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This is embarrassing, but I'm a graduate student in a mathematics program and I'm terrible at writing proofs. My computational skills are strong but proofs, not so much. I want to go on to complete a PhD in math but know this area needs improvement. Are there any texts or other resources you suggest?

  • Does this or this help? – J.G. Apr 22 '20 at 19:30
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    If you made it to graduate school you are probably not as bad at writing proofs as you think! –  Apr 22 '20 at 19:30
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    What about proof-writing do you find difficult? Do you struggle to figure out arguments for why facts are true? Or do you struggle to convert arguments that make sense in your head into writing? – Alex Nolte Apr 22 '20 at 19:34
  • Thanks, @J.G., I'll review the list later. The final semester of my degree I needed two independent math studies to graduate. I requested one on proofing techniques but my advisor felt I was fine and encouraged me to take up another topic instead. –  Apr 22 '20 at 19:35
  • Thanks, @TokenToucan. I'm sure my skills aren't inadequate but it does feel like the proof problems in graduate work make less sense. I'm sure I'll acclimate soon enough. –  Apr 22 '20 at 19:35
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    I also recommend just typing out your own proofs for practice / reference. It is a great way to make sure you actually understand something, and I also find that (I guess unsurprisingly) my own notes make the best reference material for myself. On that note, I also got a lot of practice answering questions here on stack exchange. It forces you to think about how to communicate. – pancini Apr 22 '20 at 19:35
  • @AlexNolte, I find pulling the right information to justify my claims frustrating. I took a graduate abstract algebra course I withdrew from since the instructor did not like my proofing style and I think that's where my self-consciousness originated from. I'm a very logic-oriented person (I do well in things like philosophy) and have the creative potential to see how approaches work (I'm a prolific rookie composer/film orchestrator as a hobby). –  Apr 22 '20 at 19:37
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    Adding to this, it is useful to read your own proofs several weeks after you wrote them. You will start to notice why things were not as clear as they seemed when you wrote them, and where the weak points are. The flow of language is also easy to mess up since it usually takes much longer to come up with a proof than it does to read it. – pancini Apr 22 '20 at 19:39
  • Thanks, @ElliotG. I try to do that with my homework/text problems but sometimes I feel like these resources are a crutch. I find answering questions here rough sometimes. More often than not an administrator will close my question or ban my response because they feel it didn't meet the guidelines despite fully answering the question proposed.

    I agree. I did complex analysis as an undergrad independent study and it made no sense. I have an A in the course at the graduate level (thank God it's mostly computational).

     –  Apr 22 '20 at 19:39
  • Does this answer your question? Basic book about mathematical proofs – user1110341 Oct 08 '23 at 18:45

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A really great book for acquiring the ability to write proofs, and gain confidence in doing so, is Daniel Velleman's "How to Prove it: A Structured Approach".

Even using it for self-study, or as a reference, will prove helpful. It covers logic, and is very logic-oriented, so you may really like it.

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amWhy
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    Compensatory upvote. – Brian Tung Apr 22 '20 at 19:40
  • Thanks, @amWhy. I'll definitely read this book. Despite my organised tendencies mathematical proofing is one area that remains rather entropic. –  Apr 22 '20 at 19:41
  • I encountered this only as a grad student, as a TA, after some logic, and such, and used it in a course, as a supplement, and, I've recommended it to undergrads and grads alike since. – amWhy Apr 22 '20 at 19:43
  • Excellent, I'm glad you're able to attest to the usefulness of this resource. –  Apr 22 '20 at 20:46
  • Is it related to construction Algebra? – Mikasa May 30 '20 at 10:59