Yesterday's Math, Today's Applications, fall '25

Class notes and other materials

These are the lecture slides and related materials for each of the topics we covered in class. Students did the research, prepared the presentations, and gave lectures on their topics (except for Introduction), usually in teams of two.

Introduction (Ismar Volić)

Presentation slides:

Introduction to MATH 349 Yesterday's Math, Today's Applications, covering

teasers about the mathematics of cryptography, PageRank, machine learning, AI, quantum computing, topological data analysis, robotics, molecular knotting, and gerrymandering.

Other materials:

There are no additional materials for this material.

Modeling desease and epidemics (Leah Valentiner)

Presentation slides:

Modeling disease and epidemics with differential equations slides and notes.

Other materials:

Additional materials are linked in the slides.

Google PageRank algorithm (Skylar Shi and Elisabeth Sylvestre)

Presentation slides:

Google PageRank slides and notes.

Other materials:

Cryptography and cryptocurrency (Kamya Chakravarthi and Julia Niemann)

Presentation slides:

Cryptography and cryptocurrency slides and notes on

Other materials:

Additional materials are linked in the slides.

Machine learning (Claire Cao and Ruoxi Gao)

Presentation slides:

Machine learning slides and notes on

Other materials:

Notes on gradient descent convergence theorems
Gradient descent visualizer
Gradient descent game
Notes from a machine learning class at MIT

Knots in biology and chemistry (Katie Jacques and Mia Kovan)

Presentation slides:

Coming soon...

Other materials:

Coming soon...

Topological data analysis (Elaine Yang and Leah Valentiner)

Presentation slides:

Coming soon...

Other materials:

Coming soon...

Political structures (Elisabeth Sylvestre and Valerie Zhu)

Presentation slides:

Coming soon...

Other materials:

Coming soon...

Some other applications we will cover are LLMs, gerrymandering, robotics, quantum computing, social media networks, the spread of opinion and (mis)information, and a few others.