The Higher Arithmetic: An Introduction to the Theory of Numbers

by Harold Davenport

Updated in a seventh edition, The Higher Arithmetic introduces concepts and theorems in a way that does not require the reader to have an in-depth knowledge of the theory of numbers, and also touches on matters of deep mathematical significance. This new edition includes state of the art material on the use of computers in number theory, as well as taking full account of the proving of Fermat's last theorem.

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

241 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.