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How can I learn to enjoy mathematics more?

  1. May 15, 2014 #1
    I love aspects mathematics, especially those which when I can apply it to real situations. However, when mathematics becomes so abstract like aspects of precalculus/calculus it becomes faint for me, at times. How do you keep it fresh, interesting and rewarding? I am a computer science major and I want mathematics to be my best friend. In short, I am just wondering what tips you can give me to keep mathematics interesting.

    Thank You
     
  2. jcsd
  3. May 15, 2014 #2
    This is just my opinion, but very little of the mathematics taught in "math class" beyond the arithmetic of primary school and the basic algebra of middle school is intended to be used/useful "as is". You take the classes either to become familiar with the language of math so that you can be successful in other classes or to train your brain in abstract thinking and a particular brand of problem-solving.

    The courses specific to your major will do a better job of showing you how to use the math that you learned in calculus, linear algebra, discrete math, etc. to solve "real" problem, but that's assuming you've learned the material in the first place. So one place of motivation is that if you don't learn it today, you're gonna have some catching up to do later on.

    As far as keeping it interesting ... maybe try and see which problem types lend themselves to algorithmic solutions. Write pseudo code describing how to solve them. Some problems, like finding derivatives, are (almost) purely mechanical and lend themselves to fairly straightforward algorithms. Others, like finding limits, aren't so straightforward in general. But the types of limit problems that get assigned in calculus classes usually fall into one of three or four "categories". So see if you can identify the various cases and write an algorithm for each case.
     
  4. May 15, 2014 #3

    Simon Bridge

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    I'm with gopher - the more "abstract" maths you learn is about obtaining a toolkit - or a language.
    The fun in a language comes from how you use it, and tends to be personal.

    OTOH: you can always learn to like something by reinforcement - reward/punishment, you know.
    Much of school uses this Pavlovian approach ;)
     
  5. May 15, 2014 #4

    mathwonk

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    try to avoid abstract math. i think it is a perverse exercise in turning students off. but every now and then take a few minutes to ask what concrete math is being abstracted in a particular abstract treatment, i.e. try to render some abstract math less so. abstract math is only for people who already understand a topic and who want to see what the minimal number of assumptions are to discuss it formally. it is not at all for understanding a new subject. E.g try to avoid discussions of integration that begin by telling you what a boolean sigma algebra is, rather than what it means for a subset of the real line to have measure zero.
     
  6. May 15, 2014 #5
    If you're a programmer looking for calculus applications, I'd have to say computer graphics, particularly physics simulation. Of course, that requires you to learn computer graphics if you don't know it already and a little physics. There aren't that many actual programming jobs where you get to apply calculus, but this is definitely a place where you can put it to work from a hobby point of view if you know how. So, for example, I wrote a little program recently that simulates a ball the hits the ground and bounces, using 0.5gt^2, which is a somewhat trivial application of calculus to physics. More generally, you could tell the computer what the acceleration or velocity is and have it display the ball's motion according to that. That's one of the big applications of integration.


    If you think that's abstract, you ain't seen nothing. I thought I had reached the peak of abstraction when I took my first topology class, but I hadn't seen nothing at that point, either.

    The way I keep it interesting is to try to visualize a lot of it, but it can be challenging to do that, if your teachers don't explain it that way. This might give you some hints:

    http://www.maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf

    Not all of it is going to be thrilling, though, I think. Stuff like trig integrals just isn't the most riveting thing in the world, I think. I think the "application" of that stuff, if you want to call it that, is mostly just so that you get more practice applying the concepts in different settings. You may never use some weird trig integral, but learning how to do it could breed a little more familiarity with integration by substitution and other techniques. I think if you get though your calculus class and all you remember is what a derivative is, what an integral is, enough to do some basic examples and apply the concepts, plus the fundamental theorem of calculus, then that's 90% of the point of the class right there, for most people. You'll have a new way of looking at the world. The most useful part of it is probably just the basic concepts. But if you didn't spend some time practicing with it, doing problems, it wouldn't sink in as well.
     
  7. May 16, 2014 #6

    symbolipoint

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    You can learn to enjoy Mathematics more when you use some topics of it to make decisions allowing you to control practical things that you need at the moment. This can be either a quantity and decision for an academic laboratory exercise, or a situation for a job in the real world.
     
  8. May 16, 2014 #7
    Thanks for all the great response everyone! Yeah, I think that's the key homeophorphic I need to find ways of applying the mathematics to all sorts of different situations, even when it seems abstract. Similarly, I need to put into practice all mathematics I learn in my classes to my daily routines.
     
  9. May 16, 2014 #8
    Have you tried incorporating the mathematics you are learning into simple programs? This would allow you to practice programming and also see the mathematics in practice. You don't need to write anything fancy, just something that's tangible.
     
  10. May 16, 2014 #9
    As other have mentioned, since you're a programmer, try writing programs with the math you're learning. Precalculus isn't really abstract, as your professor should be showing you examples of how it can be applied, such as exponential growths (my professor loved to use bacteria growth for these), and other such functions and algorithms to do 2D rotation and scaling and 3D rotation and scaling.

    If you're into game development and programming, think back to the basics of Pong. It uses rudimentary physics for the ball speed, direction of movement, and angle.

    Think of precalc and calc functions as writing functions in your favorite programming language. A single argument function in programming is similar to a function of X, while a multiple argument function in programming could be loosely related to a vector.

    If your professors aren't giving applied examples of the material being taught, use some critical thinking, and thinking out side of the box, to see how it can be applied in day to day events.
     
  11. May 17, 2014 #10
    That's good advice with the pong programming I didn't think about it that way but yes there is a lot of calculus/physics that could be applied to it. And yes I am learning about exponential and logarithmic growths although it seems a bit confusing at times, are they essentially interchangeable? I know a little off topic but it's something that's been bugging me.
     
  12. May 17, 2014 #11

    Simon Bridge

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    Ask in a different thread if you want details.
    Short answer: no.
     
  13. May 17, 2014 #12
    There will be some portions you may have to research a little more to understand better, especially if you are one of those students who doesn't want to feel like "that guy" and ask a bunch of questions.

    In my experience (I've only ever been to community college so far), the professors generally don't go into much detail about a lot of the constants, like e or K (plus some constants in one form of math will be completely different in others), so some portions maybe be challenging to understand.
     
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