I highly appreciate any input and thank anyone who helps.
I am a Mechanical Engineering student with a Mathematics minor, and I am in the process of starting undergraduate research with one of my previous Math professors.
His background is in Applied Math and PDEs but he has told me I do not have enough background to do work in his field
The undergraduate courses I have taken are: Calculus I through IV (includes Vector Calculus), Discrete Structures (includes Logic, Sets & Proofs), Linear Algebra, Numerical Methods, (Ordinary) Differential Equations, Probability & Statistics, and Real Analysis (includes metric topology, single-variable analysis and rigorous proofs).
I have a strong computational background and can program well. I also have a person who will work with me with very similar credentials.
We have been struggling to find a topic appropriate to my level. Ultimately we want to do work in Robotics (the applied math aspect of it). But I really want to experience mathemtical research, because math is something I really enjoy. I frequently read a lot of math beyond my level out of thirst and fun.
What would be a realistic topic, field, or problem someone with my context could work on?
I am fine with any problem either abstract or real-life based. I seriously just want something I can work on, anything accessible is good enough at this stage.
I understand I am not asking a simple question, but any input, point, or direction would be extremely helpful. I just want the insight of people who know much more than I do.
Thank you very much.