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Does a pure math major need to take ODEs?

  1. Mar 9, 2012 #1
    Right now I'm a sophomore at a state uni with hopes of getting into graduate school in pure mathematics.
    When I was a freshman, I surveyed the three major areas of math - analysis, algebra, and topology - and I decided that analysis was for me. Although I did very well in Algebra, I found it unbearably boring (is this a problem?) Anyway, as sophomore I've taken measure and lebesgue theory, complex variables, graduate group theory and rings all of which were graduate courses, and now I'm taking functional analysis, and probability, and algebraic topology.

    However, I was told I need to take ODEs - not even a proof heavy one. Just the typical "how to solve ODEs" course. I think this is ridiculous..as I could probably learn the material in a couple of weeks. Any advice on how to get exempt from this requirement?

    Thanks everyone.
  2. jcsd
  3. Mar 9, 2012 #2
    I can't comment to specifically on whether or not you should take the class but when I wanted to skip over the first semester of physics I just asked the department chair if I could and he said ok.
  4. Mar 9, 2012 #3
    If it is that easy I don't see why its that big of a problem. If however you are serious about getting rid of it, why don't you see if your school will let you challenge the course/pass out of it, then you don't have to take it. If not your kind of out of luck, not like its going to be a totally useless course.
  5. Mar 9, 2012 #4

    I like Serena

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  6. Mar 9, 2012 #5


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    What do you intend to do with that doctorate in mathematics? The great majority of doctorates become college teachers and, even if you do not intend to do that, you would certainly want to keep that option open. And if you do teach at a college you will very likely be asked to teach differential equations at some point.
  7. Mar 9, 2012 #6


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    calculus is basically about solving differential equations. indeed differential equations are one of the most basic topics in all of mathematics. take a look at the book on ode by arnol'd to find out how interesting it can be. morse theory in differential topology is basically a consequence of the fundamental theorem of ode. take a look at the little book by wallace.
    If you don't know ode it is hard to imagine understanding pde. hodge theory in geometry and topology is basically about solutions of a basic pde, the laplace equation. theta functions in algebraic geometry are best understood by their fundamental relation to the heat equation another basic pde. deRham cohomology gives the relation between topology and a fundamental differential equation. The important topic of vector fields on manifolds is the geometric version of differential equations.

    The whole subject of linear algebra, in particular the structure of jordan normal forms, is essentially describing the behavior of the simplest differential operator d/dx on a finite dimensional space of exponential and polynomial functions. the basic existence theorem in ode is usually proved by a beautiful "contraction" mapping technique in a general metric space that is very interesting. complex analysis is entirely about the solutions of one diff equation ∂/∂zbar = 0.

    i suppose someone could teach an ode course that failed to transmit any of these insights, but I think you are advised to learn as much as possible about differential equations in order to understand pure mathematics, especially analysis. I admit I was like you as a young student and hated ode, viewing it as a plug and chug course with no value. This is the fault of the curriculum which declines to point out the connections between all these subjects. Linear algebra is one of the worst for refusing to teaching differential operators as indeed the most important linear transformation. Linear algebra is not about reducing and solving trivial systems of numerical equations.
    Last edited: Mar 9, 2012
  8. Mar 9, 2012 #7


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    If it's an easy as you think it will be, just look at it as a chance to reinforce your pure mathematican's prejudices about applied math :smile:
  9. Mar 9, 2012 #8


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    Without a doubt you need it. You will learn more than you can imagine.
  10. Mar 10, 2012 #9
    Teach it to yourself over the summer. Basic no proof odes classes can be really easy. If you teach yourself they will probably let you skip it.
  11. Mar 10, 2012 #10
    I think you should take the ODE class and feel lucky that their requirements are that loose to begin with! In my university, I'm forced to take classes like Number Theory, Advanced Statistics, Mathematical Introduction to Fluid Dynamics, etc in my mathematics bachelor degree (for example I asked if I could take Functional Analysis or Measure Theory in place of one of them, but was not allowed). Not that some of them can't be interesting, but it goes to show how much more demanding a department can be. I think demanding an ODE class is pretty darn basic.
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