Talk:Number Theory

I will soon have a large amount of free time and would like to expand the book on number theory, as it is my passion, and I wish there to be an accesible way for people to learn it.

I would like to follow a plan along the lines of:

Divisibility, Unique Factorization, Multiplicative Functions, Congruences, Congruence Equations, Reduced Residue Systems, Totient Function, Polynomial Congruences, Diophantine Equations, Rational Irrational and Transcendental numbers, Continued Fractions, Quadratic Fields, and a Collection of Theorems with proof sketches

Each area would be divided into several sub chapters and each subchapter would have examples. I would hopefully highlight many theorems and their proofs, at the same time covering many basic methods of proof, with questions at the end of each section.

The Collection of Theorems at the end would contain many theorems with proof sketches, and it can be left as an excercise to the student to fill them in.

After this is complete I would be interested in expanding it to include more advanced topics, however I believe this would be a good start.

I would like to assume minimal knowledge of Calculus in the first part. Robert Carr 00:17, 8 May 2006 (UTC)

Hi, I'm not sure if anybody has been planning anything for this book, but I would like to help any construction going on. I think I will add some sections about Gaussian Integers to the template, and maybe start to fill in some of the unwritten and partially written chapters during my freetime.

Hmm.. I think that some discussion of axioms would be a good idea.

Hopefully we'll see more people tack onto this book soon, because Number Theory is truly a marvelous subject. mac (talk) 19:31, 28 September 2008 (UTC)