Undergrad maths for theoretical physics - QIT

[IahWay]

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
Stats

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 can't fit 3rd year:
Differential geometry
Metric spaces ie HilbertIt 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.

 

[DrSuage]

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).

MSc:

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 that's 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...