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What math do i need for quantum mechanics and general relativity?

  1. Aug 11, 2014 #1
    ok, so hear me out, please read the whole thing.

    so, next year im going to a new school(tams)

    i will be starting my jr year in highschool. and the classes are total only 4 hour long daily, that gives me a lot of free time.

    ive been reading a lot about quantum mechanics and some particle physics. but every time i get to the math, i get lost because i cant quite understand much of it.

    i also want to learn general relativity.

    so, what math do i need to learn in order for me to be able to fluently workout problem concerned with QED, QCD, GENERAL AND SPECIAL RELATIVITY, and also, if i eventually reached up to ideas like sting theory as well.

    ive only completed math up to algebra2, however, i have natural talent for it.

    please list everything i need and tell me what i dont need. please give lots and lots of detail and explanation. since im a noob, even little detail will go a long way. thanks.
  2. jcsd
  3. Aug 11, 2014 #2
    You will need to learn a lot more mathematics and physics to be able to tackle QM and GR.
    Trigonometry is the first thing you'll need to study.
    Then you will need to do calculus and multivariable calculus, and also differential equations.
    Some linear algebra will definitely be needed too.

    Then from the physics side you need classical mechanics and E&M.
  4. Aug 11, 2014 #3
    Micromass pretty much has it. A typical graduate course in GR will teach you the requisite differential geometry. A friend of mine took a pure math course in differential geometry before taking GR and claimed it was useless for him, but if you like pure math taking one might help you out.

    non-relativisitic QM mainly relies on PDE's and linear algebra, most of which should be covered in a mathematical physics course. I've met many physics students who seem to have a poor grasp of linear algebra unfortunately, so I would recommend taking an engineering/applied math course in linear algebra if it's available in the program you get into for college.
  5. Aug 11, 2014 #4
    First of all, welcome to PF!

    This. By the way, a course on Waves and Oscillations, pretty much like MIT OCW 8.03, could help too. If you like to watch lectures online, the MIT, UC Berkeley and other universities offer open courseware.
  6. Aug 16, 2014 #5
    For starters:

    Mathematical Methods for Physics and Engineering by K. F. Riley, M. P. Hobson, S. J. Bence
  7. Aug 16, 2014 #6
    A lot of differential geometry is taught in a hideously formal way, which may be part of the problem. One remedy is to really try to understand curves and surfaces very deeply before you try to tackle the higher-dimensional version. Then, it feels less like definitions and concepts are being pulled out of thin air all the time. It's easier to find good books on that subject, too. If someone explained it halfway decently, as opposed to just filling the board with meaningless calculations every lecture, as my differential geometry professor did all too much of the time, I can guarantee it wouldn't be useless. Uselessness is an artifact of people who don't care to explain the intuition.
  8. Aug 16, 2014 #7


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    Gold Member

    Micromass said it best. You're still in high school. Focus on true mastery of trigonometry and calculus.

    Don't skimp because TRUE MASTERY of these subjects will pay many dividends in the future.

    Also, I don't think this:
    is a healthy view to take. Perhaps you have a talent, perhaps not. I think the single greatest predictor of success is effort and grit. If you think you have talent for something, I think it is easier to rationalize not putting in one's full effort.
    Last edited: Aug 16, 2014
  9. Aug 17, 2014 #8
    Very true, I concur that the underlying material is both interesting and useful, but that this can be obscured by the perspective often taken.
  10. Aug 24, 2014 #9
    what math do i need, please help?

    ok, so i am trying to learn math for quantum mechanics and genral relativity. one guy posted giving me topics of maths i should learn. the other guy said, that i dont need all of them. only some concepts that are included in the topics.

    i dont want to waste my time doing math i dont really need, because i am really short on time. however, i come up to an chalenge that will require me to learn something new, i am willing to do so.
    its just that i want to quickly familirize myself to the math involved so i can do problems related with both qm and general relativity.

    here is the link to the old forum

    [Mentor's note: these two threads have now been merged.]

    pleaes help, include lot of detail and explanation. one good answer could make a huge difference to me. thanks :)
    Last edited by a moderator: Aug 28, 2014
  11. Aug 24, 2014 #10
    The path I took and it proven successful to me:

    First, geometry. The plain old Euclidean geometry. Some analysis also won't hurt. Then learn the normal Newtonian physics in the Lagrange (i.e. particle) picture, as they teach it in elementary school.

    Then learn a bit about metric spaces and tensor calculus and you can dive into special relativity. I recommend purely geometrical view on SR. You don't need all that EM stuff to understand it.

    At this point you should know a bit of group theory and understand the concept of geomertic transformation, its associated transformation group and the concept of symmetry. Along with some analysis it will help you to understand general relativity. This step was a bit hard for me.

    When you will have learned GR, you can start with quantum mechanics. I think it should be learned in that order. QM is much harder than GR, at least for me.

    You have to reset your mind back to Newtonian dynamics and learn it again, this time in Hamilton picture. You will need variational calculus.

    Then the most unexpected part, namely the spectral theory. I still can't believe how people got to apply spectral theory to physical problems. Armed with that, you can learn the traditional quantum dynamics.

    The last part is the group theory and topology. This will allow you to understand quantum field theory. I am currently at that point.
  12. Aug 24, 2014 #11
    This is what you should know to become a good theoretical physicist according to a well known Nobel-prize winner (van 't Hooft):


    Clicking on the list on the left side of the page gives you some descriptions with links to websites and books. Note that it will take you a couple of years (full-time university student) to go through all of this.
    Note that the first thing he lists is to learn proper English since communication with your peers is very important.
  13. Aug 24, 2014 #12


    Staff: Mentor

    I studied applied math, not physics, although my primary interest these days is QM, but I went through a phase where I was really into GR and studied Wald - which many, including me, think is THE book on GR.

    One thing I have noticed about physics that's different to math is physics books tend to teach the math as you go. In math, before you apply it you learn the math. You need PDE's to study QM - then you study PDE's first. But in physics you have books like Griffths (a very well respected QM book) that teaches you about it as you go.

    Because of that what I am going to suggest is a little different to other posters.

    First, there is no getting around it - you need a reasonable grasp of calculus - but, recognising the need, books exist with just what you need to start physics:

    After that I would get Susskinds books that are pitched at exactly that level - you have a bit of a grasp of calculus:

    There are also video lectures:

    When finished you can post here for further suggestions.

    Of course you can post here with any questions you have about those books or lectures.

    However you are advancing way ahead of what someone at your age would normally do. No need to push yourself. Take your time and enjoy it.

    I taught myself calculus at 14 and it was huge fun - especially all this stuff I was learning in math classes and seeing just how trivial it was when you know calculus.

    Last edited by a moderator: May 6, 2017
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