Abstract algebra vs. upper division mechanics for applied math: can only take one

  1. Hey all,

    I'm currently a pure math major, though I'm leaning towards going to grad school for applied math, specifically dynamical systems and climate modeling. This semester, upper division abstract algebra and upper division classical mechanics are only offered in the same time-slot. I know abstract algebra isn't *that* important for applied mathematicians, but it's still very fundamental material that every mathematician should have familiarity with.

    Which of these courses should take priority? I can make a case for both: the case for mechanics is that it's very basic physics and highly applicable to dynamical systems. The case for abstract is that it's also very basic, but for math in general, and also since I just took linear algebra and it's the natural sequel to that course.
     
    Last edited: Dec 30, 2011
  2. jcsd
  3. I think classical mechanics is pretty essential. I'd take that. Its entirely possible to do climate simulations without abstract (a professor is an example). Still if there is anyway to do both I'd do that.
     
  4. have you taken any algebra at all? If not, then you should take algebra without a second thought.. if you want to be any kind of mathematician, you will definitely need to know about algebra.
     
  5. I've taken linear algebra.
     
  6. micromass

    micromass 18,668
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    You can't call yourself a mathematician if you didn't take abstract algebra... You should at least know something about groups and rings. Even if you'll never need it again.

    Abstract algebra isn't as useless as you think it is though. It's very likely you'll never need it, but you never know.
     
  7. Abstract algebra is the proper language for many concepts in linear algebra, calculus/analysis and discrete math. If you don't have any abstract algebra under your belt, you don't really understand any of the mathematics that you've studied.
     
  8. You should read the Wikipedia articles on abstract algebra out of curiosity. However, it does not appear to be nearly as necessary for you to grind through in detail as much as the other subject, so take the other.
     
  9. Thanks for all the responses. I think the choice I'm presented with this semester is, if you will, some sort of vague sign that will indicate the direction of my career path, in that choosing algebra will pave the way towards becoming a mathematician, while choosing mechanics will nudge me towards the career of a mathematically-trained scientist. In consideration of the opinions expressing the importance of algebra, I'll keep a thorough treatment of the subject high on my list of academic priorities. However, I think my current aspirations would be much better served by the earliest possible development of physical intuition, so that classical mechanics is likely the wisest choice in my situation.
     
  10. I will add that if you take subject X, and it does NOT click for you as much, it could nudge you in the OPPOSITE direction. Never make decisions based on introductions. Go a bit deeper. Both of these subjects can be useful in various directions, and one mistake often made is oversimplifying what a field consists of.
     
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