so a bit of background info on me.
I'm a math grad student. My undergrad classes were mainly math-theory based stuff. I took Number Theory, Intro to Analysis, Intro to Abstract algebra, and such.
I did take some computationally sweaty courses such as Financial Math for Actuaries(sweaty, but fun!). I also took Intro to Probability. And of course, I have the basics such as differential equations, linear algebra, complex variables...
My professor told me he could assign me stuff related to optimization(for example a minimal-time control problem). He said if I knew my stuff, he could assign me something on single-cell RNA sequencing data analysis, which is basically a study on large scale sparse matrix. He also proposed a topic on stochastic control which would be challenging to both him and me.
Can someone let me know what I'd be getting myself into if I chose to do research with him? I honestly have no idea what I'd be getting myself into.
Appreciate any feedback. !~
To be honest, it is hard to say whether or not you are ready for this research topic. It doesn’t really have anything to do with your background, your background should be fine for a topic like optimization. I am by no means an expert in optimization, but I can say that for applications, all you really need is a working knowledge of numerical linear algebra, vector calculus, and experience with programming (in Matlab for example). Some depth in topics like convex and set-valued analysis would be a plus, but are not essential.
That being said, being ready for a research topic is not necessarily dependent on your mathematical background alone. It also has a lot to do with your attitudes towards learning as a whole, and having a growth (as opposed to a fixed) mindset. In other words, things like:
It is really subjective, so a definitive answer is hard to give. I should also note that in practice, you will learn what you need to do research on the go. I haven’t met (yet) an advisor who expects their mentees to know absolutely everything about their research the first semester.
These are my 2 cents, take with a grain of salt.