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Richa Nandra, Lovely Professional University Unit 1: Generating Sets

Unit 1: Generating Sets Notes

CONTENTS
Objectives

Introduction
1.1 Sets
1.2 Cartesian Product
1.3 Relations
1.4 Functions

1.4.1 Composition of Functions
1.5 Some Number Theory
1.5.1 Principle of Induction

1.5.2 Divisibility in Z
1.6 Summary
1.7 Keywords
1.8 Review Questions
1.9 Further Readings

Objectives

After studying this unit, you will be able to:
Explain the operations on sets

Define Cartesian products of sets

Describe the equivalence classes

Define different kinds of functions

Explain the division algorithm and unique prime factorisation theorem

Introduction

In this unit, we will discuss some basic ideas concerning sets and functions. These concepts are
elementary to the study of any branch of mathematics, in particular of algebra. In the unit, we
discuss some basic number theory. The primary aim of this section is to assemble a few facts that
will be required in the rest of the course. We also hope to give you a glimpse of the elegance of
number theory. It is this sophistication that led the mathematician Gauss to call number theory
the "queen of mathematics". Let us start explaining these concepts one-by-one.

LOVELY PROFESSIONAL UNIVERSITY 1