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Fundamentals of Number Theory (Dover Books on Mathematics)

by William J. LeVeque (Author)
4.1 out of 5 stars 10 customer reviews
ISBN-13: 978-0486689067
ISBN-10: 0486689069
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 288 pages
  • Publisher: Dover Publications (February 7, 1996)
  • Language: English
  • ISBN-10: 0486689069
  • ISBN-13: 978-0486689067
  • Product Dimensions: 5.6 x 0.6 x 8.2 inches
  • Shipping Weight: 8.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #472,997 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

5.0 out of 5 starsGood for self teaching
By A Customer on July 3, 2002
Format: Paperback
I am currently working through this book, and I really like the format, which is usually a small, digestible chapter followed by a set of exercises (usually 10 or so). Quite a wide variety of topics are covered including congruences, primitive roots, analysis of the number theoretic functions (e.g., the number of primes below x), and a little on diophantine approximations and continued fractions. Nothing post-calculus is used in the book except for some algebraic structures such as fields and rings, however, they are fully explained at the beginning of the book. (And some previous acquaintance with these would probably be good.) The exercises are especially good, being not too easy and not too hard. In response to the review below, to actually understand math like this you must be willing to do some work yourself. If you are looking to sit back in your easy chair and be entertained, then you should buy a book on the history of number theory, not a textbook.
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5.0 out of 5 starsVery detailed and interesting.
By A Customer on September 28, 1999
Format: Paperback
Although by no means an easy read, this book is very detailed and informative. Math phobic people need not apply, however, because it gets very technical after the first chapter. I absolutely loved this book and would recommend it to anyone (probably not for pre-college people) who enjoys a challenging read.
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5.0 out of 5 starsGood Book
By Indikos on July 4, 2010
Format: Paperback
This book is very well written and organized;
the author clearly loves the subject and writes with genuine feeling for it.
I found the proofs easy to follow; there are plenty of exercises.
The books covers the linear diophantine equation, quadratic reciprocity,
Fermat's theorem, Lagrange's theorem on a number expressed as a sum of 4 squares,
Pell's equation and other nice stuff.
A nice feature is the historical asides on past number theorists.
It is well suited for self-study, and is pitched at the undergraduate level
- and the price can't be beat.
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5.0 out of 5 starsGreat Number Theory Book
By Enrique Treviño and Yuliia Glushchenko VINE VOICE on April 16, 2010
Format: Paperback
This book covers all the basics in number theory. The greatest common divisor, the Euclidean algorithm, congruences, primitive roots, quadratic reciprocity and more. If one has taken abstract algebra, then this is a great introductory number theory book, if one hasn't taken abstract algebra, then a few chapters would be difficult to understand (such as chapters 3, 4 and 8), but the rest don't need abstract algebra.
I like the topics that are covered, in particular, I think Leveque does a very good job of explaining important concepts in elementary number theory in chapter 6. I really like Brun's theorem on twin primes and the order of magnitude of several famous number theory functions.
The last chapter has some interesting sections including the proof of the trascendence of e.

Another thing I like about the book, is that it has mini biographies of important number theorists throughout the history of mathematics. I've always enjoyed reading about great mathematicians.
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3.0 out of 5 starsThree Stars
By Pablo Salvajes on June 14, 2015
Format: Paperback Verified Purchase
wish the proofs were more concise and there was some background context for the motivation of the proofs
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