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.

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There are no additional materials for this material.

Presentation slides:

Modeling disease and epidemics with differential equations slides and notes.

Other materials:

Additional materials are linked in the slides.

Presentation slides:

Google PageRank slides and notes.

Other materials:

• Linear algebra of PageRank

• PageRank algorithm through graph theory

• Perron-Frobenius Theorem

• PageRank and Markov chains

• PageRank simulator

Presentation slides:

Cryptography and cryptocurrency slides and notes on 

• modular arithmetic, 

• Euler's Theorem and RSA example, 

• public key cryptography, 

• elliptic curves,

• cryptocurrency and blockchain.

Other materials:

Lots of materials and resources are linked in the slides.

Presentation slides:

Machine learning slides and notes on

• Gradient descent

• Neural networks

• Simple neural network example

Other materials:

• Notes on gradient descent convergence theorems

• Gradient descent visualizer

• Gradient descent game

• Notes from a machine learning class at MIT

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Knots and their applications slides and notes on

• Calculating the Alexander polyomial for the trefoil and figure-8 knots

Other materials:

• Lots of resources and materials are linked in the slides.

• Definition of the Jones polynomial (needed for homework) and a video that talks about it (the video also has some cool applications of knot theory, some of which were covered in class).

Presentation slides:

Topological data analysis slides and notes on

• Topology intuition, homology groups, Betti numbers

• Simplicial complexes and homology

• Real-world topological data analysis examples

Other materials:

Materials and resources are linked in the slides. The last slide in particular has links to some TDA applications.

Presentation slides:

Voting methods slides and notes on

• IRV example and more notes on class slides

• IIA example

• RCV analysis research report

Other materials:

• Notes from the Mathematics of Democracy class at Wellesley

• Notes from the Math of Voting class at St. Mary's College

• Notes from the Intro to Voting class at UPenn

• Notes on the Borda count from Notre Dame

• Making Democracy Count

• RCV and Arrow's Theorem from the Institute for Mathematics and Democracy website

• RCV explanation from the MIT Election Data and Science Lab

• Visualization of various voting methods

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