Books in ANT and Galois Theory with medium difficulty

Question

I'm interested in learning Algebraic Number Theory and Galois Theory, so I was suggested Ireland Rosen and Stewart for them respectively. But the problem with the books is that the text is very very easy to understand and almost all the exercises are trivial, so I couldn't understand things properly from this.

Then I was suggested to work on Problems in Algebraic Number Theory by Murty, and I'm finding it to be very hard. Since it's supposed to be an "introductory first read" on ANT, does the fact I'm finding Murty hard suggest I lack the required mathematical maturity to solve the problems from it ?

Also what are some Galois Theory/Algebraic Number Theory somewhere between these two ? The exposition needn't be too hard to follow, but the exercises should at least take some time to solve.

Answer 1

I might consider this set of notes written by Matt Baker for some algebraic number theory (minus Galois theory). The preface states

“Algebraic Number Theory is often presented in either a very elementary way which does not take full advantage of students’ backgrounds in Abstract Algebra, or in a very abstract and high-powered way which runs the danger of divorcing itself in the students’ minds from the concrete origins and applications of the subject. We have tried to steer a middle ground between these approaches.”

This seems like it might be a good fit for you. With regard to difficulty related to your knowledge of algebra, I would suggest you keep a copy of Dummit and Foote next to you while you read. If you don’t understand an argument, take a break and read a bit in D&F about the objects being used and then come back to whatever you end up reading.

(Moreover, D&F has some Galois theory in it. It can be a little long-winded at times depending on what you’re looking for, but it is there.)