I was looking for some good books for algebra and number theory at the olympiad level. Does anybody have any suggestions? I specifically want books that work on techniques and concepts (not just problems) and start out from a pretty accessible level and steadily build up to the desired level. An example of such a book would be 'A School Geometry' by H.S Hall and F.H. Stevens which has good problems as well as theory; and covers basic geometry quite well.
I tried out 'Problem Solving Strategies' by Arthur Engel, but that's just way over my level. I have trouble understanding the solutions presented in the book and the motivations behind them. I suspect I need to start at a simpler level.
Best Answer
For number theory I would suggest "An introduction to the theory of numbers" by Niven, Zuckerman and Montgomery. It has a very good theory and problems. Everything is nicely explained with elegant proofs.
An easier book would be "Elementary Number Theory" by Burton. However, it doesn't have any difficult problems.
However, for olympiad preparation you learn by solving problems. Therefore, I would recommend "104 Number Theory Problems" by Titu Andreescu. It has some basic theory and then progressively harder problems all with solutions.
Similarly, for algebra try "101 problems in algebra" by Titu Andreescu.