thelonewanderer

Good afternoon everyone, I'll be starting my trek into upper division mathematics next year (applied math major) and since the perquisites are essentially just multivariable calculus and linear differential equations, I can pretty much take them in any order. However, I know that I should probably take Linear Algebra first and plan on doing that, but after that, I'm at a loss.
Here are the classes I plan on taking (also if you have suggestions to switch them to something else, input would be great):

Linear Algebra
Real Analysis
Complex Analysis
Mathematical Modeling
Linear/Nonlinear Systems of DE
ODEs
PDEs
Applied Numerical Methods
Optimization
Probability Theory and Stochastic Process
Combinatorics
Methods of Applied Mathematics
Algebra for Applications
Fourier Analysis

Thanks for your time!

b@r!um

I agree with you that the linear algebra course has priority.

I would also take Real Analysis before PDEs or Fourier Analysis. It will be much easier to appreciate the rigor and format of the latter two classes if you are already familiar and comfortable with analysis-type arguments.

That's the only real recommendation I have. If it's convenient scheduling-wise, you might prefer to take one differential equations class before you dive into applied and numerical math classes. It's probably not necessary, but you'll get much more out of the classes "spiritually" if you start with a stronger background. (Knowing differential equations gives you a tool to work with in applied math, and it will show you why you care to solve certain problems that you'll see in your numerics classes.)

You might find a fair bit of overlap between your 4 classes on differential equations and fourier analysis. Maybe you could consider dropping one of them? (Several people suggested to me that I skip ODEs. Retrospectively that was a good decision for me at my school. You could consult an adviser at your own school to see if that might be a good idea for you too.)

thelonewanderer

Hey thanks for the reply. I'm required to pick two "two quarter series" which are between numerical methods AB, Probability Theory AB, and linear/nonlinear and ODEs. I guess since I only need to pick two, I can use numerical methods probability to satisfy that, and then not take the ODEs. But yeah I'll talk to my adviser in the fall, just wanted a little insight from some other people (:
I'm also considering switching to the Math/CS (ish) degree, but I'm still unsure if it holds "better" job prospects. I'll save that discussion for another thread

broken_symlink

If you do decide to go through with the differential equations stuff, you should take ODE before the linear/nonlinear class, otherwise, the dynamical systems stuff won't seem that well motivated.

WaitingForGodot

ODEs before the other DE classes, linear before Fourier (well, you don't need to, but it might help you understand Fourier analysis better). In fact, linear should probably come before everything (maybe at the same time as ODEs).

Math methods should probably be after PDEs and complex analysis.

Fourier and PDEs should probably have a large amount of overlap, possibly enough to consider only taking one of them.

I'd take algebra early too because it's a pretty huge area of math that you might want to learn more about.