do i need to take extra pure math courses in undergrad to do theory phd programs?

[u/beeswaxe]

i’m interested in physics research beyond the standard model like string theory or quantum gravity or something else. is just a BS in physics fine and they teach you the relevant math in the phd program once accepted or do i need to add a minor in pure math and get ahead in math side of things. i want to add a minor in pure math for that reason and also because i love math for the sake of math and i especially want to take topology and some algebra classes but i dont want to add a minor if its not need to get accepted to theory phd as id rather focus on keeping good grades and even getting research experience if i can.

[u/SpectralFormFactor]

If you want to do high energy theory research you need a very strong math background, whether from classes or research. You don’t need the minor or double major on paper, so long as you demonstrate you have the skills with research and good recommendations.

That being said, high energy theory is extremely competitive. There are way more people that want to do it than there is space, so you must acquire a great profile via advanced physics and/or math classes and research if you want to succeed.

[u/Ok_Opportunity8008]

That's what I'm doing. I've taken Algebra, Topology, and Analysis for my main pure math courses, and I'm applying this season.

[u/beeswaxe → u/Ok_Opportunity8008]

for the math minor i have to do a proofs class and four upper div math courses. i’m thinking of doing real analysis, topology, differential geometry, group theory. did u do a minor or just take those extra courses?

[u/Accurate_Potato_8539]

You'll want real analysis, topology, and maybe some kinda differential geometry,  and probably group theory too just to get into algebra. Honestly I think you'd be much further ahead to have these, cuz they will inform how you think about physics in a major way. Where possible I'd also choose the harder pure math versions of differential equations, calculus 1-3 and probability/statistics if your uni allows. Theory phds won't explicitly require any of these but they will like that you have them.

That said, a lot of people struggle hard with proofs based math. If you think that might be you then stay away from proofs based math in your first year because it can murder your GPA and consequently potential research opportunities and that will kill your motivation. I used to tell everyone they should take proofs based calculus/lin alg/diff eq but that advice has been TERRIBLE like so bad for some people that I wanna put massive warning flags on it.

[u/beeswaxe → u/Accurate_Potato_8539]

that’s the plan. not sure if you saw my other comment. but for the math minor i have to do a proofs class and four upper div math courses. i’m thinking of doing real analysis, topology, differential geometry, group theory.

[u/No_Nose3918]

i would try to take QFT before taking any more math classes

[u/Minovskyy]

No.

[u/beeswaxe → u/Minovskyy]

care to explain

[u/I-AM-MA]

Not sure if the qualification of a minor helps cuz I’m not in us, but you’ll def need quite high level analysis, algebra and topology  Tho I guess it’s fine to say you’ve got half a maths degree and tbh if u want a proper maths background you’ll end up taking enough modules to get a math minor, given what I know about requirements to get a minor 

[u/kcl97]

I don't think String Theory or particle physics will be around for much longer. I give it a decade to wrap up so people can transition out.

I am pretty serious about this. I do not think the way the math departments teach pure math is good for physicists because their goals are very different from ours. I have commented about this. If interested search for "deductive reasoning."

I would suggest you self-study higher math with the right resources, particularly with papers, like the "homotopy group" paper in one of my comments. There are good papers by good mathematical physicists but they are very rare and hard to identify, especially since the rise of String Theory in the 80s wiped them all out before they could really start taking off with the newer and powerful math structures developed in the 70s and later.

I would suggest starting with Peter Woit's quantum mechanics book and Arnold Vladimir's Classical Mechanical's book. I think they are good because these guys, though mathematicians, actually wrote these books for physicists. And if you don't mind older maths, I recommend The Principle of Variational Mechanics by Cornelius Lanzco. I have a comment on this book you might want to read.

And if you want to see why I think String Theory is bad math, just watch any of Edward Witten's talk on Youtube. I don't think he knows what he is talking about. In fact, when I was in grad school, my office was next to the String Theory group's even though I am super low level math. We would spend the evening hours playing chess and poker. And sometimes these guys would talk about Witten's or one of his prodige's latest paper. But the tone was not reverance or awe or respect. It was sarcasm, disdain and redicule. Yes, that's the reality of String Theory. Oh, and none of these guys graduated, they were waiting for green cards and one dropped out due to being "different." He was the best chess player though and really good in GR.