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Mathematics for Physics

  1. Dec 13, 2004 #1
    what mathematics should a physics major know? right now, im taking calculus but i also have the option of taking linear algebra, or both. any list of mathematics i should be aiming for? also, recommended text books for the subjects would be usefull. thanks.
     
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  3. Dec 13, 2004 #2

    ZapperZ

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    1. Boas "Mathematical Methods in the Physical Science" (I highly recommend this book as already stated in my "So You Want To Be A Physicist" essay).

    2. Arfken "Mathematical Physics".

    Zz.
     
  4. Dec 13, 2004 #3
    Differential Equations are incredibly important. A little linear algebra can hurt.

    Beyond that, it really depends on specialization.
     
  5. Dec 13, 2004 #4

    cepheid

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    I thought linear algebra was crucial as well, especially for QM. Heck, even in my classical mechanics course this semester, they're using the prefix "eigen" in front of all sorts of words for which I never thought it possible. :rofl: At two universities I've had experience with, engineering students take it right from first year.

    One thing I have learned...the best answer to the question asked in the thread is that ...physics requires a LOT of math!!!!!!!!!!!!
     
  6. Dec 13, 2004 #5
    so, so far we have differential equations (should i focus on this more than the rest of calc, which is integrals?) and linear algebra. what is in those books Zapper? applications from different maths, or does it teach you the maths that you use?
     
  7. Dec 13, 2004 #6
    Personally I think it is a bad idea only to learn things because it is manditory or is very important for a perticular field. The purpose of post secondary is to learn as much as you possibly can while focusing on a certain feild. If there is one thing that you are going to relize it is that mathimatics is the language of physics; to limit your ability in math will definitly limit your ablility in understanding and participating in the feild of physics.
    Just a few thoughts...
     
  8. Dec 13, 2004 #7
    well, i dont really wanna waste my time on something thats gonna be completly useless in the field i want to study.
     
  9. Dec 13, 2004 #8
    ^ if you're going into theoretical physics, and intend to do something remotely groundbreaking then its always good to know as much math as possible. but if you intend to specialize and just work in that field alone, like maybe condensed matter and be a CM researcher, then perhaps its not that important.
     
  10. Dec 13, 2004 #9

    dextercioby

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    Not necessarily groundbreaking.Just the basic knowledge of QM and QFT should ask for functional analysis (topology included),group theory,differential geometry,calculus+variational calculus,linear and abstract algebra,statistical mathematics.

    As for the condensed matter part,your're very,very wrong.Just to take the "symple" examples offered by plasma physcs and solid state physics.You'd be amazed to learn how much QFT (including too many (for my taste :tongue2: ) Feynman diagrams) is involved in solid state physics.

    Daniel.

    PS.As for CM researcher,ever heard of V.I.Arnold and his (too famous,but probably not for you :tongue2:) book:"Mathematical Methods of Classical Mechanics"???????????
     
  11. Dec 13, 2004 #10
    lol, i actually meant that,

    if say, abstract algebra is useless in SS physics as in, you probably won't be needing it, then its no point learning it. But if you're in theoretical physics, who knows what insights you can gain just by knowing that bit of math?

    But neither am I that familiar with the math involved in physics....

    : )
     
  12. Dec 14, 2004 #11
    You're right about linear algebra popping up everywhere. All the LA I've ever needed to know will came up as a supplement to the course material (the prof. will let you know all the various ways of doing calculations you need to know with your matrices, for example) so the theory from class was not particularly useful to me for my physics, I suppose.

    That said, what I listed above was probably a bare minimum knowledge of mathematics for a trained physicist. As other people have pointed out, you cannot escape lots of math when doing physics. The more math you know, the more physics will make sense. As a person who loves both, it's my personal feeling that all physics majors should be required to take courses in analysis (real and complex) as well as algebra beyond the standard calculus, ODE and linear algebra courses that are required of physics majors. The theory really compliments the physics.
     
  13. Dec 14, 2004 #12

    Dr Transport

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    For an undergrad degree you will need to have a working knowlegde of calculus, differential equations, both single variable and partial differential, linear algebra maybe some group theory, differential geometry and complex variables.

    Any calculus book will do.
    I sugest Boyce and DiPrima for dIfferential equations.
    Schaums outline for linear algebra.
    Haberman is a good choice for partial differnetial equations and Fourier series.
    Any complex vairables book will do as well as any book on differntial geometry.

    If you are short of cash, take ZZ choices, Boas and Arfken for Math Methods texts. I use my Arfken all the time for a reference.

    More difficult texts are Morse and Feshbach (well over $100 each). Group Theory for physicists can be learned out of Tinkham (more point groups and greared towards solid state and molecular physics) and Wu-Ki Tung which is greared towards particle physics because it covers the Poincare and Lie groups.


    A good math libray on your shelf is never a bad thing, I have mine spread between the house and the office and refer to both fairly regularly.

    dt
     
  14. Dec 14, 2004 #13
    Math makes it oh so clear

    As others have said on this post, the more math you know the better. To use a favorite line from the math books, it is necessary but not sufficient to know a lot of math. Rudimentary understanding of the basics of differential equations, complex analysis, vector spaces, operator theory, tensor analysis, ... is enough to allow you to do calculations, BUT as the amount of math you know increases the beauty and interconnectednes of physics becomes more and more apparent. I'm in the process of finding this out and it is really amazing. There are truly elegant things that group theory has to say about the conservation of energy, momentum and angular momentum, all of special and general relativity is formulated in terms of tensors, and there are some people who believe that quantum theory could have cleaned up if the mathematics was paid more attention during its formulation.

    There is also a practical view. If you become a career researcher there will come a time when you are confronted with some mathematical idea that is not clear to you and that you cant figure out from the books. If you want to be able to talk to the "profesional" mathematicians about it, its helpfull to be fluent in their language and be able to clearly state your question. This is getting kind of long so I'll stop, but I would say take as much math as you can stand.
     
  15. Dec 20, 2004 #14
    I used Byron and Fuller's Mathematics of Classical and Quantum Physics as an undergrad, and it's a great book. Cheap too since it's published by Dover.

    Definitely try to learn some real and complex analysis maybe at the level of Rudin's Principles of Mathematical Analysis. Knowing real analysis will give you a foundation for more difficult math courses down the line.
     
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