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Math Envy

  1. May 13, 2012 #1
    So I'm going to start my undergrad degree in applied physics this summer, and I'm having a particularly annoying case of math envy. I decided to brush up on my physics and math skills before I go to uni, but this made me realize that I'm actually very bad at proving math theorems and the like.

    For example, trigonometric formulas. In high school I learned that sin(s+t)=sin(s)*cos(t)+cos(s)*sin(t), but never learned what the proof for this was. It's much easier to remember something when you can prove it, because then you only need to remember the basic rules (which you most likely already know). However, looking at the proof of this formula made me think "wait, what? I could never come up with this kind of proof on my own!" Thus, math envy.

    Now of course I'm not even in college yet, but has anyone else who went into physics or math experienced a similar thing? Is it normal to not be able to come up with all these proofs for such formulas by yourself at this time?

    Thanks. :smile:
  2. jcsd
  3. May 13, 2012 #2
    Here's a good, innovative proof for sin(a+b) : http://oakroadsystems.com/twt/sumdiff.htm#sincosAplusmnB [Broken]

    As for math envy, I think its normal to feel it. You can't innovate everything, but you can do your bits. Keep at it, try finding your own solutions to given problems, despite what's said in the book, it doesn't matter whether you really can right now or not, just the desire is good, and someday, you can prove your own theorems!
    Last edited by a moderator: May 6, 2017
  4. May 13, 2012 #3


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    Hey KiwiKid and welcome to the forums.

    Just keep at it and don't stress too much.

    You should be aware that we all forget things and this includes mathematicians, engineers, scientists, and other people that use various mathematical machinery.

    The most important thing you should learn is enough that you can understand what is going on so that if you needed to pick up a book, then you could do it yourself (or largely by yourself) later on.

    If you eventually understand what something really means, then you will be able to get the right information to do what you need to do on your own. Even if you need some advice or a nudge in the right direction from another expert or specialist or from a colleague, the point is that you will understand what that all this really means and this is the key.

    If you feel like you don't have this kind of understanding, then ask your teachers, fellow students, professors as well as say people on this forum. Also read textbooks, blogs, and other sources of information because understanding is the thing that you will need.

    You will have to know things for your exam, but it's more important that you follow what is going on so that you can apply the right results and reasoning to do what needs to be done.
  5. May 13, 2012 #4
    I'm not sure why you'd expect to be able to do something that you have pretty much never done before in your entire life. Even people who seemingly are genius with this type of thing were in addition to their raw skill exposed to the foundational concepts at an early age -- foundational concepts you have never encountered.

    It's sort of like you have never played violin or studied even how to read sheet music. You then post a thread at violinforums.com, describing how you picked up a violin for the first time but couldn't use it to produce pleasant sound, thereby generating 'violin envy'. The post's tail then is inquiry into whether any members there have ever had the same 'violin envy'.

    People generally envy things they cannot have or are really hard to have. In this case, a regular amount of dedication will give you the experience needed to do what you apparently envy. Basically, the proposition of envy in this circumstance seems a bit far-reaching.
  6. May 13, 2012 #5


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    One of links on the page cited - http://www.maa.org/pubs/mm_supplements/smiley/trigproofs.html [Broken] - is perhaps more appropriate proof.

    With respect to the OP, if one was shown the basics, I'm sure one could arrive at the proof. It's a matter of exposure and familiarity with a subject.

    I have to wonder how many high school students are exposed to that level of detail. I'm concerned it is too few.
    Last edited by a moderator: May 6, 2017
  7. May 13, 2012 #6
    Definitely, that is a more geometric proof. I was just suggesting innovation in work, rather than stick-to-the-book-style which would hopefully bring in a love for mathematics (It worked for me :biggrin:)

    Very true. It comes down to a matter of self interest...
    Last edited by a moderator: May 6, 2017
  8. May 13, 2012 #7
    Thanks for your replies everyone. :smile:

    That's actually what bothers me. I don't know if I've learned enough in high school to do well in college, so I'm trying to learn as much as I can and getting increasingly frustrated about how little I seem to know.
  9. May 13, 2012 #8


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    In university, it readily becomes apparent how little one knows. The task/challenge is to overcome that, i.e., don't let it bother one.

    There is plenty to learn, and that will always be a fraction of what there is to know. Nature and the universe is rather vast. There is more out there than one could learn in several lifetimes.

    I realized in high school that there was a disconnect between math and the other sciences. I struggled in university to find the right math courses to cover what I wasn't getting in the physics courses. Really, it was a matter of taking the math in preparation for the physics courses ahead.

    It did learn my first year at university that there were mathematical concepts to which I had not been exposed in high school. I found that rather annoying.
  10. May 13, 2012 #9
    You're only in high school. You're not expected to come up with genius proofs for such things. The most you can do now is read the proof and understand it.
    If you advance more in your degree and get more comfortable with math, then you might be able to prove more things then you can now.

    Don't be envious, what you're going through is perfectly normal.
  11. May 13, 2012 #10
    Well, technically speaking I finished high school last year. :wink: This is a gap year, so to speak. You make some good points, though. Thanks for all the advice, everyone. :smile:
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