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.
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"Stark has written a delightful leisurely account of elementary numbertheory with little or no ideal theoreticpremeditation, included an abundantsupply of great exercises, and endedwith an exciting chapter on quadraticnumber fields," K.F. Ireland, theAmerican Mathematical Society Monthly
"... this book will furnish the student,the teacher and the specialist alike withnew methods and new insights intonumber theory It is a welcome additionto the literature " A.L. Whitman , Reviews of the American MathematicalSociety
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Most Helpful Customer Reviews
19 of 19 people found the following review helpful:
4.0 out of 5 stars
A wonderful insight into number theory,
By Sammy Choi (Hong Kong) - See all my reviews
This review is from: An Introduction to Number Theory (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.
2 of 2 people found the following review helpful:
3.0 out of 5 stars
Perhaps biased,
This review is from: An Introduction to Number Theory (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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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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