Undergraduate Algebra : A First Course

Cover

S Title

Undergraduate Algebra: A First Course

Copyright
© 1986 by C. W. Norman
ISBN 0-19-853249-0
ISBN 0-19-853248-2 Pbk
QA 154.2. N65 1986 512
LCCN 85-31057

Dedicated To Lucy, Tessa, and Timmy

Preface

Contents

Notation

1 Preliminary concepts
Sets
Exercises 1.1
Mappings
Exercises 1.2
Equivalence relations
Exercises 1.3

Part I Rings and fields


2 Rings; fields; and complex numbers
Exercises 2.1
The complex field
Exercises 2.2
Geometric properties of C
Exercises 2.3

3 Integers
Order properties
Exercises 3.1
Division properties
Exercises 3.2
Congruence properties
Exercises 3.3

4 Polynomials
Polynomial rings
Exercises 4.1
Factorization of polynomials
Zeros of polynomials
Exercises 4.2

5 Ring theory*
Exercises 5.1
Constructions
Exercises 5.2

Part II: Linear algebra

6 Vector spaces
Elementary properties of vector spaces
Exercises 6.1
Bases and dimension
Exercises 6.2
Complementary subspaces
Exercises 6.3

7 Matrices and linear mappings
Matrices
Exercises 7.1
Linear mappings
Exercises 7.2
Representation of linear mappings*
Exercises 7.3

8 Rank and row-equivalence
Rank
Exercises 8.1
Row-equivalence
Exercises 8.2
Row-reduction and inversion
Exercises 8.3
Equivalence of matrices
Exercises 8.4

9 Groups and determinants
Groups
Exercises 9.1
Subgroups and cosets
Exercises 9.2
Determinants
Exercises 9.3
Multiplicative properties of determinants
Exercises 9.4

10 Diagonalization and duality
Diagonalization
Exercises 10.1
Diagonalization (continued) and the characteristic polynomial
Exercises 10.2
Duality
Exercises 10.3
Bilinear forms
Exercises 10.4

11 Euclidean and unitary spaces
Euclidean spaces
Exercises 11.1
Unitary spaces
Exercises 11.2
Isometries and volume
Exercises 11.3

Further reading

Index