An Introduction to Abstract Algebra

AnIntroductiontoAbstract
Algebra
C.K.Taylor

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C.K. Taylor

An Introduction to Abstract Algebra

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An Introduction to Abstract Algebra
First edition
© 2013 C.K. Taylor & bookboon.com (Ventus Publishing ApS)
ISBN 978-87-403-0367-4

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An Introduction to Abstract Algebra

Contents

Contents
1

Preliminaries

7

1.1

Introduction to Abstract Algebra

7

1.2

Logic and Proof

11

1.3

Set heory

20

1.4

Mappings and Equivalence Relations

26

2

Group heory

36

2.1

Binary Operations

36

2.2

Introduction to Groups

39

2.3

Cyclic Groups

48

2.4

Dihedral Groups

51

2.5

Groups of Permutations

54

2.6

Alternating Groups

59

2.7

Subgroups

65

2.8

Homomorphisms and Isomorphisms

72

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An Introduction to Abstract Algebra

Contents

2.9

Cosets and Normal Subgroups

79

2.10

Quotient Groups

85

2.11

Direct Products

91

2.12

Catalog of Finite Groups

99

3

Field heory

103

3.1

Introduction to Fields

103

3.2

Polynomials

107

3.3

Irreduciblity

113

3.4

Vector Spaces

118

3.5

Extension Fields

122

3.6

Algebraic Extensions

125

3.7

Geometric Constructions

131

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