About

This Math 99r course is small group tutorial course with limited enrollment. The tutorial had been offered already in the Fall 2024. We live in a time where technology enables us to explore, interact with, and experience mathematics in novel ways. Within a remarkably short period, we have witnessed the emergence of powerful computer algebra systems, the development of web technologies for creating interactive laboratories, and advances in printing technologies that enable us to fabricate mathematical models. New photographic techniques, such as panoramic views and drone technologies, have become accessible to consumers in the last decade. Moreover, advancements in large language models, stable diffusion technologies, and proof verification models have entered the mainstream, offering innovative tools for shaping mathematical structures.
In this tutorial, we will first explore several of these developments. Students will then delve into the mathematical applications and/or aspects of one or two of these advances more deeply, culminating in a presentation towards the end of the semester.

Prerequisites: Multivariable calculus and linear algebra as taught in Math 19, 21, 22 or a higher numbered course is highly recommended. Any other math, computer science or applied math or statistics knowledge is helpful but definitely not required. Possible exploration topics:

• Animating or building curves and surfaces: 3D printing, visualization, art for documents or on the web
• The mathematics of photography: Different type of cameras systems, panorama photography.
• Computer vision structure: Reconstructing scenes from pictures, 3D scanning, path reconstruction.
• The mathematics of text recognition: Recognizing direction of a text, separating and matching characters.
• Network models and graph visualization: Visualization on the web, types of graph structure.
• Illustrating differential equations: Running differential equations on the browser, building a small lab
• Visualizing partial differential equations: Heat and wave equations on graphs, cellular automata, numerical visualization
• Finite versions of calculus: Discrete Stokes theorem, discrete Taylor theorem
• Discrete differential geometry: Curvature, Gauss-Bonnet, fixed point of maps
• Using intelligent bots to do mathematics: Teaching a bot, learning from a bot, using bots as an assistant
• Mathematical models in history: Collections of mathematical models, mathematics in art and film.