Introduction to Abstract Algebra

by Jonathan D. H. Smith

Overview

Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups.This new edition of a widely adopted textbook covers

Product Details

ISBN-13:	9781498731812
Publisher:	CRC Press
Publication date:	10/23/2015
Series:	Textbooks in Mathematics , #31
Sold by:	Barnes & Noble
Format:	eBook
Pages:	352
File size:	5 MB

About the Author

Jonathan Smith is a Professor at Iowa State University. He earned his Ph.D., from Cambridge (England). His research focuses on combinatorics, algebra, and information theory; applications in computer science, physics, and biology.

Table of Contents

Numbers. Functions. Equivalence. Groups And Monoids. Homomorphisms. Rings. Fields. Factorization. Modules. Group Actions. Quasigroups.

What People are Saying About This

From the Publisher

… The author goes the extra mile to build algebraic concepts by confronting the pedagogic and logical sequence groups-first or rings-first dilemma … a perfect pure math precursor to Grillet and Knapp’s works. … The book’s well-thought out sequence supports a set of useful statements on how to use its 11 chapters in a course … The book is also outstanding for self-study. … I recommend this book as second to none on abstract algebra for its content, style, and expository efficiency.
—Computing Reviews, January 2011

… a careful treatment of the principal topics of abstract algebra … This is an attractive book which could be read by everybody because the author supposes not so much knowledge from the reader and gives all the necessary information to continue the reading from [one] chapter to the next. The approach used by the author to introduce modules and group actions is new and innovative. The book is well written … students and even experienced researchers may benefit strongly from this book. …
—IACR Book Reviews, October 2010

… This compact book covers topics one would expect to find in an abstract algebra text. … Smith’s approach is carefully implemented, and topics flow logically from one chapter to the next. The writing is careful and rigorous, yet accessible to hardworking students. The problems are collected at the end of each chapter in two sets, with one set made up of shorter exercises. … This is an ideal text for an abstract algebra course comprised of mathematics students or CS students who have either a strong minor or second major in mathematics. …
—Computing Reviews, December 2009

One can trace the author’s research interests to the border between algebra and category theory, which gives the textbook its unique flavour.
—EMS Newsletter, March 2009

The book is well written and flows well. Readers looking for an alternative approach to abstract algebra should consider this volume.
—J.R. Burke, Gonzaga University, CHOICE, July 2009, Vol. 46, No. 11

This book is well written, interesting to read, and the proofs and examples are clear and clean.
—David F. Anderson, Mathematical Reviews, 2009e

Editorial Reviews

"A complete course of instruction under one cover, Introduction to Abstract Algebra is a standard text that should be a part of every community and academic library mathematics reference collection in general, and algebraic studies supplemental reading in particular."
—Reviewer’s Bookwatch, December 2015

Smith’s update to the first edition (CH, Jul'09, 46-6260) is an alternative approach to the usual first semester in higher algebra. The author accomplishes this by including many topics often absent from a first course, such as quasigroups, Noetherian domains, and modules, which, theoretically, are developed alongside their mainstream analogues, like groups, rings, and vector spaces. It is essentially a first semester wink at universal algebra. Smith’s approach to axiomatic systems is few-too-many—he starts with structures with very few axioms, like semigroups and monoids, and continues adding axioms. He finishes with more complex axiomatic systems, like unique factorization domains and fields. The book is very well written and easy to read, flowing naturally from one topic to the next. Numerous supportive homework exercises are also included to help the reader explore further topics. This book will best serve readers with a background in abstract algebra who desire to strengthen their understanding and build bridges between various topics. Unfortunately, because many similar topics are handled in tandem, an inexperienced reader might become confused, especially as many clarifying examples are missing. This book is for readers who want an under the hood view of algebra.
—A. Misseldine, Southern Utah University 2015

From the Publisher