Second Year Physics Student Seeking Advice on Math Courses

[codymcleod]

Hello everyone. I am a second year physics student at a large research university in Ontario. The math courses required for my degree are Calc 1,2,3 and vector calc, linear algebra, ODEs and PDEs. I have taken linear algebra, calc 1-2 and stats (not required) and am currently taking calc 3, ODEs and discrete math (not required). I am really enjoying my discrete math course and am planning on taking another math course next semester as well. My options are number theory, game theory, group theory and abstract algebra (all third year courses but I have the pre reqs for each). I would like to take either real analysis, lin alg 2 or complex variables but real analysis 1 and complex variables are only offered in the first term and lin alg 2 interferes with a mandatory physics course. I was considering abstract algebra, as it seems to have the biggest application to physics out of all of the options, but game theory and number theory sound very interesting as well. I am not specifically trying to get another major/minor but I feel that I will end up getting a math minor just by taking so many math/comp sci/applied math courses. I am already enrolled in comp sci 2 for next semester, which is a pre req for the rest of the comp sci courses. Does anyone have any advice for me? Thanks

 

[Student100]

Hello everyone. I am a second year physics student at a large research university in Ontario. The math courses required for my degree are Calc 1,2,3 and vector calc, linear algebra, ODEs and PDEs. I have taken linear algebra, calc 1-2 and stats (not required) and am currently taking calc 3, ODEs and discrete math (not required). I am really enjoying my discrete math course and am planning on taking another math course next semester as well. My options are number theory, game theory, group theory and abstract algebra (all third year courses but I have the pre reqs for each). I would like to take either real analysis, lin alg 2 or complex variables but real analysis 1 and complex variables are only offered in the first term and lin alg 2 interferes with a mandatory physics course. I was considering abstract algebra, as it seems to have the biggest application to physics out of all of the options, but game theory and number theory sound very interesting as well. I am not specifically trying to get another major/minor but I feel that I will end up getting a math minor just by taking so many math/comp sci/applied math courses. I am already enrolled in comp sci 2 for next semester, which is a pre req for the rest of the comp sci courses. Does anyone have any advice for me? Thanks

Is there a mathematical methods course you could take? One specifically designed for science majors?

I don't think abstract algebra, game or number theory will apply very directly to your physics course work. Ignoring when the courses are available, complex analysis has probably the most applications out of the bunch.

Is a PDE course available next semester?

 

[codymcleod]

Is there a mathematical methods course you could take? One specifically designed for science majors?

I don't think abstract algebra, game or number theory will apply very directly to your physics course work. Ignoring when the courses are available, complex analysis has probably the most applications out of the bunch.

Is a PDE course available next semester?

PDEs is only offered in the first term, and my school sadly doesn't offer a mathematical methods course.

 

[micromass]

Don't take abstract algebra because you think it might be useful for physics, it won't. Sure, physics deals with groups, and groups are studied in abstract algebra. But abstract algebra studies mostly finite groups, while for physics, you will want to study infinite groups (Lie groups). So don't expect abstract algebra to be very useful to you.

 

[DeldotB]

I would say try to get into L.A. I'm in an abstract algebra class right now, and my professor draws a lot of relations between abstract algebra and physics (mainly because his research involves non commutative geometry and lie algebras which have deep connections with physics) but i'll agree with micromass - the mathematics learned isn't immediatly useful (probably not that useful at all to an experimentalist). Although once in a while he'll be talking about some abstract group and then all the sudden say something like "and if you take the semi direct product of this group and the lorentz group, you get the poincare group - an essential symmetry group for general relativity.." which is pretty cool - it sort of snaps what he's saying back to reality for a bit.

 

[Dr Transport]

Don't take abstract algebra because you think it might be useful for physics, it won't. Sure, physics deals with groups, and groups are studied in abstract algebra. But abstract algebra studies mostly finite groups, while for physics, you will want to study infinite groups (Lie groups). So don't expect abstract algebra to be very useful to you.

How can you say that, yes, Lie groups are important, but if you study condensed matter physics, i.e. solid state (semiconductors) you'll never encounter continuous groups, only finite groups. I do agree, abstract algebra in the math department isn't too useful for a physics major, but not for the reason you state.

 

[micromass]

How can you say that, yes, Lie groups are important, but if you study condensed matter physics, i.e. solid state (semiconductors) you'll never encounter continuous groups, only finite groups. I do agree, abstract algebra in the math department isn't too useful for a physics major, but not for the reason you state.

I'm sorry, I am not at all familiar with condensed matter physics. I am very glad you corrected me on this. Can you elaborate why abstract algebra isn't useful for physics anyway?

 

[romsofia]

I took an abstract algebra course my first semester, thinking it would be helpful for physics (I also took elementary number theory the same semester). The only place where i'd see that it's useful for physics would be when you learn about cyclic, permutation, and dihedral groups (basically, symmetry stuff).

While both subjects are interesting, I've yet to encounter a spot in my courses/research where I've needed knowledge from my abstract algebra or elementary number theory course to solve a problem or understand a concept. Since you are taking comp sci classes as well, I would say take number theory because that will have more immediate applications.

 

[Dr Transport]

I'm sorry, I am not at all familiar with condensed matter physics. I am very glad you corrected me on this. Can you elaborate why abstract algebra isn't useful for physics anyway?

I personally didn't take abstract algebra, but my friends who did said after the fact during graduate school or out in the real world working that was the material they never really used at all. They wished that it wasn't a required course and that they had more time to take some other applied course.