Elements of Number Theory | 
 enlarge | Author: John Stillwell
Publisher: Springer
Category: Book
List Price: $54.95
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Rating:  2 reviews
Sales Rank: 815010
Media: Hardcover
Edition: 1
Pages: 254
Number Of Items: 1
Shipping Weight (lbs): 1.1
Dimensions (in): 9.3 x 6 x 0.7
ISBN: 0387955879
Dewey Decimal Number: 512.7
EAN: 9780387955872
Publication Date: December 13, 2002
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Product Description
This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals. The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting. These include some that have not yet appeared in textbooks, such as a treatment of the Pell equation using Conway's theory of quadratic forms. Also, this is the only elementary number theory book that includes significant applications of ideal theory. It is clearly written, well illustrated, and supplied with carefully designed exercises, making it a pleasure to use as an undergraduate textbook or for independent study. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer-Verlag, including Mathematics and Its History (Second Edition 2001), Numbers and Geometry (1997) and Elements of Algebra (1994).
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| Customer Reviews:
Extremely well-motivated and clear introduction February 20, 2005
Viktor Blasjo
5 out of 5 found this review helpful
This is a very pleasant introduction to number theory. Each chapter is preceded by a preview and concluded by a discussion to make the main ideas clear and well-motivated and to show how things fit in the big picture by discussing the historical development. The book starts with the very basics and moves via some pearls like the four square theorem and quadratic reciprocity to a culmination with algebraic number theory. A readable and elementary introduction to algebraic number theory is especially valuable today because, as Stillwell argues in his preface, this is the proper setting in which to learn of rings and ideals. Nowadays, of course, the custom is to pull these concepts out of a hat in the mysterious context of "abstract algebra" where there is no apparent reason to introduce them whatsoever. Fortunately, Stillwell has provided us with an equally enjoyable book on algebra, so now we can only hope that some day the curricula will change accordingly.
Illuminating and down to earth July 30, 2004
Anthony K. Shaw (Plymouth Meeting, PA USA)
3 out of 3 found this review helpful
One of the best introductory books I've seen. It is concise, and yet very illuminating and down to earth, leading very nicely into the beginnings of algebraic number theory.
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