Fundamentals of number theory

By William J. LeVeque

Book Overview

Basic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition.

• Format: Paperback
• Language: English
• ISBN: 0201042878
• ISBN13: 9780201042870
• Release Date: January 1977
• Publisher: Addison-Wesley
• Length: 280 Pages
• Weight: 1.26 lbs.

Customer Reviews

Recommend this book

This book on Number Theory is pitched at the undergraduate level. It is well written and organized. A nice feature is historical notes on past number theorists.

Great Number Theory Book

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.

Good for self teaching

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.

Very detailed and interesting.

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.