Maximizing My Math Classes for a Future in Theoretical Physics

[JaredEBland]

I am currently in my third year of a physics and mathematics double major. I've taken almost enough mathematics to fulfill the mathematics degree requirements. I plan on becoming a theoretical physicist and attending graduate school. I've listed the courses I've done, and registered for, and will definitely take. I've also taken almost every higher division physics class at my institution and am doing independent studies in advanced topics (another semester of E&M and quantum; survey course in modern physics applications like solid state, nuclear, etc; either QED or QFT/Fields).

I have taken:
Calc I- III
ODEs
Linear Algebra
Numerical Analysis
Foundations of Math (methods in proofs)

Registered:
PDEs
Topology (Point-set)

Will take:
Abstract Algebra (group theory)
Complex Analysis

I have worked out my schedule for math and physics classes to take, but I'm not sure which of three classes would benefit me best for one of the spaces I can take a course. The three classes I would like to do are Differential Geometry, Interrelations in Math, and Mathematical Methods for Physics.

It's worth noting a few things:

The Interrelations course is somewhat unique, the course description reads "Topics include groups, complex variables, non-Euclidean geometry and differential equations with the theme that any two areas are related. Emphasis on examples, applications, and unsolved problems in contemporary areas such as elliptic curves, geometric surfaces, group-manifolds and modern physics. Appropriate for math majors, and non math majors who are interested in seeing what lies beyond calculus."

The math-physics course would be an independent study. I attend a small liberal arts school, and I am one of two physics students double majoring in math.. I would like to do a survey of different topics, tensors, calculus of residues (I'll learn it in complex, but reviewing won't be bad), differential and integral equations, and some topics in Clifford algebras and dual spaces.

I'm currently doing a little bit of study in differential geometry, specifically of surfaces and geodesics. So I'll have some exposure to the material, although I admit I'm not extremely comfortable with it.


I'm not sure which of the options will benefit me most as a physicist. I'm fairly confident that they will all be beneficial. Any insight or advice is greatly appreciated.

 

[member 428835]

differential geometry! very helpful course in what you may see. the rigorous courses youre taking will help pave the way for it, so youll be okay with it when you see it

 

[Astrometry]

differential geometry! very helpful course in what you may see. the rigorous courses youre taking will help pave the way for it, so youll be okay with it when you see it

I agree with this post. Differential Geometry.

 

[nonequilibrium]

Differential Geometry :) (in case it helps to hear the same opinion again)

The interrelations course sounds like good fun (maybe just sit in if you're really curious?). The math in physics course sounds a bit random; the topics you mention are interesting/relevant, but a course in diff geo sounds much better. Basically the idea is: whenever you have the opportunity to learn about diff geo, do it.

 

[1MileCrash]

That interrelations class sounds extremely cool, I wish my university had something like that.

 

[JaredEBland]

Thanks for the feedback guys.

The interrelations course is somewhat unique, the professor specializes in that sort of thing. I saw one of his former students give a talk on a project. He connected two seemingly unrelated problems in math - it was in my freshman year so I could barely follow the work. Half of my motivation for taking that class is that it's something I won't likely see in other courses.

It looks like differential geometry seems to benefit me the most. I suppose it will be good to see the material in a classroom setting as well.

 

[nonequilibrium]

Just in case you're afraid we're only advising diff geo out of usefulness: it's pretty too :)

 

[JaredEBland]

Differential geometry is beautiful: I agree wholeheartedly. I'm currently learning some of it now, and the next chapter I cover will be Geodesics. I've gained a whole new appreciation for plane geometry from it.

 

[WannabeNewton]

Differential geometry is beautiful...

I can't say I agree wholeheartedly but if you really want to see a beautiful subject in the same ballpark (and one that will be indispensable to you given your interests in physics, especially if you end up studying gauge field theory) then take up differential topology/algebraic topology. You've already studied point-set topology and you're going to study group theory so you're basically set :)

 

[nonequilibrium]

A course in algebraic topology is not indispensable, but of course useful if you have the extra time. When comparing courses in diff geo and algebraic topology in usefuless for theoretical physicists, I think that's a no-brainer.

 

[WannabeNewton]

A course in algebraic topology is not indispensable, but of course useful if you have the extra time. When comparing courses in diff geo and algebraic topology in usefuless for theoretical physicists, I think that's a no-brainer.

Alright then, in what sense is a pure math course on differential geometry a "no-brainer" more of a necessity for "theoretical physics" (ignoring the fact that the term is extremely ambiguous to start with) than a pure math course on algebraic topology? I'd love to see an elucidation of this statement.

 

[nonequilibrium]

Do you think it's a controversial statement? I'm thinking of the fact that diff geo underlies gauge theories, and the latter underlies modern physics.