An Introduction to Number Theory 1st MIT Press paperback ed Edition

by Harold M. Stark (Author)

4 customer reviews

ISBN-13: 978-0262690607

ISBN-10: 0262690608

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The majority of students who take courses in number theory are mathematics majors who will not become number theorists. Many of them will, however, teach mathematics at the high school or junior college level, and this book is intended for those students learning to teach, in addition to a careful presentation of the standard material usually taught in a first course in elementary number theory, this book includes a chapter on quadratic fields which the author has designed to make students think about some of the "obvious" concepts they have taken for granted earlier. The book also includes a large number of exercises, many of which are nonstandard.

An Introduction to Number Theory

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Product Details

Paperback: 360 pages
Publisher: The MIT Press; 1st MIT Press paperback ed edition (May 30, 1978)
Language: English
ISBN-10: 0262690608
ISBN-13: 978-0262690607
Product Dimensions: 6 x 0.8 x 9 inches
Shipping Weight: 1.3 pounds (View shipping rates and policies)
Average Customer Review: 3.8 out of 5 stars See all reviews (4 customer reviews)
Amazon Best Sellers Rank: #1,094,295 in Books (See Top 100 in Books)
- #362 in Books > Science & Math > Mathematics > Pure Mathematics > Number Theory
- #8320 in Books > Textbooks > Science & Mathematics > Mathematics

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Customer Reviews

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23 of 23 people found the following review helpful

A wonderful insight into number theory

By Sammy Choi on May 12, 2000

Format: Paperback

In general, this book gives a comprehensive account on elementary number theory. The first few chapters include some fundamental concepts like divisibility and congruences (i.e. a simple kind of modular arithmetic), as well as famous yet basic theorems like the fundamental theorem of arithmetic. Important topics in number theory such as Diophantine equations, fractional approximations for irrational numbers and Quadratic fields are there, and if you're interested in magic squares, I'd like to say that a whole chapter is devoted to it.
There're some good points featuring this book. It assumes no prerequisite in number theory. Just a bit knowledge about numbers and operations on them are needed. Results and theorems are closely related, allowing you to observe how things are connected. Although not many examples are available, some are really instructive and helpful enough to avoid misconceptions.
However, it's a pity to say that the materials contained are not really well-organized, especially those in Chapter 7: the geometric arguments used in the development of the continued fraction algorithm lack concision, and a few proofs are quite annoying because the author failed to justify some claims that shuold not be treated as something "obvious". It can be motivating just to provide readers guidelines about how to work out those minor stuff, but such things shouldn't have been misleadingly called "proofs". Another problem is that the illustratons presented are occasionally insufficient, and this is particularly the case in the chapter about Diophantine equations. Novices in the subject can hardly rely on the text to solve harder exercises contained without tracing out more technique which is not emphasized.
Overall, the book deserves to be a fine reading for the interested ones new to number theory. But if you're serious about the topic, find an even better book instead.

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4 of 4 people found the following review helpful

Perhaps biased

By K. Frye on May 17, 2009

Format: Paperback

This book was the required text for an independent study class I enrolled in. The class has been more difficult than I thought it would be, as has the text. It is complex material and doesn't provide a lot of clear-cut examples - instead assuming that you make the connection yourself. However, I am learning all on my own and the material may be more understandable with the help of a live professor.

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Excellent introduction to number theory.

By Anon on May 23, 2015

Format: Paperback

I used this book for an undergraduate course on number theory at Stanford. It starts off how you would expect it to with sections on the Euclidean algorithm, linear diophantine equations, Euler's totient function, congruences and primitive roots. It seemed pretty conventional but then it got interesting with the chapter on magic squares, which is pretty cool. I remember being asked to construct a 9-by-9 filled, magic square using integers from 0 to 80 with the property that when divided into ninths, each 3-by-3 subsquare is also magic. While you are most likely to encounter exercises at the beginning of the book that deal with topics such as Fermat's little theorem and perhaps proving that a number like 1729 is a pseudoprime or verifying that there are infinitely many primes of the form 4n-1 and 4n+1, there are some unique problems in this book that explore topics like the sieve of Eratosthenes and continued fractions. I find this book incorporates a lot of neat topics like this and the later chapters on quadratic fields prove to be a good insight into algebraic number theory.

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1 of 2 people found the following review helpful

Old but still good

By Russell Taylor on April 15, 2014

Format: Paperback Verified Purchase

If numbers are over your head, you might not enjoy this book... But, if you want to take your good math skills and make them better, a good study of number theory will do it and this book is a good way to get moving down that path... Now, it is a bit dated, being almost as old as I am... Some of the discussion of work done in the field may be out of date... but the internet can help you check those facts... Otherwise, numbers haven't changed since Adam (1) & Eve (1) = Couple (2)... Did Adam understand number theory... I don't know, but if he had this book, he certainly would have...

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