The content of the course will focus on mathematical models of infectious diseases, primarily viruses. You may have read about 'herd immunity' and “R_0” in the past couple of years; these are classic results from population-level epidemic models. In the first half of the class, we will study models like these. Then we will move to models of the interaction between a virus and the immune system in a single infected individual. We will study how mathematical models are developed and analyzed, and how they can be modified for a wide range of situations. We will explore what can and can’t be learned from models – the strengths and weaknesses of this approach to science. Mathematical modeling in biology is a relatively young field, and biology is vast. Thus, it isn’t hard to develop your own research questions, the answers to which may not yet be known.

People have been writing numbers for as long as they have been writing. This course traces the use of numbers from ancient civilizations to modern times and examines how our view of numbers has changed over that period: natural numbers, prime numbers, rational numbers, Fibonacci numbers, real numbers and complex numbers, as well as the way in which our ability to calculate has evolved.

What is reason? This course examines the philosophical and psychological dimensions of the various epistemological platforms upon which we believe our capacity to think is based. Logic, science and mathematics are just a few of the paradigmatic examples of reasoning we will explore, along with failures of reasoning, such as conspiracy theories, logical fallacies and mythology.

Mathematical models have been used to explain, predict, and control the dynamics of infectious diseases for nearly a century. Beginning with early attempts to explain cholera outbreaks, mathematical epidemiology grew rapidly during the global spread of HIV in the 1980s. In 2020, the spread of novel coronavirus made phrases like 'basic reproductive number' and 'SIR modeling' part of our everyday discourse. This class will explore the construction, analysis, and application of mathematical models of infectious diseases. We will study the relationships between model assumptions and conclusions and learn about what mathematical models can and cannot tell us about the spread of infectious diseases, and about the course of an infection within an individual.

What is the best or most fair way to make choices as a group? How can we quantify or measure fairness? Can we mathematically describe power and equity? How can mathematics play a role in identifying and combatting gerrymandering? This course will consider these questions and hopefully generate many more. We study how mathematicians have attempted to understand fairness and power, how mathematics underlies important aspects of voting and representation, and how math can help illuminate many important social and political issues. Topics: Fairness, Gerrymandering, Voting Systems, Arrow’s Theorem, Apportionment, Power, and additional topics as time allows

This course examines the philosophical and psychological dimensions of the various epistemological platforms upon which we believe our capacity to think is based. Logic, science and mathematics are just a few of the paradigmatic examples of reasoning we will explore, along with failures of reasoning, such as conspiracy theories, logical fallacies and mythology.