# Learning Real Analysis outside a classroom setting

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.]

• Check the tag "proof-verification". Aug 25, 2018 at 15:16
• 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.
– xbh
Aug 25, 2018 at 15:19
• Oskar Tegby -- done, and thanks! Aug 25, 2018 at 16:29
• 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? Aug 25, 2018 at 16:31
• 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. Aug 25, 2018 at 23:29