Re: Heuristics for number theory?

if you're looking for a more practical approach to number theory in terms of cryptographic type things, you should check out a book like "Cryptography: Theory and Practice" by doug stinson. it's a very good read, and it will give you many of the same mathematical insights, only with a lot of really good practical insight as well. other than that one, any basic crypto book will give you good applications of the supposedly unthemed material.

having strong mathematical background, i would say number theory is a very beautiful (maybe one of the most beautiful) area of mathematics, but it should be approached carefully. if you're in it for the application, a number theory course in mathematics will probably just confuse you (as it apparently did), and something like a graduate course in cryptography/network security from an electrical engineering or computer science department may do more for you.
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