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I want to build very solid foundation of modern mathematics.

resources and activities all I know so far are below. please advice me what to add and what to remove. 1. read Euclid's Elements (book) 2. watch math foundation youtube video

as you see, I have very poor knowledge on what I have to do.

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  • $\begingroup$ I'd recommend learning some fairly basic set theory (e.g. from one of those "introduction to proofs" books; I used amazon.com/Transition-Advanced-Mathematics-Douglas-Smith/dp/… which was adequate) and then just...learning the math that interests you, rather than trying to work too hard on foundations. $\endgroup$
    – Ian
    Commented Jul 25, 2015 at 13:19
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    $\begingroup$ (Cont.) The notion of building up all of mathematics from a common foundation is fraught with mathematical problems (encapsulated in the incompleteness theorems) and human problems (the resulting structures contain a huge amount of redundant information, such as whether $e \in \pi$). $\endgroup$
    – Ian
    Commented Jul 25, 2015 at 13:19
  • $\begingroup$ I'm not sure what your level is, but eventually you should try Rudin's books on real and complex analysis. $\endgroup$ Commented Jul 25, 2015 at 13:24
  • $\begingroup$ You should start by familiarizing yourself with some basic concepts and proof techniques, for example by working through one of the books mentioned here. Then you can choose a topic, like abstract algebra or calculus, and dive in (you can find many good book recommendations by searching this site, also consider looking at questions tagged reference-request). $\endgroup$
    – A.P.
    Commented Jul 25, 2015 at 14:58

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