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Courses Undergrad maths for theoretical physics - QIT

  1. May 18, 2016 #1
    Hi all I am a second year maths and physics student from Australia.

    I am hoping to complete a PhD in an interesting area of theoretical physics. At the moment I am interested in particles and quantum information theory. Though it is worth keeping in mind that I am only in second year.

    I know a few grad students who managed to get into PhD spots with only second year classes in linear algebra, vector calc (I think calc 3 for the US) and a PDE class.

    Maybe I am putting too much pressure on the content of an undergrad degree but my math sequence looks like this (from second year onwards honours stream maths - has a focus on rigour)

    First year:
    Diff Calc (mix of calc 1 and 2)
    Linear algebra
    Integral calc

    Second year:
    Real and complex analysis
    Vect calc and linear alg
    Stats and prob
    into to PDE
    Abstract algebra

    Third year
    Lagrangian and Hamiltonian dynamics
    Mathematical computing
    partial diff eq and waves
    non linear ODE's

    Missing but cant fit 3rd year:
    Differential geometry
    Metric spaces ie Hilbert

    It seems like I am doing more maths than physics just to do physics.
    Am I doing it right? Is it normal to fit all of this into an undergrad or are these grad topics for a physics PhD candidate? (read: not a maths PhD candidate)
    Perhaps I would be better with some comp sci too?

    Appreciate any help and time you have to offer.
    Last edited: May 18, 2016
  2. jcsd
  3. May 18, 2016 #2
    Hello IahWay! I'm starting a PhD in Theoretical Cosmology and Relativity this September, so I can give you a little perspective on what applying for Theory is like.

    Those courses all look very worthwhile to someone wanting to continue in theory, however I would be concerned about the lack of physics on your transcript. You have only cited Analytical Mechanics, and I suspect that you've chosen a more math oriented version than most physicists would encounter. If you wish to do particle physics, I would expect to see at least one course in Quantum Field Theory, and one in Gauge Field Theory on your transcript. If you wanted to apply for Quantum information then certainly a class in that subject would seem appropriate, and at least a couple of courses in Quantum Mechanics seem like an absolute must to me for both directions

    Have you considered string theory at all? If you're more mathematically bent perhaps that would be an appropriate direction. I know some string theorists who basically didnt do any undergrad physics but have just picked it up as they went along. They all work on Algebraic Geometry applications to M-Theory though.

    Caveat: You'd probably have to maintain an average mark of over 80% to get a place anywhere. (They only take the most hardcore - I tried and failed to get into that area ;) ).
    It took a 4 year undergraduate degree, a break to get some money from a job and an MSc from Imperial College to get me a PhD at what is realistically not one of the best schools in the UK in theoretical physics - its pretty darn competitive - but if you really love it you'll get there. (I got a First in my undergrad degree but I undershot 85% quite significantly due to pure idleness and lack of direction).

    I did a physics undergraduate degree rather than a maths one but I'll give you a list of the courses I took.

    First Year
    Core Maths A&B (Calculus up to multivariable calculus with a bit of ODE's and PDE's thrown in the mix, Linear Algebra, Probability and Analysis)
    Core Physics A&B (Newtonian Mechanics, Thermodynamics, Waves, Optics, Electricity and Magnetism, Special Relativity, Introduction to Quantum Physics)
    Labs (euurgh - you can sack this one off - wish I had been able to!)
    Intro to Astronomy

    Second Year
    Quantum Mechanics & Electromagnetism (This was the first proper course on either of those subjects - wave mechanics and emag from a vector calculus perspective)
    Thermodynamics, Condensed Matter Physics
    Vector Calculus, More Linear Algebra, Differential Equations proper, Intro to PDE's.
    Theoretical Physics 2 (Theoretical Classical Mechanics & Quantum Theory)
    Labs (oh god please no more)
    Stars and Galaxies

    Third Year
    More Quantum Mechanics & Introduction to Nuclear and Particle Physics (NB this is from an experimentalist perspective - no group theory or QFT in this course)
    Statistical Mechanics, Optics & More Condensed Matter Physics
    Complex Analysis, Infinite Dimensional Vector Spaces, Introduction to Group Theory, Integral Transforms, Mathematical Trickbag
    Theoretical Physics 3 (Relativistic Electrodynamics, Relativistic Quantum Mechanics, Quantum Scattering Theory)
    Planets and Cosmology
    Key Skills A (this was a bullshit course that they made everyone take to check they hadn't forgotten first year)

    Fourth Year
    Quantum Optics & Advanced Condensed Matter Theory (Superconductivity, Superfluids, Bose Einstein condensates)
    Particle Theory (Basic QFT, Little taste of gauge theory, Intro to Phenomenology)
    Theoretical Astrophysics (General Relativity and More Cosmology)
    Project (I did mine on Renormalons in QFT).


    Quantum Field Theory
    Quantum Electrodynamics
    Advanced Quantum Field Theory (probably the hardest course I've ever taken)
    Advanced General Relativity & Black Holes
    Gauge Field Theory, Unification & The Standard Model
    Differential Geometry
    Lie Algebras and Representation theory

    Now I didnt start off knowing I wanted to do theoretical physics - in fact I had no plans to do a PhD until I had a life changing accident that made me shift my priorities somewhat, but thats another story.
    Of the courses I took, you can sack off pretty much all the undergrad physics non theoretical stuff (i.e all the astronomy stuff and condensed matter, labs, thermodynamics, optics etc), but if going into particle theory, you need QFT courses and Gauge field theory courses, and to take those you need quantum theory, special relativity and relativistic electromagnetism courses.
    For QIT you will need a Quantum Information course which will require quantum theory. I would also recommend quantum optics in that case - there is some crossover.
    The rest you are free to fill with mathematics as you see fit.

    Hope that helps! Bear in mind that my path was somewhat more longwinded since I didnt know what I wanted to do at the start...
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