Good problem books at a relatively advanced level?

Asked Apr 01 '15 at 23:37

Active Aug 12 '15 at 13:18

Viewed 791 times

I have been searching for problem books on advanced topics.

By advanced I am referring to the undergraduate level and above. I am looking for something analogous to the olympiad type problem books found at the high school level. I am hoping to supplement my learning with challenging problems in these topics and I have so far found a few, namely:

Putnam and Beyond by Razvan Gelca
Problem-Solving Through Problems by Loren C. Larson
Linear Algebra Problem Book by Halmos.

But with the exception of Halmos, these books do not cover the topics I am interested in deeply enough, these include:

Abstract Algebra
Real Analysis
Differential Equations

and a few other topics.

Just to reiterate, I am looking for books that entirely consist of difficult problems. Thanks.

edited Aug 12 '15 at 13:18

Martin Sleziak

53,687

asked Apr 01 '15 at 23:37

J.Gudal

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1

Halmos' book on Hilbert spaces is pretty grueling. – Mnifldz Apr 01 '15 at 23:39
Definitely the sort of the thing I am looking for, but alas it is seems to be quite a bit beyond my level right now. Perhaps I may end up using it one day though. Thanks. – J.Gudal Apr 01 '15 at 23:44
See IMO Math and Putnam Archive. – Lucian Apr 02 '15 at 01:00
Maybe it would be better to post (or even better to search for) a separate question for abstract algebra, real analysis, ODEs. – Martin Sleziak Aug 12 '15 at 13:21
Abstract algebra: Good problem book on Abstract Algebra and maybe some of the questions linked there. – Martin Sleziak Aug 12 '15 at 13:22
These questions are about calculus/analysis, but the answers include books about real analysis. (It is probably worth adding that various people will understand real analysis a bit differently.) Book recommendation for analysis problems, Suggest books in calculus to improve problem solving skills – Martin Sleziak Aug 12 '15 at 13:25
And here is a post somewhat similar to yours - i.e., not directed towards one specific area: Problem books in higher mathematics. – Martin Sleziak Aug 12 '15 at 13:30

Good problem books at a relatively advanced level?

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