I am looking for books on these two topics at the undergraduate level, an absolute must is that they contain problems with solutions. I hate when books give you 50 exercises after a chapter and then don't provide solutions to any of them.

Alternatively, could you suggest a book for the theory part and a separate exercise book with solutions?

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    $\begingroup$ Im enjoying a lot Understanding analysis by Abbott. It dont provide solutions but you can search solutions in the net. Anyway it dont have too much exercises, just a few but very good ones. $\endgroup$ – Masacroso Jun 10 '16 at 21:46
  • $\begingroup$ It's pretty rare for math textbooks to have solutions. But you wouldn't have a hard time finding solutions online for any of the "standard" books for analysis or linear algebra. Naturally it's best to try to solve them yourself. $\endgroup$ – carmichael561 Jun 10 '16 at 21:48
  • $\begingroup$ Of course I would solve them myself, but sometimes, especially when it comes to proofs it would be great for my confidence to have a solution included. So there are books with solutions to popular books? Excuse my ignorance, I'm not from an English-speaking country. $\endgroup$ – n4869 Jun 10 '16 at 21:53
  • $\begingroup$ @Masacroso Actually, all of the solutions are pretty easy to find. $\endgroup$ – Daniel W. Farlow Jun 10 '16 at 21:55
  • $\begingroup$ I don't know if there are books of solutions, but for instance if you were to Google solutions to Rudin's Principles of Mathematical Analysis I'm sure you'd find plenty. $\endgroup$ – carmichael561 Jun 10 '16 at 21:56

Jim Hefferon's book Linear Algebra is provided for free, along with all of the solutions, on his website. It also happens to be a really good introductory book (not quite Linear Algebra Done Right good, but I'd still put it above average).

I haven't ever read a real analysis book with solutions but a quick Google search has provided a couple:

  • A Problem Text in Advanced Calculus by John Erdman seems to be freely available, though I don't know if he actually meant for his directory to be public or not.
  • Problems and Theorems in Analysis, Vol I and II by Polya and Szego. Both authors are very well known mathematicians so I'd hazard a guess that it's a pretty good book.
  • $\begingroup$ Thank you so much, Jim Hefferons book seems to be in the ballpark of what I'm looking for. As for Erdman, it looks like a very comprehensive text. I know about Polya, will try to find those books, should be very good too. $\endgroup$ – n4869 Jun 11 '16 at 18:37

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