Which courses should I take for a BS in physics: more math or more physics?

[eep]

Hi,

I basically have to decide whether to take introduction to analysis, partial differential equations, and complex analysis while taking the minimum number of physics classes to graduate with a BS in physics. Or, I can take "Mathetmatical Methods for the Physical Sciences" and take a few extra physics classes (solid state physics and atomic physics). I'm currently taking an upper-division course in linear algebra. I'm not sure whether I want to pursue theoretical or experimental work, and my advisors seem split both ways. What would you pick and why?

 

[Stephan Hoyer]

Do you really need to choose one entire course set or the other?

I think Mathematical Methods would probably be worth it for physics whether you do theory or experiment.

My Mathematical Methods class is covering differential equations, PDEs, Fourier Series, Fourier and Laplace Transforms, complex integration and intro material on tensors and group theory (as used in physics). It's quite a bit, but it's all (killer) problem sets and no theory. There's just not enough time to learn all the necessary math for physics in math courses (and I'm a math major, too, even).

 

[eep]

It doesn't *have* to be one or the other, the reason why I picked the courese the way they are is because I need the Intro to Analysis in order to take Partial Differential Equations and Complex Analysis. The mathematical methods course covers pretty much exactly the same material you listed. My advisor (a particle physicist) told me that I might not want to take these upper-division math courses as I'm not pursuing a math degree, however one of my professors (works on dark matter) said that he thinks the math is more important, especially from what he's seen of his grad students. I've gotten mixed opinions from others too.

 

[tmc]

Id take both. The mathematical methods class will show you more practical applications of what youll see in your other math classes. But youll need those math classes to see more advanced math which might become useful (and which you wouldn't be able to learn from just the math methods class since youll never see a rigorous introduction to it).

You might do some analysis, but probably not enough to do manifold theory. Youll see some group theory, but probably not enough to be able to learn lie groups.

Now if you were to never use any manifolds or lie groups, id tell you to take math methods. But seeing as youre not sure, no need to risk it.

And besides, the math. methods is just 1 extra class.

 

[eep]

what sort of math classes cover manifold theory and group theory? is this sort of stuff usually taken at the physics undergrad level, or is it more something that's seen in grad school?

 

[tmc]

group theory is definitely undergrad (2nd year for math majors).

Lie Groups and Manifold, normally either 4th year undergrad or in grad school.

Theyre whole subjects by themselves, so each spans quite a few classes (mostly group theory which is really the basis to a bunch of other classes, hence being taught so early).

 

[eep]

Hrm, I don't see anything in any of the offered classes that relate to group theory, except maybe "Introduction to the Theory of Sets". Sets could be completely different from groups, though, for all I know. What areas of physics are described by group theory and manifolds?

 

[tmc]

manifolds is advancad analysis (which itself is advanced / theoretical calculus).

Group theory really is group theory. Check for courses such as Abstract Algebra, Modern Algebra, Ring Theory.