Contents

1. Modular Arithmetic

1. Introduction

2. Relations   

3. Congruence  

4. Applications

5. Fermat’s Little Theorem

6. Congruence and Groups

2. Two Principles of Counting

1. Introduction

2. The Pigeonhole Principle

3. Graph Theory

1. Introduction

2. Graph  

3. Special Types of Graphs

4. Connected Graphs 

5. The Konigsberg Seven Bridge Problem    

6. Isomorphism of Graphs

7. Trees  

8. Applications

9. Coloring Problems

10.Planar Graphs

4. Recurrence Relations   

1. Introduction

2. Recurrence Relation    

3. General Linear Recurrences  

4. Other Classical Recurrences 

5. Generating Functions