Customer Reviews

Theory of Numbers: A Text and Source Book of Problems

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Adler and Coury's text on elementary number theory is one of the best I've ever seen; certainly for the purpose of independent reading or study. Aside from an otherwise standard flow of theorems, proofs, exercises, etc, there are approximately 800 problems all with solutions. Numerous historical and incidental notes are included as well, making this a rewarding book to read and use.

Anyone who works through the material should have no difficulty with the more challenging classics, like those of Hardy and Wright or the more recent one by Hua.

Any undergraduate textbook that says the proof of Bertrand's Postulate is beyond the scope of the text (p201) is remiss. Proofs easier than quadratic reciprocity exists. Not surprising, this was my text at a school known for engineering, not pure math.

In 400 pages you'll only go one-third the distance covered in Hardy and Wright, or Niven and Zuckerman. There is almost no emphasis on the more advanced areas of number theory, nor even a hint that such branches exist. Although many of the elementary, but unsolved conjectures are mentioned.

But wait! The book does have some merit. The book is broken into bite-size pieces - number theory for Attention Deficit Disorders. Everything is broken up into these pieces, notes, problems, further readings. Even the proofs that aren't "beyond its scope" are broken up into lemmas. This book has more "problems with solutions" than any I've seen, which would make it a good study guide for more concise texts that leave all the problems to the reader. It is these problems and solutions that fill out the bulk of the text and limit its depth of coverage. (Hardy and Wright has only 24 more pages but covers so much more).