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Breaking a habit

  1. Dec 3, 2009 #1
    I've been skimming some upper level (undergrad) math texts, and I have a feeling I'm in for a big surprise.

    Up until now I've been able to just glance at a question and understand how to get to the solution, and sometimes figure it out on the spot. As math becomes more symbolic, I feel as though I can't just look at a question and figure it out, the symbols are freaking meaningless. I actually have to ... understand? the question, to the point where reading the question itself seems to be half the battle. Does anyone have tips on how to get past the at-a-glance method of solving? It works for now, but I fear that it won't work for long.
  2. jcsd
  3. Dec 3, 2009 #2
    Develop proper study habits, even if it seems trivial it will help you be able to quickly focus and understand as you progress in math. Math definitely does not stay as something that you can glance at and understand quickly (for most people). However with the proper study habits you can develop this it'll take time and plenty of focus though... which if you don't help develop now (even while it seems easy) you may never get the hang of it until it's too late.

    As well don't be shocked you don't know what undergraduates learn in math... you haven't even learnt about that stuff yet probably what grade are you in? I would be much more surprised if you had said you DID understand it. :tongue:
  4. Dec 3, 2009 #3
    I have always thought of it in this manner, if you are a musician you should understand easily my point. What makes a good musician is one who is able to go beyond technical performance, and concentrate on interpretation. In order to be able not to worry about the handling of the instrument (technical performance), one has to play the instrument every day, repeat fundamentals over and over again, until the instrument is almost another part of the body, until it feels natural.

    When reading for the first time significantly higher level math concepts, you are not yet aware of them, you do not yet have a natural mental picture of those objects, they do not yet fit into your mathematical landscape. You certainly do not have to worry about that, on the contrary you should be excited, because you are on the verge of expanding your mathematical horizon. In order to be familiar with those new constructions, the only way is to manipulate them by yourself. Yes, all I am saying is : work.

    I often repeat this quotation from one of my math teacher
  5. Dec 4, 2009 #4


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    read (or at least skim) the chapter first, then look at the questions, then you'll know where to go back and look in the chapter for particular challenges in the question.
  6. Dec 5, 2009 #5


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    Heh, welcome to the world of having to work to understand and achieve something! It's how higher learning is supposed to be. If you're willing to actually keep up with it, don't freak out about it too much, you're not there yet. Remember, everything you are good at now you were once a complete amateur.

    Also, yes, math does become more symbolic and, at first glance, more meaningless as you go up in rank. The focus becomes less about concrete computation and more about rigorous definition and treatment of concepts and patterns, regardless of their possible practical applications. I guess it's part of what they mean when they say "pure mathematics."
  7. Dec 5, 2009 #6
    When I was in grade 6 .. grade 10 math had really strange and scary symbolic characters .. now whenever I try to read grad level books, I feel the same.
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