Concrete Abstract Algebra: From Numbers to Groebner Bases | 
 enlarge | Author: Niels Lauritzen
Publisher: Cambridge University Press
Category: Book
List Price: $50.00
Buy New: $29.95
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Rating:  1 reviews
Sales Rank: 203329
Media: Paperback
Pages: 254
Number Of Items: 1
Shipping Weight (lbs): 0.9
Dimensions (in): 9.4 x 5.4 x 0.5
ISBN: 0521534100
Dewey Decimal Number: 512.02
EAN: 9780521534109
Publication Date: October 20, 2003
Availability: Usually ships in 1-2 business days
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Product 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.
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.
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| Customer Reviews:
Very suitable textbook for courses in abstract algebra March 20, 2007
Charles Ashbacher (Marion, Iowa United States(cashbacher@yahoo.com))
5 out of 5 found this review helpful
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.
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