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Elementary Number Theory

Underwood Dudley
Publisher: 
Dover Publications
Publication Date: 
2008
Number of Pages: 
249
Format: 
Paperback
Edition: 
2
Price: 
14.95
ISBN: 
9780486469317
Category: 
Textbook
BLL Rating: 
BLL*

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Herbert E. Kasube
, on
08/12/2009
]

What can you say about a classic? Dudley’s number theory text was first published in 1969; this volume is a faithful reprint of the second edition, from 1978. The writing style is engaging and at a level which makes this book accessible to a wide audience. There are 23 chapters that offer a variety of choices for coverage. The selection of exercises is excellent. There are enough “easy” problems so as not to discourage a student, but also enough that challenge as well. A perfect balance!

Even if you choose not to use Dudley’s book as the required text, its availability in paperback makes it an excellent resource available to everyone.

Herbert Kasube is Professor of Mathematics at Bradley University in Peoria, IL.

 

Preface

Integers

Unique Factorization

Linear Diophantine Equations

Congruences

Linear Congruences

Fermat's and Wilson's Theorems

The Divisors of an Integer

Perfect Numbers

Euler's Theorem and Function

Primitive Roots

Quadratic Congruences

Quadratic Reciprocity

Numbers of Other Bases

Duodecimals

Decimals

Pythagorean Triangles

Infinite Descent and Fermat's Conjecture

Sums of Two Squares

Sums of Four Squares

x2 – Ny2 = 1

Bounds for π(x)

Formulas for Primes

Additional problems

Proof by Induction

Computer Problems

Factor Table for Integers Less Than 10,000

References

Answers to Selected Exercises

Answers to Selected Odd-Numbered Problems

Comments on Selected Odd-Numbered Problems

Index

 

Tags: 
Elementary Number Theory

Comments

fqgouvea@colby.edu's picture

Submitted by fqgouvea@colby.edu on Fri, 2015-09-11 13:30

Just the other day I heard a top-notch mathematician mention this book as an inspiration. It's a great way to begin learning number theory.