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Good day. I am working in IT-related field, has a bachelor degree and intend to get graduate degree in Computer Science. Since it requires passing some math test I need to prepare for this exam.

During my university time I studied math, but I studied how TO SOLVE problem. For example: "Ok, I have a definite integral, so need to use Newton – Leibniz formula". Problem is that I did not understand why I use this formula, what does this formula mean - have no fundamental understanding of all.

During the weekends I read an article about Shinichi Mochizuki's and his work related to ABC-theory. I did understand nothing from a lot of math formulas, proofs, but was really impressed.

I have enough time to prepare for the exam. But I would like ask a question about some way not just to learn how TO SOLVE some task but about how TO UNDERSTAND mathematics? Not just for the exam but also for self-development. It is interesting I think.

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    $\begingroup$ This question seems to be about learning mathematics and this site is about teaching mathematics. This question belongs on math.stackexchange.com $\endgroup$
    – Amy B
    Nov 2 '15 at 0:40
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    $\begingroup$ @AmyB, there it will get closed as "opinion based". In fact, I believe it is a better match here than there... even if it is awkward. $\endgroup$
    – vonbrand
    Nov 2 '15 at 1:44
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    $\begingroup$ I have followed the other votes of moving to MSE, but, in fact, the problem would need to be greatly re-formulated there, too. The jump from evaluating university Calc integrals to Mochizuki's work on the abc-conjecture is (to understate) tremendous. And the question of "how to understand mathematics" is too broad to be tractable on any Q&A site. $\endgroup$ Nov 2 '15 at 2:03
  • $\begingroup$ This question was previously asked at mathoverflow.net/q/222396/12357 and I suggested that the OP ask it here after making it narrower in scope. Unfortunately, the OP copied the question verbatim (without editing it as I suggested). $\endgroup$ Nov 2 '15 at 5:58
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Get hold of some higher-level texts in the areas you need to work yourself into. Graduate level texts tend to be more on the "understand why, so you can extend" more than "use to" outlook. But for Computer Science, unless heavy on theory, won't go too much into mathematics except as a tool.

See if you can get your hands on William Dunham's books (Journey through genius, for instance), also take a peek at Aigner and Ziegler's "Proofs from THE BOOK". They should help you to find out what mathematics is all about.

Lehman, Leighton and Meyer's class notes for MIT's 6.042 course ("Mathematics for Computer Science") is an encyclopaedia at more than 900 pages. A new edition of sorts comes out each fall or so. More tuned to "apply", but still geared towards "understand".

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