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.

 

[Mene]

To be a good applied mathematician, there are several key areas that you should focus on. First and foremost, a strong foundation in mathematics is essential. This includes a solid understanding of calculus, differential equations, and linear algebra. It is also important to have a good grasp of probability and statistics, as these are fundamental to many applications of mathematics.

In addition to these core math courses, it is beneficial to have a strong background in computer science and programming. As you mentioned, you already have some programming experience, but it would be helpful to continue developing your skills in this area. This will allow you to effectively implement mathematical algorithms and models, as well as analyze and visualize data.

In terms of specific courses to take, the ones you have listed seem like great options. Computational astrophysics will give you hands-on experience with numerical techniques, which are crucial in many applied math fields. Methods of applied math will introduce you to important concepts such as dynamical systems and perturbation methods. Foundations of computational math will provide a rigorous understanding of the methods used in computational math, which will be useful for developing your own algorithms and models. Intro to fluid dynamics and financial math are also valuable courses, as they apply mathematical concepts to real-world problems in these specific fields.

In addition to these courses, it may also be beneficial to explore other areas of mathematics such as optimization, graph theory, and topology. These areas have applications in a wide range of fields and can help you develop a more well-rounded understanding of mathematics.

Ultimately, the key to becoming a good applied mathematician is to have a strong foundation in mathematics, programming skills, and a willingness to continuously learn and adapt to new techniques and methods. By taking a variety of courses and exploring different areas of mathematics, you will be well-prepared for a career in applied mathematics.