discrete structures of computer science...

Outline Course Info What is Discrete Mathematics?

Discrete Structures of Computer ScienceIntroduction

Gazihan Alankus(Based on original slides by Brahim Hnich)

July 23, 2012


1 Course Info

2 What is Discrete Mathematics?Continuous MathematicsDiscrete Mathematics


Course Info

Instructors:

Asst. Prof. Dr. Gazihan AlankusTeaching assistant: NoneCourse Webpage

http://homes.ieu.edu.tr/∼galankus


Course Info

Instructors:Asst. Prof. Dr. Gazihan Alankus

Teaching assistant: NoneCourse Webpage



Course Info


Teaching assistant: None

Course Webpage



Course Info


Teaching assistant: NoneCourse Webpage



Course Info

Course objective

Introduce basic concepts and applications of discretemathematics

Syllabus

Logic and formal reasoningSet theoryRelations and functionsMathematical inductionCombinatoricsFinite probabilityGraphs and Trees


Course Info

Course objectiveIntroduce basic concepts and applications of discretemathematics

Syllabus

Logic and formal reasoningSet theoryRelations and functionsMathematical inductionCombinatoricsFinite probabilityGraphs and Trees


Course Info


SyllabusLogic and formal reasoning

Set theoryRelations and functionsMathematical inductionCombinatoricsFinite probabilityGraphs and Trees


Course Info


SyllabusLogic and formal reasoningSet theory

Relations and functionsMathematical inductionCombinatoricsFinite probabilityGraphs and Trees


Course Info


SyllabusLogic and formal reasoningSet theoryRelations and functions

Mathematical inductionCombinatoricsFinite probabilityGraphs and Trees


Course Info


SyllabusLogic and formal reasoningSet theoryRelations and functionsMathematical induction

CombinatoricsFinite probabilityGraphs and Trees


Course Info


SyllabusLogic and formal reasoningSet theoryRelations and functionsMathematical inductionCombinatorics

Finite probabilityGraphs and Trees


Course Info


SyllabusLogic and formal reasoningSet theoryRelations and functionsMathematical inductionCombinatoricsFinite probability

Graphs and Trees


Course Info


SyllabusLogic and formal reasoningSet theoryRelations and functionsMathematical inductionCombinatoricsFinite probabilityGraphs and Trees


Textbook

Discrete and Combinatorial Mathematics (An AppliedIntroduction) by Ralph. G. Grimaldi, Addison-Wesley: 5th

Edition

We will not cover all the chapters of the bookWe will not cover all sections of all covered chaptersWe will not follow the order of the bookIn few cases the notation and terminology will be differentfrom that of the bookThe contents uncovered in slides/lectures are not required


Textbook


EditionWe will not cover all the chapters of the book

We will not cover all sections of all covered chaptersWe will not follow the order of the bookIn few cases the notation and terminology will be differentfrom that of the bookThe contents uncovered in slides/lectures are not required


Textbook


EditionWe will not cover all the chapters of the bookWe will not cover all sections of all covered chapters

We will not follow the order of the bookIn few cases the notation and terminology will be differentfrom that of the bookThe contents uncovered in slides/lectures are not required


Textbook


EditionWe will not cover all the chapters of the bookWe will not cover all sections of all covered chaptersWe will not follow the order of the book

In few cases the notation and terminology will be differentfrom that of the bookThe contents uncovered in slides/lectures are not required


Textbook


EditionWe will not cover all the chapters of the bookWe will not cover all sections of all covered chaptersWe will not follow the order of the bookIn few cases the notation and terminology will be differentfrom that of the book

The contents uncovered in slides/lectures are not required


Textbook


EditionWe will not cover all the chapters of the bookWe will not cover all sections of all covered chaptersWe will not follow the order of the bookIn few cases the notation and terminology will be differentfrom that of the bookThe contents uncovered in slides/lectures are not required


Grading

6 Homeworks each worth 5%

1 Midterm exam worth 30%

Midterm will be on August 23

1 Final exam worth 40%


Grading

6 Homeworks each worth 5%1 Midterm exam worth 30%

Midterm will be on August 23

1 Final exam worth 40%


Grading

6 Homeworks each worth 5%1 Midterm exam worth 30%

Midterm will be on August 231 Final exam worth 40%


Two Mathematics

Continuous mathematics

Discrete mathematics


Two Mathematics

Continuous mathematicsDiscrete mathematics


Calculus

Calculus (Latin, calculus, a small stone used for counting)

It is a branch of mathematicsIt includes the study of limits, derivatives, integrals, andinfinite series


Calculus

Calculus (Latin, calculus, a small stone used for counting)It is a branch of mathematics

It includes the study of limits, derivatives, integrals, andinfinite series


Calculus

Calculus (Latin, calculus, a small stone used for counting)It is a branch of mathematicsIt includes the study of limits, derivatives, integrals, andinfinite series


Trigonometry

Trigonometry (from Greek trigo-non ”triangle” + metron”measure”)

It is a branch of mathematics that deals with triangles,It deals with relationships between the sides and the angles oftrianglesIt also deals with the trigonometric functions, which describethose relationships.


Trigonometry

Trigonometry (from Greek trigo-non ”triangle” + metron”measure”)It is a branch of mathematics that deals with triangles,

It deals with relationships between the sides and the angles oftrianglesIt also deals with the trigonometric functions, which describethose relationships.


Trigonometry

Trigonometry (from Greek trigo-non ”triangle” + metron”measure”)It is a branch of mathematics that deals with triangles,It deals with relationships between the sides and the angles oftriangles

It also deals with the trigonometric functions, which describethose relationships.


