# COMP 106 (Spring 24) • Discrete Mathematics for Computer Science and Engineering • Final

Ders Tanıtımı

Introduction

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Homogenous Recurrence Relations

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Example 1

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Example 2

Example 3

Example 4

Non Homogenous Recurrence Relations

Example5

Example 6

Creating Recurrence Relations

Example 7

Example 8

Example 9

Definition

Example 1

Example 2

Example 3

Example 4

Example 5

Extended Binomial Theorem

Counting Problems with Generating Functions

Example 6

Example 7

Example 8

Example 9

Example 10

Definition of Relation

Example 1

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Example 2

Example 3

Example 4

Reflexive Relations

Example 5

Example 6

Symmetric Relations

Antisymmetric Relations

Example 7

Transitive Relations

Example 8

Properties of Relations

Example 9

Example 10

Example 11

Composition of Relations

Example 12

Example 13

Combining Relations

Inverse and Complementary of a Relation

Example 14

Matrix Representation of a Relation 1

Matrix Representation of a Relation 2

Example 15

Operations on Zero - One Matrices

Example 16

Reflexive Closure

Symmetric Closure

Example 17

Transitive Closure & Connectivity Relation

Matrix Representation of Transitive Closure

Example 18

Equivalence Relation

Example 19

Example 20

Example 21

Example 22

Example 23

Example 24

Partially Ordered Set

Example 25

Example 26

Recurrence Relations 1

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Recurrence Relations 2

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Recurrence Relations 3

Recurrence Relations 4

Generating Functions 1

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Generating Functions 2

Generating Functions 3

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Generating Functions 4

Relations 1

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Relations 2

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Relations 3

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Relations 4

Relations 6

Relations 7

Relations 8

Relations 9

Relations 10

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Introduction

Example 1

Graph Terminology

Example 2

Handshaking Theorem

Example 3

Example 4

Special Graphs

Example 5

Example 6

Bipartite Graphs

Example 7

Example 8

Complete Bipartite Graph

Matching

Example 9

Subgraph

Example 10

Subgraph Induced

Edge Contraction

Example 11

Complementary Graph

Example 12

Example 13

Example 14

Example 15

Example 16

Incidence Matrices

Example 17

Isomorphism of Graphs

Example 18

Example 19

Example 20

Example 21

Definition of Paths and Circuits

Connected Graphs

Euler Paths and Circuits

Example 22

Hamilton Paths and Circuits

Example 23

Example 24

Planar Graph

Planar Graph - Euler Formula

Example 25

Example 26

Kuratowski's Theorem

Example 27

Example 28

Example 29

Language and Grammar

Phase-Structure Grammar

Grammar -> Language Example 1

Grammar -> Language Example 2

Grammar -> Language Exam Like Question 1

Grammar -> Language Exam Like Question 2

Language -> Grammar Example 1

Language -> Grammar Example 2

Language -> Grammar Exam Like Question 1

Language -> Grammar Exam Like Question 2

Language -> Grammar Exam Like Question 3

Finite State Machines with Output

Example 1

Example 2

Exam Like Question 1

Finite State Machines with NO Output

Example 3

Example 4

Example 5

Exam Like Question 2

Exam Like Question 3

Turing Machine

Example 6

Example 7

Exam Like Question 4

Graphs 1

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Graphs 2

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Graphs 3

Graphs 4

Graphs 5

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Graphs 6

Graphs 7

Graphs 8

Graphs 9

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Graphs 10

Graphs 11

## Eğitmen

İhsan Altundağ
Eğitmen

2007 yılında Galatasaray Üniversitesi Bilgisayar Mühendisliği bölümünden birincilikle mezun olduktan sonra Fransa'da Kriptoloji üzerine Fransa hükümeti tarafından verilen bursla yüksek lisans yaptım. Devamında ikinci kez sınava girerek Boğaziçi Matematik bölümünü de bitirdim. Yaklaşık 15 yıldır üniversite öğrencilerine dersler vermekteyim.

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