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This is a little bit of an open ended question, but I'm curious none the less..

A few years ago, I remember seeing a blog of an individual who periodically (probably a lot quicker in the beginning, and much slower as things progressed) would progress through mathematical proofs and eventually find his way into proving some more advanced analytic topics.

I'm interested in doing something similar... starting with some theorems and axioms in basic set theory, and maybe eventually finishing off with proving advanced calculus, maybe even some complex analysis. I've proven most of the basic calculus theorems in my advanced calculus course in college, so I'm not looking for a proofs guide as much as a set of problems.

I'm looking for resources that might provide theorems for me to work through at my leisure. I'm already working on ProjectEuler problems, but nothing is as satisfying as a mathematical proof.

Any suggestions on websites / resources to get me started?

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  • $\begingroup$ [Possible plug] You should check out Brilliant.org which provides weekly challenging math problems for high school students to work on, further asks them to submit their proofs. We've avoiding 'university' topics like analysis/topology/abstract algebra, but I can assure you that the questions will still intrigue you. $\endgroup$ – Calvin Lin Jul 17 '13 at 16:15
  • $\begingroup$ Thanks! I'll definitely check that out $\endgroup$ – jameselmore Jul 17 '13 at 16:15
  • $\begingroup$ I don't know about mathematics, but in computer science there is a great archive of problems from various Polish contests here. Be aware that a number of them might be actually quite hard, e.g. this (it's not very hard, just hard and fun), and some were even published at conferences. $\endgroup$ – dtldarek Jul 17 '13 at 16:24

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