Introduction to Abstract Algebra

By W. Keith Nicholson

Book Overview

Praise for the Third Edition

". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."--Zentralblatt MATH

The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text.

The Fourth Edition features important concepts as well as specialized topics, including:

The treatment of nilpotent groups, including the Frattini and Fitting subgroups

Symmetric polynomials

The proof of the fundamental theorem of algebra using symmetric polynomials

The proof of Wedderburn's theorem on finite division rings

The proof of the Wedderburn-Artin theorem

Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises.

Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.

• Format: Hardcover
• Language: English
• ISBN: 1118135350
• ISBN13: 9781118135358
• Release Date: March 2012
• Publisher: Wiley
• Length: 560 Pages
• Weight: 2.50 lbs.
• Dimensions: 1.3" x 7.1" x 10.1"

Customer Reviews

Very good introductory text

The first time I took Abstract Algebra. I used Herstein's text the most cryptic text I have yet to use. I read the book cover to cover several times and still lacked a firm grasp on the material. Nicholson's book takes the time to present many examples and to thoroughly cover each topic. The examples of groups most frequently discussed are all placed at the beginning allowing the reader to have many examples to go on. While the book is not a terse reference it is a great introduction to the world of abstract algebra. It gives the undergraduate a chance to make that large step to this higher level of abstraction. However, the exercises are a little easy and the counterside to the above is that it is quite long.