Where to go next? (applied mathematics and physics)

[Avatrin]

Hi

I have a bachelor in mathematics, but I just do not know where to go next. The reason I decided to study mathematics was because I have been a puzzle solver since I learned to read (mathematical puzzles, mechanical puzzles etc). So, I wanted to see how I could make a living using that kind of thinking. I tried physics and chemistry, and in the end, I settled on mathematics.

Not all mathematics gives me the kind of joy puzzles do. Functional analysis seems too abstract (however, this may change if I ever get used to the abstractness). For some reason, multivariable calculus just does not feel very satisfying (again, this may just be because I am not very "fluent" in the methods of multivariable calculus).

On the flip side, solving problems on projecteuler.net is amazing. Game theory is great. Discovering mathematical biology is one of the greatest things that happened to me in 2013. Complex analysis was fun.

I also want to make things (part of the reason is probably that I wasted three semesers in business school before going to a university to study science). It doesn't matter if it is software or machines.

So, I am completely stuck. Sometimes I consider mechanical engineering (I only lack fluid mechanics to take a master in mechanical engineering). Other times I consider computer science. I have also, due to mathematical biology, considered biophysics (but, imaging does not appeal to me).

If I seem confused... Well, yes, I am. Any suggestions on what I should do next?

 

[jedishrfu]

How about everything on Differential Geometry from vectors, tendons to differential forms? It's useful math for a lot of upper division physics.

 

[flawesome]

You sound like a programmer to me. One who would be very good and making software to analyse complex biological systems. Neurological systems might be right up your ally. Check out the free edX course called "Neuronal Dynamics - Computational Neuroscience of Single Neurons". One course of action might be to pursue a masters in biophysics and get some IT certificates in the programming languages of you choosing. Imaging is one small facet of biophysics, so don't let it deter you. I do think all of the options you mentioned are good ones in any case.

 

[homeomorphic]

I just have a couple comments on functional analysis. To overcome the abstraction, I think it helps to study physics, certain aspects of engineering, PDE, numerical analysis, integral equations, and stuff like that--particularly integral equations. The functional analysis class that I took in grad school was horrifyingly abstract, but the good thing about it was the very interesting and difficult problems that were assigned, so I think that would appeal to a problem-solver type of mathematician. I am more of a theory-building type of guy, myself, more interested in seeing how things work and fit together than in cracking hard nuts, but I strongly dislike unmotivated abstractions. I think the solution for both types of mathematicians who don't like abstraction should be pretty similar. Another thing you can do is read the book by Dieudonne on the history of functional analysis, which is not very readable but gives you an idea of where the subject comes from. What I haven't tried yet that might be very helpful is to find more books that say "applied functional analysis" or books that cover functional analysis, but use it more as a tool than as an end in itself. I still need to search for those books and read them, though.

 

[jedishrfu]

Another avenue to consider is Computational Physics and related disciplines. Take a look at the Open Source Physics website. They provide a large collection of Java programs that simulate various kinds of physical systems. You'd getmto play with Java, differential equations and geometry all in one package.

Http://www.compadre.org/osp

Alternatively you could look at pyzo.org IDE which is a python based framework for doing scientific applications. There are no examples but they use established Python modules for doing computational physics...

 

[Avatrin]

I just have a couple comments on functional analysis. To overcome the abstraction, I think it helps to study physics, certain aspects of engineering, PDE, numerical analysis, integral equations, and stuff like that--particularly integral equations. The functional analysis class that I took in grad school was horrifyingly abstract, but the good thing about it was the very interesting and difficult problems that were assigned, so I think that would appeal to a problem-solver type of mathematician. I am more of a theory-building type of guy, myself, more interested in seeing how things work and fit together than in cracking hard nuts, but I strongly dislike unmotivated abstractions. I think the solution for both types of mathematicians who don't like abstraction should be pretty similar. Another thing you can do is read the book by Dieudonne on the history of functional analysis, which is not very readable but gives you an idea of where the subject comes from. What I haven't tried yet that might be very helpful is to find more books that say "applied functional analysis" or books that cover functional analysis, but use it more as a tool than as an end in itself. I still need to search for those books and read them, though.

Thanks! Do you also have advice for measure theory? That is probably the worst for me (I even managed to get past abstract algebra by tying it up to theory of equations. Measure theory, however, seems unassailable).

Also, thanks for all the other advice! I think I will continue towards mathematical biology/biophysics and see where that leads me.

If anybody else have any advice, I would like to know! I have not completely settled on biology, but currently, it seems like that's where I should venture off to.

 

[jedishrfu]

How about computational biology?

http://en.wikipedia.org/wiki/Computational_biology