Elementary Number Theory

by David M. Burton

This text provides a simple account of classical number theory,as well as some of the historical background in which the subject evolved. It is intended for use in a one-semester,undergraduate number theory course taken primarily by mathematics majors and students preparing to be secondary school teachers. Although the text was written with this audience in mind,very few formal prerequisites are required. Much of the text can be read by students with a sound background in high school mathematics.

Genres: Mathematics, Number Theory, Science, Nonfiction, Academic, Textbooks, Computer Science

Paperback

First published January 1, 1976

Reviews

[Richard]

Great book, but on page 42, 315 is actually the gcd of 4725 and 17640, not 17460 (The gcd of 4725 and 17460 is 45.). And 2^3 X 3^2 X 5 X 7^2 is 17640, not 17460 (The factorization of 17460 is 2^2 X 3^2 X 5 X 97, the largest prime less than 100). This typo has survived between at least 2 editions. It made me scratch my head and peck at my calculator for a while as well.

[Saquib Mohammad · Rating 5 out of 5]

A very helpful book. The book has few drawbacks if you are looking for a more modern perspective on number theory. However, those drawbacks are barely noticeable. One of the most beautiful features besides the mathematical ease of reading and presentation is the little stories about Euler, Fermat, Lagrange, and multitude of other mathematicians. It is a story of developments of number theory in the hands and minds of few brilliant number theorists distributed across the ages scattered across the globe. A marvelous book!

The book is extremely constructive and helpful. Burton helps you every step of the way with his hints littered across every exercise. A very easy read. However, lack of recent developments might be wanting but any undergraduate getting introduced to number theory will appreciate the number of open problems Burton introduces in his text with relevant information. Topics covered include Euclid's theorem, Mobius' inversion, primality, primitive roots (a glimpse in to Group Theory), modular arithmetic/congruences, quadratic reciprocity, Legendre and Jacobi symbols, QNR, Pell's equation, Pythagorean numbers, Fermat conjectures and theorems, Wilson' theorem, infinite fractions, CRT, and several minor topics, not necessarily in order of mentioning.

I would recommend this book to any student taking a first course in Number Theory despite the lack of some topics in any elementary Number Theory Course. Simply because of the excellent ease of reading and writing style.

[Lawrence · Rating 4 out of 5]

As far as I can remember, and surprisingly enough, this is the first math textbook I've ever read straight through, so that feels like a real accomplishment, after trying and failing to get through several textbooks beforehand. As far as math textbooks go, I found it fairly readable, and there weren't really any sophisticated techniques used in the book's numerous proofs (which I suppose is why it's "elementary"). Burton does an adequate job, if not a stellar one, of contextualizing and historicizing various developments in number theory, which did end up making a big difference to me in how exciting the book was to read.

At some points, I'm thinking Burton could have contextualized his demonstrations even more: various proofs he presents, for example, seem fairly unmotivated, and at times I felt like I was lost in a blizzard of meaningless symbols. By that, I don't mean I didn't know what they meant mathematically; however, I couldn't zoom out and describe how they figured into the larger context of the topic (e.g., the numbers t_n in the continued fractions chapter).

... It was also kind of a shock, in Burton's timeline of number theorists at the end of the book, to see no women and only three mathematicians of color!

[Dan · Rating 5 out of 5]

This was the textbook for my Elementary Number Theory class. That class, in no small part due to this book, is the reason why I decided to major in Mathematics and hence why I am (as of writing this) getting a graduate degree in the field.

This book is an excellent introduction to elementary number theory. The problems are very challenging, but illuminate the material deeply. Furthermore, this book serves as an excellent reference when I want to look up proofs of facts in elementary number theory.

[Ym.R. · Rating 5 out of 5]

ספר מהנה רצח, מובן וכולל גם מעט היסטוריה נחמדה פה ושם

[Fri · Rating 5 out of 5]

كان بمثابه [الهدية من الله]

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2- الأسبوع الثالث من شهر 4. وضعت خطة دراسة فصوله الــ16 بتمارينها ومسائلها.
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5- الأسبوع الثاني من شهر 8. أتممته. {النهاية}

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طشعر بــ[السعادة] وربي يستر ههههههه

[Hmys · Rating 4 out of 5]

I think it is a completely standard intro to Number Theory. It doesn't use any algebra or any fancy analytical tools. I like the fact that it has relatively lengthy historical intros to each chapter. I think some of the proofs were rather difficult, but that might be in the nature of the subject.

[DJ]

book for math 430

[Cedric · Rating 5 out of 5]

Excellent explanations, excellent exercises, excellent background information. Best book on the subject!

[Christina · Rating 2 out of 5]

A bit wordsy. Nice inclusion of history at the beginning of each chapter though, among other anecdotal jaunts throughout the text.

Don't miss the part on Chinese Remainder Theorem! It's a must-read!

[Eric · Rating 4 out of 5]

Very good introductory text. Excerises seem to have an appropriate level of difficulty.

[Harshith Avasarala]

It's a good book.

[Ben · Rating 5 out of 5]

I enjoyed this textbook more than any other I can recall. It could just be my love for the subject though.

[Avisha Singla]

best book ever

[Insaf Turkmani · Rating 5 out of 5]

This book includes the base of number theory which is the most important branch in mathmathics. All its chapters are interesting because the most includes open problems which acquire deep studying.

[Dhiraj Kumar · Rating 5 out of 5]

Didn't read the entire book but whatever I read was enough to convince me that this is a great book and if I ever read number theory again I will surely come back to this book.