I'm studying Herstein's Topics in algebra and Hardy&Wright's An introduction to the theory of numbers, and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as companions.
The books I am searching for should be:
- full of hard, non-obvious, non-common, and thought-provoking problems;
- rich of complete, step by step, rigorous, and enlightening solutions.
Roughly speaking, something similar (in some sense) to George Pólya and Gabor Szegő's Problems and Theorems in Analysis.
Update: I would appreciate some suggestions in reference to the answers given to these questions too: 1 & 2
Best Answer
You could try 'The Red Book of Mathematical Problems' and 'The Green Book of Mathematical Problems' by Kenneth Hardy and Kenneth S. Williams.
These contain numerous problems, with hints and solutions.
Available directly from Dover Publications.
An on-line selection of problems by Yang Wang is here, but no hints or solutions.