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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.

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    $\begingroup$ Halmos' book on Hilbert spaces is pretty grueling. $\endgroup$ – Mnifldz Apr 1 '15 at 23:39
  • $\begingroup$ 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. $\endgroup$ – J.Gudal Apr 1 '15 at 23:44
  • $\begingroup$ See IMO Math and Putnam Archive. $\endgroup$ – Lucian Apr 2 '15 at 1:00
  • $\begingroup$ Maybe it would be better to post (or even better to search for) a separate question for abstract algebra, real analysis, ODEs. $\endgroup$ – Martin Sleziak Aug 12 '15 at 13:21
  • $\begingroup$ Abstract algebra: Good problem book on Abstract Algebra and maybe some of the questions linked there. $\endgroup$ – Martin Sleziak Aug 12 '15 at 13:22

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