Suggestion regarding transition to Mathematics

Question

I have studied mathematics upto High school level and also studied Calculus 1 and 2. I also have studied basic ODE. Recently i read a book "The Heart of Mathematics : Invitation to effective thinking". Now i feel like pursuing mathematics especially number theory area on my own. I would welcome suggestions of experienced mathematicians so as to what should be the pathway to it. Thanks

Answer 1

I'm glad you liked "Heart of Mathematics", it's one of my favorite books.

You might try a book like "Elementary Number Theory and Its Applications" by Rosen. Hardy and Wright, recommended in another reply, is an excellent book, but it's a big jump from "Heart of Mathematics" to Hardy and Wright. Rosen's book is simpler, and the only prerequisite is high-school algebra.

Answer 2

You could start by working your way through one or two of the classic texts on number theory such as

An Introduction To The Theory Of Numbers by G.H. Hardy and E.M. Wright

Number Theory by George E. Andrews

The Higher Arithmetic: An Introduction to the Theory of Numbers by H. Davenport

An Adventurer's Guide to Number Theory by Richard Friedberg

As with all mathematics textbooks, it is important to work through the problems at the end of each chapter to confirm and consolidate your understanding.

Also worth a mention is A Pathway into Number Theory by R.P. Burn, which consists of a series of problems which lead you to discover the basic results of number theory for yourself.