Learning Algebraic Number theory

Question

I am looking for a good reference to self study algebraic number theory, as no undergraduate course is given at the university. I've web-searched a lot of online notes and courses, and I don't seem to understand what's happening. Could anyone who took/is taking/teaching a course in algebraic number theory say what are the prerequisites and the corequisites to tackle the subject in an efficient way? Further, could anyone suggest a good reference to learn the subject?

Answer 1

At the University of New South Wales (UNSW), which is considered to house the best school of mathematics in Australia, we have a third-year undergraduate course entitled Algebraic Techniques in Number Theory.

Having read the course outline, it appears that a background of linear algebra and discrete mathematics comes in handy.

Unfortunately, they don't recommend any textbooks as the course is self-contained, and claim that any textbook on number theory would be useful. However, it appears as though A Classical Introduction to Modern Number Theory by Ireland and Rosen is a popular choice.

Answer 2

Algebraic Number Theory by Jarvis could be a good option. It has an appendix containing extensive hints and solutions to the exercises (handy for self-study) and has modest prerequisites: linear algebra, some elementary number theory and parts of abstract algebra (groups up to Lagrange's theorem and some acquaintance with rings and fields). It's aimed at advanced undergraduates.

Answer 3

Answer: A bit more advanced is Neukirch, "Algebraic Number Theory". You need background in commutative algebra (Atiyah-Macdonald or Matsumura). Its a good book.