# MAT 2033 • Discrete Mathematics • Final

Ders Tanıtımı

Definition and Notation

Subset

Example 1

Union and Intersection of Two Sets

Difference of Two Sets

Example 1

Symmetric Difference

Example 1

Set Identities

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Power Set

Example 1

Example 2

Cartesian Product

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Generalized Intersections and Unions

Example 1

Example 2

Example 3

Definition of Function

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Number of Functions

Injective Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Surjective Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Bijective Function

Composition of Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Inverse Function

Example 1

Example 2

Example 3

Example 4

Example 5

Image of a Set

Example 1

Proof Example For Image of a Function

Preimage of a Set

Example 1

Example 2

Example 3

Proof Example for Preimage of a Function

Example 1

Definition of Relation

Example 1

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

Example 12

Example 13

Composition of Relations

Example 14

Example 15

Example 16

Equivalence Relation

Example 17

Example 18

Example 19

Example 20

Example 21

Example 22

Example 23

Example 24

Definition of Divisibility

Ücretsiz

Example 1

Example 2

Ücretsiz

Example 3

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

Example 1

Example 2

GCD Greatest Common Divisor

LCM Least Commun Multiple

Example 1

Euclidian Algorithm

Example 1

Bézout Identity

Example 1

Example 2

Example 3

Inverse of a Number in Modular Arithmetic

Primitive Root

Discrete Logarithm

Fermat's Little Theorem

Solving Linear Congruences

Example 1

Example 2

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

Ceasar Cipher

Ücretsiz

Affine Cipher

Ücretsiz

Example 1

Ücretsiz

Example 2

Example 3

Example 4

Transposition Cipher

RSA Algorithm

Example 1

Example 2

Example 3

Exam-like Question 1

Exam-like Question 2

Diffie - Hellman Protocol

Example 1

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

Adjacency Matrices - Undirected Graphs

Adjacency Matrices - Directed Graphs

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

## 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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