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3 maths

  1. Apr 25, 2007 #1
    would it be a bad idea to take these three math classes together for next fall semester (Fall 'o7)

    Number Theory
    Ordinary Differential Equations
    Introduction to Real Analysis

    I have heard good things about every one of the teachers, So I cam confident the teaching will be good.

    My thought was that number theory will go well with real analysis

    I'm just afraid the homework load may be too much.

    I have taken Linear Algebra already, and calc 1-3 so I have some minimal knowledge of Diff Eq already from linear algebra, calc 2, and my physics classes

    what are your thoughts
     
  2. jcsd
  3. Apr 25, 2007 #2

    AKG

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    Number theory will have nothing to do with real analysis. In fact, I don't think any two of those courses will complement each other in any significant way, nor will any two conflict with each other (I can't imagine how a course would conflict with another anyways). Also, none of those courses are prerequisites for either of the other two, although depending on what is covered during real analysis, it might be slightly helpful to have a very basic familiarity with the theory of ODE's. However, the minimal knowledge you claim to have already is probably close enough.

    And it's entirely absurd to ask whether the homework load will be too much, it all depends on the teachers and how much homework they give.
     
  4. Apr 25, 2007 #3
    I don't know, it seemed to me when I took number theory, that really it was more of a class on how to write good proofs - the actual "number theory" part is in some sense really easy and straightforward. The hard part of the class was learning how to use all the theorems and lemmas and such to prove interesting facts about numbers. Of course, it depends entirely on how the course is taught where you go.

    Also, this probably doesn't matter, but it might be worth considering whether the ODE's course is the kind that engineers/scientists take (primarily applications) or if it's more mathematical (proving existence/uniqueness, formal methods, etc)

    you should contact your professors, though, because they will know best how rigorous and heavy these courses are. Plus, it depends a lot on how heavy a load you're able to bear, personally- some people can manage 6 classes per semester, others top out at 4.
     
  5. Apr 25, 2007 #4
    I know for a fact that you're not British, so why are you saying "maths?" :biggrin:

    From what I recall of my own ODE class, it was really easy. Really easy. It might be different at your school, but I wouldn't think that it would take that much time, because the subject matter isn't all that difficult. As for the other two, even though I've studied the material, I can't say that I've taken the classes.
     
  6. Apr 25, 2007 #5
    My ODE class was for engineers and was super easy as well in my opinion. Just know how to integrate well and memorize a few things and your set.
     
  7. Apr 25, 2007 #6

    t!m

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    I also found ODEs to be really easy, but am now taking PDEs and it is very challenging - though enjoyable nonetheless. I feel a background in analysis (which I do not have) would actually really help with PDEs, especially in dealing with Fourier series and issues of convergence.
     
  8. Apr 29, 2007 #7
    Interestingly enough, more advanced real analysis jogs well with PDE's. Once you start dabbering around in Lebesgue's theory of integration, you move on to explaining Lp spaces, where the L2 space (Hilbert space) is the natural environment for fourier series... a normal topic in PDE's.

    It's nice knowing some of the background behind the things you do in applied math and physics (i.e. quantum mechanics and it's formalization to Hilbert space).

    Like everyone has been saying, an intro course to ODE's is usually cakewalk. Nothing is overly hard to understand and can be learned quickly.

    Lastly, the workload for those 3 courses combined doesn't seem like it'd be outrageous if it's the standard one assignment per week/midterm/final. I guess it depends on what your definition of outrageous is... and probably how the prof gauges work load.
     
  9. Apr 29, 2007 #8
    Stupid question, but, what grade are u in? I mean are u a sophomore, senior or? Just curious, to know..
     
  10. Apr 29, 2007 #9
    if you planned to do any applied science or simulations science, ODE is a must...
    number theory is really fun with apps in cryptography
    analysis...well it woulc complement understanding of how math is built. But you could always learn it on your own.
     
  11. Apr 29, 2007 #10
    If you have never done proofs before then you might have a tough time. I would recommend learning a little about proving things before you enter Analysis and Number Theory.

    This thread has some online resources for learning how to write proofs: https://www.physicsforums.com/showthread.php?t=166996
     
  12. Apr 29, 2007 #11
    Thanks for the responses, I am going to be a sophomore in college next year, this year I took Multi-variable Calculus (Calc 3) and Linear Algebra. The only real background I have in proofs comes from possibly high school geometry and my Linear Algebra class I just took. Unfortunately My Lin Alg class didn't focus much on formal proofs.
     
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