DISCRETE MATHEMATICS

Mathematical logic

INTRODUCTION

Logically Equivalent using Truth Table

Logically Equivalent without using Truth Table

Normal Forms(DNF,CNF,PDNF,PCNF)

Predicates And Quantifiers

Rule of inference

Proofs in Propositional Logic

Functions

Introduction

One TO One Functions

Onto Function or Surjection

Bijective

Identity Function

Inverse Function

Compostion of Function f&g

The Graphs of functions

Floor functions

Ceiling Functions

Relations

Introduction

Complement of a Relation

Inverse of Relation

Types of Relation

      Reflexive Relation
      Irreflexive Relation
      Symmetric Relation
      Anti Symmetric Relation
      Asymmetric Relation
      Transtive Relation

Closure of Relation

      Reflexive Closure
      Symmetric Closure
      Transtive Closure
        Transtive Closure Using Warshall's Algorithem

Equivalence Relation

      Equivalence Classes

Partial Ordering

      Hasse Diagram
Graph theory

Basic concepts

Bipartite Graph

Handshaking Theorem

representation of graph

      incidence matrix
      Adjacency Matrix

Graph isomorphism

Euler's Theorem

Hamiltonian Graph

Planar Graph

      Euler's formula
      Kuratowski's Theorem

Graph Coloring

      Chromatic Number

Shortest Path

      Dijkstra's Algorithm
Trees

Definition Of Tree

Rooted Tree

Terminology for Rooted Tree

Spaning Tree

      Depth-First Search
      Breadth-First Search

Minimum Spanning Tree

      Prim's Algorithm
      Kruskal's Algorithm

Tree Traversal

Traversal Algorithms

      Preorder Traversal
      Inorder Traversal
      Postorder Traversal

Infix, Prefix, and Postfix Notation

Applications Of Trees