Which Classes Should I Take for My 3rd Year: Pure Math or Mathematical Physics?

[proton]

i'm about to enter my 3rd year, and i have been planning for a physics major during my entire college career, until recently, where i have decided to pursue pure math instead. i may decide to switch back to physics, or pursue mathematical physics, however

i plan to take for sure this upcoming fall: abstract algebra and numerical analysis.
but i don't know which of these to take: german A (i heard math phD students need to know another foreign language, i don't plan on taking this to fulfill a GE requirement since I've already done so), differential geometry A, quantum mech A, or E&M B. my school uses the trimester system, so 'A' refers to the 1st quarter, and 'B' refers to the second quarter of that class

i plan to take quantum mech A and german A so far, since my school doesn't offer diff geom B until the 3rd quarter (spring), and offers diff geom A again next quarter (winter), so i figure i might as well wait, since i may forget the stuff if i don't take B right after A. also, i kinda look forward to quantum mech A, but it isn't offered again until spring

any advice? i guess what's making this all complicated is that i don't know wheter to pursue mathematical physics or pure math

 

[tmc]

How many courses are you comfortable taking? You've listed four main choices (german, QM, algebra, num.analysis), will take diff geo later, so I guess the only point up for debate is taking E&M or not? Four courses seems quite normal, especially with one of them being intro german (at least I think, maybe that's high for quarter systems?)

Why are you so sure about numerical analysis? I assume you're taking it through the math department, in which case it would neither really belong in pure math, nor in mathematical physics really (since the whole course might be based on proving convergence of algorithms and the likes, though it's hard to say without an outline). It depends a lot on the kind of mathematical physics you want to do (i.e., writing numerical physics programs or doing theoretical, mathematical physics), but I personally would ditch that for E&M. Then again, you might need the math credits to graduate if you were to choose math...

That being said, if E&M B is the last semester of E&M there is, you can always delay it; if there's a C, then you should probably take it now. But then I don't know if four hard courses is too much.

As a last resort, you could drop german and learn it casually on your own (you still have a lot of time until grad school), since my experience with freshman introductory courses to languages is that they don't really do that much.

 

[proton]

i may be able to handle 4, considering that the algebra class is an honors course, similar to that taught at the level of ivy league schools

i'm pretty sure the intro german should be an easy class

i thoughtt numerical analysis seems useful since its applicable regardless of what field i go into my career with

my goal is to do theoretical stuff, but i want backup plans, hence why i consider taking numerical analysis

E&M B is offered again in the spring. there is no C part

dont grad schools expect you to have reading level of another foreign language? i figure that would take awhile, hence the need to learn a year-long class in german. if i learn german on my own, how much will i likely have to study? also, when will i have the time? i still haven't taken the GREs, which i plan on studying for in my future breaks from school

 

[tmc]

Some grad schools (a few top ones, really) require something like that I think, yes. Or at least a lot of people seem to think they do. In any case, learning german is a useful thing to do.

If you can take E&M later, and don't have other classes that you think might conflict with it, then go ahead and do that. However, I personally don't believe that numerical analysis will be much use to someone in theoretical physics or pure math. At least, not any more useful than an adv. stats course for example. Learning the basics of numerical analysis is good, especially knowing how some of the methods work, but really all you're going to need to know is how to use the numerical methods, which is both very easy (i.e., you look it up on wikipedia), and may not even be touched on much in your course, which might be more concerned about proving that these methods work. Not to mention, unless you really insist on coding everything in an obscure language, you can probably quite easily find libraries which already contain all the code you need.

For example, a most-used method would be the Runge-Kutta method. A 10-second look at wiki and two minutes in your favourite programming language will give you everything you want. http://en.wikipedia.org/wiki/Runge-Kutta

To give an idea, we had a 12-hour seminar on applications of numerical methods, which was way more than I'll ever need provided I stay away from building my own solvers and find supervisors who can afford matlab.

If you insist on it, a programming course on numerical methods would probably be much better, if there is such a thing offered. That would focus on writing the algorithms well and efficiently, and learning the basics of how / why they work without going to a full-blown proof.

 

[proton]

i figured numerical analysis would be good for me in case i decide to go into industry instead of academia. but if not, then i figure to take german and E&M B instead of it

 

[tmc]

Does your school offer a Computational Physics course? That's the one you'd want.

 

[proton]

my school does, but not this fall.

i could take combinatorics or probablity theory instead of numerical analysis, if theyre useful for pure math. based on what I've seen from the prob theory class though, it looks very basic and elementary, so i don't want to take it

 

[tmc]

Then you should take the computational physics course whenever it's offered. So you could take E&M now in order to make sure you'll have room for computational physics, or take a pure math course which has uses in theoretical physics (which is where I think you're leaning). For these, I'd probably recommend some sort of abstract algebra or topology; both of which have quite a lot of use in both pure math and theo. physics. However, neither are employable in industry, which would probably prefer something in applied math (like combinatorics, probability, stats...).

 

[will.c]

Just a side note; numerical analysis does not consist of using canned routines to solve trivial problems. If you can learn how to do it on wikipedia in 10 minutes, chances are professional mathematicians and scientists are not terribly interested in it.

If you're interested in industry work or computational science, the numerical analysis class will actually be very useful.

 

[proton]

my TA mentioned that I could learn Maple on my own, so he recommended I take probability instead of numerical analysis in my situation. I still don't know about E&M and german though..