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Real Analysis after Multivariable Calculus a bad idea?

  1. May 26, 2013 #1
    I studied from Multivariable Calculus by James Stewart this past year and thought that it would be worth reading another calculus text to fill in the gaps and to keep my skills sharp. While reading Advanced Calculus by David Widder, I came across this problem:

    (Paraphrased from text)
    Suppose a homogeneous polynomial of the nth order and of m variables. Show that the number of terms in the homogeneous polynomial can be described by [itex]\stackrel{m + n - 1}{n}[/itex]

    This seems like a question that would require some knowledge of mathematical analysis, a course I have not taken. As a physics student, would I gain anything by studying real analysis? If not, what would you suggest?
     
  2. jcsd
  3. May 26, 2013 #2
    In my experience, real analysis is useful as a gateway course to more advanced analysis courses that are directly useful for physics. It was also indirectly useful by forcing a higher level of mathematical maturity.

    Whether or not you should take analysis depends, what course would you have to give up to take it? If none, then it's absolutely worth it.

    Also, that question does not need analysis, it can be treated with combinatoric arguments.
     
  4. May 26, 2013 #3
    I do not think this requires mathematical analysis at all. Consider a couple of test cases. Example suppose we have 2 variables and second order. Sucha polynomial looks like:

    [itex]ax^2 + bxy +cy^2[/itex].
     
  5. May 26, 2013 #4
    Why would that be a bad idea? In many schools, multivariable calculus is actually a prereq for real analysis.
     
  6. May 26, 2013 #5
    I am also confused by the thread title. It seems like asking whether it is a good idea to open the door before getting into a car.
     
  7. May 26, 2013 #6
    The title is bad, I know. To make it clearer: I've made it through the first 2 chapters of Real Mathematical Analysis by Pugh and I'm thinking that my time would be better spent with a book on Linear Algebra or Differential Equations. That being said, I'll be taking courses on those two topics next semester so maybe I should study something I won't see in school.
     
  8. May 27, 2013 #7
    Well, it really depends on what you are wanting to do with it. Analysis will take you further in to the rigor behind calculus. As others have said, it is a pre-requisite for going deeper into mathematics, particularly anything in the mathematical side of physics.

    However, one can never have too much Linear Algebra. Sometimes it just takes a little time before you want to attack a subject like Analysis, and brushing up on other subjects can give you more tools (and confidence). I don't think there is one right answer.
     
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