Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics.
Author(s): Peter J. Cameron
Edition: 2
Publisher: Oxford University Press, USA
Year: 2008
Language: English
Commentary: 68766
Pages: 353
Contents......Page 10
What is mathematics?......Page 12
Numbers......Page 21
Elementary algebra......Page 34
Sets......Page 43
Modular Arithmetic......Page 59
Matrices......Page 63
Appendix: Logic......Page 69
Rings and subrings......Page 74
Homomorphisms and ideals......Page 85
Factorisation......Page 98
Fields......Page 110
Appendix: Miscellany......Page 114
Groups and subgroups......Page 121
Subgroups and cosets......Page 130
Homomorphisms and normal subgroups......Page 135
Some special groups......Page 143
Appendix: How many groups?......Page 158
Vector spaces and subspaces......Page 161
Linear transformations and matrices......Page 172
Introduction......Page 193
Modules over a Euclidean domain......Page 201
Applications......Page 207
6. The number systems......Page 220
To the complex numbers......Page 221
Algebraic and transcendental numbers......Page 231
More about sets......Page 241
Further group theory......Page 248
Further ring theory......Page 267
Further field theory......Page 279
Other structures......Page 289
Coding theory......Page 310
Galois Theory......Page 328
Further reading......Page 345
C......Page 348
F......Page 349
L......Page 350
P......Page 351
V......Page 352
Z......Page 353
