
- 456 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
About this book
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and the information and physical sciences. In addition to introducing the main concepts of modern algebra â groups, rings, modules and fields â the book contains numerous applications, which are intended to illustrate the concepts and to show the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems, error correcting codes and economics are described. There is ample material here for a two semester course in abstract algebra. Proofs of almost all results are given. The reader led through the proofs in gentle stages. There are more than 500 problems, of varying degrees of diffi culty. The book should be suitable for advanced undergraduate students in their fi nal year of study and for fi rst or second year graduate students at a university in Europe or North America. In this third edition three new chapters have been added: an introduction to the representation theory of fi nite groups, free groups and presentations of groups, an introduction to category theory.
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Information
Table of contents
- Title Page
- Copyright
- Contents
- Preface
- 1âSets, Relations and Functions
- 2âThe Integers
- 3âIntroduction to Groups
- 4âQuotient groups and Homomorphisms
- 5âGroups Acting on Sets
- 6âIntroduction to rings
- 7âDivision in Commutative Rings
- 8âVector Spaces
- 9âIntroduction to Modules
- 10âThe Structure of Groups
- 11âThe Theory of Fields
- 12âGalois Theory
- 13âTensor Products
- 14âRepresentations of groups
- 15âPresentations of groups
- 16âIntroduction to category theory
- 17âApplications
- Index