Trigonometry

Trigonometry (from Greek trigo-non ”triangle” + metron”measure”)It is a branch of mathematics that deals with triangles,It deals with relationships between the sides and the angles oftrianglesIt also deals with the trigonometric functions, which describethose relationships.


Dynamic Systems

The dynamical system concept is a mathematicalformalization for any fixed ”rule” which describes the timedependence of a point’s position in its ambient space

Examples include the mathematical models that describe

1 the swinging of a clock pendulum2 the flow of water in a pipe3 the number of fish each spring in a lake


Dynamic Systems

The dynamical system concept is a mathematicalformalization for any fixed ”rule” which describes the timedependence of a point’s position in its ambient spaceExamples include the mathematical models that describe



Dynamic Systems


1 the swinging of a clock pendulum

2 the flow of water in a pipe3 the number of fish each spring in a lake


Dynamic Systems


1 the swinging of a clock pendulum2 the flow of water in a pipe

3 the number of fish each spring in a lake


Dynamic Systems




Differential Equations

A differential equation is a mathematical equation for anunknown function of one or several variables that relates thevalues of the function itself and of its derivatives of variousorders

They play a prominent role in engineering, physics, economicsand other disciplines


Differential Equations

A differential equation is a mathematical equation for anunknown function of one or several variables that relates thevalues of the function itself and of its derivatives of variousordersThey play a prominent role in engineering, physics, economicsand other disciplines


Chaos Theory

Chaos theory describes the behavior of certain systems whosestate evolves with time

These systems may exhibit dynamics that are highly sensitiveto initial conditions (popularly referred to as the butterflyeffect)


Chaos Theory

Chaos theory describes the behavior of certain systems whosestate evolves with timeThese systems may exhibit dynamics that are highly sensitiveto initial conditions (popularly referred to as the butterflyeffect)


Logic and Formal Reasoning

Logic is the study of the principles of valid demonstration andinference

Logic investigates and classifies the structure of statementsand arguments

through the study of formal systems of inference and the studyof arguments in natural language


Logic and Formal Reasoning

Logic is the study of the principles of valid demonstration andinferenceLogic investigates and classifies the structure of statementsand arguments

through the study of formal systems of inference and the studyof arguments in natural language


Set Theory

Set theory is the branch of mathematics that studies sets(collections of objects)

It is the most common foundational system for mathematicsThe language of set theory is used in the definitions of nearlyall mathematical objects


Set Theory

Set theory is the branch of mathematics that studies sets(collections of objects)It is the most common foundational system for mathematics

The language of set theory is used in the definitions of nearlyall mathematical objects


Set Theory

Set theory is the branch of mathematics that studies sets(collections of objects)It is the most common foundational system for mathematicsThe language of set theory is used in the definitions of nearlyall mathematical objects


Combinatorics

Combinatorics is a branch of pure mathematics concerning thestudy of discrete (and usually finite) objects


Combinatorics

Aspects of combinatorics include

”counting” the objects satisfying certain criteria (enumerativecombinatorics)deciding when the criteria can be metconstructing and analyzing objects meeting the criteria (as incombinatorial designs)finding ”largest”, ”smallest”, or ”optimal” objects(combinatorial optimization)finding algebraic structures these objects may have (algebraiccombinatorics)


Combinatorics

Aspects of combinatorics include”counting” the objects satisfying certain criteria (enumerativecombinatorics)

deciding when the criteria can be metconstructing and analyzing objects meeting the criteria (as incombinatorial designs)finding ”largest”, ”smallest”, or ”optimal” objects(combinatorial optimization)finding algebraic structures these objects may have (algebraiccombinatorics)


Combinatorics

Aspects of combinatorics include”counting” the objects satisfying certain criteria (enumerativecombinatorics)deciding when the criteria can be met

constructing and analyzing objects meeting the criteria (as incombinatorial designs)finding ”largest”, ”smallest”, or ”optimal” objects(combinatorial optimization)finding algebraic structures these objects may have (algebraiccombinatorics)


Combinatorics

Aspects of combinatorics include”counting” the objects satisfying certain criteria (enumerativecombinatorics)deciding when the criteria can be metconstructing and analyzing objects meeting the criteria (as incombinatorial designs)

finding ”largest”, ”smallest”, or ”optimal” objects(combinatorial optimization)finding algebraic structures these objects may have (algebraiccombinatorics)


Combinatorics

Aspects of combinatorics include”counting” the objects satisfying certain criteria (enumerativecombinatorics)deciding when the criteria can be metconstructing and analyzing objects meeting the criteria (as incombinatorial designs)finding ”largest”, ”smallest”, or ”optimal” objects(combinatorial optimization)

finding algebraic structures these objects may have (algebraiccombinatorics)


Combinatorics

Aspects of combinatorics include”counting” the objects satisfying certain criteria (enumerativecombinatorics)deciding when the criteria can be metconstructing and analyzing objects meeting the criteria (as incombinatorial designs)finding ”largest”, ”smallest”, or ”optimal” objects(combinatorial optimization)finding algebraic structures these objects may have (algebraiccombinatorics)


Theory of Computation

Is the branch of computer science that deals with whether andhow efficiently problems can be solved on a model ofcomputation, using an algorithmThe field is divided into two major branches: computabilitytheory and complexity theory


Graph Theory

Graph theory is the study of graphsGraphs are mathematical structures used to model pairwiserelations between objects from a certain collection


Probability Theory

Probability theory is the branch of mathematics concernedwith analysis of random phenomena

discrete structures of computer science...

Documents