Gentle introduction to algebraic number theory

Question

For context, I am a undergraduate majoring in math. I've taken two semesters of algebra (though I am still a bit shaky on Galois theory). I just finshed a course in elementary number theory which used George Andrew's text.

This introductory course in number theory has been my favorite math class and I hope to learn a bit of algebraic number theory this summer to hopefully do an independent study/senior thesis in the next school year.

What are the best gentle introductory algebraic number theory texts that give an overview of the subject?

Answer 1

Not sure if it's gentle, but A Classical Introduction to Modern Number Theory by Ireland and Rosen appears to have received excellent reviews on Amazon.com, so perhaps that might be worth a look.

Alternatively, I found another one by William Stein's Elementary Number Theory: Primes, Congruences, and Secrets.

Answer 2

With a background in introductory algebra (groups, rings, fields) and some introductory number theory, and presumably also linear algebra, you are well-prepared to read Algebraic Number Theory by Jarvis. It's aimed at advanced undergraduates with a little, but not a huge amount, of abstract algebra under their belts. See here for a review.

Answer 3

A recently-published gem is John Stillwell's Algebraic Number Theory for Beginners: A Path from Euclid to Noether. It is particularly gentle, even going over the necessary parts of linear algebra. It also does a great job of putting the subject in a historical perspective, as one would expect from Stillwell.