Need help/tips/advice from someone who has a degree in Applied Mathematics

Solution 1:

It depends broadly with what you want to do next, since mathematics are literally applied everywhere...

If you want to do things close to engineering, you probably want to invest heavily into subjects that are used in finite elements (FEM). Those would be functional analysis, PDEs and linear algebra.

If you want to do things close to dynamical systems (Control theory, chaos, ...), you probably want to invest into ODEs, differential geometry and calculus. Also a little topology.

If you want to do things in data science (ML, ...) , I would encourage you to go for linear algebra, probability theory, statistics and optimization.

Despite all of this, I find as a mathematician that everything is useful, even the subjects that are the most theoretical. I myself am in the finite element world (so 1st category) applied to HPC, and even though it is very applied you definitely need things like topology, differential manifolds, functional analysis, group theory and much more. Having a broad understanding of every field of mathematics (even if you are not an expert) is paramount in order to get the full picture.

Cheers!