Nate Pinsky
Harvey Mudd College Mathematics 2013
| Thesis Proposal: | Differential Geometry through Discrete Approximations: A Video Pedagogy |
|---|---|
| Thesis Advisor: | Prof. Weiqing Gu |
| Second Reader: | Prof. Darryl Yong |
| E-Mail: | npinsky@hmc.edu |
Differential Geometry through Discrete Approximations: A Video Pedagogy
In my project, I will examine the pedagogy underlying modern uses of technology in the classroom, determine the efficacy of various approaches, and apply these principles by developing a video-based introductory course to differential geometry based around MATLAB. I expect to spend the majority of this project developing the introductory course. Since many of the precise definitions used in differential geometry rely on advanced and abstract ideas from calculus, linear algebra, and topology, the course will present much of the content, which is by nature continuous, by way of discrete approximants. By teaching the content as a discrete subject, I will also be able to discuss uses of differential geometry in the analysis of real-world problems for which only discrete data is available, thereby motivating students who focus on appliction. For these reasons, I will use MATLAB, a tremendous tool in processing data as well as visualizing mathematics, to explore the concepts in the course. I hope that this course will be able to serve as a first introduction to differential geometry for undergraduates, as a tutorial for using differential geometric tools to analyze discrete data, or as a review of these topics for more advanced students.
Download the CDF file and open it with Mathematica or CDF Player.