Spring 2022 Program

Meet the Mentors

Kate Donahue

PhD Student in Computer Science at Cornell University

Description: Game theory studies the interaction of strategic agents. For example, consider the famous Prisoner's Dilemma example: two people, Alice and Bob, each who are under suspicion of committing a crime. Each can either remain silent or confess to the crime. While it would be individually best for each of them to remain silent, game theoretic analysis has shown that in many cases, both Alice and Bob are incentivized to take the worse choice of confessing. Game theory helps analyze situations like this: when rationale, intelligent actors might end up in sub-optimal situations. Phenomena like this might occur in business, in health, or in international relations. The mathematics of game theory involves analyzing such games and proving results about the kind of outcomes we can expect. In this reading course, we'll read through introductory game theory, moving to more specific models and potential open questions based on the interest of the student. 

Prerequisites: Experience writing mathematical proofs, some probability background helpful but not necessary.

Description: Machine learning studies how to learn patterns and rules from data, in order to make more accurate predictions about the world. Machine learning theory is the theory of how we can create such rules - and guarantees around how accurate the rules we learn are. In this reading course, we'll work through an introduction to machine learning theory, as well as discussing avenues of ongoing research.

Marlin Figgins

PhD Student in Applied Math at the University of Washington

Description: Mathematical models of infectious diseases have been essential in developing our modern understanding of how and why infectious diseases continue to spread. Infectious disease systems are often described as a dynamical system and there are various ways of modeling infectious diseases using ordinary differential equations, stochastic processes, agent-based models, and machine learning. In this project, we will study models of infectious disease and learn how to use mathematics to describe and simulate infectious disease systems.

We will read from the book "Modeling Infectious Diseases in Humans and Animals" by Keeling and Rohani.

Prerequisites: There's various sub-projects here depending on students interest as this is quite the big field, but at minimum: any student with calculus and linear algebra should be able to handle this as well as exposure to probability (not necessarily a class). 

Programming experience would also be a plus for simulating these models and discussing data, but it is not strictly necessary.

Micah Henson

PhD Student in Applied Math at the University of Washington

Description: Mathematics can be used to solve real world problems. Researchers in many fields including economics, biology, computer science, and many social sciences rely on mathematics to gain deeper insights into their fields. For example, math models have helped us with the COVID pandemic. Social networks, marriage, climate change and much more can be studied using math models. In this project, you will be able to choose a topic you would like to explore with math models. We can go really in-depth into one model, or explore many different models. The choice is yours!

We will read from the book "Topics in Mathematical Modeling" by KK Tung.

Prerequisites: Some differential equations would be nice, but not necessary

Elizabeth Newman

Postdoc in Math at Emory University

Description: Whether hiring a new employee or distributing vaccination doses, there is inherent bias to human-based decision making. If we want decisions to be made fairly, we should remove the humans and have machines and algorithms to make decisions, right? Wrong! In fact, algorithms can make decisions that are equally unfair.  In this project, we will explore fairness in machine learning. We will learn how to describe fairness mathematically and some sources of unfairness that arise in machine learning. Through many concrete, real-world examples, we will come to understand the importance of incorporating fairness into machine learning algorithms.

We will read from the book "FAIRNESS AND MACHINE LEARNING Limitations and Opportunities," by Barocas, Hardt, and Narayanan, available here.

Prerequisites: An interest in fairness and machine learning is the only prerequisite. Some experience with probability could be useful, but is not required.

Chelsea Walton

Associate Professor of Math at Rice University

Description: Representation theory is an old and beautiful field that boils down to finding matrix solutions to equations. It connects abstract algebraic structures (such as groups) to matrix theory (linear algebra). In this project, we will start with a review of group theory and the theory of vector spaces, and continue into Group Representation Theory with use of the book “Representation Theory and Characters of Groups” by James and Liebeck. It will be self-paced, and extra topics could be introduced based on your interests. 

For a preview of what Representation Theory is all about, you can check out the first half of the talk available here, or Sections 1 and 3 of the article available here. 

Don’t worry about not knowing some of the terms— that’s part of the fun and what you’ll gain throughout the semester!

Prerequisites: Linear Algebra + the first course of Abstract Algebra covering Group Theory

Meet the Students

Edmond Anderson

Mika Campbell

Storm Chin

Kristen Mosley

Cameron Thomas