# Teaching

Math 123 a: Principles of Mathematical Modeling.
Spring 2018; Spring 2020.

Come join the discussion on what is a mathematical model, how we design equations to describe natural, social or economic phenomena, and how to study models described by discrete or continuous dynamical systems! Learn about fixed points, periodic orbits and… chaos (see below!)

The Mandelbrot set

Chaotic orbits of the standard (Chirikov–Taylor) map

You will be given the opportunity to study your own model, either from a research article or one you make up! Examples of cool projects chosen include, in 2018, the dynamics of religious communities, the impact on demographics of sex selection during one-child policy periods, or, in 2020, the dengue fever infection or models of the covid-19 pandemic and ways to limit the number of infected individuals. Checked out those two featured projects from 2020:

Dengue Fever transmission model – by Chloé Shiff, Class of 2022

COVID-19 models and impact of policies – by Shaoqian Chen and Monica Zhu, Class of 2022.

Math 126 a: Stochastic Processes
Spring 2018, Spring 2020.

From the movement of a pollen grain in water to financial stock markets, from birth and death of plants to brain’s activity, some laws of nature combine with random phenomena, yielding complex, sometimes seemingly unpredictable dynamics. