week Lecture Topics Practice/Lab/Field1 Fundamental concepts of group theory
2 Homomorfisms and quotient groups
3 Endomorphisms and aotumorphisms of groups
4 Permutation groups and group actions
5 Generating groups, semidirect products
6 Wreath product, direct limit
7Free groups
8 Midterm
9 Sylow Theorems
10 Classification of finite groups
11 Series and composition series, Simple groups, direct decompositions
12 Abelian and central series
13 Nilpotent groups, Groups of prime power order
14 Soluble groups
Course assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Complex Variables and ApplicationsDepartment MathematicsDivision in the Dept. Mathematics
Code Term Level Type Language Credit hours/week
Lecture Lab Credit ECTS CreditMAT570 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Complex Variables and Applications including Complex numbers, functions, limits, continuity, complex differentiation, Cauchy- Riemann equations, complex integration, Cauchy’s theorem, Cauchy’s integral formulas, infinite series, Taylor’s and Laurent series, Residue theorem, conformal mapping, physical applications of conformal mapping.
Textbook and Supplementary readings1 Complex Variables with an introduction to conformal mapping and its applications, by M. R. Spiegel,
1991.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Complex numbers
2 Functions
3 Limits
4 Continuity
5 Complex differentiation
6 Cauchy- Riemann equations
7 Complex integration
8 Cauchy’s theorem
9 Cauchy’s integral formulas
10 Infinite series
11 Taylor’s and Laurent series
12 Residue theorem
13 Conformal mapping and physical applications of conformal mapping
14 Final ExamCourse assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these
FACULTY OF ARTS AND SCIENCES
Course Title Theory and Applications of Infinite SeriesDepartment MathematicsDivision in the Dept. Mathematics
Code Term Level Type Language Credit hours/week
Lecture Lab Credit ECTS CreditMAT572 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Theory and Applications of Infinite Series including Principles of the theory of real numbers, sequences of real numbers, sequences of positive terms, sequences of arbitrary terms, power series, the expansions of the elementary functions, infinite products, closed and numerical expansions for the sums of series, series of positive terms, series of arbitrary terms, series of complex terms, the elementary analytic functions.
Textbook and Supplementary readings1 Theory and Applications of Infinite Series, by K. Knopp, 1990.234
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Principles of the theory of real numbers
2 Sequences of real numbers
3 Sequences of positive terms
4 Sequences of arbitrary terms
5 Power series
6 The expansions of the elementary functions
7 Infinite products
8 Closed and numerical expansions for the sums of series
9 Series of positive terms
10 Series of arbitrary terms
11 Series of complex terms
12 The elementary analytic functions
13 The elementary analytic functions
14 Final Exam
Course assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these
FACULTY OF ARTS AND SCIENCES
Course Title Topology and GeometryDepartment MathematicsDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hour/week
Lecture Lab Credit ECTS Credit
MAT574 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Prof. Dr. Hatice Kandamar, Assist. Prof. Dr. Selma Altınok
InstuctorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected]
Course Objective and brief Description
Its aim of this course inntroduces the fundamental concepts of topology and geometry, and calculates fundamental groups of differentiable manifolds and mention De Rham Cohomology of Riemannian Geometry.
Textbook and Supplementary readings1 Lecture Notes on Elementary Topology and Geometry, I. M. Singer, J. A. Thorpe, Springer, 1976.
COURSE CALANDER/ SCHEDULE
Week Lecture Topics Practice/Lab/Field
1 Topological spaces
2 Connected and compact spaces
3 Continuity, Product spcases, the Tychanoff Theorem
4 Speration axioms, complete metric spaces
5 Homotopy
6 Fundamental groups, covering spaces
7Fundamental groups, covering spaces
8 Midterm
9 Geometry of simplicial complexes and groups
10 Manifold
11 Simplicial homology, De Rham’s theorem
12 Simplicial homology, De Rham’s theorem
13 Riemann geometry of surfaces
14 Riemann geometry of surfaces
Course assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Advanced Module Theory Department Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT 576 Spring MS Elective Turkish 3 0 3 10Course Prerequisites Introduction to Module Theory
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Semra Doğruöz,
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected],
Course Objective and brief Description
This course gives the fundamental concepts of modules
Textbook and Supplementary readings1 Rings and Categories of Modules, F.W. Anderson-K.R. Fuller, Springer Verlag 1991
2 Moduln und Ringe, F. Kasch, B.G.Teubner Stuttgart 1977.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Artinian and Noetherian Modules and Homomorphisms
2 Hilbert’s Basis Theorem
3 Decomposition of Modules over Noetherien and Artinian Modules
4 Local Rings, Local Endomorphism Rings
5 Krull-Remark-Schmidt Theorem
6 Semisimple Modules and Rings
7 Socle ve Radical
8 Tensor Product and Flat Modules (EXAM)
9 Regular Rings
10 Semiperfect Modules
11 Nil Ideals and t-Nilpotent İdeals
12 Injectivity and the Cogenerator Property of Ring
13 Quasi-Frobenius Rings and Characterization of Quasi-Frobenius Rings
14 Quasi-Frobenius Algebras and Characterization of Quasi-Frobenius Algebras
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Differentiable Manifolds IIDepartment MathematicDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 578 Spring MS Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Leyla Onat
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü 09010-AdınTel:02562128498 [email protected]
Course Objective and brief Description
The main goal is this course to provide a working knowledge of Differentiable Manifold
Textbook and Supplementary readings1 Brickell,F., Clark,R. Differentiable manifolds, Windson House, Condon S.W.12 Boothby, William M. An Introduction to Differentiable Manifolds and Riemannian Geometry Academic
Press, New York,1975COURSE CALANDER / SCHEDULE
Week Lecture topics Practice/Lab/Field1 Submanifolds
2 Vector fiels on a manifold
3 The Lie algebra of vector fields on a manifold4 Orientation of manifolds
5 Integration on manifolds
6 Stokes Theorems
7 Solve the problem about what he has learned
8 Differentiation on Riemannian Manifolds
9 Tangent bundle
10 Curvature
11 Gauss and mean curvature
12 Equations of structure
13 Solve the problem about what he has learned
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Artificial Neural NetworksDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 580 Spring MS Elective Turkish 3 0 3 8
Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Rıfat Aşlıyan
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected]
Course Objective and brief Description
Nowadays the methods of artificial intelligence are widely used in computer science. Artificial neural networks (ANN) are very advantageous in most systems, especially in the systems which has very complex mathematical structures. In this course, the aim is to teach the fundamental ANN subjects.
Textbook and Supplementary readings1 Foundations of Neural Networks, T. Khana2 Fuzzy and Neural Approaches in Engineering, L. H. Tsoukalas, R. E. Uhrig3 Neural Networks for Control, W.T Miller,. R.S Sutton,.and P.J. Werbos4
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction
2 Fundamentals of Artificial Neural Networks (ANN)
3 Multilayered Feedforward Neural Nets
4 Back Propagation Algorithms
5 Competitive Learning and Other Special Neural Networks
6 Self- Organizing Systems
7 Radial Basis Function
8 Generalized Regression Neural Networks
9 Dynamic Systems and Recurrent Neural Networks
10 ANNs in System Identification
11 Adaptive Processors and Neural Networks
12 Neural networks for Control; Applications: Modelling, Neural networks in Spectral Analysis and Time-Series Prediction
13 Neural networks for Control; Applications: Modelling, Neural networks in Spectral Analysis and Time-Series Prediction
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Mathematical Methods of Physics IIDepartment Mathematics Division in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT 582 Spring MS Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors
Assist. Prof. Dr. İnci Ege
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN, [email protected]
Course Objective and brief Description
This course gives the fundamental concepts of generalized functions
Textbook and Supplementary readings1 Generalized Functions, Vol. I, I. M. Gelfand and Shilov, Academic Press, 1964
2 Distributions, Ultradistributions and Other Generalized Functions, R. Hoskins and J.S. Pinto, Ellis
Horward, Chichester, 1994
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Canonical functions
2 Taylor’s and Laurent Series for ve
3 Taylor’s series for ,
4 Convolutions of generalized functions
5 Convolutions of generalized functions
6 Elementary solutions of differential equations with constant coefficents
7 Fourier transforms of test functions
8 EXAM
9 Fourier transforms of test functions
10 Fourier transforms of generalized functions . A single Variable
11 Fourier transforms of generalized functions . A single Variable
12 Fourier transforms of generalized functions .Several Variable
13 Fourier transforms of generalized functions . Several Variable
14 Fourier transforms and differential equations
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Data CompressionDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 584 Spring MS Elective Turkish 3 0 3 8
Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Rıfat Aşlıyan, Assist. Prof. Dr. Korhan Günel
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected], [email protected]
Course Objective and brief Description
In this course, the fundamental data compression subjects will be presented .
Textbook and Supplementary readings1 Introduction to Data Compression, K.Sayood, Morgan Kauffman, 19962 Data Compression, D.Salomon, 199834
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to data compression and source coding
2 Block coding
3 Arithmetic coding
4 Huffman coding
5 Huffman coding
6 Dictionary based coding
7 Dictionary based coding
8 Scalar quantization
9 Vector quantization
10 Predictive coding
11 Transform, subband and wavelet based coding
12 In class presentations of image, audio, video and computer graphics compression methods
13 In class presentations of image, audio, video and computer graphics compression methods
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Function theory of real variableDepartment MathematicsDivision in the Dept. Analysis and Function Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab. Credit ECTS CreditMAT601 Fall PhD Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of function theory of real variable including measures, construction of measures, measure and topology,continuous linear functionals, duality, bounded operators, Banach algebras, Hilbert spaces, integral representations, unbounded operators.
Textbook and Supplementary readings1 Introduction to Modern Analysis, Shmuel Kantorovitz
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Measures
2 Construction of measures
3 Measure and topology
4 Continuous linear functionals
5 Duality
6 Bounded operators
7 Bounded operators
8 Banach algebras
9 Banach algebras
10 Hilbert spaces
11 Hilbert spaces
12 Integral representations
13 Unbounded operators
14 Final Exam
FACULTY OF ARTS AND SCIENCES
Course Title Algebra Department Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT603 Spring Ph. D. Obligatory Turkish 3 0 3 10Course Prerequisites None
Name of Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma
Instructors Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz
Instructor Information
[email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
Introduction to advanced algebra
Textbook and Supplementary readings1 Algebra, Thomas W. Hungerford2 Algebra, S. Lang34
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Structure of groups
2 Free groups
3 Free groups
4 Finitely generated groups
5 Classification of finite groups
6 Classification of finite groups
7 Fields and Galois theory
8 Cyclic extension
9 Structure of fieldsExam
10 Structure of fields
11 Structure of rings
12 Structure of rings
13 Simple and Primitive rings
14 Jacopson radical
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Advanced TopologyDepartment MathematicsDivision in the Dept. Topology
Code Term Level Type LanguageCredit hours/week
Lecture Credit ECTS creditMAT 605 Fall Ph. D. Obligatory Turkish 3 3 10Course Prerequisites None
Name of Assist. Prof. Dr. Adnan MELEKOĞLU
Instructors
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]
Course Objective and Brief Description
The aim of this course is to present General Topology subjects at advanced level.
Textbook and Supplementary Readings1 Willard S. (1970) General Topology, Addison-Wesley Publishing Company2 Munkres, J.R. (1999) Topology, Prentice Hall
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Convergence
2 Countability and separation axioms
3 Countability and separation axioms
4 Compactness and connectedness
5 Tychonoff theorem
6 Compactifications
7 Metrization theorems
8 Midterm Exam
9 Paracompactness
10 Paracompactness
11 Complete metric spaces and function spaces
12 Complete metric spaces and function spaces
13 Uniform spaces
14 Baire spacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Group Theory IDepartment MathematicsDivision in the Dept. Algebra and Number Theory
Code Term Level Type Language Credit hours/WeekLecture Lab. Credit ECTS Credit
MAT607 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma
Instructors Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz
InstructorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
To prepare the students to current resarch in group theory and study some special groups
Textbook and Supplementary readings1 A course in the theory of the groups, Derek R. J. Robinson
2 An introduction to theory of the groups Rotman J.J.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Abelian groups
2 Torsion, divisible, torsion-free groups
3 Pure groups
4 Finitely generated abelian groups
5 Soluble groups
6 Nilpotent groups
7 Hall Pi-groups
8 Permutation groups
9 Representations
10 Fixed-point-free automorphisms
11 Locally nilpotent groups
12 Locally soluble groups
13 Finiteness properties
14 Infinite soluble groupsCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Module Theory IDepartment Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT609 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Algebra I-II
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya
İnceboz Günaydın
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
Working in Advance Modüle Theory
Textbook and Supplementary readings1 Rings and Categories of Modules, F.W. Anderson-K.R. Fuller, Springer Verlag 1974
2 Lectures on Modules, T.Y. Lam, Graduate Texts in Mathematics, Springer 1998
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to Module Theory
2 Cartesian Products and Direct Sums of Modules
3 Homomorphisms
4 Split Exact Sequences
5 Projective and Injective Modules
6 Length of a Module
7 Artinian and Noetherian Modules
8Artinian and Noetherian Rings
9 Simple and Semisimple Modules-EXAM
10 Simple and Semisimple Rings
11 Radicals of Modules and rings
12 Finitely Generated Modules
13 Von Neumann Regular Rings
14 The Group Ring
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ART AND SCIENCES
Course Title Differantial and Inregral EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 615 Fall Ph. D. Elective Turkish 3 0 3 10
Course Prerequisites Theory of Integral Equations
Name of Instructors
Assist. Prof. Ali IŞIK, Asist. Prof. Ali FİLİZ
Instructor Adnan Menderes Üniversity, Faculty of arts and science 09100 Aydın
Information Tel:256 2128498 [email protected], [email protected]
Course Objective and brief Description
This course aims to acquaint students with the advanced knowledge of integral equations. Students will be familiar with classification of equations Volterra and singular Volterra method of solutions. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to physics, and other sciences.
Textbook and Supplementary readings1 V.S.VLADIMIROV (1971)Equations of Mathemetical Physics , Marcel Dekker, NewYork2 Ram P. KANWAL (1971) Linear integral equations, Academic Pres, New York and London3 Ram P. KANWAL (1971) Linear integral equations, Academic Pres, New York and London
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Basic Equations of Mathematical Physics
2 Classification of Linear (Second Order ) Differential Equations
3 Formulation of Boundary value Problems for Linear Second Order Differential Equations
4 Fundamental Solutions of Linear Differantial Equations,
5 The Cauchy Problem for the Wave Equations
6 The Cauchy Problem for the Equation of Heat Conduction,
7 The Method of Successive Approximation,
8 Fredholm’s Theorems
9 The Sturm-Liouville Problem,
10 Spherical Functinos
11 Sobolev Methods for Solving Wave Equations,
12 Singular Volterra integral equations.
13 Singular Volterra integral equations.
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Tauberian TheoryDepartment MathematicsDivision in the Dept. Analysis and Functions Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab. Credit ECTS CreditMAT617 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Tauberian theory including the Hardy-Littleweood theorems, Wiener’s theory, complex Tauberian theory, Karamata’s Heritage: Regular variation, Borel summability and general circle methods and Tauberian remainder theory.
Textbook and Supplementary readings1 Tauberian theory, Jacob Korevaar
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Hardy-Littleweood theorems
2 Hardy-Littleweood theorems
3 Wiener’s theory
4 Wiener’s theory
5 complex Tauberian theory
6 Complex Tauberian theory
7 Karamata’s Heritage: Regular variation
8 Karamata’s Heritage: Regular variation
9 Borel summability and general circle methods
10 Borel summability and general circle methods
11 Tauberian remainder theory
12 Tauberian remainder theory
13 Tauberian remainder theory
14 Final Exam
FACULTY OF ARTS AND SCIENCES
Course Title Gödel’s TheoremsDepartment MathematicsDivision in the Dept. Foundations of Mathematics and Mathematical Logic
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS credit
MAT 619 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Ali Filiz
Instructor Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDIN
Information Tel: 256 2128498 [email protected] Objective and Brief Description
To introduce the student to Gödel’s two incompleteness theorems and to their most important corollaries.
Textbook and Supplementary Readings1 H.B. Enderton, A Mathematical Introduction to Logic, (especially chapter 3). Academic Press.2 J.R. Shoenfield, Mathematical Logic, (chapters 4 and 6). Addison-Wesley, 1967.3 G.T. Kneebone, Mathematical Logic and the Foundations of Mathematics. Van Nostrand, 1963.4 Hao Wang, From Mathematics to Philosophy. RKP, 1974
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 The completeness theorem for the predicate calculus: a review
2 First order theories
3 Recursive functions and relations. Basic properties.
4 Basic properties. Primitive recursion
5 Closure under bounded quantification
6 Gödel’s Coding of finite sequences
7 . Recursively enumerable sets and the arithmetic hierarchy
8 Midterm exam
9 Church’s Thesis
10 Gödel numbering and the arithmetization of logic. The recursiveness of the proof predicate. Gödel’s first
11 . Tarski’s undefinability theorem
12Applications of the incompleteness theorem to show the undecidability of the predicate calculus and other axiom systems. Examples of decidable theories: Presburger arithmetic
13 Gödel’s second incompleteness theorem. The philosophical impact of Gödel’s work. The limitations of the axiomatic method
14 Final exam
FACULTY OF ARTS AND SCIENCES
Course Title Conformal MappingDepartment MathematicsDivision in the Dept. Analysis and Functions Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab. Credit ECTS CreditMAT621 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of conformal mapping including harmonic funtions, analytic functions, the complex integral calculus, families of analytic functions, conformal mapping of simply-connected domains, mapping properties of special functions and conformal mapping of multiple-connected domains.
Textbook and Supplementary readings1 Conformal Mapping, Zeev Nehari.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 harmonic funtions
2 harmonic funtions
3 analytic functions
4 analytic functions
5 complex integral calculus
6 complex integral calculus
7 families of analytic functions
8 families of analytic functions
9 conformal mapping of simply-connected domains
10 conformal mapping of simply-connected domains
11 mapping properties of special functions
12 conformal mapping of multiple-connected domains
13 conformal mapping of multiple-connected domains
14 Final Exam
FACULTY OF ARTS AND SCIENCES
Course Title Category Theory IDepartment Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT623 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt. Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected],
[email protected], [email protected], [email protected] Objective and brief Description
Introduction to Theory of Category
Textbook and Supplementary readings1 Theory of Categories, Barry Mitchell, Academic Pres, New York and London, 1965
2 Categories fort he Working Mathematics, S. Mac Lane, Graduate Texs in Mathematics 53
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to Category Theory
2 Duality, Special Morphisms, Equalizers
3 Pullbacks and Pushouts, Intersections, Unions
4 Images, Kernals, Normality
5 Exact Categories, The 9 lemma, Producs
6 Variety of Categories
7 Diagrams, Limits, Functors
8 Preservation Properties of Functors
9 Limit Preserving Functors, Faithful Functors-EXAM
10 Natural Transformations, Equivalence of Categories
11 Diagrams as Functors
12 Categories of Additive Functors, Modules
13 Projectives, Injectives
14 Generaters, Small Objects
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Homological Algebra IDepartment Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT625 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites It is necessary to know module theory
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective Introduction to Homological Algebra and some fundamental properties
and brief Description
Textbook and Supplementary readings1 Basic Homological Algebra, M. Scott Osborne, Springer Verlag
2 Homology, Saunders Mac lane, Springer Verlag3 Introduction to Homological Algebra, Rotman, J.J.
4 Relative Homological Algebra, Edgar E. Enochs, Overtoun M. G. Jenda
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Categories
2 Modules (Generalities, Tensor Products, Exactness of Functors)
3 Modules (Projectives, Injectives and Flats)
4 Ext and Tors ( Complexes and Projective Resolutions )
5 Long Exact Sequences
6 Flat Resolutions and Injective Resolutions,
7 Consequences
8 Dimension Theory
9 Dimension Theory-EXAM
10 Change of Rings (Computational Considirations,
11 Change of Rings (Matrix Rings, Polynomials, Quotients and Localization)
12 Additive Functors
13 Derived Functors
14 Long Exact Sequences ( Existence)
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Riemannian ManifoldsDepartment MathematicsDivision in the Dept. Topology
Code Term Level Type LanguageCredit hours/week
Lecture Credit ECTS creditMAT 627 Fall Ph. D. Elective Turkish 3 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Adnan MELEKOĞLU
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]
Course Objective and Brief Description
The aim of this course is to introduce Riemannian Manifolds
Textbook and Supplementary Readings1 Lee J.M. (1997) Riemannian Manifolds, Sringer2 Gallot S., Hulin D., Lafontaine J. (1990) Riemannian Geometry, Sringer
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Manifolds
2 Vector bundles
3 Riemannian metrics
4 Model spaces of Riemannian geometry
5 Connections
6 Vector fields
7 Riemannian geodesics
8 Midterm Exam
9 Geodesics of the model spaces
10 Lengths and distances on Riemannian manifolds
11 Lengths and distances on Riemannian manifolds
12 Completeness
13 Curvature
14 Manifolds of constant curvature Course assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Graph TheoryDepartment MathematicsDivision in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Credit ETSC credit
MAT 629 Fall Graduate Elective Turkish 3 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Asst. Prof. Dr. Semra Doğruöz, Asst. Prof. Dr. Erdal Özyurt
Instructor Information
Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, 09010 AYDIN, Tel: 256 2128498, E-mail: [email protected], [email protected], [email protected] , [email protected]
Course Objective and Brief Description
The aim of this course is to give some properties for graph theory.
Textbook and Supplementary Readings1 Graph Theory , Reinhard Diestel
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Graph Theory
2 Graph Theory
3 Path Theory4 Algebraic and Topological methods
5 Algebraic and Topological methods
6 Nets7 Graph Algorithma8 Midterm Exam
9 Hamilton and Euler Graphs
10 Hamilton and Euler Graphs
11 Extremal Graph Theory
12 Extremal Graph Theory
13 Random Graphs
14 Random GraphsCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on
instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCİENCES
Course Title Differential and Riemannian Manifolds IDepartment MathematicsDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT631 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Leyla Onat
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü 09010-AydınTel:02562128498 [email protected]
Course Objective and brief Description
The main goal is this course to provide a working knowledge of Riemanniann manifolds, tensors and differential forms.
Textbook and Supplementary readings1 Lang S. Differential and Riemannian Manifolds,Springer-Verlag 1995.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Basic Properties
2 Define Manifold
3 Submanifold and İmmersions
4 Tangent Bundle
5 Operations on Vector Bundles
6 Operations on Vector Fields
7 Solve the problem about what he has learned
8 Lie Derivative
9 Killing Vector Fields
10 Covariant Derivatives
11 Metrics
12 The Metric Derivative
13 Solve the problem about what he has learned
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
.
FACULTY OF ARTS AND SCIENCES
Course Title Semi- Riemannian GeometryDepartment MathematicDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 633 Fall Ph.D. Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Leyla Onat
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü 09010-AdınTel:02562128498 [email protected]
Course Objective and brief Description
The main goal is this course to provide a working knowledge of Semi-Riemannian Geometry.
Textbook and Supplementary readings1 O’Neill,B., Semi-Riemannian Geometry with Application to Relativity Academic Press.Inc.New York
1983COURSE CALANDER / SCHEDULE
Week Lecture topics Practice/Lab/Field1 Symmetric bilinear form and scalar producrs
2 Isometry
3 The Levi-Civita connections4 Geodesics
5 Exponential maps
6 Curvature
7 Solve the problem about what he has learned
8 Semi-Riemannian surfaces
9 Metric contraction
10 Tensor derivation
11 Differential operator
12 Ricci and scalar curvature
13 Solve the problem about what he has learned
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Discrete GeometryDepartment MathematicsDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Cre
dit ECTS credit
MAT 635 Fall Graduate Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Asst. Prof. Adnan MELEKOĞLU
Instructor Information
Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, 09010 AYDIN, Tel: 256 2128498, E-mail: [email protected]
Course Objective and Brief Description
The aim of this course is to introduce Discrete Geometry at the graduate level.
Textbook and Supplementary Readings1 Matousek, J. (2002) Lectures on Discrete Geometry, Springer. 2 Pach J. and Agarwal P.K. (1995) Combinatorial Geometry, John Wiley & Sons, Inc.
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Convex sets
2 Minkowski’s Theorem
3 General lattices
4 Convex independent subsets
5 Polytopes
6 Convex polytopes
7 Intersection patterns of convex sets
8 Midterm Exam
9 Geometric selection theorems
10 Transversals
11 Epsilon nets
12 High dimensional polytopes
13 Volumes in high dimension
14 Embedding finite metric spaces into normed spacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Advanced Neural NetworksDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 637 Fall Ph. D. Elective Turkish 3 0 3 8
Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Rıfat Aşlıyan
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected]
Course Objective and brief Description
Nowadays the methods of artificial intelligence are widely used in computer science. Artificial neural networks (ANN) are very advantageous in most systems, especially in the systems which has very complex mathematical structures. In this course, the aim is to teach the fundamental ANN subjects.
Textbook and Supplementary readings1 Foundations of Neural Networks, T. Khana2 Fuzzy and Neural Approaches in Engineering, L. H. Tsoukalas, R. E. Uhrig3 Neural Networks for Control, W.T Miller,. R.S Sutton,.and P.J. Werbos4
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction
2 Fundamentals of Artificial Neural Networks (ANN)
3 Multilayered Feedforward Neural Nets
4 Back Propagation Algorithms
5 Competitive Learning and Other Special Neural Networks
6 Self- Organizing Systems
7 Radial Basis Function
8 Generalized Regression Neural Networks
9 Dynamic Systems and Recurrent Neural Networks
10 ANNs in System Identification
11 Adaptive Processors and Neural Networks
12 Neural networks for Control; Applications: Modelling, Neural networks in Spectral Analysis and Time-Series Prediction
13 Neural networks for Control; Applications: Modelling, Neural networks in Spectral Analysis and Time-Series Prediction
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Automatic Speech Recognition and Synthesis Department MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 639 Fall Ph.D. Elective Turkish 3 0 3 8
Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Rıfat AŞLIYAN
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected]
Course Objective and brief Description
This course introduces students to the rapidly developing field of automatic speech recognition and synthesis. The content is divided into two parts. Part I deals with background material in the acoustic theory of speech production, acoustic-phonetics, and signal representation. Part II describes algorithmic aspects of speech recognition systems including pattern classification, search algorithms, stochastic modelling, and language modelling techniques.
Textbook and Supplementary readings1 Rabiner and Juang, “Fundamentals of Speech Recognition,” Prentice-Hall, 1993.2 Thierry Dutoit, “An Introduction to Text-to-Speech Synthesis”, Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-4498-7,1997.34
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Acoustic Theory of Speech Production, Human hearing, acoustics, and phonetics
2 Signal Representation, Vector Quantization
3 Speech spectrum analysis (Fourier analysis, cepstral analysis, spectrogram reading)
4 Fundamental frequency analysis (F0 estimation, prosody models)
5 Speech synthesis
6 Linear Prediction (all-pole model, LPC, PARCOR, LSP analysis)
7 Learning algorithms and application (Viterbi algorithm, Bayes’ Theorem)
8 Speech coding (waveform coding, PCM, LPC)
9 Dynamic time warping and acoustic modeling
10 Hidden Markov Modeling, expectation-maximization, and search
11 Language Modeling
12 Graphical Models
13 Segment-Based ASR, Finite State Transducers
14 Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Expert Systems Department MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 641 Fall Ph.D. Elective Turkish 3 0 3 8
Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Rıfat AŞLIYAN
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected]
Course Objective and brief Description
In this courses fundamental concepts of expert systems, some techniques and their application will be introduced to students. Also, some tools for developing expert systems will be explained.
Textbook and Supplementary readings1 P. Jackson, "Introduction to Expert System", Addison-Wesley Publishing Company, ISBN 0201876868,
1998. 2 J. P.Egnizo, "Introduction to Expert System", ISBN 0-079-09785-5, McGraw Hill, 1990.34
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Overview of Artificial Intelligence. What are Expert Systems?
2 Knowledge Representation
3 Rule-Based Systems
4 Associative Nets and Frame Systems
5 Logic Programming
6 Representing Uncertainty
7 Knowledge Acquisition
8 Heuristic Classification
9 Constructive Problem Solving
10 Tools for Building Expert Systems
11 Machine Learning
12 Belief Networks
13 Case-based reasoning
14 Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Radical TheoryDepartment MathematicsDivision in the Dept. Algebra
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT 643 Fall Ph. D. Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assoc. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın, Assist. Prof. Dr. Erdal Özyurt
Instructor Information
Adnan Menderes University, Faculty of Art and Sciences, Department of Mathematics-09010 Aydın Tel: 256 218 20 00, E-posta : [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
In this course, it is aimed to present fundamental subjects of radical theory.
Textbook and Supplementary readings1 Rings and Radicals, N. J. Divinsky2 A Radical Approach to Algebra, M. Gray3
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Construction of a Radical Property, Ordinal Numbers
2 Construction of a Second Radical Property, Partitions of the Simple Rings
3 Nil and Nilpotent, The Descending Chain Condition
4 Ideals in Nil Semisimple Rings with Descending Chain Condition
5 Direct Sums, Central Idempotent Elements
6 First Structure Theorem, Idempotent Elements, Second Structure Theorem: Simple Rings
7 Generalizations: Radical Properties that Coincide with Nil on Rings with Descending Chain Condition
8 Arasınav
9 Relationship Between Ascending Chain Condition and Descending Chain Condition
10 The Baer Lower Radical, Prime Rings, Prime Ideals
11 Subdirect Sums, Prime and Semiprime Rings with Ascending Chain Condition
12 Jacobson Radical
13 Brown-McCoy Radical, Levitzki Nil Radical
14 Final ExamCourse assessment will be weighted 40 % for mid-term exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Gamma Rings
Department MathematicsDivision in the Dept. Algebra
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT 645 Fall Ph. D. Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assoc. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın, Assist. Prof. Dr. Erdal Özyurt
Instuctor Information
Adnan Menderes University, Faculty of Art and Sciences, Department of Mathematics-09010 Aydın Tel: 256 218 20 00, E-posta : [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
In this course, it is aimed to present fundamental gamma ring subjects
Textbook and Supplementary readings1 Gamma Rings, S. Kyuno2 Structureof Rings, N. Jacobson3 Theory of Rings, N. McCoy
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Definitions and Examples of Gamma Rings,
2 Operator Rings, Ideals, Homomorphisms and Residue Class Gamma Rings
3 Prime, Primitive and Simple Gamma Rings
4 Density Theorem
5 Semi-Prime Gamma Rings with Min-r Condition
6 Simple Gamma Rings with Min-r Condition, Gamma Rings with Min-r and Min-l Conditions
7 Prime Radical, Levitzki Nil Radical, Jacobson Radical
8 Arasınav
9 Relation Among Radicals of R, of L and of M
10 Relations Among the Various Radicals
11 Relations Between Gamma Rings and Other Algebraic Systems
12 Morita Pairs and Morita Equivalences
13 Subdirect Sums of Gamma Rings, Commutative Gamma Rings
14 Final ExamCourse assessment will be weighted 40 % for mid-term exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Function Theory of one Complex VariableDepartment MathematicsDivision in the Dept. Analysis and Functions Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab. Credit ECTS CreditMAT602 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of function theory of one complex variable including fundamental concepts, complex line integrals, applications of Cauchy integral, meromorphic functions and residues, the zeros of holomorphic function, holomorphic functions as geometric mappings, harmonic functions, infinite series and product, applications of infinite sums and products, analytic continuation, rational approximation theory, special classes of holomorphic functions, special functions.
Textbook and Supplementary readings1 Function Theory of One Complex Variable, Robert E. Grene, Steven G. Krantz.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Complex line integrals
2 Applications of Cauchy integral
3 Meromorphic functions and residues
4 The zeros of holomorphic function
5 Holomorphic functions as geometric mappings
6 Harmonic functions
7 Infinite series and product
8 Applications of infinite sums and products
9 Analytic continuation
10 Rational approximation theory
11 Special classes of holomorphic functions
12 Special classes of holomorphic functions
13 Special functions
14 Final Exam
FACULTY OF ARTS AND SCIENCES
Course Title Commutative AlgebraDepartment Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT604 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Algebra I
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
To give necessary fundameltal properties of commutative algebra for algebraic geometry.
Textbook and Supplementary readings1 Introduction to Commutative Algebra, M.F. Atiyah ve I.G. MacDonald
2 Değişmeli Cebire Giriş, A. Harmancı, M.Akgül, H.I. Tutalar, K.Taş (Çeviri)
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Modules
2 Exact Sequences
3 Tensor Product of Modules
4 Algebras
5 Rings and Modules of Fractions
6 Localizations
7 Primary Decomposition
8Integral Dependence and Valuations
9 Chain Conditions- EXAM
10 Noetherian and Artinian Rings
11 Dedekind Domains
12 Completions
13 Dimension Theory
14 Non Algebraic Dimensions
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Algebraic Geometry
Department Mathematics Division in the Dept. Algebra and Number Theory, and Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT606 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Commutative Algebra
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma Altınok
Instructor Information [email protected]
Course Objective and brief Description
Algebraic geometry is the study of Geometry coming from Algebra and Rings. Algebra, polynomials rings and geomety are roots of polynomials. In the last centurary, it is discovered that Algebraic Geometry can be applied to Commutative Rings with unity. As a result of this , Algebraic Geometry can be applied into many areas, a specially Number Theory. For example, Andrew Wiles used Algebraic Geometry tools to prove the Fermat Last Theorem. This course’s aim is to teach the fundamental concepts of Algebraic Geometry
Textbook and Supplementary readings1 Algebraic Geometry, Hartshorne2 Using Algebraic Geometry, Cox, Little, O’Shea
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Affine varieties
2 Affine varieties
3 Projective varieties
4 Projective varieties
5 Morphisms, Rational maps
6 Nonsingular varieties
7 Divisors, Projective Morphism. Curves; Riemann-Roch Teorem, Hurwitz’s Theorem
8 Divisors, Projective Morphism. Curves; Riemann-Roch Teorem, Hurwitz’s Theorem
9 Clasification of Curves in 3- dimentional Projective SpaceExam
10 Clasification of Curves in 3- dimentional Projective Space
11 Clasification of Curves in 3- dimentional Projective Space
12 Surfaces; Geometry on a Surface, Ruled Surfaces, Cubic Surfaces in 3-dimensional Projective Space
13 Surfaces; Geometry on a Surface, Ruled Surfaces, Cubic Surfaces in 3-dimensional Projective Space
14 Clasification of Surfaces
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Group Theory II
Department MathematicsDivision in the Dept. Algebra and Number Theory
Code Term Level Type Language Credit hours/WeekLecture Lab. Credit ECTS
CreditMAT608 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz
InstructorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
To prepare the students to current resarch in group theory and study some special groups
Textbook and Supplementary readings1 A course in the theory of the groups, Derek R. J. Robinson
2 Group Theory I-II Michio Suzuki
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Locally finite groups
2 Maximal and minimal conditions
3 Cernikov groups and automorphisms of Cernikov groups
4 Direct limit of groups
5 Inverse limit of groups
6 Linear groups
7 Classical simple groups
8 Locally finite simple groups
9 Hall universal group MIDTERM
10 Finite simple groups
11 Lie types of simple groups
12 Centralizers of elements in simple locally finite groups
13 Centralizers of elements in simple locally finite groups
14 Centralizers of elements in simple locally finite groups
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Module Theory II
Department Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT610 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Module Theory I
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
Working in Advance Modüle Theory
Textbook and Supplementary readings1 Lectures on Modules, T.Y. Lam, Graduate Texts in Mathematics, Springer 1998
2 Rings and Categories of Modules, F.W. Anderson-K.R. Fuller, Springer Verlag 1974
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Free Modules( Invariant Basis Number, The Rank Conditions)
2 Projective Modules
3 Projective Modules
4 Injective Modules
5 Injective Modules
6 Injective Modules
7 Flat Modules
8 Faitfully Flat Modules
9 Homological Dimensions-EXAM
10 Injective Dimensions
11 Global Dimensions of Semiprimary Rings
12 Global Dimensions of Local Rings
13 Uniform Dimensions
14 CS-Modules
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Functional AnalysisDepartment MathematicsDivision in the Dept. Analysis and Functions Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab. Credit ECTS CreditMAT612 Spring Ph. D. Obligatory Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Functional Analysis including Differentiation, Lebesgue Integral, Stieltjes Integral and its generalizations, Integral Equations and Linear transformations, Hilbert and Banach spaces, Completely contınuous symmetric transformations of Hilbert space, Bounded symmetric, Unitary, and normal transformations of Hilbert space, Unbounded linear transformations of Hilbert space.
Textbook and Supplementary readings1 Functional Analysis, Frigyes Riesz, Bela Sz. –Nagy, 1990.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Differentiation
2 Lebesgue Integral
3 Stieltjes Integral and its generalizations
4 Stieltjes Integral and its generalizations
5 Integral Equations and Linear transformations
6 Integral Equations and Linear transformations
7 Hilbert and Banach spaces
8 Hilbert and Banach spaces
9 Completely contınuous symmetric transformations of Hilbert space
10 Completely contınuous symmetric transformations of Hilbert space
11 Bounded symmetric, Unitary, and normal transformations of Hilbert space
12 Bounded symmetric, Unitary, and normal transformations of Hilbert space
13 Unbounded linear transformations of Hilbert space
14 Final Exam
FACULTY OF ARTS AND SCIENCES
Course Title Special FuctionsDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit EC TSCreditMAT 614 Spring Ph. D. Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors
Assist. Prof. Ali IŞIK, Assist. Prof. Ali Filiz
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDIN Tel: 256 2128498 [email protected], [email protected]
Course Objective and brief Description
The aim of this course is to introduce special functions of mathematics.
Textbook and Supplementary readings1 W. W. Bell, Special Functions for Scienlisls and Enginccrs, Dover I ublications, 2004.
Larry C. Andrevvs, Ronold L. Phillips, Mathematical Techniques for Engineers and Scientists, Spie Press,2003.
2 Larry C. Andrews, Special Functions of Mathematics for Engineers, Spie Press, 1998.3 lan N. Sneddon, Fourier Transforms, Dover Pub., 1995.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Series solutions of ordinary differential equations,
2 Intergral Functions: Gamma function.
3 Beta function., Error function..
4 Exponential integrals, Elliptic integrals;
5 Special functions: Bessel function.
6 Legendre, Hermite, Laguerre
7 Chebyshev,
8 Gegenbauer,
9 Jacobi polinomials,
10 Hipergcometric functions
11 Integral transforms: Fourier
12 Laplace, Mellin, Hankel,
13 Kontorovich-Lebedev, Mehler-Fock transforms.
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Numerical Solution of Differential and Integral EquationsDepartment MathematicsDivision in the Dept. Foundations of Mathematics and Mathematical Logic
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS credit
MAT 616 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites MAT527
Name of Instructors Assist. Prof. Dr. Ali FİLİZ
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]
Course Objective and Brief Description
To provide a unified account of numerical methods for solving integral, differential and partial differantial equations.
Textbook and Supplementary Readings1 E Hairer, S P Norsett and G Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, (2nd edition),
1993, Springer-Verlag.2 E Hairer and G Wanner, Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems, (2nd
edition), 1996, Springer-Verlag.3 A Iserles, Numerical Analysis of Differential Equations, 1996, Cambridge University Press.4 K W Morton and D F Mayers, Numerical Solution of Partial Differential Equations, 1994, Cambridge University
Press.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Discrete methods for solving ODEs: Review of Runge-Kutta methods, linear multistep methods (Adams) convergence and order
2 Review of Runge-Kutta methods, linear multistep methods (Adams) convergence and order.
3A number of practical ODE/PDE problems from different areas of applications will be introduced. They will be used and solved to illustrate ideas throughout the course. Implicit Runge-Kutta methods.
4 Stability regions, A-stability and other stability concepts. The BDF methods. Finite difference methods for linear equations and for more general problems.
5 The BDF methods. Finite difference methods for linear equations and for more general problems.
6 Implicit Runge-Kutta methods, deferred correction. Numerical solution of integral equations using different numerical methods.
7 The comparasion LaTeX and Word
8 Finite difference methods for heat equation, wave equation and Poisson's equation: The 5-point Formula
9 Finite difference methods for heat equation, wave equation and Poisson's equation: The 5-point Formula
10 Existence and order of convergence for the grid-solution. Curved boundaries and derivative boundary conditions.
11 Existence and order of convergence for the grid-solution. Curved boundaries and derivative boundary conditions.
12 Numerical solution of parabolic Volterra integral equations using Finite difference methods
13 Numerical solution of parabolic Volterra integral equations using Finite difference methods
14 Final exam
FACULTY OF ARTS AND SCIENCES
Course Title Tauberian Theory and its ApplicationsDepartment Mathematics
Division in the Dept. Analysis and Functions Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab. Credit ECTS CreditMAT618 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assoc. Prof. Dr. İbrahim Çanak
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]
Course Objective and brief Description
This course aims to acquaint students with the fundamental notions of Tauberian theory and its applications including the Laplace-Stieltjes transform, convergence and absolute convergence of the Laplace-Stieltjes transform, uniform convergence of the Laplace-Stieltjes transform, Abelian theorems for power series, Abelian theorems for the Laplace-Stieltjes transforms, Tauber’s theorem, the remainder term in Tauber’s theorem, Littlewood’s theorem, the theorem of Hardy and Littlewood, Fatou’s theorem, Korevaar’s proof of Fatou’s theorem, the Haryd-Littlewood theorem in the complex domain and Ikehara’s theorem.
Textbook and Supplementary readings1 Tauberian theory and its applications, A. G. Postnikov
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Laplace-Stieltjes transform
2 convergence and absolute convergence of the Laplace-Stieltjes transform
3 uniform convergence of the Laplace-Stieltjes transform
4 Abelian theorems for power series
5 Abelian theorems for the Laplace-Stieltjes transforms
6 Tauber’s theorem
7 the remainder term in Tauber’s theorem
8 Littlewood’s theorem
9 the theorem of Hardy and Littlewood
10 Fatou’s theorem
11 proof of Fatou’s theorem
12 the Haryd-Littlewood theorem in the complex domain
13 Ikehara’s theorem
14 Final Exam
FACULTY OF ARTS AND SCIENCES
Course Title Algebraic Curves
Department MathematicsDivision in the Dept. Topology
Code Term Level Type LanguageCredit hours/week
Lecture Credit ECTS creditMAT 620 Spring Ph. D. Elective Turkish 3 3 10Course Prerequisites None
Name of Instructors Asst. Prof. Adnan MELEKOĞLU
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]
Course Objective and Brief Description
The aim of this course is to introduce Algebraic Curves
Textbook and Supplementary Readings1 Kirwan F. (1992) Complex Algebraic Curves, Cambridge University Press2 Fulton W. (1989) Algebraic Curves, Addison-Wesley
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Real algebraic curves
2 Complex algebraic curves in
3 Complex algebraic curves in
4 Complex projective spaces
5 Complex projective curves in
6 Affine and projective curves
7 Bézout’s theorem
8 Midterm Exam
9 Degree-genus Formula
10 Weierstrass P-function
11 Riemann surfaces
12 Riemann surfaces
13 Abel’s theorem
14 Riemann-Roch theoremCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Lie AlgebraDepartment MathematicsDivision in the Dept. Algebra and Number Theory
Code Term Level Type Language Credit hours/WeekLecture Lab. Credit ECTS Credit
MAT622 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar , Prof. Dr. Gonca Güngöroğlu ,Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz
InstructorsInformation
ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected],[email protected],, [email protected], [email protected]
Course Objective and brief Description
This course is to introduce the students to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0. Besides being useful in many parts of mathematics an Phiysics, the theory of semisimple lie algebras inherently attractive.
Textbook and Supplementary readings1 Introduction to Lie Algebras and Representation Theory
2
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Basic concepts: Definitions and first examples
2 Ideals and homomorphisms,
3 Soluble and nilpotent Lie algebras
4 Semisimple Lie Algebras: Theorems of Lie and Cartan
5 Killing form
6 Complete reducibility of representation
7 Representation of SL(2,F)
8 Root space and decompositons MIDTERM
9 Root systems: Axiomatics
10 Simple roots and Weyl group
11 Classification
12 Construction of root systems and automorphisms
13 Abstract theory of weights
14 Borel subalgebraCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Category Theory IIDepartment Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT624 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Category Theory I
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
Advance Category and Aplications
Textbook and Supplementary readings1 Theory of Categories, Barry Mitchell, Academic Press, New York and London, 1965
2 Categories fort he Working Mathematics, S. Mac Lane, Graduate Texs in Mathematics 5
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Complete Categories (C_i Categories, Injective Envelopes)
2 Existence of Injectives
3 Adjoint Functors (Generalities)
4 Existence of Adjoints
5 Functor Categories
6 Reflections
7 Projective Classes
8 Application to Limits
9 Tensor Product-EXAM
10 Full Imbedding Theorem
11 Ext^1, Ext^n
12 The Relation
13 The Exact Sequences
14 Global Dimension
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Homological Algebra IIDepartment Mathematics Division in the Dept. Algebra and Number Theory
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT626 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites It is necessary to know module theory and take Homological Algebra I before
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
Advance Homological Algebra
Textbook and Supplementary readings1 Basic Homological Algebra, M. Scott Osborne, Springer Verlag
2 Homology, Saunders Mac lane, Springer Verlag3 Introduction to Homological Algebra, Rotman, J.J.
4 Relative Homological Algebra, Edgar E. Enochs, Overtoun M. G. Jenda
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Abstract Homological Algebra ( Living without Elements)
2 Additive Categories
3 Kernels and Cokernels
4 Cheating with Projectives
5 Arrow Categories
6 Homology in Abelian Category
7 Long Exact Sequences
8 An alternative for Unbalanced Categories
9 Limits and Colimits-EXAM
10 Adjoint Functors
11 Directed Colimits Tensor product and Tor
12 Lazard’s Theorem
13 Weak Dimension Revisited
14 Injective Envelops
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Compact Riemann SurfacesDepartment MathematicsDivision in the Dept. Topology
Code Term Level Type LanguageCredit hours/week
Lecture Credit ECTS creditMAT 628 Fall Ph. D. Elective Turkish 3 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Adnan MELEKOĞLU
Instructor Information
Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]
Course Objective and Brief Description
The aim of this course is to introduce compact Riemann surfaces
Textbook and Supplementary Readings1 Jost J. (1997) Compact Riemann Surfaces, Springer2 Jones G.A. and Singerman D. (1987) Complex Functions, Cambridge University pres
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Manifolds
2 Riemann surfaces of analytic functions
3 Riemann surfaces of analytic functions
4 Topological classification of compact Riemann surfaces
5 Topological classification of compact Riemann surfaces
6 The theorems of Gauss-Bonnet and Riemann-Hurwitz
7 The theorems of Gauss-Bonnet and Riemann-Hurwitz
8 Midterm Exam
9 Harmonic maps
10 Metrics and conformal structures
11 Teichmüller spaces
12 Teichmüller spaces
13 Hyperelliptic Riemann surfaces
14 Geometric structures on Riemann surfacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCİENCES
Course Title Differential and Riemannian Manifolds IIDepartment MathematicsDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT632 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Leyla Onat
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü 09010-AydınTel:02562128498 [email protected]
Course Objective and brief Description
The main goal is this course to provide a working knowledge of Riemanniann manifolds, tensors and differential forms.
