I was wondering if there is a good way to learn "maths in english". I am studying mathematics in Germany (I am from Germany, so english is not my native language) and have recently started to work with english papers, textbooks etc. Reading them is alright so far, although I had to get used to some sentence constructions (but this was also the case when I started studying maths, as mathematicians tend to have their own grammar, so that is fine with me).
My question aims to writing/speaking "mathematical english". As far as I'm concerned there are (at least) two things I'd like to learn:
- Get the "basic theorems" right. For example if someone wants to show that there exists a unique solution to $x=\cos(x),x\in\mathbb R$, I'd suggest to use the "Zwischenwertsatz". Using wikipedia I can find that the "Zwischenwertsatz" is the "Intermediate value theorem" and of course I can do that for every specific theorem and eventually learn the translations, but I find it rather annoying to consult wikipedia whenever I want to talk about a specific theorem. I guess I'm looking to suggestions for good textbooks that cover these basics; they don't need to be "good" in a way that they have lots of exercises including solutions, online support or anything like that, but have a "good style" of mathematical writing, which ties to my second point.
- Get the "style of writing" right. Of course, learning by doing should be a good thing here, but living in a german environment so far I didn't have many chances to write in english. My first attempt to writing maths in english actually happened yesterday here on stackexchange, and it took me quite a while until I was satisfied (and at least thought it to be "readable"), much longer that it would have taken me to write the same thing in german.
Can you suggest anything that I should read/do to achieve this?