Additional Math Classes for Physicists | Marshall

[Mhorton91]

I've seen several threads related to my question, and I have tried to utilize the information found within them to answer part of my own question.

I'm a physics major, and after looking through my universities requirements I've realized that the physics major leaves me just a few classes shy of a mathematics minor.

The mathematics requirements for my physics program are:
Single variate calculus 1 & 2
Multivariate calculus
Differential equations (according the the course catalog this is ODE, not PDE)

The mathematics minor requires:
Single variate calculus 1 & 2
Algebraic structures
15 hours of additional course work numbered above 300:

So after finishing off my multivariate and ODE class from my program, and taking the required algebraic structures class, that leaves me with 9 hours remaining to finish off a math minor.Now, from what I've read, Linear algebra and PDE are both classes that "should" be required for the physics degree... so I plan to take those...

Also from what I've read my future goals are important to take into account when choosing with maths will be most valuable. So, my goal is to someday do research in particle physics!

Also after taking Linear and PDE, the minor will only require 3 more hours (1 class), however I will still have a few general elective spots to fill, so if there are multiple different courses that will benefit me in the long run, I can definitely take more than required!

Thanks for any advice!
Marshall

 

[Dishsoap]

Discrete math. It's fun, it's useful, it'll teach you to think, and also come in handy.

 

[Incand]

If there's a course in complex variables it's probably the one most useful for physics beyond those you already mentioned. It may also benefit you in the PDE course.

 

[S.G. Janssens]

Functional analysis. It's fun, it's useful, it'll teach you to think, and also come in handy.

 

[jtbell]

I second the suggestion for complex variables. During my first year of grad school, I wished that I had had the chance to take that course as an undergrad, because my E&M professor was fond of using conformal mapping to solve electrostatics problems. I ended up taking complex variables as one of my two elective non-physics "cognate courses." The other one was intermediate differential equations, which happened to go over a lot of the territory that I was also covering in my QM course at the same time... all those special functions (Legendre, Laguerre, hypergeometric, etc.).

 

[Mhorton91]

We have a class called "Theory of Functions of a Complex Variable" I will add that to my list of classes to take for sure.

Also we have a class called "Intro to Non - Euclidean Geometry" which is something I've been interested in learning about since I took high school geometry, but I'm curious if it will have any benifit to a physics career.

 

[micromass]

We have a class called "Theory of Functions of a Complex Variable" I will add that to my list of classes to take for sure.

Also we have a class called "Intro to Non - Euclidean Geometry" which is something I've been interested in learning about since I took high school geometry, but I'm curious if it will have any benifit to a physics career.

Depends on the course, but it usually won't. It might be useful to general relativity if it covers a bit of differential geometry, curvature, metrics, etc. but it seems unlikely it will go in that territory. That said, it is pretty fascinating, so if you're into it, then take it.

 

[Mhorton91]

Depends on the course, but it usually won't. It might be useful to general relativity if it covers a bit of differential geometry, curvature, metrics, etc. but it seems unlikely it will go in that territory. That said, it is pretty fascinating, so if you're into it, then take it.

Alright thanks! I'll have to see if I have time some semester to take it, I'm not going to force it in somewhere and sacrifice a useful course.

Also as I mentioned, we have a Theory of Functions of a Complex Variable, which is a prerequisite for a higher class just called Complex Analysis. Would you suggest stopping at Theory of Functions of a Complex Variable, or taking a full Complex Analysis course?

 

[micromass]

Please list the contents and description of the classes

 

[Mhorton91]

Please list the contents and description of the classes

MTH 506 Theory of Functions of a Complex Variable
Prerequisite: MTH 280 and MTH 315.

Theory of elementary functions-polynomial, trigonometric, exponential, hyperbolic, logarithmic-of a complex variable; their derivatives, integrals; power series; other selected topics. May be taught concurrently with MTH 605. Cannot receive credit for both MTH 605 and MTH 506.MTH 706 Complex Analysis
Prerequisite: MTH 503 or MTH 603.

Analytic functions, power series, Cauchy's theorem and its applications, residues. Selected topics from conformal mapping, analytic continuation, harmonic functions, Fourier series, and Dirichlet problems.

 

[micromass]

Wow yes, I definitely recommend the complex analysis course. I don't understand why the complex variables course is even a course...

 

[Mhorton91]

Awesome, thank you!

My issue really seems to be that there are a lot of courses that seem super interesting, but won't have much to do with physics research (the main 2 I'm referring to right now are non Euclidean Geometry, abstract algebra). I don't mind taking a few extra classes. Being a 24 year old sophomore, I've moved past worrying about speed of degree... but I don't want to lose focus either.

So I guess all these answers have left me with a final question.

Does knowing more math ever become a hinderance? It seems like the answer is no, but I want to be sure.

 

[Incand]

Yes you need both. I'm actually surprised as well, complex variables is a required course at my university and contains the contents of both those courses except for Fourier series and dirichlet problems that's instead covered in Fourier analysis (I would assume you see this in a PDE course). Which are the course you list as prerequisites? If you already are somewhat familiar with complex numbers you may not even need the first course. It pretty much just shows that complex numbers for a lot of things behave like the real numbers.

 

[micromass]

No, of course not. More knowledge can never become a hindrance. One should however not approach a physics problem like a math problem or vice versa. Some people do a physics problem and start worrying about all kind of things like convergence of series. This attitude can become a hindrance. Not that it's bad to adopt that attitude, but it will result in you going too slowly and not caring about the physics as much as you could. So as long as you realize that math and phyics are two different worlds which do interact, you should be fine.

 

[Mhorton91]

Yes you need both. I'm actually surprised as well, complex variables is a required course at my university and contains the contents of both those courses except for Fourier series and dirichlet problems that's instead covered in Fourier analysis (I would assume you see this in a PDE course). Which are the course you list as prerequisites? If you already are somewhat familiar with complex numbers you may not even need the first course. It pretty much just shows that complex numbers for a lot of things behave like the real numbers.

The prerequisites for complex variables MTH 280 is Calculus 2, and MTH 315 is Algebraic Structures.

The complex variables course (which is MTH 507, and MTH 607) is the only prerequisite for Complex Analysis.

 

[micromass]

The prerequisites for complex variables MTH 280 is Calculus 2, and MTH 315 is Algebraic Structures.

The complex variables course (which is MTH 507, and MTH 607) is the only prerequisite for Complex Analysis.

This course structure literally makes no sense. Why need algebraic structures for this complex variable course??

 

[Incand]

The prerequisites for complex variables MTH 280 is Calculus 2, and MTH 315 is Algebraic Structures.

The complex variables course (which is MTH 507, and MTH 607) is the only prerequisite for Complex Analysis.

Sounds good! I would guess they use algebraic structures as some sort of gateway course. It's similar at my university where algebraic structures is required for a lot of things (although in practice it's usually not that formal). From what I'm told it may be useful to have seen a little bit of it from a math perspective as well (I'm also thinking about possibly taking a similar course myself).