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Advice on taking ODE without calc III (goal is math grad school)

  1. May 19, 2012 #1
    I feel very comfortable doing this because I've taken numerical analysis and written a short term paper on numerical approximations for PDEs. I am very strong in linear algebra and have calc I/II.

    The reason I ask for advice is because I have just graduated from undergrad with a degree in comp sci but I'm taking extra courses through a non-degree program at Columbia which will let me skip calc III. I want to apply to graduate school in a few years for a masters in something like applied mathematics. Assuming I can do well, would it reflect poorly if I've taken upper-level mathematics courses without calc III under my belt?

    The most math I have is calc I/II, linear algebra, and intro statistics (economics focus).
  2. jcsd
  3. May 19, 2012 #2
    You don't honestly need much knowledge of multivariable calculus for ODE's to my recollection.

    Multivariable calculus is pretty important though, especially for applied mathematics. In the physical world, many systems are modeled by PDEs (for this you should have a decent knowledge of vector analysis, linear algebra, surfaces, etc. [some of which is covered in calc 3]). I recommend you take calc 3 and ODE, and then PDE.

    Just my 2 cents.
  4. May 19, 2012 #3
    Thanks for your reply. So what you're saying is that I would be lacking a fundamental piece of my mathematical education by skipping calculus III entirely, is this correct?

    The session I'm looking at is in fact condensed in to a month-long semester. I think it may be difficult to do both calculus III and ODE at the same time unless you suspect there will be significant overlap in the material or my linear algebra/numerical analysis background will help me through one or the other?
  5. May 19, 2012 #4
    You don't need calcIII for ODE but you should take Calc III for your future goals. There were a few things from calc III in ODE but they were quite simple and you probably already know them since you dealt with some PDEs.
  6. May 20, 2012 #5
    Calc III is fairly straightforward, he can learn any concept form it at any time when needed.
  7. May 20, 2012 #6
    My main concern is that an admissions committee would disapprove if I took upper-level courses and never finished the calculus sequence, even though I can do well in the upper-level math courses like ODE.
  8. May 20, 2012 #7
    Disclaimer: I have never been a part of an admissions committee so take my words with a grain of salt.

    If you ace a class like ODE, I don't see how the committee would look bad at you. If you do bad, however, I can see how they might think that you haven't achieved a good level of mastery of the material.

    Though, there are people who test out of calculus and other classes, and I'm sure their only more competitive because it shows maturity and that you can handle the material.

    Broccoli21 for example tested out of the whole calculus sequence along with differential equations, and I'm sure the admission committee wouldn't disapprove of that. It is all the more impressive.
  9. May 20, 2012 #8
    Usually, if you've handled other classes that show your foundation is probably not lacking, they don't care. If you handled linear algebra, then you have the sophistication needed to deal with most multivariable ideas.

    None of this would be an issue if you studied, say, differential topology, which effectively combines linear algebra and multivariable calculus in its foundations.
  10. May 27, 2012 #9
    I just took a diff eq class, and although it was technically a prerequisite, we hardly used multivariable calculus at all--just for the last week or two when we looked at PDEs. Linear algebra, which was only a suggested prerequisite, actually showed up way more often.

    That being said, I don't know how severe the long-term consequences of skipping multivariable calculus would or wouldn't be.
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