Second Course in Number Theory - Self Study

Question

I just finished a first course in number theory using Dudley's Elementary Number Theory. This was by far my favorite math course and I want to learn more number theory this summer. As far as prerequisites, I've taken introductory courses in algebra and complex analysis. As such,

• What topics are covered in a second number theory course?
• What is a good textbook (or lecture notes, etc) for a second course in number theory?

Answer 1

How about Number Fields by Marcus. It covers algebraic number theory. You can read concurrently Analytic Number Theory by Apostol.

Answer 2

There's a book by Harvey Cohn called A Second Course in Number Theory (although I think recent editions have been renamed, An Advanced Course in Number Theory).

There's also a book by Paul Pollack called Not Always Buried Deep, and subtitled, A Second Course in Elementary Number Theory.

Some other books that might work for you are Ireland and Rosen; Apostol's introductory Analytic Number Theory text; Stewart and Tall --- I'm not going to copy out tables of contents, I'm sure you can find those. Or, you can just walk into the library and look at QA 241 through 247 (if you're on Library of Congress system).

Or ask the person who taught you the 1st course.