Math Proof Training Camp and Practice Guidelines

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Math Proof Training Camp and Practice Guidelines

We frequently get questions on how and where to learn to prove statements. The vast majority of scientists learnt them by doing. It is a try and error approach trained in tutorials and exams. This forum is meant to practice these techniques on a playground without the risk of bad marks or silly questions in a real tutorial. The goal is: e.g. How to Read and Do Proofs made interactive. Certain areas of science have typically certain proof techniques. Physics forums are naturally biased towards analysis in its widest sense, which mainly uses inequalities and limit processes. But linear algebra is also necessary, and that brings in different techniques: dimension considerations, specific properties, and often indirect reasoning. This forum is meant to practice proofs in all their presentations. Ideally you won't be surprised anymore when switching the field.

This forum is meant for young students to improve and practice their capability to write rigor proofs. Senior students and science advisors should be on the other side of the desk: posting simple problems which show a particular proof technique or request such a solution to practice. It is not meant for seniors to solve more or less simple problems, or answer what we can expect them to know anyway.

Proof techniques can also be important in the non academic world. E.g. if you have to staff a project, then it is necessary to distinguish person, role and function. These are three different properties and requirements. Practising proofs sharpens your eye to recognize such things. If you listen to e.g. politicians (country or party doesn't matter), you will note that they often turn around the implication in their arguments. "See it has rained, the road is wet." is such an example. True is, that if it had rained, the road would have been wet. But the statement in italics is wrong. There is a loophole which prevents the true statement to be turned around: Rain isn't the only possible cause for a wet road! Practising proofs means to sharpen your mind not to fall for such cheap tricks,

  1. All PF guidelines applicable to any forum apply here, plus the following.
  2. This forum is meant to practice mathematical proofs. Homework questions or textbook exercises are not allowed.
  3. We only use first-order predicate logic, and the Zermelo-Fraenkel system with the continuum hypothesis and the axiom of choice (ZFC+AC).
  4. Discussions about this or other logical systems belong in the appropriate mathematics forum.
  5. Posts which are welcomed:
    a. Examples to discuss a certain proof technique according to the available prefixes.
    b. Challenges to practice a certain proof technique according to the available prefixes. (not the challenge prefix)
    c. Questions about a certain proof technique according to the available prefixes.
    d. Discussions about a certain proof technique according to the available prefixes.
    e. Literature tips about proofs. (no prefix)
  6. Copyright restrictions have to be respected. If in doubt, quote where a reference is available, e.g. on amazon.
  7. Possible mistakes and errors are no problem, since this forum is meant as a tutorial and training camp.
  8. Only post a challenge if you know the solution. It is very unlikely that we will be able to prove the ERH.
  9. The Challenge prefix is reserved for the common challenge threads.
    Challenges according to a certain proof technique should get the prefix of that technique.
  10. In case of doubt, i.e. you are not sure whether your question is on the targeted meta level about proofs, or simply a specific question in a given proof, please contact a mentor to decide.
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