How to Read Mathematics

There's a few books on how to approach books and problems, e.g. don't strain on first seeing new material. Lara Alcock wrote 2 books on studying math which seem to have the same ToC, a lot of undergrad programs have materials on proofs and how to transition from high school problem solving: http://web.archive.org/web/20150319020039/http://www.maths.c... Mathoverflow and math.stackexchange soft-questions tag has lots of mini-essays, e.g. https://mathoverflow.net/questions/143309/how-do-you-not-for... and…

If you like this, you might enjoy this delightfully funny, yet effective, introduction to calculus book from 1914: http://www.gutenberg.org/files/33283/33283-pdf.pdf It starts by ranting about uppity mathematicians and academics while showing how simply you can get your head around basic calculus.

" Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis? " -Paul Halmos, inventor of "iff" and the ∎ symbol ( http://en.wikipedia.org/wiki/Paul_Halmos )

I wish I had this advice when I started university! Back then there was no web. Kids these days, they are spoiled!