Concrete Abstract Algebra: From Numbers to Gröbner Bases [Paperback]

Niels Lauritzen (Author)

Book Description

ISBN-10: 0521534100 | ISBN-13: 978-0521534109 | Publication Date: October 20, 2003

Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course. In addition, there is a rich supply of topics such as cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials, and systems of non-linear equations. A special feature is that Gr"obner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications, and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experienced teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly.

Editorial Reviews

Review

"Lauritzen does a great job of motivating the concepts covered. The title of the book seems to be contradictory, but after reading the book, you will really have the feeling that Lauritzen achieved his goal: to concretize the abstract without losing rigor and depth. The text is very readable, and the well-chosen exercises help the reader understand the material. I highly recommend this book as a text for teaching abstract algebra. If you are looking for a solid introduction to the topic of abstract algebra, this is the book for you." Computing Reviews

Book Description

Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course. In addition, there is a rich supply of topics such as cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials, and systems of non-linear equations. A special feature is that Gr"obner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications, and exercises. The basic philosophy is that inspiring, non-trivial applications, and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experienced teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly.

Product Details

• Paperback: 254 pages
• Publisher: Cambridge University Press (October 20, 2003)
• Language: English
• ISBN-10: 0521534100
• ISBN-13: 978-0521534109
• Product Dimensions: 9.4 x 5.4 x 0.5 inches
• Shipping Weight: 14.6 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #540,205 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

8 of 8 people found the following review helpful:

5.0 out of 5 stars Very suitable textbook for courses in abstract algebra, March 20, 2007

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Concrete Abstract Algebra: From Numbers to Gröbner Bases (Paperback)

The subject matter of a first course in abstract algebra is almost universally the same to all people. It begins with some fundamental background in number theory, relations, functions and a survey of notation. After this, it is groups, rings, fields in their various incarnations. Within these categories, the coverage is also generally the same, the pedagogical examples are well known and they are used in all books. Therefore, when making a choice concerning what book to adopt for a class, the decision is based largely on the clarity of the explanations and how one reacts to it on an emotional level.
The quality of the exposition in this book is excellent; it is easy to follow the explanations and proofs from start to finish. A large number, generally over 50, of exercises are included at the end of each chapter. If and when I teach abstract algebra again, this book will be given the most serious consideration for adoption.