Hey all,

I have found this forum very helpful over the past two years of my PhD, so I am hoping to get advice on how to transition from a schedule of two courses plus research to full research. I am one of the few computer science students in my program who studies theory. I will just list a few of my concerns that I would greatly appreciate advice on.

- As a theory researcher, I will not have the structure of going into a lab or regularly collaborating with colleagues. Any advice on keeping with a research schedule and monitoring self-progress?

- My adviser says that anything I need to learn at this point I should just teach myself. Is there an effective way to split time between learning new topics and focusing on research? Should I just learn things as I encounter them in research?

- Although I have an undergrad background in math, I feel behind students of math. Part of me wants to take a math course just to see how I compare with other students, but this seems like a bad reason to spend so much time in a class. Am I right to be concerned that I am under-prepared going into a math-dominated area as a comp sci researcher?

- If I want to pursue a professor position in math or comp sci with an equal focus on research and teaching, what are some goals to keep in mind before graduating?

Thanks for any advice you can give!

I would imagine that you need a strong background in Linear algebra, discrete maths and algorithm development to start with.
Are you solid on these things? I would have thought a CS course would have given you a decent background in these things but you obviously feel a bit vulnerable there.

I found that lectures were almost completely useless once I started my PhD. I found them too slow and prefer to learn at my own pace with online videos and problem solving from books.

As for planning, I would identify the subjects you want to learn, make a reading list, allocate 3 to 4 hours per day perhaps and keep a diary of progress.

I am definitely strong in the areas you mentioned. However, a lot of the research in my area uses topology, algebraic geometry, matroid theory, and many other topics that I don't have a deep knowledge of. I know a lot of the basics though.

Maths students will presumably have some basics in topology or algebraic geometry but they are probably not as far ahead of you as you think. Are they likely to know about things like Matroid Theory?
If it was me I'd get that reading list sorted and then mapped into my diary. That'll tell you how many months it will take you to get those things on board.
Presumably you don't need to be an expert in any of them at this stage.

If I were you, I would start to independently learn matroid theory (I think Günther Ziegler has a book or notes on this), topology (I guess Munkres for basic topology) and algebraic geometry (try Hartshorne's book). If you do theoretical CS, I'm sure that with enough motivation you can know the relevant areas of these fields as well as math students studying these fields (I know many math students who don't know any of these fields besides some basic topology). I like the idea of learning things as you encounter them in research in order to understand their significance. If there is a math course which is relevant to your research, maybe you can take it. Often times courses provide good structure.