The Higher Arithmetic: An Introduction to the Theory of Numbers

by Harold Davenport

Now into its Eighth edition, The Higher Arithmetic introduces the classic concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers The theory of numbers is considered to be the purest branch of pure mathematics and is also one of the most highly active and engaging areas of mathematics today. Since earlier editions, additional material written by J. H. Davenport has been added, on topics such as Wiles’ proof of Fermat’s Last Theorem, computers & number theory, and primality testing. Written to be accessible to the general reader, this classic book is also ideal for undergraduate courses on number theory, and covers all the necessary material clearly and succinctly.

Genres: Mathematics, Number Theory, Reference, Science, Nonfiction

250 pages, Paperback

First published January 1, 1982

Reviews

[Hassan Zayour · Rating 4 out of 5]

This book serves as an outstanding introduction to the theory of numbers, a fascinating field that attracts the lover of wisdom into its magnanimous arbitrary fields of gold. In that higher realm, numbers become the pillars upon which we build everything we know. Once you see them, you cannot un-see; once you taste the sweetness of their harmony, honey becomes dull. Yours eyes find their glimpse in the faintest of shadows, and through them, higher sciences are obtained.

The book is designed to cover the fundamentals, and I claim that it is not very friendly to those who are not previously acquainted with the skill of extracting theorems and definitions from mathematical texts. This is how it differs from a conventional textbook: it does not tell you that it is providing you with a valuable definition or theorem at the moment of doing so; it rather allows you to extract it by providing an insightful motivation in the process. Arguably, by doing that, the reader will grasp the more comprehensive perception, and the knowledge obtained in this process is thus trapped in one's memory.

I loved it so much.

[Matt Young · Rating 4 out of 5]

A good introduction to Number Theory, not in a rigorous way; but, in an informal and enjoyable tone. I do however prefer "Excursions into Number Theory." This book was a bit drier and slightly more technical.

[Wissam Raji · Rating 4 out of 5]

A very good introduction to number theory with a nice treatment of the elementary topics. The only issue is that one needs to supplement it with problems from other sources. It is a very good book to be used for an undergraduate course in number theory.