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I am studying Real Analysis -- using Baby Rudin -- on my own in a community that does not have a university near (if the "why" is important, see below). I recently worked through standard texts for Calculus, (basic) Differential Equations, Linear Algebra, Vector Calculus and [Eccles] "Introduction to Mathematical Reasoning" in preparation. Most of those were fairly easy to do in a self-study environment, because it was reasonably easy to tell, when doing the problem-sets, whether I'd gotten it right or not. (Student & Instructor answer books and Chegg helped a good bit when I got stuck; which was not often, but more often than I'd like .)

However: while I have the answer-book for Rudin, I'm finding it much harder to tell -- where most problems are of the form "Prove X" -- whether my proofs are valid unless they match precisely those in the answers. Sometimes they do. Usually there are subtle (or greater) differences. And I cannot reliably tell whether those 'subtle differences' are inconsequential or horrifyingly stupid (plus WRONG). Anyone with thoughts or experience on how this subject can best be learned in a self-study environment? Or is it likely I'm going to have to develop a resource -- one way or the other -- to 'grade' my efforts and help keep me on track? Thanks for considering.

[Possibly unnecessary framing information: Mostly I just want to spiff up my mathematical understanding. But there exists a research project that I'd like to join, in my field (Medicine), which really needs at least some ability to think topologically about the problems, and which often involve (somewhat) the math of Chaos. Thus I think I need to bring myself up to at least that level to participate.]

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    $\begingroup$ Check the tag "proof-verification". $\endgroup$ Aug 25 '18 at 15:16
  • $\begingroup$ Baby rudin is hard to use as a first course text, since it has eliminated most of comments and remarks, which make it pretty dry to read. However the examples and method of proofs are undoubtedly classic, it is a better choice to use it as a companion. $\endgroup$
    – xbh
    Aug 25 '18 at 15:19
  • $\begingroup$ Oskar Tegby -- done, and thanks! $\endgroup$ Aug 25 '18 at 16:29
  • $\begingroup$ xbh -- I have been so-told; I've a copy of S. Lay's "Analysis", which additionally has the advantage of having worked-answers on Chegg (though I've not been able to lay (sic) my hands on the Instructors' manual). Maybe I should work through that before I tackle Rudin? $\endgroup$ Aug 25 '18 at 16:31
  • $\begingroup$ I am no expert on medical research but I suggest you ought to,(if you haven't yet), acquire some considerable expertise in analytic methods of Statistics. $\endgroup$ Aug 25 '18 at 23:29
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My opinion: I think it is a hard, maybe impossible, task to succeed completely alone. In university, proof-heavy courses are what makes many students reconsider their subject. And they do have tutors to ask questions and get feedback on their proofs.

Maybe one possibility is to post your proofs here and ask for review.

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  • $\begingroup$ Thank you, both for the thoughts and for the suggestion of using this site to vet my answers (though that may also be a sure way to de-inflate my ego (a task which my nurses are pretty good at already!)). Also, see above in my response to 'xbh' for another possibility I might pursue. $\endgroup$ Aug 25 '18 at 16:34
  • $\begingroup$ I have to disagree a bit here. Proof oriented courses are not hard inherently, but rather most of the school education is not proof oriented at all which makes such courses seem hard. If someone wishes to study such a course like real analysis then it is better to encourage him to get good books which have detailed explanations. $\endgroup$
    – Paramanand Singh
    Aug 26 '18 at 10:26

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