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Applicability of Algebraic Geometry (and all the rest of math that goes with it)

  1. Nov 5, 2009 #1
    Applicability of Algebraic Geometry (and all the rest of math that goes with it)

    Hello fellow mathematicians and physicists. I’m at that crossword in my university life right now, fall semester of sophomore year, and I really could use some advise in my next load of classes. I have always wanted to be a math major. Apart from choosing a subject which to me carries a lot of mystic (maybe second to Quantum Mechanics – but hey, group theory is also a subset of that), I knew that one day, whatever math I learn will give me a new angle in attacking whatever physical problem be it in engineering, physics or economics. In that regard, I always seeks to learn math both in breath and depth.

    Well, I starting to loose confidence in this path of mine. Unlike most college students who try to graduate with the highest GPA or join the honor society, my goal is somewhat unique: I want to come out of Duke university getting an ‘A’ in Algebraic Geometry. I understand that this class is perhaps the last class you’ll take in the list of graduate requirements but realistically speaking, I came into college having done multivariable calculus. So having 4 years to march through Real Analysis -> Algebra -> Topology -> Algebraic Topology -> Complex Analysis -> Commutative Algebra -> Algebraic Geometry (as the sequence in my school) seemed quite reasonable.

    Now, here is where I need some help. I don’t have a clear understanding of what Algebraic Geometry is in particularly it’s usefulness in the other sciences. All I hear are phrases such as ‘The subject that leads us to the deepest waters of math’ or ‘Mathematicians learn Algebraic Geometry to conquer the world’. Sure, that sounds impressive and it surely adds to the mystic factor I so desire in learning math. Yet I need to know the answer to a more practical question, one which answers my intent of learning math in the first place: “Will I one day look at a engineering problem, say Aerodynamics or Control Systems, and say “Yes, let’s employ an Algebraic Solution””

    The answer does depend on the level of advancement in Algebraic Geometry and this I totally have no idea of. Calculus has certainly matured where double integrals are undoubtedly fused with engineering. My question is that as of NOW or maybe in the next 2 years, does Algebraic Geometry already have its practical uses in Engineering.

    If the answer is no or perhaps it’s usefulness will come in say 10 years later, then I would have missed the mark because with all the respect I have for Pure Mathematicians, I would love to learn math so as to use math and not prove a theorem which only exist in the abstract realm (which I sometimes do but that’s not where my main interest lie).

    Thanks for listening and any advice is greatly appreciated.
  2. jcsd
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