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Reading proofs - impeding learning?

  1. Apr 5, 2007 #1
    When solving a problem, the last thing you want to do is look at the solution. When you're trying to prove a theorem, axiom or whatever, is looking at a proof something that would impede your learning? To me it seems that the answer is yes. Looking at a proof removes the thinking process so essential to learning. What's you're take on that?
     
  2. jcsd
  3. Apr 5, 2007 #2
    reading a proof helps you try to learn the process to prove a similar problem or to learn tricks that may combine on a totally different problem in math.

    Hence when reading a proving techniques proof. You read through them and then apply it to the text problems.
     
  4. Apr 5, 2007 #3
    Just take a minute to think of how you would attack the problem. If you've been working through a textbook and you come to a new result, you should usually know everything required for the proof. So it never hurts to give it a little bit of thought on your own before going ahead and reading it.
     
  5. Apr 5, 2007 #4

    JasonRox

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    Hmmm... I disagree with that.

    There are many proofs that have many spins on them that not that many people would have thought of it. In fact, usually only one person has thought of it.
     
  6. Apr 5, 2007 #5
    It is important to solve proofs to build skills, but it is also important to read proofs so that you have a body of knowledge and techniques to draw from.
     
  7. Apr 5, 2007 #6
    If you are trying to prove an axiom you have much bigger problems than "looking ahead"
     
  8. Apr 5, 2007 #7
    Is your question about when trying prove theorem A and can't do it. It would be bad to just look up theorem A in a book?

    So it's just like looking up a solution to a problem that you can't do. That is always not recommanded but compare to spending 3 or more hours doing that problem when you have other subjects as well, I would look up the solution. At least you can learn something from looking at the solution. But make sure you have a good go at the problem or proof first.
     
  9. Apr 5, 2007 #8

    JasonRox

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    Also, when you're doing a problem, it's ok to look at the solution after awhile of not solving. Just think about the techniques you think you would take, but just can't finish it up. And see if they used that technique, if not, you learn a new, if yes, then you know you're going in the right direction and learn how to apply it.
     
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