1
$\begingroup$

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?

$\endgroup$
  • 1
    $\begingroup$ If you don't have time for reading, then what's the point of asking for literature that you might find helpful? $\endgroup$ – Gerry Myerson Nov 8 '15 at 11:38
  • $\begingroup$ I mean, I think it is better in this moment reading books about real analysis and linear algebra, instead of books about proof tecniques in general. As I said, I've got the last ones too and started to read them but now I realize I have only time for the first ones, for which I am asking advice here, and for the homeworks, which are mandatory. $\endgroup$ – Always learning Nov 8 '15 at 11:51
  • 1
    $\begingroup$ @Alwayslearning: Are you a math student in university? :) $\endgroup$ – H. R. Nov 8 '15 at 11:54
  • 1
2
$\begingroup$

How to read and do proofs by Daniel Solow is pretty helpful. But learning to proofs, like anything in mathematics requires A LOT OF PRACTICE.

$\endgroup$
  • $\begingroup$ Yes, I have got this book already and liked it. $\endgroup$ – Always learning Nov 8 '15 at 11:52
  • $\begingroup$ do you have a recommendation for linear algebra as well? $\endgroup$ – Always learning Nov 8 '15 at 11:53
  • 1
    $\begingroup$ If you're going to learn a subject, make sure you're studying from the books written by the best people in the field. I would recommend Manin's linear algebra. $\endgroup$ – Brandon Thomas Van Over Nov 8 '15 at 12:02
  • 1
    $\begingroup$ @Alwayslearning, that sounds like another question... but look for Treil's "Linear Algebra done Wrong" (it's available for free in the 'net). $\endgroup$ – vonbrand Nov 8 '15 at 12:08
  • $\begingroup$ Thank you! But it is not another question! If you read again the body of my post, as well as the keywords, you should get it $\endgroup$ – Always learning Nov 8 '15 at 12:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.