A First Course in Abstract Algebra
Rings, Groups, and Fields, Third Edition
3rd Edition
Published on 7. November 2014
Book
Hardback
556 pages
978-1-4822-4552-3 (ISBN)
Description
Like its popular predecessors, A First Course in Abstract Algebra: Rings, Groups, and Fields, Third Edition develops ring theory first by drawing on students' 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, warm-up exercises following the chapter that test fundamental comprehension, and regular exercises concluding the chapter that consist of computational and supply-the-proof problems. Historical remarks discuss the history of algebra to underscore certain pedagogical points. Each section also provides a synopsis that presents important definitions and theorems, allowing students to verify the major topics from the section.
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, warm-up exercises following the chapter that test fundamental comprehension, and regular exercises concluding the chapter that consist of computational and supply-the-proof problems. Historical remarks discuss the history of algebra to underscore certain pedagogical points. Each section also provides a synopsis that presents important definitions and theorems, allowing students to verify the major topics from the section.
Reviews / Votes
"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
More details
Edition
3rd edition
Language
English
Place of publication
Boca Raton
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Illustrations
40 s/w Abbildungen
40 Illustrations, black and white
Dimensions
Height: 260 mm
Width: 183 mm
Thickness: 34 mm
Weight
1228 gr
ISBN-13
978-1-4822-4552-3 (9781482245523)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Marlow Anderson | Todd Feil
A First Course in Abstract Algebra
Rings, Groups, and Fields, Third Edition
E-Book
11/2014
3rd Edition
Chapman & Hall/CRC
€125.99
Available for download
Marlow Anderson | Todd Feil
A First Course in Abstract Algebra
Rings, Groups, and Fields, Third Edition
E-Book
11/2014
3rd Edition
Chapman and Hall
€125.99
Available for download
Previous edition
Marlow Anderson | Todd Feil
A First Course in Abstract Algebra
Rings, Groups and Fields, Second Edition
Book
01/2005
2nd Edition
CRC Press
€69.51
Article exhausted; check for reprint
Persons
Marlow Anderson, Todd Feil
Content
Numbers, 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.