Another choosing a math class question

[phun]

I'm planning on going to grad school for soft condensed matter/biological physics. I'm generally interested in learning as much math as possible, but being a senior, I don't have much time.. I was hoping to hear some opinions/advises about which of the following courses would be most benefitial to me. I've pretty much decided that I want to do experiment, but I think some modeling skills would be good to have, even for an experiementalist. Also, it is possible that biological physics would become pretty theoretically advanced during my career span, so I would want to be able to understand what theoreticians say..
Thanks in advance for any input!

1. Abstract Algebra (a year long course)
Groups and their structure, including the Sylow
theorems; elementary ring theory; polynomial rings; basic field theory; Galois
theory; Module theory, including application to canonical form theorems of linear algebra.

2. Real Analysis (year long)
Rigorous analysis in Euclidean space and on metric spaces. Metric space topology, properties of Euclidean spaces, limits and continuity, differentiation and integration, sequences and series, the inverse and implicit function theorems. Lebesgue integration with applications

3. Differential equations of mathematical physics (2 quarters)
Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion equation, wave equation, maximum principles, and variational methods.

4. Numerical solution of partial differential equations (1 or 2 quarters)
Numerical solution of partial differential equations by finite difference methods and spectral methods. Construction of algorithms, consistency, convergence, and stability of numerical methods. Matrix iterative analysis.

It would be nice if you can even rank them in the order of usefulness :)

 

[joelperr]

Given your choices to go into condensed matter physics and biophysics, I would say that this following order would be best: 3, 4, 1, 2.

Biophysics sometimes has to deal a lot with bioinformatics, where #4 will come in quite handy. #3 is essential to any physicist, but especially in biophysics (since some real-life biological systems can be modeled by non-linear PDE's). #1 sounds like a very good algebra class, which is essential if you want to do any theoretical work, but I'm not sure as to it's uses in bio/condensed. #2 is a very interesting class, but not very useful to you, even if you go into theoretical. If you go into experimental as you intend, then this class will serve no purpose.

Well, that's my 2 cents.

 

[Daverz]

Apart from the idea of a group itself, the group theory in the typical abstract algebra course is not very applicable to Physics. I'd just pick up a book on "Group Theory for Physicists". Dover has some inexpensive ones.

Real Analysis is helpful for building confidence in mathematics, and I just plain enjoy the subject myself, but the other courses are going to be most immediately useful to you.

Is there no complex analysis course available? That is very useful in the sciences (particularly contour integration), and one of the most beautiful subjects in the undergraduate curriculum.

 

[phun]

Thanks for the reponses. I've always been wondering why some undergrad physics curriculums include courses in analysis. Is it only for building mathematical rigor and confidence? I have taken complex analysis, in which I learned about analytic functions and some fancy integration techniques, but unfortunately my physics curriculum never utilized anything I learned in that class (at my school physics and math profs don't seem to talk about to each other's curriculum at all), so the material is pretty faint in my memory. I guess grad level courses must have something to do with those things.

 

[Poop-Loops]

God, I hated that at my old school. I went up through 4 quarters of calc, linear algebra, and Diff EQ (ODE's), and the physics was stuff like "integrate Edx" or whatever for an electric field. It pissed me off that we never got to use what we learned, since now I've forgotten most of it.

 

[phun]

Yup, it's annoying. But the weird thing is, standard texts such as marion&thornton, griffiths, or even some of the easier chapters of ashcroft&mermin don't use anything that I learned in complex analysis. And yet my physics dept recommends complex analysis for students intending to go to grad school. I wonder if they even know what is being taught in that class.

 

[Daverz]

Thanks for the reponses. I've always been wondering why some undergrad physics curriculums include courses in analysis. Is it only for building mathematical rigor and confidence?

It does make reading the mathematical literature easier.

I have taken complex analysis, in which I learned about analytic functions and some fancy integration techniques, but unfortunately my physics curriculum never utilized anything I learned in that class (at my school physics and math profs don't seem to talk about to each other's curriculum at all), so the material is pretty faint in my memory. I guess grad level courses must have something to do with those things.

Yes, it doesn't get used in the undergraduate physics curriculum, but you will encounter it in your graduate courses. Don't worry, it won't take you long to relearn how to do contour integrals.