MAT 2033 • Final • Discrete Mathematics

Big-O Notation

Example 1

Example 2

Example 3

Example 4

Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

Example 1

Example 2

What is an algorithm?

Algorithm and Pseudocode 1

Algorithm and Pseudocode 2

Algorithm and Pseudocode 3

Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

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

GCD Greatest Common Divisor

LCM Least Commun Multiple

Euclidian Algorithm

Example 1

Bézout Identity

Example 1

Example 2

Example 3

Inverse of a Number in Modular Arithmetic

Ceasar Cipher

Affine Cipher

Example 1

Example 2

Example 3

Example 4

Growth of Functions 1

Growth of Functions 2

Growth of Functions 3

Growth of Functions 4

Growth of Functions 5

Algorithms 1

Algorithms 2

Algorithm and Complexity

Algorithm and Complexity

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example 1

Identical Objects Example 2

Identical Objects Example 3

Combination

n choose r

Committee Example 1

Committee Example 2

Ball Example 1

Ball Example 2

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Binomial Theorem

Example 1

Example 2

Example 3

Pascal Identity

Vandermonde's Identity

Example 1

Combinatorial Proof

Example 1

Counting Standard Models 1

Counting Standard Models 2

Counting Standard Models 3

Counting Standard Models 4

Counting Standard Models 5

Counting Standard Models 6

Counting Standard Models 7

Counting Standard Models & Binomial Coefficients 1

Binomial Identities

Combinatorial Proof 1

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 5

Pigeonhole Principle 6

Introduction

Homogenous Recurrence Relations

Example 1

Example 2

Example 3

Example 4

Non Homogenous Recurrence Relations

Example5

Example 6

Creating Recurrence Relations

Example 7

Example 8

Example 9

Definition of Relation

Example 1

Example 2

Example 3

Reflexive Relations

Example 4

Symmetric Relations

Antisymmetric Relations

Example 5

Transitive Relations

Properties of Relations

Example 6

Example 7

Composition of Relations

Inverse and Complementary of a Relation

Matrix Representation of a Relation 1

Matrix Representation of a Relation 2

Example 1

Reflexive Closure

Symmetric Closure

Example 2

Transitive Closure & Connectivity Relation

Equivalence Relation

Example 3

Example 4

Partially Ordered Set

Example 5

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

Complementary Graph

Example 9

Example 10

Example 11

Adjacency Matrices - Undirected Graphs

Adjacency Matrices - Directed Graphs

Example 12

Example 13

Incidence Matrices

Example 14

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relations 4

Recurrence Relations 5

Recurrence Relations 6

Recurrence Relations 7

Recurrence Relations 8

Relations 1

Relations 2

Relations 3

Relations 4

Relations 5

Adjacency Matrices

Incidence Matrices

Bipartite Graphs & Euler Circuits

Euler Path, Induced Subgraph & Incidence Matrix

Isomorphism 1

Isomorphism 2

Isomorphism 3

Isomorphism 4