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Proofs- what should I do?

  1. Jun 1, 2005 #1
    I want to be a physicist when I'm out of college, but I see a humongous obstacle in proofs. See, I had taken Calc III and Diff Eq earlier this year, and aced them, but when I got to linear algebra, my first proof-based course, my grade dropped to a C+. (I have my final tomorrow, btw, and I'm dead there. You can see my thread there in the linear algebra section. Help would be appreciated :smile: ), but the purpose of this post is how do I learn to do proofs well? Any books you would recommend? Will physic's students math courses involve proofs? If so, I can't be a physicist. :biggrin:
    Thanks.
     
  2. jcsd
  3. Jun 1, 2005 #2

    honestrosewater

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    Others will probably recommend that you practice and be observant- try to glean as much as you can from the proofs you read. While I agree with that, I think you should also learn some basic logic. If you can't find a decent book at the library, I can teach you some things that have helped me. Seriously, if you want, I'll start another thread. It pains me to see people stuck on problems that would be obvious if they just knew some basic logic. (BTW, I'm not saying the problems you posted are obvious- I haven't looked at them.)
     
  4. Jun 1, 2005 #3
    from what i remember the "math for physics" courses weren't as proof-intensive as the "math for math" courses. i think generally the "math for physics" courses had much more computation than the others. there were some easy proofs, but generally i think the emphasis was on computations.

    as for learning to do proofs, learn some logic, set theory and proof techniques like induction, contradiction, etc & work on that stuff. those are the basics that you'd need to do any proofs no matter what subject. i would do that first & then maybe you won't be so mystified when it comes to proofs.
     
  5. Jun 2, 2005 #4

    matt grime

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    And you need to learn to distinguish between tools for proving things, ie understanding induction, contradiction and what "the contrapositive" is and actually working out how to do a proof.

    A proof is 'simply' a series of logically valid deductions from a premise to a conclusion. You need to get used to recognizing what things can be deduced from statements, and experience is the best way to do that.

    Finally, for now, something that is key, and that few people seem to understand first time out, when you're asked to prove something is true in general, say for all vectors in R^3, then you cannot just pick a specific vector, eg (1,0,1), and just check it for that case.
     
  6. Jun 2, 2005 #5
    there is a course called Introduction to Logic which comes seperately ...Does that help in mastering Proofs.
     
  7. Jun 2, 2005 #6

    matt grime

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    It would entirely depend upon what the course was teaching. As I told you in a PM, the content of a course is not deducible simply from its title. With my educational background I would not expect to see a course on "logic theory" in a mathematics program until at least two years after having to "prove" your first theorem. In the US it may well be that such a course is a precursor to "proving" things.
     
  8. Jun 2, 2005 #7
    here's a book for you
    Larson- "Problem solving"...I hope you get the right book from that. I'm to lazy to walk 2m to get the book
     
  9. Jun 2, 2005 #8
    that book is all about solving putnam-style problems, not the fundamentals/basics of doing proofs. one thing at a time....
     
  10. Jun 5, 2005 #9

    Meir Achuz

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    Mathists like proofs. Physicists like to use math. Become a physicist.
    I teach Math Physics. While there are proofs, they are only proofs with a point.
    You should take a Math Physics course or look "Math Methods of Physics" by Arfken (any edition, the earlier the better). It is a grad text, but I don't know of any good UG text. Stop worrying. Just get on with it.
     
  11. Jun 5, 2005 #10
    Meir Achuz:
    Sorry to butt in on this thread, but could you answer my question here:

    https://www.physicsforums.com/showthread.php?t=77380 (bottom of the page)

    thanks
     
  12. Jun 6, 2005 #11

    Meir Achuz

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    I just answered in that thread. Your question there, asking for a mathematical answer to a problem (air resistance) that an untutored child could answer from experience, illustrates the difference in approach of a mathist and a physicist.
     
  13. Jun 6, 2005 #12
    Good, maybe you'll be able to answer my untutored reply to your answer. Where did you do your physics PhD, if you don't mind my asking? I need a backup school to apply to.

    edit: by the way, are you implying that I'm a mathist? Why, I've never been so insulted! :biggrin:
     
    Last edited: Jun 6, 2005
  14. Jun 7, 2005 #13

    Meir Achuz

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    Sorry, but if you quack like a duck...
    I'm glad you're planning further study.
     
  15. Jun 7, 2005 #14
    Can you at least tell me what equation a guitar string satisfies in the model you were talking about? Is it a nonlinear one?
     
  16. Jun 8, 2005 #15

    Meir Achuz

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    The vibration of a guitar string is linear if there is no air resistance.
    Air resistance is generally non-linear. The force on a moving object varies
    (I recall) with velocity to some power between two and three, depending on the shape of the object. The flow is usually turbulent, so no simple equation applies, although you sometimes see one in an elementary book. But that is usually a gross simplification. In Math Physics books, the dissipation is often described by a term
    \gamma(dy/dt) in the wave equation. That is a gross simplification, but leads to simple equations for the "twang".
     
  17. Jun 8, 2005 #16
    Yes, that is the linear damping term I was talking about. And I believe it leads to the prediction that the different modes die out uniformly. That is why I was asking you how you model the string to predict the "twang" phenomenon, in which the higher modes die out faster.

    edit: perhaps we should continue in the original thread?
    https://www.physicsforums.com/showthread.php?t=77380
     
    Last edited: Jun 8, 2005
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