Enough Maths for Physics Grad School?

[Mike K]

I am currently in a theoretical astrophysics research group. By the end of my undergrad, I plan to have done 3 years there. However, only recently did I consider doing theoretical, not experimental, physics. But I am worried that I won't have completed enough maths to be accepted anywhere. Right now, by the end of my undergrad, I should have taken:
Calculus I, II, & III
Differential Equations
Matrix Algebra
Engineering Mathematics
Methods of Theoretical Physics I & II (which focuses on PDEs and Group Theory)

Unfortunately, most math courses require a foundations in math prerequisite, so I don't have much room to take more maths. Is this enough to get into grad school to study theoretical physics? I could try to shuffle around my schedule to fit in the foundations course and another math like analysis or topology. I have taken many upper level physics electives already, so I guess I could reluctantly cut back a few.

 

[SteamKing]

I am currently in a theoretical astrophysics research group. By the end of my undergrad, I plan to have done 3 years there. However, only recently did I consider doing theoretical, not experimental, physics. But I am worried that I won't have completed enough maths to be accepted anywhere. Right now, by the end of my undergrad, I should have taken:
Calculus I, II, & III
Differential Equations
Matrix Algebra
Engineering Mathematics
Methods of Theoretical Physics I & II (which focuses on PDEs and Group Theory)

Unfortunately, most math courses require a foundations in math prerequisite, so I don't have much room to take more maths. Is this enough to get into grad school to study theoretical physics? I could try to shuffle around my schedule to fit in the foundations course and another math like analysis or topology. I have taken many upper level physics electives already, so I guess I could reluctantly cut back a few.

It's not clear what 'Engineering Mathematics' covers that isn't already covered in the other courses you have listed. If it duplicates the material in the other courses, it would seem like a good course to drop and substitute something more relevant to your grad school work.

 

[radium]

For most theorists, if you have a solid foundation in basics (maybe have take a few more specialized courses), you can learn the rest you need ok your own. The way the average theorist thinks about math is a lot different than the way mathematicians do. This includes many theorists who use a lot of advanced math in their research.

For example, in my field there are a lot of people who use notions from topology, representation theory, differential geometry, projective symmetry groups, etc. but when you talk to many of them, they don't seem to think of themselves as very mathematical. This is because they are applying math to physical problems in a way which may not be rigorous. I've asked several of these people if I should take more math, but they all seem to say it is more useful to learn it on my own.

If you talk to mathematicians about things like path integrals, renormalization, or the AdS/CFT correspondence, for example, they will be very disturbed by the techniques used since from my understanding, many of these things have never been proven to work in a mathematically rigorous way, they just seem to work.

 

[Mike K]

It's not clear what 'Engineering Mathematics' covers that isn't already covered in the other courses you have listed. If it duplicates the material in the other courses, it would seem like a good course to drop and substitute something more relevant to your grad school work.

I agree. Conviently, I planned to take it next semester; instead I will the foundations course and maybe I will find time in my last semesters for a higher level math.

 

[Mike K]

For most theorists, if you have a solid foundation in basics (maybe have take a few more specialized courses), you can learn the rest you need ok your own. The way the average theorist thinks about math is a lot different than the way mathematicians do. This includes many theorists who use a lot of advanced math in their research.

For example, in my field there are a lot of people who use notions from topology, representation theory, differential geometry, projective symmetry groups, etc. but when you talk to many of them, they don't seem to think of themselves as very mathematical. This is because they are applying math to physical problems in a way which may not be rigorous. I've asked several of these people if I should take more math, but they all seem to say it is more useful to learn it on my own.

If you talk to mathematicians about things like path integrals, renormalization, or the AdS/CFT correspondence, for example, they will be very disturbed by the techniques used since from my understanding, many of these things have never been proven to work in a mathematically rigorous way, they just seem to work.

Interesting; well I am certainly willing to learn such maths on my own.
Thank you, it is good to know that I will be able to still conduct theoretical research (and, less importantly, not be viewed as behind for lack of maths in admissions).