Found 2 comments on HN
timwiseman · 2010-08-05 · Original thread
I do not know if it is exactly what you want, but Chapter Zero ( http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Math... )comes close. It talks about a lot of the foundational mathematics that and symbolism that is often never taught to non-math majors, but it does so in an easily understood way.

Proofs and Refutations by Lakatos also touches on this topic, though it is not the primary or sole discussion there.

tokenadult · 2009-10-28 · Original thread
This Chapter Zero,

http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Math...

right? I have not read this particular book, but in general most students who desire to study math should take a look at a "transitions course" textbook or two, to fill in the gaps left by studying only in the fast lane to calculus.

http://www.amazon.com/Mathematical-Proof/lm/R3LUNI80ZOUYK4/

http://www.amazon.com/Mathematical-logic-and-foundations/lm/...

http://www.amazon.com/How-solve-prove-books-useful/lm/31B4QV...

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