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I am very very interested in mathematical proof. I have learned basic proof techniques such as contradiction, mathematical induction, inclusion-exclusion etc.

So, I want a list of mathematical proofs which must be basic to advanced. Example...

  1. Pythagorean Theorem.

  2. Mathematical induction.

  3. Proof by contradiction.

  4. pigeonhole principle.

    ................................

    ................................

    The second question is: Proofs that every mathematician should know. I am also want to apply this proofs techniques to prove the equation that comes in math Olympiad.

SKL
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  • The Pythagorean theorem is not a proof technique. It is a theorem. – Bernard W Jun 06 '17 at 07:04
  • Oh.Sorry..It may be.. – SKL Jun 06 '17 at 07:06
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    You should probably break this up into two separate questions. Firstly, is there a list of 'proof techniques', if not can someone provide one. Secondly, is there a list of proofs that every mathematician should know.

    They are separate questions with separate answers.

     – Bernard W Jun 06 '17 at 07:06
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    Even your first question is too broad, probably. The second should definitely be formulated as another question. –  Jun 06 '17 at 07:17
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    I also think that you need to better define your focus. Very loosely speaking, but in a way math Olympiads are geared towards "sprint runs", while longterm math aptitude is more of a "marathon". The two are not the same, and don't necessarily work on the same optimal training curve. – dxiv Jun 06 '17 at 07:19
  • @dxiv is completely right...! But if you like math Olympiads then you can see as an example, an interesting proof technique, called Vieta Jumping. – Marios Gretsas Jun 06 '17 at 07:49
  • https://en.wikipedia.org/wiki/Vieta_jumping – Marios Gretsas Jun 06 '17 at 07:50
  • Wow this list can be very long... – Yanko Jun 08 '17 at 21:59

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