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Algebra and Geometry (Term I)

BI 861

New

Algebra and Geometry

Includes: Sets, Function, The Integers, Complex Number, Polynomials

According to New Revised Syllabus w.e.f. 2008 PUNE, Maharashtra (INDIA)

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Contents

1. Sets

1.1 Introduction

1.2 Power set of a set

1.3 Product of sets

1.4 Relations

1.5 Equivalence relation

1.6 Equivalence classes and partitions of a set

2. Function

2.1 Introduction

2.2 Function

2.3 Composition (Or Product) of two functions

2.4 Inverse of a function

2.5 Binary operations

3. The Integers

3.1 Introduction

3.2 Divisibility

3.3 Division algorithm

3.4 Greatest common divisor (G.C.D)

3.5 Least common multiple (L.C.M.)

3.6 Primes

3.7 Congruences

4. Complex Number

4.1 Introduction

4.2 Algebra of complex numbers

4.3 Some definitions

4.4 Geometric representation of complex numbers

4.5 Properties of modulus and argument

4.6 Geometric representation of the addition, subtraction, product and quotient

4.7 De moivre’s theorem

4.8 Power and roots of a complex number

5. Polynomials

5.1 Introduction

5.2 Polynomial

5.3 Algebra of polynomials

5.4 The remainder and factor theorems

5.5 Divisibility in the set Q [x]

5.6 Common divisors

5.7 Roots of a polynomial

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