I work as a programmer. After finishing my Bachelors in Statistics I have to choose a Masters.
I want to boost my Math knowledge, both theoretical(I enjoy numerical methods, optimization and topology) and applied(Neural Networks, Models). Maybe write a little bit of code. I guess I would love to do some Data Science work in the future but I believe I have to learn the hard stuff, first .. but getting a better job isn't the reason I am chasing a Masters.
NUMERICAL METHODS/DIFFERENTIAL EQUATIONS:
On the one hand I could study numerical methods, differential equations. I think I will learn a lot about the Finite element method. I like that there will be a lot of code and direct implication in biology/physics models. I also think this would have some implications on my Neural Networks knowledge, as things like the adam optimizator could be explore and I could have a cool practical topic for weather prediction on which I could improvise.
On the other hand I could study topology, functional analysis, Game Theory and some other very heavy theoretical math which in the end could result personal clarifaction of how certain phenomenons work. I like how after a lot of theoretical math you get inspired aboutthe world, how you see things from a different perspective. It sound edgy.
I think that some problems like the biological SIR method could be solved with different approaches. I think the two Master degrees would take 2 different approaches for solving this problem, one being very empirical and the other theoretical. Are they contradicting each other in the sense that they are are using different approaches to solve the same problem?
I feel numerical methods is more practical, I feel that the future is numerical methods but I find Optimization more impactful, it sounds harder and just ... more respectful.
People tell me to choose what I like, but I like both, what would you choose?