MAT 1006 (Spring 24) • Engineering Mathematics I • Final

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

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

Relations 1

Relations 2

Relations 3

Relations 4

Relations 6

Relations 7

Relations 8

Relations 9

Relations 10

Introduction to Counting

Combination & Permutation: Intuition

Combination

Permutation 1

Permutation 2

Binomial Theorem

Example 1

Example 2

Example 3

Pascal Identity

Combinatorial Proof

Example 4

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Example 5

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Counting 7

Counting 8

Counting 9

Binomial Coefficients and Identities 1

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 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

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

Planar Graph

Planar Graph - Euler Formula

Example 25

Corollaries about Planar Graph

Example 26

Kuratowski's Theorem

Example 27

Example 28

Example 29

Graphs 1

Graphs 2

Graphs 3

Graphs 4

Graphs 5

Graphs 6

Graphs 7

Graphs 8

Graphs 9

Graphs 10

Graphs 11

What is an algorithm?

Algorithm and Pseudocode 1

Algorithm and Pseudocode 2

Algorithm and Pseudocode 3

Algorithm and Pseudocode 4

Exam Like Question 1

Exam Like Question 2

Big-O Notation

Example 1

Example 4

Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

Example 1

Example 2

Big-Omega Notation

Big-Theta Notation

Example 1

Complexity 1

Complexity 2

Complexity 3

Complexity 4

Complexity 5

Complexity 6

Algorithms 1

Algorithms 2

Algorithms 3

Algorithms 4

Algorithms 5