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.

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    $\begingroup$ Higher Algebra by Hall and Knight is quite good. It also has good problems. $\endgroup$ – user53167 Jun 22 '14 at 7:22
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    $\begingroup$ Besides Hall/Knight, see also the books by George Chrystal, Elias Loomis, Charles Smith, Aldis William Steadman, and Isaac Todhunter that I posed links to in this 5 November 2009 sci.math post at Math Forum. All of these books are freely available on the internet. $\endgroup$ – Dave L. Renfro Jun 24 '14 at 16:11

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.

  • $\begingroup$ please add more books like 101 problems in algebra, 104 Number Theory Problems. $\endgroup$ – mnulb Jan 17 '17 at 16:55

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