How to learn writing proofs? Could you give me some advice and sources, please? I have to learn how to prove, if I want to continue to study science. For now, the fields I am studying are real analysis and linear algebra.
I guess some of the tips are:
1) finding good books - appropriate for my level of knowledge, with a comprehensible style, yet introducing the concepts to the reader by definitions and proofs. I think a good book in this regard is: Calculus in one variable by Tom Apostol. Still, I am not sure if I've found the right one for learning linear algebra. Any suggestions?
2) Get in used with the mathematical language, which for me is very difficult, as I am a scholar coming from the humanities.
3) Learning definitions well and trying to make a mental picture of everything. Trying to put some effort in solving proof-exercises before asking for any help.
4) In my case, as I don't think I am very intuitive in math and as I miss some background, it would be really good to have a tutor. i.e. private lessons - of course, this means spending money but if this is the only way for me for learning better and faster and passing exams...
5) I have also got some books which introduces the reader to proof writing and learning how to prove but I don't have much time for that readings, unluckily, as I am already overwhelmed by homeworks.
Could you please add some pieces of advice as well as some literature I might find of more help, please?