Textbook and Supplementary readings1 Lang S. Differential and Riemannian Manifolds, Springer-Verlag 1995.
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Basic Properties
2 The Riemannian Distance
3 The Riemannian Tensor
4 The Second Variation Formula
5 The Riemannian Volume Form
6 Covariant Derivatives
7 Solve the problem about what he has learned
8 The Jacobıan Determinant of the Exponential Map
9 Orientation
10 Stoke’s Theorem on a Manifold
11 The Divergence Theorem
12 Cauch’y Theorem
13 Solve the problem about what he has learned
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
.
FACULTY OF ARTS AND SCIENCES
Course Title Tensor AlgebraDepartment MathematicDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 634 Spring Ph.D. Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors Assist. Prof. Dr. Leyla Onat
Instructor Information
Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü 09010-AdınTel:02562128498 [email protected]
Course Objective and brief Description
The main goal is this course to provide a working knowledge of Tensor Algebra
Textbook and Supplementary readings1 Greub,W.H. Multilinear algebra, Springer-Verlag New York 1967
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Multilinear mappins
2 Tensor Product
3 Linear mappins4 Dual spaces
5 Tensors
6 Tensor algebra
7 Solve the problem about what he has learned
8 Mixed tensors
9 Symmetry in the tensor algebra
10 Exterior algebra
11 The Poincare isomorphism
12 Symmetric tensor algebra
13 Solve the problem about what he has learned
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Digital Geometry Department MathematicsDivision in the Dept. Geometry
Code Term Level Type LanguageCredit hours/week
Lecture Lab
Credit ECTS credit
MAT 636 Spring PhD Elective Turkish 3 0 3 10Course Prerequisites None
Name of Instructors Asst. Prof. Adnan MELEKOĞLU
Instructor Information
Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, 09010 AYDIN, Tel: 256 2128498, E-mail: [email protected]
Course Objective and Brief Description
The aim of this course is to introduce Digital Geometry at the graduate level.
Textbook and Supplementary Readings1 Klette, R. and Rosenfeld, A. (2004) Digital Geometry: Geometric Methods for Digital Picture Analysis,
Elsevier. 2 Herman G.T. (1998) Geometry of Digital Spaces, Birkhauser.
COURSE CALENDAR / SCHEDULEWeek Lecture Topics
1 Grids
2 Digitization
3 Metrics
4 Adjacency Graphs
5 Digital Topology
6 Combinatorial Topology
7 Topology of curves and surfaces
8 Midterm Exam
9 Geometry of curves and surfaces
10 Digital arc length
11 Digital curvature
12 Digital planes
13 Transformations
14 DeformationsCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.
FACULTY OF ARTS AND SCIENCES
Course Title Advance Artificial IntelligenceDepartment MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 638 Spring Ph. D. Elective Turkish 3 0 3 8
Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Rıfat Aşlıyan
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected]
Course Objective and brief Description
In this course, it is aimed to present fundamental artificial intelligence subjects
Textbook and Supplementary readings1 Artificial Intelligence: A Guide to Intelligent Systems, M. Negnevitsky2 Artificial Intelligence: A Modern Approach, S. J. J. Russell and P. Norvig34
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to AI
2 Programming languages
3 Knowledge representation: Production rules, inclusion hierarchies, prepositional and predicate calculus
4 Knowledge representation: Rules of inference, frames, semantic networks, constraints and syntactic approaches.
5 Searching: Hypothesis and test, depth-first search, breadth-first search
6 Searching: Heuristic search, optimal search
7 Searching: Game trees and adversarial search: minimax search and alpha-beta pruning
8 Learning: Identification trees
9 Learning: Neural nets, perceptrons
10 Learning:Genetic algorithms
11 Expert systems, robotics, computer vision, natural language processing, speech recognition
12 Expert systems, robotics, computer vision, natural language processing, speech recognition
13 Expert systems, robotics, computer vision, natural language processing, speech recognition
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Digital Signal Processing Department MathematicsDivision in the Dept. Applied Mathematics
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS CreditMAT 640 Spring Ph.D. Elective Turkish 3 0 3 8
Course Prerequisites None
Name of Instructors Asst. Prof. Dr. Rıfat AŞLIYAN
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected]
Course Objective and brief Description
This course will introduce the basic concepts and techniques for processing signals on a computer. By the end of the course, you be familiar with the most important methods in DSP, including digital filter design and transform-domain processing. The course emphasizes intuitive understanding and practical implementations of the theoretical concepts using the Matlab environment.
Textbook and Supplementary readings1 McClellan, J. H., et al. “Computer-Based Exercises for Signal Processing Using MATLAB® 5”, Upper
Saddle River, NJ: Prentice Hall, 1998. ISBN: 0137890095.2 Emmanuel C. Ifeachor, Barrie W. Jervis, 2002; “Digital Signal Processing, A practical Approach”. Second
Edition, Prentice Hall.3 Sanjit K. Mitra ,” Digital Signal Processing: A computer-based approach” (3rd ed.), McGraw-Hill, 2005
(ISBN 0-07-304837-2, international edition ISBN 007-124467-0)4
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Introduction to digital signal processing and its applications
2 Analog/digital input/output interfaces for real time systems
3 Discrete transforms, Discrete Fourier transform
4 Fast Fourier transform, inverseFFT, and discrete transforms
5 Z-transorm and applications
6 Extracting correlation and convolution function
7 Training algorithms for digital signal processing and speech recognition
8 Digital filter design
9 Finite impulse response (FIR) digital filter design
10 Window-based FIR filter design
11 FIR filter design by frequency sampling
12 Recursive (IIR) digital filter design
13 Adaptive digital filters
14 Final Exam
Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.
FACULTY OF ARTS AND SCIENCES
Course Title Special RingsDepartment MathematicsDivision in the Dept. Algebra
Code Term Level Type LanguageCredit hours/week
Lecture Lab Credit ECTS Credit
MAT 642 Spring Ph. D. Elective Turkish 3 0 3 10
Course Prerequisites None
Name of Instructors
Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assoc. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın, Assist. Prof. Dr. Erdal Özyurt
Instructor Information
Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 218 20 00, E-posta : [email protected], [email protected], [email protected], [email protected], [email protected]
Course Objective and brief Description
In this course, it is aimed to introduce some special rings and to present fundamental ring strucrute
Textbook and Supplementary readings1 Noncommutative Rings, I. N. Herstein2 Algebra, T.W. Hungerford
COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field
1 Jacobson Radical, Artinian Rings
2 Semisimple Artinian Rings
3 Density Theorem
4 Semisimple Rings, Applications of Wedderburn’s Theorem
5 Wedderburn’s Theorem and Some Generalizations
6 Some Special Rings
7 The Brauer Group
8 Midterm Exam
9 Maximal Subfields
10 Representations of Finite Groups
11 A Theorem of Hurwitz, Applications to Group Theory
12 Polynomial Identities
13 Standart Identities, A Theorem of Kaplansky
14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.