Abstract Algebra: An Introduction with Applications

Derek J.S. Robinson

Published by De Gruyter 2022

Abstract Algebra

An Introduction with Applications

Derek J.S. Robinson

In the series De Gruyter Textbook

https://doi.org/10.1515/9783110691160

Overview
Contents

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 – 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.

Very gentle, user-friendly and skillful introduction, suitable for private study and exam preparation.

For students in mathematics and in various other fields of science.

Author / Editor information

Derek J.S. Robinson, University of Illinois, Urbana-Champaign, USA.

Reviews

"Altogether, this book represents a very gentle, user-friendly and skillful introduction to undergraduate abstract algebra for students in various fields of science. [...] a very experienced teacher has here presented a valuable introductory text on abstract algebra that can universally be used as a source for a one or two semester course on the subject for students in their second or third year of study: Without any doubt, this text is also very suitable for private study and exam preparation of undergraduates." Werner Kleinert in: Zentralblatt MATH 2003/10

***

"Robinson's textbook Abstract Algebra: an introduction with applications is an abstract algebra textbook written for advanced undergraduates and beginning graduate students. The book covers all of the standard topics that one expects such a book to cover (groups, rings, modules, tensor products, fields, Galois theory), as well as a number of interesting applications (the Polya enumeration theorem, latin squares, error correcting codes, as well as an interesting and far less standard application to algebraic models of accounting systems)." Benjamin Linowitz in: MAA, https://www.maa.org/press/maa-reviews/abstract-algebra-an-introduction-with-applications-0 (03.06.2022)

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	IX
List of symbols Publicly Available Download PDF	XIII
1 Sets, Relations and Functions Requires Authentication Unlicensed Licensed Download PDF	1
2 The Integers Requires Authentication Unlicensed Licensed Download PDF	20
3 Introduction to Groups Requires Authentication Unlicensed Licensed Download PDF	35
4 Quotient groups and Homomorphisms Requires Authentication Unlicensed Licensed Download PDF	58
5 Groups Acting on Sets Requires Authentication Unlicensed Licensed Download PDF	86
6 Introduction to rings Requires Authentication Unlicensed Licensed Download PDF	102
7 Division in Commutative Rings Requires Authentication Unlicensed Licensed Download PDF	125
8 Vector Spaces Requires Authentication Unlicensed Licensed Download PDF	144
9 Introduction to Modules Requires Authentication Unlicensed Licensed Download PDF	180
10 The Structure of Groups Requires Authentication Unlicensed Licensed Download PDF	220
11 The Theory of Fields Requires Authentication Unlicensed Licensed Download PDF	243
12 Galois Theory Requires Authentication Unlicensed Licensed Download PDF	261
13 Tensor Products Requires Authentication Unlicensed Licensed Download PDF	292
14 Representations of groups Requires Authentication Unlicensed Licensed Download PDF	309
15 Presentations of groups Requires Authentication Unlicensed Licensed Download PDF	332
16 Introduction to category theory Requires Authentication Unlicensed Licensed Download PDF	354
17 Applications Requires Authentication Unlicensed Licensed Download PDF	380
Bibliography Requires Authentication Unlicensed Licensed Download PDF	429
Index Requires Authentication Unlicensed Licensed Download PDF	431

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 3rd, extended edition
Audience: Students and lecturers in Mathematics, Information and Physical sciences; Academic libraries.
Pages
- Front matter: 16
- Main content: 440
Keywords: Algebra; Gruppentheorie; Angewandte Mathematik

eBook

Published: February 7, 2022
ISBN: 9783110691160

Paperback

Published: February 21, 2022
ISBN: 9783110686104