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Introduction to Abstract Algebra, by W. Keith Nicholson
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This Third Edition of the acclaimed self-study text lets you learn abstract algebra at your own pace
The Third Edition of Introduction to Abstract Algebra continues to provide an accessible introduction to the basic structures of abstract algebra: groups, rings, and fields.The text's unique approach 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.
As in the previous editions, the Third Edition offers many special features to help readers learn and apply their developing knowledge of abstract algebra:
- Historical notes and biographies of mathematicians provide context and perspective
- Some 500 worked examples help readers understand key concepts and their applications
- Almost 1,500 computational and theoretical exercises ranging from basic to complex challenge readers to apply their knowledge to solve problems. Many answers are provided in the text
- Applications to real-world problems in such areas as coding theory and combinatorics help readers grasp the topic's relevancy
- Special topics such as symmetric polynomials, nilpotent groups, semidirect products of groups, and the Wedderburn-Artin theorem for rings are included for more advanced study
This Third Edition includes thoroughly revised chapters and much new material, including new sections covering free, semisimple, and projective modules; modules over principal ideal domains; as well as semidirect products and the Wedderburn-Artin theorem. Two new appendices have been added on Zorn's lemma and the proof of the recursion theorem.
Numerous worked examples, exercises, and real-world applications make this text perfect for upper-level undergraduate and graduate courses. Moreover, with this book's self-contained chapters, students can learn at their own pace, and instructors can adapt the text to meet a variety of course objectives.
- Sales Rank: #2173740 in Books
- Published on: 2006-11-28
- Original language: English
- Number of items: 1
- Dimensions: 10.02" h x 1.23" w x 7.26" l, 2.37 pounds
- Binding: Hardcover
- 534 pages
Review
"For those seeking a sound introduction to abstract algebra, or a handbook on the basic ideas, this third edition of Nicholson's book is highly recommended." (MAA Reviews, April 13, 2007)
"…an expository masterpiece of highest didactic value which has gained additional attractivity through the various improvements…(ZentralblattMATH, 1107,1)
From the Back Cover
This Third Edition of the acclaimed self-study text lets you learn abstract algebra at your own pace
The Third Edition of Introduction to Abstract Algebra continues to provide an accessible introduction to the basic structures of abstract algebra: groups, rings, and fields.The text's unique approach 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.
As in the previous editions, the Third Edition offers many special features to help readers learn and apply their developing knowledge of abstract algebra:
- Historical notes and biographies of mathematicians provide context and perspective
- Some 500 worked examples help readers understand key concepts and their applications
- Almost 1,500 computational and theoretical exercises ranging from basic to complex challenge readers to apply their knowledge to solve problems. Many answers are provided in the text
- Applications to real-world problems in such areas as coding theory and combinatorics help readers grasp the topic's relevancy
- Special topics such as symmetric polynomials, nilpotent groups, semidirect products of groups, and the Wedderburn-Artin theorem for rings are included for more advanced study
This Third Edition includes thoroughly revised chapters and much new material, including new sections covering free, semisimple, and projective modules; modules over principal ideal domains; as well as semidirect products and the Wedderburn-Artin theorem. Two new appendices have been added on Zorn's lemma and the proof of the recursion theorem.
Numerous worked examples, exercises, and real-world applications make this text perfect for upper-level undergraduate and graduate courses. Moreover, with this book's self-contained chapters, students can learn at their own pace, and instructors can adapt the text to meet a variety of course objectives.
About the Author
W. KEITH NICHOLSON, PhD, is a Professor in the Department of Mathematics and Statistics at the University of Calgary in Alberta, Canada. Dr. Nicholson has published numerous textbooks and monographs throughout his career. He received his PhD in Pure Mathematics from the University of California at Santa Barbara, and his current research interests include clean rings, morphic rings, and module theory.
Most helpful customer reviews
0 of 2 people found the following review helpful.
Five Stars
By Jeff
Mensa
18 of 18 people found the following review helpful.
Very good introductory text
By A Customer
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.
3 of 4 people found the following review helpful.
Hard to read
By Andres Ramon
As a new student that is new to proofs and Abstract algebra, I found this book hard to read and hard to follow. The language itself is very difficult and spares a lot of words.
Granted, if you are somewhat familiar with abstract algebra and the terminology the book might not be as difficult. However, I had to buy two other books in order to understand the material.
Although it's loaded with information and even covers the basic information, my other books expressed it in clearer language and walked me thorough the beginning proofs, much better than this book did.
If you are brand new to the subject, I don't recommend using this book.
In addition the glue/binding in the middle of the book starts to tear, so groups of pages will become lose if you are not careful. It happened to my book, as well as the books of my class mates even though we bought it from different sources.
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