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What math are people referring to

  1. Jul 19, 2007 #1
    ...when physicists and educators say most potential physics major fear the math the most that physics majors need to learn. Physics undergraduates only need to learn 3 courses of calculus, Differential Equation courses , and to a lesser extent , linear algebra. I haven't taken linear algebra yet, but I didn't really find DE or Calculus very difficult or even merely difficult. Am I missing something ?
     
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  3. Jul 19, 2007 #2
    For a BS degree, there's not a lot of need for more math (other than perhaps complex analysis). However, for a master's or higher, there are many more classes that, while not absolutely necessary, are absolutely helpful, such as functional analysis on Hilbert spaces, toplogy, differential geometry, etc.
     
  4. Jul 19, 2007 #3
    so what math do I need to study in order to better understand string theory. I am both majoring in physics and applied math so does it really matter whether or not if I study applied math or pure math in order to understand string theory. Would there be any dire cosequences for not majoring in pure math if I chose to go to graduate school to study string theory and other high energy related topics
     
  5. Jul 19, 2007 #4

    cristo

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    This may be a rather wild suggestion, but it would be useful for you to study pure maths in order to understand string theory. Of course it depends upon what "applied maths" consists of, but many pure courses such as differential geometry, topology, metric spaces, etc.., will be more beneficial than, say, fluid mechanics.
     
  6. Jul 19, 2007 #5
    Yeah, I had this same question when I started college and could never get a straight answer. Absolutely study pure math. And you need a whole lot of it, from all three branches. It's probably best to start with a real analysis course, since you already know calculus the 'abstractness' will seem less chaotic and much more motivated.
     
  7. Jul 19, 2007 #6

    mathwonk

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    i thought physicists needed liegroups, group representations, and riemann surfaces, and general differential geometry.
     
  8. Jul 19, 2007 #7

    Dr Transport

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    They might if they are studying Relativity, QFT, QCD or String theory. I used group representations in my research but non of the others mentioned as a condensed matter physicist.
     
  9. Jul 19, 2007 #8

    mathwonk

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    what did you use?
     
  10. Jul 19, 2007 #9
    what about for other areas of physics, such as atomic, molecular, optical, and astrophysics? would applied or pure math be better?
     
  11. Jul 20, 2007 #10
    Physicist might fear math, but mathematicians fear a far more redoubtable enemy: time. Or so do I say.
     
  12. Jul 20, 2007 #11

    Dr Transport

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    Group theory, linear algebra and numerical analysis.

    Applied for optical, molecular and atomic physicists. An astrophysicist may use differential geometry.

    It must be remembered that every discipline is different. The professor I got my masters under uses Lie groups (Poincare, Lorentz etc...) in his work and converts almost every equation into an integral equation for solution. My PhD advisor knew enough about continuous groups to work with rotations but waqs a whiz at linear algebra and differential equations, both linear and non-linear.

    My strong points are in point groups for condensed matter, i.e. semiconductors and thier properties. I spend alot of time working in special functions and linear algebraic computations.
     
  13. Jul 20, 2007 #12
    whats nonlinear dynamics and chaos used for in physics?
     
  14. Jul 20, 2007 #13

    Dr Transport

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    There is a whole subdivision of nonlinear dynamics and chaos in physics. The Lorenz oscillator is an example. Another example is the van der Pol equation is a model for circuits. Many problems in physics today have to be treated using non-linear techniques, non-linear optics comes to mind initially.
     
    Last edited: Jul 21, 2007
  15. Jul 21, 2007 #14
    PHYSICS & MATHS are unseparated, not so?
    There was an imperfection to a physicist who doesn't like math.
     
  16. Jul 21, 2007 #15
    I think what most Physics educators will say is that many students that struggle in physics don't necessarily have problems with understanding the physical concepts, but get bogged down in the math. They forget to use or apply the physics because they get so caught up with the math.

    And if they cannot do the math they have very little hope of getting any kind understanding of the actual physics.
     
  17. Jul 23, 2007 #16
    I covered 4 basic calculus courses, some Linear Algebra (laughably called, it basically consisted of how to operate on simple matrices) and that's it.

    There are math courses within the physics department that are more tailored to physics problems, so are made up of math skills (like using tensors). I also think that if I'd taken a combined option I would have preferred to cover pure math instead of applied, it's more thorough, difficult and if coped with, gives better understanding of the whole field.

    Even then, I know quite a few physicists that graduated in pure math and started physics post-grad.
     
  18. Jul 23, 2007 #17
    IF I wanted to more fully understand:
    http://www.math.utah.edu/~milicic/lie.pdf
    What class/topic would I start with? Assume I only know calculus/differential equations up to PDE/BVP's, Linear up to basic Tensor analysis, and Complex Analysis.
    Where does one get started with the whole group-theory branch?
     
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