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When do you learn abount Tensors?

  1. Jul 9, 2010 #1
    Hi everybody,

    I just finished a intro to modern physics recently where we covered SR, but didn't touch on GR. From what I've read, you have to have an understanding of tensors before you can understand Einstein's equations and most of the math behind GR. I go to Stony Brook, and I haven't found any specific math courses that covers tensors, so I was wondering when you guys learned it. Is it touched on in linear algebra, abstract algebra, maybe diff geometry, or grad school? I want to learn about GR, but I'm curious about how much background I need.

  2. jcsd
  3. Jul 9, 2010 #2


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    You might touch on it in your upper division electrodynamics course. If not, then you'd see them in graduate e/m or classical mechanics. As far as in what math class you might see them in, I'm not sure, if you even would.
  4. Jul 9, 2010 #3


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    A lot of physics students, probably even most of them, learn about tensors while studying GR, from their GR textbook. So if you want to learn about GR, get hold of a suitable textbook and get to work! :smile:

    In our Science Book Discussion forum you'll probably find any number of threads about GR textbooks.

    Or maybe the Stony Brook physics department has a GR course that's accessible to undergraduates (I haven't looked in your catalog).
  5. Jul 10, 2010 #4
    I'm actually taking a junior division e&m class, but I don't think it will be touched on there.

    In terms of GR textbooks, I do have Basic Relativity by Mould (which I bought for SR) and they do touch on Tensors a little bit there, but it seems like they expect you to know some stuff already. I'll check out the science books threads to see any other books/ideas.

    We do have an upper division relativity course, but its not dedicated just to GR (same textbook is actually used). Easier for the teacher I guess.

    Thanks for the advice, I was just worrying that my university was lacking a course (at first I thought they didn't have a PDEs course, but its just given a strange name like applied real analysis instead of just...PDEs :) )
  6. Jul 10, 2010 #5
    In undergrad I tacked a whole math major onto my physics program, and didn't learn too much about tensors. I guess we touched on it in differential geometry. I worried about tensors again when I took cosmology, and one last time in my third year of grad school when I took quantum field theory. Strangely, I've yet to actually study tensor calculus comprehensively.
  7. Jul 10, 2010 #6
    Download this text. http://arxiv.org/abs/gr-qc/9712019" [Broken]
    Last edited by a moderator: May 4, 2017
  8. Jul 10, 2010 #7
    A lot of them tend to see it in their math methods course. We covered them in my course, then saw them again for GR.
  9. Jul 10, 2010 #8


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    In physics, I learned about them in the course "Classical Field Theory" (but I don't think many undergraduates have such a course).
    In mathematics, we covered tensors in a course on Smooth Manifolds.
  10. Jul 10, 2010 #9
    in my school the physics majors touch upon tensors in a course called 'methods in theoretical physics', maybe your school offers that course?
  11. Jul 10, 2010 #10
    Yeah, my school calls it 'Mathematics of Physics'. Or something like that.
  12. Jul 10, 2010 #11
    I first got in touch with them in Classical Mechanics in my second year, the professor didn't say any word about the properties. Then in the second semester I encountered them in electrodynamics (intro to electrodynamics by David Griffiths) and began to understand. This year I had Particle Physics (intro to elementary particles by David Griffiths) and now I finally feel that I can really work with them. Never had any explanation about it from any of my professors in my three years of physics...

    The problem in physics is that nobody takes the time to explain to students what tensors really are. They are of utmost importance, but somehow physics professors keep them mysetrious for their students.
  13. Jul 10, 2010 #12
    Unfortunately, stony brook doesn't have a mathematical methods course, but rather seem to relegate the task to the Math department in two classes, applied real and applied complex analysis. The classes seem pretty similar to mathematical methods courses.

    They cover:

    Partial differential equations of mathematical physics: the heat, wave, and Laplace equations. Solutions by techniques such as separation of variables using orthogonal functions (e.g., Fourier series, Bessel functions, Legendre polynomials). D'Alambert solution of the wave equation


    Functions of a complex variable, calculus of residues including evaluation of real integrals, power and Laurent series, conformal mappings and applications, Laplace and Cauchy-Riemann equations, the Dirichlet and Neumann problems, and the Laplace and Hilbert transforms and their applications to ordinary and partial differential equations

    Thanks for that, I'll make sure to go over it.

    Thats good to hear actually, I'll be getting the Griffiths electrodynamics course for next semester and i think the griffith one for elementary particles is recommended for the particles class. I guess I was wrong about it being touched on in that class. It seems like their important for E&M and GR, but stony doesnt mention them on any course page. Guess you gotta learn while you go.
  14. Jul 11, 2010 #13
    "Mathematical Methods in the Physical Sciences" by Boas has a chapter on tensors.
  15. Jul 11, 2010 #14
    At my school we have a course titled "Vector and Tensor Analysis", which hopefully will introduce me to tensors well enough to take a course in GR. To be honest I have no idea what a tensor is at the moment, but luckily have enough time to learn.
  16. Jul 12, 2010 #15
    The first time I properly learned about tensors was in my first course in general relativity, otherwise I had touched on them in electrodynamics.

    For GR, I recommend A First Course in General Relativity by Schutz - affectionately known as 'green Schutz'. A very nice book.
  17. Jul 13, 2010 #16
    I first learned what a tensor really was (i.e. beyond the usual heuristic discussions given in many undergrad physics books) in a grad GR course. Almost all of the standard texts for such courses cover tensors in some degree of detail.

    If you want to learn about them right now, I second the recommendation above of Carroll's lecture notes. They have a fantastic, no-nonsense introduction to tensors for physicists.
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