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In recent times, I have been studying mathematics (topics related to mathematical logic, more specifically) independently and I feel a great deal of passion about it. However, although I have made peace with the fact that it's a lonely endeavor and my motivation is enough to carry on, I have also become preoccupied with the veracity and quality of my learning; basically, I'm worried about misinterpreting things I read and/or that my proofs are fallacious.

For example, currently I'm reading [1] and working on the exercises with great pleasure (these are some of my notes). I also worked through some of [2] (again, some of my notes). I tried to contact several professors in my area asking for advice and available programs, but I never got a reply from them. Unfortunately I do not have a university degree and my current life situation doesn't allow me enrolling in one.

How can one make progress as an independent student and gain the additional confidence/reassurance that could be attained, perhaps, with the help of an advisor, a teacher or fellow students?


[1] Shoenfield, J.R. Mathematical Logic. Reading, Mass., Addison-Wesley Pub. Co (1967)

[2] Knuth, D. E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Pearson Education (US) (2015)

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    $\begingroup$ This is one of those situations where it's not totally clear to me whether your question will get better help from math.SE, matheducators.SE, or maybe even mathoverflow or academia.SE. I hope you are able to find some assistance either here or one of those places. $\endgroup$
    – Chris Cunningham
    Oct 12 at 16:23
  • $\begingroup$ If you wanted to pick a proof you're not sure of, and post your work on math.SE, I'm guessing you'd get some valuable feedback there. $\endgroup$
    – Sue VanHattum
    Oct 12 at 18:01
  • $\begingroup$ @SueVanHattum I guess I can start doing that. I was asking for more general guidance, but I guess asking in math.SE is a valid (general) strategy as well. Thank you for your suggestion. $\endgroup$
    – ale64bit
    Oct 12 at 19:18
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    $\begingroup$ @Chris This question is unlikely to be well received on Math SE---we typically don't entertain questions which ask for personal or career advice, and this seems to riding that line pretty closely. ale64bit: I very firmly believe that mathematics is a collective endeavor, and that it is basically impossible for all but a very tiny minority to learn in isolation. My advice would be to find peers and mentors (an independent study group, classes, or a course of study with institutional support). $\endgroup$ Oct 13 at 13:18

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