Description
Book SynopsisLike its popular predecessors, A First Course in Abstract Algebra: Rings, Groups, and Fields, Third Edition develops ring theory first by drawing on studentsâ familiarity with integers and polynomials. This unique approach motivates students in the study of abstract algebra and helps them understand the power of abstraction. The authors introduce groups later on using examples of symmetries of figures in the plane and space as well as permutations.
New to the Third Edition
- Makes it easier to teach unique factorization as an optional topic
- Reorganizes the core material on rings, integral domains, and fields
- Includes a more detailed treatment of permutations
- Introduces more topics in group theory, including new chapters on Sylow theorems
- Provides many new exercises on Galois theory
The text includes straightforward exercises within each chapter for students to quickly verify facts, wa
Trade Review
"I am a fan of the rings-first approach to algebra, agreeing with the authors that students’ familiarity with the integers and with polynomials renders rings more intuitive and accessible than groups. But this book has many other virtues besides presenting the material in this order. For example, each section is preceded and followed by short sections that try to put the material into a broader context. … This is definitely a book worth considering for textbook adoption."
—MAA Reviews, November 2014
Praise for the Second Edition:"I was quickly won over by the book … . The book is very complete, containing more than enough material for a two semester course in undergraduate abstract algebra … . Even though there was a great deal of material presented, I found the book to be very well organized. … There are a lot of things that I like about this book. … [It is] well written and will help students to see the big picture. … All in all it seems that a lot of thought went into this book, resulting in a comprehensive, well-written, readable book for undergraduates first learning abstract algebra."
—MAA Online
"A remarkable feature of the book is that it starts first with the concept of a ring, while groups are introduced later. The reason of that is that students are usually more familiar with various number domains rather than the mappings and matrices. There is a huge number of examples in the book … . The book contains a lot of nice exercises of various degrees of difficulty so that it can also be used as a practice book."
—EMS Newsletter, March 2006
Table of ContentsNumbers, Polynomials, and Factoring. Rings, Domains, and Fields. Ring Homomorphisms and Ideals. Groups. Group Homomorphisms. Topics from Group Theory. Unique Factorization. Constructibility Problems. Vector Spaces and Field Extensions. Galois Theory. Hints and Solutions. Guide to Notation. Index.
