Rank Courses for BS Statistics & Increase Math Understanding

[transphenomen]

I am getting my B.S. in statistics in a few years and will then try for a PhD, and I happen to have 1-4 spots where I can take additional courses. I am taking all my stat courses as well as a year of real analysis and a year of abstract algebra and want to take these other courses, but I may need to prioritize in case I don't have enough time.

Introduction to Partial Differential Equations. This is not a proof class.
Fourier series, orthogonal expansions, and eigenvalue
problems. Sturm-Liouville theory. Separation of variables
for partial differential equations of mathematical physics,
including topics on Bessel functions and Legendre polynomials.

Elements of Complex Analysis. This is not a proof class.
Complex numbers and functions. Analytic functions,
harmonic functions, elementary conformal mappings.
Complex integration. Power series. Cauchy’s theorem.
Cauchy’s formula. Residue theorem.

Number Theory. Proof class.
Elementary number theory with applications. Topics
include unique factorization, irrational numbers, residue
systems, congruences, primitive roots, reciprocity
laws, quadratic forms, arithmetic functions, partitions,
Diophantine equations, distribution of primes. Applications
include fast Fourier transform, signal processing, codes,
cryptography.

Differential Geometry. Not a proof class.
Differential geometry of curves and surfaces. Gauss and
mean curvatures, geodesics, parallel displacement, Gauss-
Bonnet theorem.

Introduction to Topology. Proof class.
Topological spaces, subspaces, products, sums and quotient
spaces. Compactness, connectedness, separation
axioms. Selected further topics such as fundamental group,
classification of surfaces, Morse theory, topological groups.

These are all undergraduate courses and so should not be too hard. I would like for you guys to help rank them not just in how useful they are for statistics, but how well they would increase my breath of understading of mathematics in general. These courses also have an additional course or two that continue on from the last class in case you guys think that studying a specific subject in depth would be better than just skimming many subjects.

 

[twofish-quant]

If you are getting a degree in statistics, I'd recommend that you take a class on econometrics with time series or something that will get you exposure to setting up a medical or educational studies. If you do econometrics you will get exposure to time series models which are critical in a lot of fields. In setting up education and medical studies, you will have to learn about stuff like human experimental rules.

In addition to that, I think the class that would be most useful if you are at all interested in finance is the PDE class. Mathematical finance talks in two languages, PDE's and statistics, and I don't know of anyone that is an expert in both. If you are an expert in statistics but you can understand and deal with PDE's and stochastic different equations, that looks really good on a resume.

As far as understanding math in general. Just pick the hardest class. It's like asking which is going to be better for your health, swimming or mountain climbing. As far as building general mathematical ability, it doesn't much matter as long as you go out and exercise.

 

[chiro]

I recommend you take the PDE class unless for some reason you are interested in one of the other subjects.

However you look at it, more maths is good: even for the sake of expanding your thinking and perspective and letting you become aware of what is out there.