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After college, it has been very difficult to continue learning math as a hobby, I have the time for it, but I get incredibly frustrated when I run into something that it feels like I will never ever understand.

As an undergraduate you are basically shielded from this kind of stuff. The reality that you are climbing a mountain which extends into space is replaced by the illusion of grades and homework and it makes it a lot easier to keep marching forward. I don't want to carry this anxiety into a graduate program.

Is there an online resource that is dedicated to the partial ordering of the topics of the undergrad/graduate curricula? Ideally, I want an exhaustive list of mathematical topics which are not, to mix metaphors, out of my depth.

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  • $\begingroup$ Khan academy has the sort of thing you describe, but unfortunately only for roughly grades 6-12. $\endgroup$ – vadim123 Jun 4 '13 at 20:21
  • $\begingroup$ I like this idea, but I imagine it would be difficult for sufficiently advanced material. For example, some parts of advanced group theory require background in complex analysis (and not combinatorics) while others require combinatorics (and not complex analysis). Furthermore, how can we quantify the "intuition" or "mathematical maturity" prerequisites in a well-defined way? After all, ideally, one should be able to pick up any math book and learn from the ground up, as most books begin with a multitude of definitions. $\endgroup$ – Alexander Gruber Jun 4 '13 at 20:27
  • $\begingroup$ The Reddit site www.reddit.com/r/math gets a lot of requests for these, e.g. reddit.com/r/math/comments/16spn5/… I don't understand how your request is related to your frustration -- if you see something you don't understand, look it up, and if you don't know any of the words in the definition, you're probably in the wrong place. $\endgroup$ – Adam Saltz Jun 4 '13 at 20:45
  • $\begingroup$ Take a look at an answer I gave not too long ago. 1st and 2nd year are essential and open the doors to a variety of different areas: math.stackexchange.com/questions/394639/… $\endgroup$ – user70962 Jun 4 '13 at 21:32
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    $\begingroup$ I actually found a pretty good resource here:hbpms.blogspot.com.br $\endgroup$ – Zackkenyon Jun 5 '13 at 17:50

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