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I am about to get my undergraduate degree in (pure) mathematics, but I feel like I'm ill prepared to go through a graduate program. This is why I'm looking for texts like this one http://www.math.kent.edu/~white/qual/list/all.pdf in other fields (algebra, analysis and topology.)

I've already looked at "Berkeley problems in mathematics", and I found it pretty tough.

Sorry if this question is too broad, or the site is not really for these kinds of questions (I've seen some in related topics, though).

Edit: I don't know how to make this question community wiki. Do you still have that feature?

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According to the Help Center page on privileges, creating a community wiki is a privilege requiring 10 reputation. –  Albert Zhang Oct 13 '13 at 3:13
    
@AlbertZhang Thank you for the information. –  user100507 Oct 13 '13 at 3:15

2 Answers 2

up vote 2 down vote accepted

http://homepages.uconn.edu/~rib02005/real.html

This one, titled Real Analysis for graduate students (don't be scared by the title, it's not a graduate level textbook!), is a good book full exercises that I discovered surfing randomly on amazon. As you can see the index is amazing: measure theory, lebesgue integration, topology, probability, harmonic functions, distributions, basic functional analysis and so on. The level, as I was saying, is not extremely high, so it could be more enjoyable that the berkeley one. Just a needless remark: the author included so many things that you can't expect that everything is detailed as it would be in a course on that subject, but it is a good starting point (and it is free :D).

I hope you'll find it interesting :D

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1  
Thanks for the link. I'm reading it and it seems great! :) –  user100507 Oct 13 '13 at 3:57

I would suggest

http://www.ams.org/bookstore-getitem/item=STML-4

http://www.ams.org/bookstore-getitem/item=STML/12

http://www.ams.org/bookstore-getitem/item=STML/21

I am actually solving them now and i feel that they are useful.

They have solutions to all problems :P

Good Luck!

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