What do i need to know to be a good applied mathematician

[ice109]

the applied math curriculum is very weak at my school so I've been fishing around in other departments trying to cobble together some useful skills. as of right now that I've only taken the basics but next semester i have seemingly decent choices for classes. available to me are:

computational astrophysics: introductory numerical techniques class in the context of astrophysics

methods of applied math: dynamical systems and perturbation methods

foundations of computational math 1: what it sounds like, rigorous explanation of the methods used in computational math.

intro to fluid dynamics

intro to financial math

all of these are at the graduate level. there's also a graduate QM class I'm considering taking for fun so at most i could take 2 of the above or 1 and the QM class.

additionally if i want to have a well rounded applied math preparation coming out of undergrad what should i be studying? I've taken the usual calc sequence including differential eqns and linear algebra and I've got the programming aspect covered and i know i should learn PDEs. what else?

 

[maverick_starstrider]

I'd say to have a strong applied math undergrad you'd probably need the following:

-ODE's
-PDE's
-Probability and Statistics
-Real Analysis
-Complex Analysis
-Possibly functional analysis (although you may only see that in grad) or else simply the Calculus of Variations
-Elementary Number Theory (groups and such)
-Potentially Differential Geometry and Tensor Analysis

so I guess of your choices (which aren't great) you'd probably want:
-Intro to Fluid Dynamics
- Computational Math
-Methods of Applied Math

Financial math is a lot of stochastic calculus which is neat and can be a useful tool but is generally not consider part of the standard 'package' that an ungrad amath major should have. and Computational Astrophysics is so general a field that that course could be about anything (and the numerical computation you learn would probably be picked up from that computational math course).

Hope that helps. Feel free to disagree.