Insights on future prospects: Applied vs Computational Math

[PhysicsKid0123]

Hello Physics Forums community, I'm looking for opinions, advice, really anything, to help me better understand what I'm going into and what may be better for me after gradation. I am posting this under academic guidance because these are decisions that I need to make while I am in college. This may not be important, but just FYI, I am currently studying physics at UT-Austin. Additionally, I am also studying mathematics as a double major - applied mathematics to be specific. I am wondering what exactly could I do with a degree in applied mathematics that I could not in computational math. Conversely, what could I do with a degree in computational math that I could not do in applied math. How would these fields diverge in an academic setting and in a career like setting, for instance industry. I've read some articles here and there after a quick Google search. However, I'd like to get some opinions from people I could interact with and has some experience in what these degrees could lead and not lead too. I'm currently undecided as to what I want to do after graduation.

A few things I am considering right after graduation are:

1) Grad school (a master's in physics, electrical or aerospace engineering, and MAYBE a PhD later, but only if I get into a good school, otherwise I rather not go that route)

2) Teaching math or physics at high school. I probably won't want to do this for a very long time, but know knows that could change.

3) Work as a quantitative analyst for a financial company or MAYBE an actuary.

4) Work at a tech company like SpaceX, NASA, Radeon, LockHeed Martin, Google, something of that nature. Not necessarily as an engineer, whatever gets me to work on interesting projects (I know NASA is a government agency, but you know what I mean.) Also, I'm not interested in making weapons-- or as long as there not deadly weapons involved non-fatal self defense systems I am okay with.

5) I would also like to make an attempt at starting a tech company myself. I know some very talented individuals that would join me in the pursuit of this endeavor. This one may be the most difficult of all. Furthermore, I would probably have to expand my knowledge in computer science like SQL, Java, and so on. All I really know at the moment is C++, some HTML, some JavaScript, and some Ruby, but not very much like I know C++. I don't know any Matlab or anything like that. I know very little Mathematica.

6) Go to Medical School. This was suggested to me by my mother and sister. I think it's a good idea, but I am not entirely sure. I do love to help people, and gaining the ability and skills to save lives would be an utter blessing.

These considerations are not in any kind of order. If anyone has any other suggestions as to what other kinds of careers I might be interested, given what I have provided, please let me know.

One final note;
I love to learn virtually about everything-- I'm very curious and knowledge is like food to me. Regardless of the outcome, I will still be motivated to learn and read books on topics in advanced math, in the sciences like chemistry, biology, physics, in engineering, in psychology, in business, et cetera--for the rest of my life. Ultimately, I plan to focus on physics or self-study-- "on my own," if you will, because I want to make an attempt at solving some of physics' toughest unsolved problems even if I'm not in academia. Sort of like a long-life hobby, but given that I do not pursue a PhD in physics. Now that I've mentioned the PhD, the reason I do not want to do this is because it seems like a lot of school-- especially if its physics. Don't get me wrong, I LOVE PHYSICS, but the routine might get boring which is why I want to see what a Master's would be like. Exposure to other fields might be good for me since I also hold interests there.

I think I have elaborated enough, and I hope someone can relate or offer some good insights. Forgive me if I provided too much, I like to be thorough and I'm also very indecisive when it comes to my future career. If you have any questions, I'd gladly answer. And thank you to all who have taken the time to read about my situation, and also to those who offer advice or what have you. I greatly appreciate it, thank you.

 

[RUber]

Really, these days applied math and computational math are becoming synonymous. However, from the broadest view, comp. math is a focus area within applied math. That is to say, you would get more specialization toward computational methods, algorithms, and speed in a comp. math program.
In the area of computational physics, methods for simplifying large matrix problems and/or parallel processing are drawing a lot of attention.
In applied math, you might focus more on the general problem and methods. Once you apply the methods to a computational problem, you will be doing the same stuff.
If your goals are as broad as you say they are, I would recommend less specialozation in your academics to maximize transferability.