Math Advice for Physics Majors: What Math Courses to Take

[DClancy]

Ok, here's my issue; I'm a physics major just finishing up my first year, but I also love math, and I've been considering doing a double major. What math courses, other than those required by a physics degree, should I take? I have read that learning Fourier series would come in handy.
I'm basically just looking for advice on what additional math topics will make my life easier down the road. What math courses did you (grad students and beyond) wish you had learned as an undergrad? I'm considering theoretical physics and from what I have read, a solid understanding of math is a must.

 

[confinement]

A dual math major is a good idea if you want to be a theoretical physicist. Every course at the math department is useful (all of them up to the 2nd year of graduate study in some cases!) if you want to understand the most mathematically demanding areas of theoretical physics. Here is a list of udergraduate classes in order of benefit/difficulty:

1. Basic Calculus
2. Multivariable and Vector Calculus
3. Ordinary Differential Equations
4. Statistics and Probablity
5. Compex Analysis
6. Partial Differential Equations (includes Fourier Series)
7. Real Analysis
8. Abstract Algebra (group theory)
9. Topology General/ Algebraic
10. Graph theory /Knot theory
11. Number Theory / Theory of Equations

In addition there will be a physics elective called "Mathematical Methods" and you must take it, it contains a survey of many of the topics listed above. If you are going to graduate school in physics then a year long course in complex analysis will make a huge difference, head and shoulders above the practical importance of the rest.

If you continue on to be a professional theoretician, the most important classes in the list will be real analysis and abstract algebra. Courses in topology and geometry, especially differential but also algeraic, are a great bonus that will make you abetter professional one day but with not as much practical importance as complex analysis.

 

[physics girl phd]

Confinement's list is great. I took through 7 myself (I had minors in math and chem with my physics degree... not a double major with anything). I'd highly suggest upper-level math courses in 5&6 as complementary to physics.

 

[Coto]

Personally I would add:

Differential Geometry/ Tensor Analysis in between #7 and #8.

I would also clarify that algebraic topology is more beneficial (for the physicist) then point-set topology would be and it could be argued that it would be more beneficial for you then abstract algebra would be depending on what type of stuff you were doing, so personally I would switch #8 and #9 around...

but the list is very comprehensive.

As a #12 you could say functional analysis, but at this point you're usually looking at introductory grad studies classes.

 

[qspeechc]

Linear algebra?

 

[Coto]

Linear algebra?

Put that somewhere in the top 3 :)

 

[owlpride]

Harmonic Analysis?

 

[confinement]

Linear algebra?

Yes, Linear Algebra was a major oversight in my original list. It has often been said that the importance of linear algebra in college level math is similar to the importance of arithmetic in high school --- it forms a foundation for everything and you should learn it backwards and forwards!

 

[Troponin]

What about differential Geometry? If you're going with knot theory and want to do some of the more abstract mathematical physics, Diff Geometry would be a nice addition.

*Edit...I see someone else already said this

 

[Cantab Morgan]

Get some exposure to exterior calculus. Div grad curl and all that are nice, but differential forms have advantages. Plus, they are beautiful.

 

[Coto]

Exterior calculus arises naturally in differential geometry.

I'm taking an introduction to harmonic analysis right now and to be honest, I don't see where the applications are. Harmonic analysis is the natural generalization of Fourier series and the Fourier transform to groups. This course is much much much more pure math in nature.