I really do not know if this is the place to ask, if it isn't, I would appreciate if you steer me in the right direction.
So I am a math grad student dropout, sad but true. I really love math, and even though I will most likely not fulfill my dream of invetigating, I still want to learn. So after some time of mourning, I am rady to study math again.
I have basic knowledge of complex analysis, and all basic algebras (Rings, modules, Galoi theory, etc.).
considering this list of what seems to be areas relative to number theory:
What books would you recomend?
Best Answer
My favorite book——by far——on number theory is: An illustrated theory of numbers by Martin Weissman. This will help you understand and think about number theory. However, it isn't comprehensive, and there are several key ideas that it omits because there are no natural visualizations of them. So I would supplement this book with Elementary number theory and its application by Kenneth Rosen.
If you're working on your own, it is essential you solve problems. Without a teacher, you'll likely need solutions. For this reason I recommend the following two books:
Introduction to number theory by Mathew Crawford, which has a nice Solution Manual.
I also like Elementary number theory: A collection of problems with solutions by V K Krishnan. You won't learn number theory from Krishnan's book, but you'll learn to solve problems, which is of course essential for any deep understanding.
Good luck!