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What math areas I need to see for graduate-level physics?

  1. Jul 23, 2015 #1
    I'm have already learn some of Differential,Integral,Multivariable Calculus(with Vector Calculus to), Ordinary Differential Equations, and something in PDEs(i know solve some by the Method of Separation of Variables:woot:), so what should i need to learn in math for areas like Eletromagnetism, Quantum Physics, Condensed Matter Physics, Astrophysics, General Relativity grad-level physics? and if it's possible, recommend so book for self-study, i'm not in the university yet :frown:
  2. jcsd
  3. Jul 23, 2015 #2
    Linear algebra. Numerical analysis.
  4. Jul 23, 2015 #3


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    For the stuff you're interested in from a mathematical standpoint? Get Mary's Boas book "Mathematical Methods in the Physical Sciences", one in linear algebra as Dr. Courtney suggests (there's a good book by Gilbert Strang), and a book in differential geometry. In lieu of that, just get books in the physic subjects you're interested in. Most books in, say, GR do the math justice. Or so I'm told. I didn't understand some (cough..most) of the stuff, myself.

    That said you seem to be interested in a wide breadth of physics, you might to narrow some of that energy down into one field while you self study. Why aren't you in university? You could just obtain syllabuses from courses you plan to later attend and self study the material. It'll make the actual course easier.
  5. Jul 24, 2015 #4


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    Does this mean you haven't even started your undergraduate (bachelor's degree) yet? And you're already worried about graduate school? If so, I suggest you take a deep breath and slow down a bit. :smile:

    During my first year of grad school, the math topic I most regretted not having studied as an undergraduate was calculus of complex variables. In my grad school E&M course, our professor liked to use conformal mapping to solve electrostatics problems.
  6. Jul 24, 2015 #5
    Thank you all!!, and yeah, i don't even started a undergraduate course., i 'm high-school right now, so linear algebra, matematical methods and diferential geometry is the only thing necessary to these fields?? What about Tensor Calculus, Complex Analysis?? I've seen many aplications of tensors in some fields...
  7. Jul 24, 2015 #6


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    Hey Andreol,

    Why're you worried about graduate courses if you're still in high school?

    For the most part you'll learn what you need to know in the physics courses themselves, or when taking a course like mathematical methods. Even my recommendations aren't necessary. Most physics graduates entering grad school having taken the basic calculus series, linear algebra, and ODE and/or PDE's. It's certainly possible to study further in things like topology, differential geometry, complex analysis, numerical analysis, and so on from a mathematical standpoint, but isn't in itself required.

    Take your example of tensors, I was very worried about them before taking GR. I wasted my time and money buying tensor study material and books on the topic. When I actually took GR I realized what a mistake it was. The course itself was more than adequate.

    You're still in high school, keep your eye on the horizon and study things you'll end up taking for your bachelors first. If you haven't already, look at the courses offered by the universities you'd like to attend and build a schedule. Then you can start studying those courses to gain familiarity/better understanding to make your life easier when you take those courses.
  8. Jul 24, 2015 #7
    I Think i will learn Linear Algebra by the MIT OCW Courses, cause that Strang's Book is friendly and use easy math, but it's confusing, i REALLY need to read that book and follow the course in MITOCW, or only by the book Boas' Mathematical Methods i can learn what's is necessary in the field of Linear Algebra?
  9. Jul 24, 2015 #8
    It really depends on what kind of physics you'll end up doing. But I think that the vast majority of physicist will find Boas sufficient. It's a good introduction too, so if you ever need something more, you'll be able to pick that up quickly.
  10. Jul 24, 2015 #9
    I see.., thank you!!, but what fields you are talking about? that fields that need advanced linear analysis, it's QFT right?
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