MATH 2103 • Final • Discrete Mathematics

Definition of Divisibility

Example 1

Example 2

Example 3

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

Example 1

Example 2

Prime Numbers

Example 1

Example 2

Example 3

GCD Greatest Common Divisor

LCM Least Commun Multiple

Example 1

Euclidian Algorithm

Example 1

Bézout Identity

Example 1

Example 2

Example 3

Fermat' Little Theorem

Ceasar Cipher

Affine Cipher

Example 1

Example 2

Example 3

Example 4

Transposition Cipher

RSA Algorithm

Example 1

Example 2

Example 3

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Cryptography 1

Cryptography 2

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

Composition of Relations

Example 13

Example 14

Combining Relations

Inverse and Complementary of a Relation

Example 15

Matrix Representation of a Relation 1

Matrix Representation of a Relation 2

Example 16

Operations on Zero - One Matrices

Example 17

Equivalence Relation

Example 18

Example 19

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 1

Example 2

Incidence Matrices

Example 3

Isomorphism of Graphs

Example 4

Example 5

Example 6

Example 7

Introduction

Rooted Tree

Terminology for Rooted Trees

Full m-ary Trees

Some Formulas

Properties of Relation 1

Properties of Relation 2

Properties of Relation 3

Combining Relations

Equivalence Relation 1

Equivalence Relation 2

Equivalence Relation 3

Equivalence Relation 4

Equivalence Relation 5

Equivalence Relation - Proof

Graph Theory 1

Graph Theory 2

Graph Theory 3

Graph Theory 4

Graph Theory 5

Graph Theory 6