As someone coming to mathematical topics like analysis and number theory from outside, I found I was really limited by not having been taught
- the special use of English my mathematicians, eg "if and only if", "implies"
- the structure of a good proof
I was recently recommended Keith Devlin's Introduction to Mathematical Thinking which addresses these directly. The course is free on coursera.
After working through it, I realised that I was not fully understanding what I had been reading previously - for years! It also helped me understand when a proof needed to show implication in two directions, to prove an "if and only if" statement, for example.
As an aside, it also got me thinking deeper about the truth table for implication, which I'm still working out in my head... that will come up again during the exercises.
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