Abstract Algebra: An Introduction with Applications (De Gruyter Textbook)

✍ Scribed by Robinson, Derek J.S.

• Publisher: De Gruyter
• Year: 2022
• Tongue: English
• Leaves: 456
• Edition: 3
• Category: Library

✦ Synopsis

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 – groups, rings, modules and fields – 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.

✦ Table of Contents

Preface
Contents
List of symbols
1 Sets, Relations and Functions
2 The Integers
3 Introduction to Groups
4 Quotient groups and Homomorphisms
5 Groups Acting on Sets
6 Introduction to rings
7 Division in Commutative Rings
8 Vector Spaces
9 Introduction to Modules
10 The Structure of Groups
11 The Theory of Fields
12 Galois Theory
13 Tensor Products
14 Representations of groups
15 Presentations of groups
16 Introduction to category theory
17 Applications
Bibliography
Index