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Courses Help choosing math courses

  1. Jan 20, 2010 #1
    Hi all,

    I am finishing my last semester of undergrad as a geosciences major with a minor in mathematics. I have applied to graduate programs in Physical Oceanography. I have found (a bit too late) that I really enjoy mathematics and would like to make the most of my last semester in two (perhaps contradictory) ways: coming out with a well-rounded math background, but also having a useful arsenal of mathematics for graduate courses in geophysical fluid dynamics, modeling, etc. Obviously finishing this task up in one semester isn't really possible, but I was hoping some of you might have some insight into courses I might take.

    I have taken: Calculus sequence, vector calculus, linear algebra, ODE, PDE, real analysis I, fluid dynamics (taught through our applied math department).

    My options are: Numerical methods (I am quite certain I will take this one), real analysis II, abstract algebra I, complex variables, probability theory.

    While abstract algebra likely won't be particularly useful, I believe having a semester each of algebra + analysis would show me some of the highlights of mathematics. I have room for two, maybe three, classes total in the list above.

    Thank you for your time.
     
  2. jcsd
  3. Jan 20, 2010 #2
    Hey Chasing_Time..

    Obviously strengthening your PDE background would be the most beneficial for someone working with fluids.

    Fortunately PDEs span a large area of mathematical disciplines (in fact it has even created some of them) and so I would aim to take a sequence of courses which give you a better foundation with PDEs.

    Since you have most of the applied sequence of math courses I would then aim to take some of the more theoretical (pure) courses. In this case I would focus on strengthening your background in analysis through taking both complex analysis and real analysis II. If you can I would supplement these with a course on topology.

    Numerical methods are obviously helpful for many cases when an analytical solution is not possible.

    Later on you might want to check out the beginnings of functional analysis, tensor analysis, asymptotic methods, and similarity theory.
     
  4. Jan 20, 2010 #3
    numerical methods and probability theory. abstract is garbage (i took the first and am taking second semester right now), complex variables is only useful for cauchy integration which does come up i guess in doing fourier integrals which you know are used to solve certain classes of pdes. probability theory (as long as it includes stats) is way useful for empirical scientists. real analysis 2 is fun but it's not useful. stick to whats useful. you can always self study the other stuff as a hobby.
     
  5. Jan 20, 2010 #4
    Hi Coto and ice109:

    Two responses and two very different opinions! You each give me more angles to consider!

    Coto- Agreed on the application to PDE's (which is why I even took Real Analysis I to begin with). I hadn't before seriously considered Real Analysis II since here, the applied math curriculum (which I have used as a 'model' in my self-constructed minor) only requires Real Analysis I. If it is any help, the first semester covers Baby Rudin ch 1-7, the second covers ch 8-11. I attended the first complex variables lecture today and it seems very exciting. Topology isn't offered this semester, unfortunately. And yes to the additional topics you mention- we did much work with tensors in my fluid dynamics course, as well as used similarity solutions and asymptotics when dealing with boundary layers! From surveying the curricula of some of the programs I have applied to, I will have the opportunity to study some of these.

    ice109- Agreed on numerical methods. This has always seemed like an essential course for someone dealing with models. The probability theory course is pretty much just that- probability theory. It isn't a probability + statistics course. My intentions for considering this course would be for possible future work involving stochastic processes in ocean / climate dynamics (but I don't know if this warrants taking a full course).

    It seems safe to say Abstract Algebra I has been ruled out.
     
  6. Jan 21, 2010 #5
    I really enjoyed Complex Variables, and have already been surprised how many times I have used it for various forms of "real" integrals. Up to this point, it was probably my favorite course and I'd definitely recommend it.

    So, if you're going for math you'll probably 'use' later...I'd go with Numerical Analysis and Complex Variables.

    However, if you're taking them just for enjoyment and not for future 'purpose,' I'd actually think abstract algebra is something that you might enjoy and could actually help you later on with how you tackle problems (or it may not help you at all. lol)

    I suppose it comes down to taking classes that you think will benefit you and choosing which classes seem the most interesting, without worrying about future application.
     
  7. Jan 21, 2010 #6
    wow, you sound like a great student!

    probability theory is very fun in terms of pure maths, but in terms of applying it to your field you can probably pick up any counting arguments and knowledge of distributions without taking the course. except perhaps in rare cases, you do not need to understand sigma algebras and the like to get into the ocean and calculate any relevant probabilities...(I'm guessing)

    good luck!
     
    Last edited: Jan 21, 2010
  8. Jan 21, 2010 #7

    cronxeh

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    Definately probability. Stochastic modeling, dynamic systems, and numerical methods. Come to think of it, you are going for applied math areas, so real analysis, abstract algebra are not really useful unless you doing pure math track.
     
    Last edited: Jan 21, 2010
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