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I'm a college student majoring in Mathematics. This term, I'm taking my second proof-based course, real analysis. Unlike my first proof-based course, this one feels a lot more challenging, for the following reasons:

  • Time management disaster. The professor said explicitly that we should spend 10 hours on average per week on the problem set. Sure, but given 6 hours of lecture and reading per week, one could easily go up to 20 hours per week on just one course. I'm taking 3 courses this term (just the normal load for students at my college), none of which are easy.

  • No time for reviewing. As mentioned in the last bullet point, there's absolutely no time for going back to previously stumbled-upon problems and practice again.

  • No confidence. I don't feel like I own the material after trying very hard.

Can someone help me develop strategies around how to be successful in hard, time-consuming proof-based courses?

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    $\begingroup$ The best strategy is to do what the professor suggests. He/she has done this before, and seen which students succeed - he/she has more information on this than either of us. $\endgroup$ Oct 1 '20 at 0:30
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    $\begingroup$ In my 35 years of university teaching and advising (often 50 math majors a year), I rarely suggested real analysis as the first upper-level proof-based course. I'm assuming that your first course was a typical "Introduction to Higher Mathematics" course, which teaches you the language of mathematics and easy proofs. Most students find that real analysis is very challenging, often because the basic definitions involve many layers of quantifiers. You should consider taking a proof-based linear algebra course and a proof-based modern algebra or number theory course before embarking upon analysis. $\endgroup$ Oct 1 '20 at 0:33
  • $\begingroup$ @DavidC.Ullrich Too many professors are not good at teaching. $\endgroup$
    – zhw.
    Oct 1 '20 at 19:28

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