Contents

1. Integers

1. Introduction

2. Division Algorithm

3. Euclid's Lemma

4. Equivalence Relation

2. Groups

1. Introduction

2. Binary Operation

3. Properties of Binary Operators

4. Groups

5. Elementary Properties of Group

3. Finite Groups and Subgroups

1. Introduction

2. Order of Group, Order of an element

3. Examples (Zn, +n)

4. Subgroup, Finite Subgroup Test

5. Cyclic Group, Generator, Finding Generator of Zn

6. Permutation Groups

7. COSETS and their Properties

8. Stabilizer of a Point

4. Groups and Coding Theory

1. Introduction

2. Coding of Binary Information and Error Detection

3. Decoding and Error Correction

4. Public Key Cryptography