Elementary Number Theory

by Underwood Dudley

Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems—some computational and some classical, many original, and some with complete solutions.
The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.

Genres: Mathematics, Reference, Textbooks, Number Theory

272 pages, Paperback

First published January 1, 1969

Reviews

[Jose Moa · Rating 5 out of 5]

Number theory is a especial branch of mathematics,is a branch where a child can propose a problem that professional mathematicians need hundreds of years to solve,are well known the Goldbach conjecture , the twin prime conjecture or the Fermat theorem;the two first yet unsolved.This branch is subdivided in three branches :analitical number theory (that one worked by Hardy),algebraic number theory and elementary number theory,this last has the special caracteristic that not needs mathematical background except elementary aritmetics and a certain mathematical maturity,is a entertainig and full of beauty and striking results branch ,yet elementary not always means easy.

This book is ideal for begining and self study,humbly the best book i know,is composed of short chapters foollowed by accesible exercises and begins from zero is to say the divission algoritm.The demostrations are very easy to follow and makes very accesible the demostration of the cuadratic reciprocy thorem,a not easy theorem that taked a year to the genial Gauss to solve.

The book developes Diophantine equations ,linear and cuadratic congruences,Fermats and Wilsons therems ,perfect numbers,infinite descent method,sums of two and four squares,a rudimentary form of the prime number theorem and formules for primes.The book dont explain the RSA or public key encoding method nor continued fractions

[Hobart Mariner · Rating 4 out of 5]

Lightweight introduction to number theory written with a wry sense of humor. Covers a fair amount of topics, but doesn't enter anything in real depth (the deepest it goes is the n =4 Fermat, sum of squares characterization, and four-squares theorems). I think the author's generally witty, low-tech approach could have made a good fit with continued fractions, rather than the silly stuff like duodecimals, but he says it would be too much machinery. Huge supply of good exercise at a nice difficulty calibration for undergraduates; a great resource for teaching. His historical asides sometimes make certain discoveries seem like a stroke of genius (for example, the characterization of sum of two squares). There's certainly a huge amount of ingenuity, but the geniuses of that era (18th/early 19th c) were, among other things, great calculators, essentially Mentats with sitzfleisch out the wazoo. But this misjudgment doesn't detract too much from the book.

[Deniz · Rating 3 out of 5]

Hat mich damals als Kind begeistert

[Becky Carlan · Rating 4 out of 5]

A great classical text in arithmetic.

[Keith Eldridge · Rating 1 out of 5]

I know this book is old, but it is hard to believe a math book where all of the samples of materials covered are left as exercises for the reader.

[powei · Rating 4 out of 5]

first math book outside of classes i've ever read and loved it. it opened up my world.

[James Fearn · Rating 5 out of 5]

Awesome book. Contains information on patterns that numbers take and interesting factoids like 2^5*9^2=2,592. Required read for my BA, reread for practice.