Elementary Number Theory in Nine Chapters [Paperback]

James J. Tattersall (Author)

Book Description

ISBN-10: 0521585317 | ISBN-13: 978-0521585316 | Publication Date: October 28, 1999

This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.

Editorial Reviews

Review

"In contrast to far too many mathematics books, this book has lots of text surrounding all the mathematical formulas. It's all a very rich mix, and I suspect students would enjoy using this book; I also suspect they would find it quite challenging. Tattersall's Nine Chapters came out just a week or so late for me to select it for my Number Theory course this spring. Next time around, it'll be high on the list of possible textbooks for the course." MAA Online "An appropriate addition to a number theory collection." Choice "Written in a rousing style...many exercises--I counted 891--and many of them are rather ingenious!" Monatshefte fur Mathematik "Written in a rousing style...many exercises--I counted 891--and many of them are rather ingenious!" Monatshefte fur Mathematik

Book Description

This book is intended to serve as a one-semester introductory course in number theory and it includes a wealth of exercises. A historical perspective has been adopted and emphasis is given to some of the subject's applied aspects. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.

See all Editorial Reviews

Product Details

• Paperback: 416 pages
• Publisher: Cambridge University Press (October 28, 1999)
• Language: English
• ISBN-10: 0521585317
• ISBN-13: 978-0521585316
• Product Dimensions: 9 x 6 x 0.9 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #554,096 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

15 of 15 people found the following review helpful:

5.0 out of 5 stars Excellent and Entertaining Textbook, December 21, 2002

By 

JLP (Schaumburg, IL USA) - See all my reviews

This review is from: Elementary Number Theory in Nine Chapters (Paperback)

For its freshness and originality of exposition and material, I give this book 5 stars despite some minor weaknesses noted below.

The book covers classical material in an unconventional manner; for example, it adopts the historical approach, begins with polygonal numbers and number sequences, and contains much recreational material, aside from the "serious" classical results. It also treats some applied aspects of number theory such as public-key cryptography. There is an abundance of problems, ranging from easy and computional to challenging. Solutions are provided.

Some strengths of the book are:
1. Strong continuity of topics and motivation behind the ideas and theorems.
2. Extensive coverage of recreational and "fun" number theory, and computer developments.
3. Historical approach: the book begins with the earliest number theory, that is, polygonal numbers and prime numbers; it has a lot of historical references and anecdotes, and gives some credits to the contributions of China, Iran, etc.
4. Many numerical examples and some neat algorithms, for example, Sanderson's algorithm to express the gcd of two numbers as a linear combination of these numbers, and heuristic methods for Diophantine equations and the Chinese Remainder Theorem.
5. Very clear and entertaining introduction to cryptology and its history.

Some weaknesses of the book are:
1. There are a considerable number of minor typographical errors, but nothing you can't correct yourself.
2. A little long (about 400 pages)--I prefer more conciseness in a textbook--but then it has a lot of history in it....

Overall, this is a very good number theory textbook for classroom use or self-study.

12 of 13 people found the following review helpful:

4.0 out of 5 stars Who knew math could be such a roller-coaster ride?, March 21, 1999

By 

Brendan LeFebvre - See all my reviews

This review is from: Elementary Number Theory in Nine Chapters (Paperback)

I took Dr. Tattersall's number theory class in the fall of 1998, for which we used a bound draft of this text. Its composition matches his frenetic and exhilarating lecture style, both in the presentation of the material and the frequent side-trips into math history. If you are math-mad, it's worth buying for fun, and if you must buy it for a class, it's worth hanging onto after that last exam. Good stuff!

6 of 7 people found the following review helpful:

5.0 out of 5 stars A Personal Accomplishment, February 16, 2001

By 

Matthew R Carreiro (Westport, MA USA) - See all my reviews

This review is from: Elementary Number Theory in Nine Chapters (Hardcover)

Never has a course of study gotten me so interested in mathematics as this course by Dr. Tattersall. This particual book has given me incredible insight into the fascinating world of numbers and has enabled me to think about mathematics as both a historical progression and a personal endeavor. It envolopes the student and holds on right through the semester.

PS. If there were any mistakes in the table of prime numbers don't come looking for me!