Update: This question has been closed by the votes of 5 privileged users because it does not meet stackexchange's guidelines (it is considered off-topic). For questions about choosing a course / career / academic program you should reach out to faculty and individuals at your institution who can better help you figure out potential career paths / research topics. I myself will reach out to my advisor again and will see if he can help me see what research areas each of these fall into/ what options I have. That being said, it seems this has been categorized as me asking for help with choosing my courses/career path. This might be a misunderstanding, as I was asking what research areas match specific courses, not asking for help deciding on which courses to take. Regardless, that is probably also considered off-topic, and so I will keep any questions regarding research strictly between me and my university.
I just finished my first semester in a PhD program in Pure and Applied Mathematics and I need to figure out what research area I want to focus on.
The crux of the issue is that I need to figure out what courses I need to take. These courses should match my research area, so I have to figure out my area of research first.
I originally was very interested in modeling, predictions, and statistics, and machine learning, but due to my performance in my courses this semester (B, B+, A) my adviser suggested maybe considering a different area of focus, stating that he thinks I will struggle to pass the qual. This has been a rather crazy semester, and was my first semester in the program and working as a Teaching Assistant (which was a lot of fun).
Even if this still were my main focus, my area of research needs to be more specific. Moreover, my school seems to offer a few fixed pairs of courses that have good synergy that you would take and then have on the qualifying exam. I have to take two pairs of them I believe. I might be able to customize it somewhat but I would need to have a very good grasp on what area / problem I want to work on.
Those pairs are:
- Probability / Mathematical Statistics or Probability / Stochastic Processes
- Nonlinear Optimization / Dyn. Prog. & Reinforcement Learning (Something about machine learning, etc)
- Numerical Analysis / ODEs
- PDEs / Complex Analysis
- Discrete Math (& Combinatorial stuff) / Graph Theory
- Algebra-focused courses, but I was told they have little synergy with the other courses and are thus not very recommended.
Rather than determining my area of research so I can choose two matching pairs of courses to focus on, I thought it might be easier to go in reverse, to come here and ask the community what areas of research match these pairs. I was hoping I could get some insight into possible areas of research and what makes them interesting/beautiful/exciting. If you have any other areas to consider I would love to hear about them, as I think I can probably customize my focus (assuming the courses are being offered).
If you want to know more about my course history / timeline, please let me know. I removed it from this post in the interest of being concise.
Please let me know your thoughts / ideas on possible research areas, and please share any links/resources you would recommend to help me decide.
I am very grateful for your time and help!
(P.S. I am still leaning towards a Probability and Nonlinear Optimization based focus, but I believe I would have to do a lot of studying / asking Professors for help to get where I need to be with those subjects)
