The long and short of this questions is that I’m someone with a pure mathematics background (albeit at a junior-undergrad level) who wants to learn a set of applied math topics in a way leverages what I already know. Perhaps there are books targeted to people like me?
To be specific, and I’m starting to do some work where I will need to get up to speed on a variety of applied math topics fairly quickly (in my case, for a summer job). Importantly, I would need to know the material well enough not just to have a vague idea of the concept, but also to do creative work with these concepts. I believe part of what will enable this is
- having an idea of how applied topics tie to theoretical foundations and
- working on exercises to reinforce what I learn.
I am afraid that in most resources to learn what I am trying to learn, one of these two things are missing. Either it’s wikipedia, or the Princeton Companion, which are missing (2), or it’s an applied math textbook which all too often lacks (1)--though maybe I just haven’t been reading the right ones.
Some topics that I know will be relevant to my work this summer are:
- Stochastic differential equations
- Inferring functions from data
- Gaussian processes
- Statistical techniques like bootstrapping, monte carlo methods, etc.
And more generally, subject areas of interest to me are
- Probability theory
- Differential equations
- Stochastic processes
- Information theory
Does the Stackexchange community know of any resources in the vein that I am describing?
Appendix Here is a more specific list of courses I’ve taken, if this is at all helpful
Theoretical side:
- Linear Algebra
- Group theory
- Two courses in real analysis
- Topology
Applied side:
- Two algorithms courses
- A discrete math course
- Nonlinear Dynamics course (lots of function iteration, fixed points, applications of topology)