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Fundamentals of Number Theory (Dover Books on Mathematics), by William J. LeVeque
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This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect.
The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, p-adic numbers, algebraic number fields, Brun's theorem on twin primes, and the transcendence of e, to mention a few.
Readers will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes — containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols — and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.
- Sales Rank: #846075 in eBooks
- Published on: 2014-01-05
- Released on: 2014-01-05
- Format: Kindle eBook
Most helpful customer reviews
25 of 28 people found the following review helpful.
Good for self teaching
By A Customer
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.
23 of 30 people found the following review helpful.
Very detailed and interesting.
By A Customer
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.
4 of 4 people found the following review helpful.
Good Book
By Indikos
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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