MATH 99R: Tutorial

Topic: Visualizing mathematics

Creative technology enables us to explore, interact with, and experience mathematics in new ways. Within a short period of time we have seen for example the rise powerful computer algebra
systems, the development of web technologies for creating interactive laboratories. Advances in printing technologies that enable us to fabricate mathematical illustrations. New photographic techniques allow to produce panoramic views, remote sensing technology allows to produce reliefs. Advancements in large language models, stable diffusion or proof verification offer innovative tools for shaping and visualizing mathematical structures. In the tutorial, these developments are first covered theoretically and with examples.

Outcome: Each Student picks a topic of choice culminating in a final paper with a presentation towards the end of the semester. Ample support will be provided, as the instructor brings several decades of experience in working with, exploring, and programming in each of these areas.

Prerequisites:
Multivariable calculus and linear algebra as taught in 21, 22 or higher is required, as topics in differential equations or linear algebra come up. Any other math, computer science or applied math or stats knowledge is helpful.

About:

The website from last semester gives an idea of what we have done in 2024: it is the following link:  Math 99: Fall 2024. While some topics will return, we will also explore new topics in 2025.  For more information about this course, send an email to Oliver Knill.