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