I'm a junior majoring in applied math computation at UCLA, and I was wondering what exactly constitutes a viable mathematics education? That is, what kinds of mathematical topics should an applied math major know for industry? Have any studies been carried out on this?
The reason I'm asking this is that I'm allowed to take 6 math/stats electives for my major, and I wanted input advice to see what should an applied math major know after college.
My plans as a career are currently to become a computer programmer/software engineer. I'm also interested in jobs dealing with finance and the like, but am not sure about anything yet. I expect if I do work in CS, I don't think I would use a lot of my math knowledge, but I'd still like it to be complete.
What I am sure is that I do not plan on going to graduate school in mathematics whatsoever, so I'm very much edging away from the whole precise, theoretical math.
What would you say constitutes as a "well-knowledged" applied math major? Like, what topics should I know?
My major only requires (1) all the calculus series obviously, (2) linear algebra and diff eq (3) linear algebra with proofs (4) Analysis/complex analysis (5) numerical analysis -> so I have to take/have taken these classes already.
Math electives I can take: The more theory math: - Algebra - Linear algebra - Cryptology - Topology - Geometry - Fourier analysis - ODE's - PDE's
More applied math: - Math imaging - Math modeling - optimization - game theory - probability theory - stochastic processes - finance/actuarial math stuff
Stats: - probability - data analysis -> regression -> experimental design -> data mining/stat models
I am honestly not too great at math so far, so I was planning on taking the easy way out by taking just optimization and the rest of my electives being stats, but I want to know what constitutes a full applied math education. Sorry if I'm being vague in my questioning. Thanks.