A Pathway Into Number Theory

by R.P. Burn

Number theory is concerned with the properties of the natural 1,2,3,.... During the seventeenth and eighteenth centuries, number theory became established through the work of Fermat, Euler and Gauss. With the hand calculators and computers of today, the results of extensive numerical work are instantly available and mathematicians may traverse the road leading to their discoveries with comparative ease. Now in its second edition, this book consists of a sequence of exercises that will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A modern high school course in mathematics is sufficient background for the whole book which, as a whole, is designed to be used as an undergraduate course in number theory to be pursued by independent study without supporting lectures.

Genres: Number Theory, Mathematics

280 pages, Paperback

First published January 1, 1982

Reviews

[Kbs · Rating 5 out of 5]

I'll say right away that this is a slog of a read, and I only made it through the first two chapters.

That said -- I was quite intrigued with the teaching approach, I wish there were more books written in this style.

It works roughly like a series of little number puzzles that gives you glimpses of underlying patterns, and then nudges you to uncover, and then prove those patterns. It's hard mental work for sure (and it seems like my brain cells have atrophied to the point where I'm not able to plug away at it for very long.) But whatever you pick up sticks around for longer; and there's the little joy of discovery every time you break through each puzzle. Good stuff, but recommended only when you have some brain cycles to spare.

[Liquidlasagna · Rating 5 out of 5]

I'm pleased to report there is a new edition of R. Burn's A Pathway into Number Theory, a book that takes readers quickly and painlessly from simple facts about whole numbers to the wonders of the quadratic forms, Pell's equation and Minkowski's theorem.
Ian Stewart