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UIUC's NetMath online program?

  1. Dec 20, 2007 #1
    I'm thinking of taking Multivariable Calculus through UIUC's NetMath online program:
    The course is taught largely through Mathematica notebooks:
    Does anyone have any experience with this program or have any advice on whether it's a good way to learn math? It's difficult for me to attend courses in-person, and I'm not really cut out for self-study. So this seems like a good compromise.

    I am not looking for a theoretical understanding of math, I'm more interested in it as it applies to physics. I'm not looking to earn a degree, I just want to learn.
  2. jcsd
  3. Dec 21, 2007 #2
    "I am not looking for a theoretical understanding of math, I'm more interested in it as it applies to physics. I'm not looking to earn a degree, I just want to learn."

    If your end goal is to crank out some integrals to solve intermediate mechanics style problems, then you don't need a good understanding of the math. On the other hand if you want to learn modern physics (or even old physics, e.g. GR), you will certainly need a deeper understanding of the math. For example you need to know advanced calculus well so that you can go on to learn differential topology and geometry. You'll want to learn 'multivariable calculus' at the level of Munkres (https://www.amazon.com/Analysis-Manifolds-James-R-Munkres/dp/0201315963/ref=pd_bxgy_b_text_b) for this.
  4. Dec 21, 2007 #3
    It depends on whether or not he wants to go into theoretical physics. I won't ever have to look at differential topology. So it depends on your goals.
  5. Dec 21, 2007 #4
    I looked at a few of the sample Mathematica notebooks and wasn't impressed. The tools they use to generate pictures are unintuitive enough that they could be hard to pick up on your own. You're also always focused on nitty-gritty examples, which may obscure important aspects of the big picture that are helpful whether you're interested in theory or applications. I hope there is also some sort of companion text.

    I think conventional textbooks would probably be a better approach, but I'm not sure if there are online courses available that use them. Certainly taking an course in whatever way it is designed is helpful, and UIUC is a respected institution, so you should learn things. If it's the best option you have, you certainly nothing to lose and you can always learn the math at a higher level later if necessary.

    Whether it will be good enough to make you comfortable with applied math for physics is impossible to say. Multivariable calculus is relied on virtually everywhere in physics above the introductory university level, so having a solid understanding of it is important to future studies. To some extent, a "solid understanding" means knowing how things relate theoretically, just not how to calculate things.

    Still, if you're just starting out learning multivariable calculus, a text like Munkres is far above the level you will need for quite some time -- it will be at least several years until you arrive at fields like particle physics and general relativity. Even then, I'm not convinced that knowing math at that level of theoretical sophistication is necessary.

    My background: undergraduate physics/math major in my final year.
  6. Dec 21, 2007 #5
    Thanks for looking over the coursework. I'm planning to use a paper textbook along side the online work, just to make sure I'm getting a full perspective. This will be my first exposure to vector calculus.
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