Maths Options for Theoretical Physics Path

[a.powell]

I'm about to go into my final(3rd) year of a maths BSc in the UK at Warwick university, and am currently looking at what options I'd like to take given that I'm hoping to go down the path into theoretical physics academia. I currently hold offers for Imperial College's "Quantum Fields and Fundamental Forces" MSc, Durham's "Particles, Strings and Cosmology" MSc, KCL's "Theoretical Physics" MSc, and Sussex's "Particle Physics" MSc, with Imperial's QFFF course as my first choice - I already have these offers because I began my final year this year but had to withdraw on medical grounds, and my offers have been transferred to start in September 2013 rather than 2012. I'm not naive enough to assume I know exactly what direction I will take myself, but I was wondering what sort of maths modules I should be picking based on my current path? The list is here: http://www2.warwick.ac.uk/fac/sci/maths/undergrad/ughandbook/year3/.

My current drafted list contains "Groups and Representations", "Introduction to Topology", "Manifolds", "Essay" (I did the Essay module this year on my chosen topic of basic solutions in general relativity), and "Complex Analysis". I'm also hoping to take several modules from the Physics department and will list my current list of them if you wish to know.

I know it's a fairly long first post and a lot to ask, but I'm finding it difficult to find the guidance here at uni of what to take, and was hoping you might be able to offer some useful advice. Also bear in mind that I'm pretty good at teaching myself some topics, as I have done in the past and had to do quite a bit this year since the medical problems I've been having stopped me from being able to attend lectures and seminars. I am willing to put in whatever work is required outside of lecture halls as well as in.

 

[a.powell]

Oh, and I can give any information on my background if it'll help such as what I've already studied.

 

[kloptok]

I'm a fourth year student with the intention of going into particle theory and I think your math choices look good, based on the choices you had these were probably the best. My feeling tells me that the courses on Groups and Representations and Complex Analysis will be the best ones, especially if you haven't had any complex analysis that is. Obviously a course on manifolds is good for General Relativity (GR). You want to focus on the physical applications, so taking a few Physics courses is vital.

Personally I would focus on understanding the theory and the models you study if you want to go into theory, their pros and cons and areas of application. Eventually you want to be able to come up with your own theories and then you need a sound understanding of the work already done (which paths in research were "wrong" and more importantly, why were they?).

Good luck with your studies!

 

[a.powell]

Yeah I'm taking physics options as well, namely ones on general relativity, the Standard Model, relativistic quantum mechanics, gauge theories in particle physics, and cosmology. Thanks for the advice, it's good to have confirmation that the maths options I've listed so far fit my intended path. Any ideas on good books I can study from relating to these courses and/or the future that I can get a head-start on?

 

[a.powell]

I usually hate to bump, but..anyone?

 

[kloptok]

I don't know any math references, but Howard Georgi has written a book called something like "An Introduction to Lie Algebra in Particle Physics". This is obviously inclined towards particle physics so you might also want to look at more general references (and as I understood it, this is a math course and not a physics course).

I don't know how much GR you've studied. As an intro I like Schutz's "A First Course in General Relativity". Wald's "General Relativity" is supposed to be a good, more mathematical book suitable for graduate students.

It seemed like the course pages you linked to in your first post contains a lot of info and tips concerning literature, the obvious thing to do is to look at the syllabus/course info to see if you can find what literature to look at.

 

[saim_]

I would strongly recommend the Variational Principles course for any sub-field in theoretical physics and you should also take a look at the Functional Analysis series; it should be quite useful for QM and QFTs.
I feel obligated to tell you that I haven't taken either of these courses and I'm not exactly from this field :D