I am a senior at Worcester Polytechnic Institute. After asking another question on this website, I have decided to become a professor of practice. To do this, I will pursue a Ph.D.
A Ph.D. project that I have already started in my free time this summer is developing an application and website that would help with calculus education. The application has
- A computer algebra system which solves the calculus problems
- A system which shows the work that the computer algebra system performs
- A system which gives hints for the user
- A system which allows the reader to type in each line of their work for the system to check for correctness and possibly identify the reason the answer is incorrect. This would include a system which would allow the user to draw graphs with their mouse for curve sketching problems.
- A website where the application would be available for free use.
- If there is still time left, typed notes and maybe even video lectures to correspond with the application.
I already have done 3,014 lines for the computer algebra system over the summer and I would love to make this my research project. I think that this would make an awesome research project because I would do it even if I didn't get a Ph.D. (I originally was considering making a level with the website as an alternative to the Ph.D.)
However, I worried that it would not be eligible as a Ph.D. project because I'm creating something rather than discovering a new theorem, numerical algorithm, or mathematical model. This made me even consider not getting a Ph.D. as my previous experience with research in numerical analysis was not enjoyable.