Suitable Math Course For 2nd year Astrophysics?

[Screwdriver]

The Exposition

I'm an Astrophysics major going into my second year of University this September. I have room for one other course in fall and one course in the winter (so I have two spaces to fill.) I'm already required to take every physics course offered (6 total), and the two requisite math courses are Differential Equations and Advanced Calculus.

The Options

i) An introductory computer science course in the fall and "Intro to Real Analysis" in the winter. Here's the course description for Real Analysis:

Taylor's theorem, optimization, implicit and inverse function theorems. Elementary topology of Euclidean spaces. Sequences and series of numbers and functions. Pointwise and uniform convergence. Power series.

ii) A full year math course called "Algebraic Methods." Here's the course description for Algebraic Methods:

Algebraic techniques used in applied mathematics, statistics, computer science and other areas. Polynomials, complex numbers; least squares approximations; discrete linear systems; eigenvalue estimation; non-negative matrices - Markov chains; permutation groups; linear Diophantine equations; introduction to algebraic structures.

iii) Something completely different.

The Issues

I don't know anything about computer science, and the course assumes you've seen it in High School, so I'd have to do some reading this summer. Also, Real Analysis looks way too much like pure math. If it's relevant, I didn't really like the theory of Lin Alg, but I found the applications very interesting (eigenvalues and stuff.) I also have no idea what the course description for either one is talking about. It's like you have to have taken the courses to understand the course description

The Question

What should I do? Thanks to anyone who even bothered to read all that!

 

[Nabeshin]

\Also, Real Analysis looks way too much like pure math.

Yep, real analysis is what us physicists would call pure maths. It's really not relevant to doing physics.

If it's relevant, I didn't really like the theory of Lin Alg, but I found the applications very interesting (eigenvalues and stuff.)

Linear algebra, however, is very useful in physics. Presumably you've already had an introductory course, and continuing on with that education will serve you well when you get to upper level quantum mechanics.

If it's between the two, I'd say the second class (but I hate real analysis .

Really depends on what you're going for. If you're trying to apply the maths to physics, then find the most applied class you can, maybe something on PDE or numerically solving equations. In the same vein, a computer science class or two would likely be helpful (not really the CS theory, but just knowing how to program at all is an extraordinarily useful skill). On the other hand, if you're interested in maths for maths, then you should probably do real analysis.

 

[Screwdriver]

Linear algebra, however, is very useful in physics.

*sigh* I was afraid of that. Good thing I decided not to burn those notes...

Actually, there is another option that I didn't mention, which seems to be more or less what you suggested. The course is "Applications of Numerical Methods."

An introductory course on the use of computers in science. Topics include: solving linear and nonlinear equations, interpolation, integration, and numerical solutions of ordinary differential equations. Extensive use is made of MATLAB, a high level interactive numerical package.

I knew it was too good to be true though, because if you take this, you can't take "Computational Methods in Physics," which is a 3rd year course that I'm required to take that presumably covers the same things.

I was also leaning towards Algebraic Methods, mainly because it seems like it'll be applications (I think?), and I definitely want math that applies to Physics. It'd be nice if I knew what I was getting myself into though

 

[SpiffyKavu]

Do you know your interests in astronomy? You're in your second year, so it is very likely that you don't. I just finished my first year of graduate school, and I've just narrowed down my interests.

But you also seem like you aren't the biggest fan of pure math. The course description for that algebraic methods seems like it is more applied mathematics, which may be better for you right now. A bunch of the topics that are supposed to be covered are relevant to physics/astronomy.

I don't think the real analysis course is very important for the vast majority of astronomy. If the topics really interest you, then take it. Physics does some real analysis without really calling it by that name, so you'll learn some of those topics in the course of your educational career.

But you could also ask a faculty member at your school for recommendations. You'll be able to explain your situation better, and they certainly know what your school offers better than we do.

 

[Screwdriver]

Do you know your interests in astronomy? You're in your second year, so it is very likely that you don't.

Guilty as charged. I figure I'll learn what I'm interested in over the years. I didn't even realize that I thought Physics was genius until 3/4 of the way through first year.

But you also seem like you aren't the biggest fan of pure math.

Right again.

But you could also ask a faculty member at your school for recommendations.

I did actually do that, and he suggested the options I presented in the OP. The only other thing I can thing of that's math-related is Statistics. How do you, or anyone else, feel about that? I don't think I'd mind a few stats courses. Thanks so much for the responses by the way.

Course descriptions for Stats and Probability I and II (in that order) if they help at all:

Basic ideas of probability theory such as random experiments, probabilities, random variables, expected values, independent events, joint distributions, conditional expectations, moment generating functions. Main results of probability theory including Chebyshev’s inequality, law of large numbers, central limit theorem. Introduction to statistical computing.

Basic techniques of statistical estimation such as best unbiased estimates, moment estimates, maximum likelihood. Bayesian methods. Hypotheses testing. Classical distributions such as the t-distribution, F-distribution, beta distribution. These methods will be illustrated by simple linear regression. Statistical computing.

 

[chiro]

For something that complements astro, I would recommend anything with statistics, and courses that deal with or lead up to signal processing. If you can get a computer subject where you do signal processing coding: that would be beneficial as well.

 

[Screwdriver]

For something that complements astro, I would recommend anything with statistics...

Sweet deal. The stats course fits with my timetable as well.