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In my math tests, I often miss little edge cases or exclude details that I would not have in homework. For example, my proof of why the root of a prime is irrational was:

Take some prime p. Suppose root p is rational. There exist some integers m and n such that root p is $m/n$ with n not equal to 1, so $m^{2}/n^{2}$ is equal to p. Since the integers are closed to multiplication, p is prime.

I find no issues with homework-- the gift of time seems to fix my problems (literally).

  1. What should I be practicing? Is my issue a weak grasp of logic?
  2. How do I practice whatever my issue is?

I've read and reread this post ad nauseum; it's helped but I don't think problem solving is my issue anymore.

EDIT: per the comment below by (dbx), I realize that the issues for me are:

  1. I struggle to be organized with my thoughts under pressure. It makes me make mistakes of logic. I also need to organize how I write notes so that I can
  2. I'm struggling to be "honest" with myself when I review my answers before submission. I can't seem to spot my own errors.

Do you have suggestions on how to practice each of these? I've been trying to simulate time pressure, but I was hoping for a process on how to organize my thoughts and notes.

skm
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  • Read the arguments you wrote down, forgetting that it was you who wrote them. Are they sound and convincing? – The "proof" you gave for $\sqrt{p}$ being irrational surely isn't convincing: it starts by assuming the claim is false but never reaches a contradiction. – Christoph Dec 18 '20 at 14:39
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    think about what resources you are using when you work on homework that aren't available to you during a test. Are you referring to definitions or theorems that you don't have memorized? Are you referring to other proofs, or glancing through your notes? The true test of whether you're prepared is whether you can do the homework, etc., in similar conditions to an exam. – Sort of Damocles Dec 18 '20 at 15:23

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