Contents

1. Numbers, Sets and Functions
1. Introduction
2. The Quadratic Formula
3. Elementary Inequalities
4. Sets
5. Set Operations
6. Functions
2. Logic
1. INTRODUCTION
2. Propositional Logic
3. Propositional Equivalences
4. Predicates and Quantifiers
5. Rules of Inference
3. Lattices and Boolean Algebra
1. Poset (Partially Ordered Set)
2. Lattices
3. Boolean Functions
4. Duality
5. Representing Boolean Function
4. Counting Principles
1. Introduction
2. Cardinality of Set
3. Cartesian Product of Sets
4. Basics of Counting
5. The Pigeonhole Principle
6. Generalized Permutations and Combinations
5. Recurrence Relations
1. Introduction
2. Recurrence Relation
3. Linear Recurrence Relations with Constant Coefficients
4. Homogeneous Solutions
5. Particular Solutions
6. Total Solutions
6. Graphs
1. Introduction
2. Graph
3. Special Types of Graphs
4. Isomorphism of Graphs
5. Adjacency and Incidence Matrix of a Graph
7. Operations on Graphs
1. Introduction
2. Subgraphs
3. Induced Subgraphs
4. Complement of a Graph
5. Self Complementary Graph
6. Union, Intersection and Product of Graphs
7. Fusion of Vertices
8. Connected Graphs
1. Introduction

2. Walk, Trail, Path Cycle in Graph
3. Connected Graphs
4. Some Definitions in Connected Graph
5. Isthmus and Cut Vertex
6. Connectivity
7. Weighted Graph and Dijkstra’s Algorithm
9. Eulerian and Hamiltonian Graphs
1. The Konigsberg Seven Bridge Problem
2. Fleury’s Algorithm
3. Hamiltonian Graphs
10. Trees
1. Definitions and Simple Properties
2. Centre of a Tree
3. Binary Tree
4. Tree Traversal
5. Spanning Tree
11. Directed Graphs
1. Introduction
2. Directed Graph
3. Special Types of Digraphs
4. Connectedness of Digraphs
5. Network and Flows