How much math is needed as an undergrad to de theoretical physics?

[xbomber88]

If I'm interested in going to grad school to do theoretical physics how much math am I expected to pick up as an undergrad? I know theory requires a lot more math than experiment but how much more and do I need to do it while I'm still an undergrad or will I be able to pick it up along the way while I'm in grad school. I wish I had time to take more math courses but I didn't take my first physics course until my sophomore year of college so now I'm trying to cram all my physics courses into 3 years which gives me little room to take extra math courses. The courses I'll have for sure by the time I graduate are vector calculus, linear algebra, and differential equations. I might have room to take like 2 more math courses but probably not more than that. Which do you think would be the most useful? And do I have any realistic shot at getting into a good grad school and doing theory with my limited background in math?

 

[arunma]

What type of theory are you planning to do? For example, if you're a theorist in my field (particle astrophysics), all you need is differential equations and vector calculus. On the other hand, if you go the high energy or nuclear route, you'll need more advanced math like group theory. In condensed matter, you do a lot of quantum mechanics, which means you'll need linear algebra.

But based on my experiences in my own department, I would say that you're better off taking more physics classes as an undergrad rather than taking math. Physicists need to take single and multi-variable calculus and a class in differential equations. Besides that, all the math we need to know we learn in our physics classes. My department even offers its own group theory class, specially tailored to physicists. If you've taken vector calculus, sophomore level linear algebra, and sophomore differential equations, you should be just fine for theory. Spend your time taking extra physics classes, especially in the field that you're interested in. In fact, I think it might even be worth your time to squeeze in a programming course or two. C++ would be a good class to take. When I started grad school, my biggest hurdle wasn't the physics, but the computer stuff I needed to pick up.

Of course, take everything I say with a grain of salt. I'm an experimentalist, and other departments might not be exactly like mine.

 

[mordechai9]

I think this sort of subject gets totally misunderstood by beginning physicists and engineers. Don't get me wrong, I misunderstood it myself when I was starting out.

The key point is that theoretical physics itself actually consists in a great deal of math. In many cases there's no separation between setting up an integral to solve a problem, and solving the problem. The mathematics is the physics. Alternatively, you might need to formulate the problem or make assumptions which aren't necessarily that mathematical. But even in this case, you almost inevitably eventually wind up with an equation or a relation which must be manipulated with using mathematics. The punch line is that you will need a tremendous amount of math to do theoretical physics, but obviously a lot of that math will come from your physics courses.

To be honest, you probably need about as much math as you need to feel comfortable with the material which you encounter. This can vary wildly between different people depending on their curiosities and interests. Some people are really content to see results set out, and then use the results, whereas other people are more neurotic/curious about seeing these results to be proved. Personally, I advocate for as much mathematical training as possible, and I think every physicist/engineer should double major in math. Aside from the courses you mentioned I would recommend some fundamental proof based courses, especially real analysis or advanced calculus, partial differential equations, differential geometry, and maybe topology or algebra if you want to really get more comfortable with abstract math.