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Continuing on in Math

  1. Nov 11, 2006 #1

    mrjeffy321

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    At the end of this semester, I will have completed all the “mathematics” classes I am required to take on paper for my Physics degree. However, I think that it certainly would be a good idea to continue on in math considering the importance of the subject within physics.
    Now I am faced with the decision of which math classes to take and, to a lesser extent, in which order to take them.

    Additional, real, math classes which I was thinking about or have seen referenced here as a good idea to take are: Abstract Algebra, Complex Variables, Partial Differential Equations, and Methods in Applied Mathematics (<-- description specifically mentions an emphasis on how the topics can be applied to the physical sciences and engineering).
    Would taking these classes be a good idea? Are there more I should consider? Is there something in the list which might not be necessary? I think the Partial Diff Eq and the methods in applied […] classes might be a good idea, but I am don’t really know, I yield to you-all’s judgment.

    But just because I am done with classes whose course prefix starts with “MATH”, does not really mean I am done with math. There are a couple physics classes which are, in actuality, math classes in disguise, near as I can tell (“Theoretical Physics” and “Numerical Methods in Physics and Computational Techniques”).
    There is likely to be some overlap between the pure math courses and the math-physics courses. I know this is probably very difficult for you to answer but might the topics covered in the math-physics courses cover the material sufficiently enough so as to not require the pure math courses (i.e. everything I need to know and none of the extra stuff I don’t)?

    Of course you might think that asking one’s academic advisor would be a good idea in a case like this, and normally you would probably be right. However, in my experience, the advisors are close to worthless in giving any type of useful advice (but I will try that too).

    I have already taken…
    Calc. I, II, Linear Algebra, Differential Equations, and Multivariable [/Vector] Calculus.

    I can provide course descriptions if needed.
     
  2. jcsd
  3. Nov 11, 2006 #2
    IF your school offers in you should take a mathematical physics course. Complex analysis is also a very interesting course.

    Also check out real analysis (aka advanced calculus). Hard, but good course
     
  4. Nov 11, 2006 #3
    I second the notion that you should take a mathematical physics course. If your department doesn't have one listed, you should ask around and see if any course have lots of math hidden in it. For example, my electrical engineering department requires the same math courses that you listed. However, one of the required EE courses, which is actually called "Analog Signal Processing," covers a lot of mathematical topics not necessarily garnishable from the title (albeit not rigorously).

    However, if you're really into mathematical rigor, you're probably going to want to take the math department's version anyway. Basically, I subscribe to what I call "common-sense rigor:" if something doesn't immediately appeal to my idea of common sense, I require a proof from principles that do. For example, I'm fine with the fairly intuitive differential version of calculus, even though it's not really justified. (Real numbers? Who needs 'em: I only deal with very small rationals. :biggrin:) Obviously I occasionally run into trouble at infinities, but other than I'm usually okay. In the end, I seem to end up learning topics with a lot more rigor than most EEs care for, a little bit less than most physicists care for, and quite a bit less than mathematicians.

    And to any detractors out there: I own a real analysis book, and I've tried working through it at least five times in the past two years I've owned it. However, by the second chapter, I'm always bored to tears, so I stop, even though I know that it gets more interesting thereafter.
     
    Last edited: Nov 11, 2006
  5. Nov 11, 2006 #4
    You don't have to take PDE's to get a physics degree? Yikes how do you even get E and M?
     
  6. Nov 11, 2006 #5
    yeah -- I'm partial to partial diff eq's myself.
     
  7. Nov 12, 2006 #6
    How can they not be required? Solving laplace's equation, heat conduction problems are almost essiential, no?
     
  8. Nov 12, 2006 #7
    Yeah I also find that odd, they require it in engineering of all types and in Computer Science I don't see why a physics major wouldn't.
     
  9. Nov 12, 2006 #8

    mrjeffy321

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    I don’t know what to say about PDEs other than I am looking at the list of required classes as well as through pre-requisites for the required classes and, unless I am missing something, I do not see it.
    Perhaps it is one of the subjects hidden within one of the math-physics classes.
    So Partial Differential Equations should defiantly be taken, OK.

    I am not sure what is meant by a "mathematical physics" or what it covers, so it is hard to say whether or not it is offered.
    As for complex/real analysis, I don’t see anything like that by name, but there are other analysis classes (Mathematical / Numerical analysis).

    How about the other classes I mentioned (Algebra, Complex Variables)?

    EDIT:
    Looking over a past syllabus I see that in one of those math-physics classes I was describing earlier, PDEs are indeed covered and the book uses is entitled "Mathematical Methods in the Physical Sciences". So rest assured, I'll get a dose of PDEs even if I don’t take a formal class devoted to the subject.
     
    Last edited: Nov 12, 2006
  10. Nov 12, 2006 #9

    quasar987

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    complex analysis=complex variables
     
  11. Nov 13, 2006 #10

    mrjeffy321

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    OK, good to know.
    So with complex variables (/analysis), I will also be required to take (as a pre-req) "Theoretical Concepts of Calculus" as well which might be something along the lines of what leright was talking about, an advanced calculus course/real analysis, it is suppose to cover topics which sound similar to those covered in Calc. I and II, but I assume in more detail and more emphasis on theory.
     
  12. Nov 13, 2006 #11
    Partial Diff. Eqs. are not required for engineering majors. I am in heat transfer, and you don't need to know how to solve them.

    Grad class will go into that level of detail for heat transfer if you want to go into that much depth.

    Like you, I have taken the required courses, which are exactly as yours less the linear (although I have taken linear for the hell of it).

    I want to take PDE's, and Complex Calc though. These are going to be handy.

    I dont care what area of science you study, all the equations are the same with different symbols for the constants. So you can't go wrong in picking ANY math course on your list.

    Oh, and a good stat class. I took one that was junk, but I would recomend a good stat class.
     
    Last edited: Nov 13, 2006
  13. Nov 13, 2006 #12
    a PDE course (well, a semester course which is 1/3 PDE's) is required for both my EE and physics. It has the core of what applied math you need to know, like Laplace's eqn, Poisson eqn, wave and heat equations, D'Alembert's method, method of characteristics, separation of variables, and power+fourier series/fourier transform solutions.

    Linear algebra is a strict requirement for the physics, and it's a practical requirement for EE, meaning that if you really wanted to, you could avoid taking it, but you have to take the advanced circuits if you don't (placing your emphasis in that area)
     
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