0

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.

Taeyun
  • 109
  • I'd recommend learning some fairly basic set theory (e.g. from one of those "introduction to proofs" books; I used http://www.amazon.com/Transition-Advanced-Mathematics-Douglas-Smith/dp/0534399002/ref=sr_1_fkmr0_1?ie=UTF8&qid=1437830301&sr=8-1-fkmr0&keywords=douglas+smith+introduction+to+proofs which was adequate) and then just...learning the math that interests you, rather than trying to work too hard on foundations. – Ian Jul 25 '15 at 13:19
  • 1
    (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 $e \in \pi$). – Ian Jul 25 '15 at 13:19
  • I'm not sure what your level is, but eventually you should try Rudin's books on real and complex analysis. – TorsionSquid Jul 25 '15 at 13:24
  • 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 [tag:reference-request]). – A.P. Jul 25 '15 at 14:58

0 Answers0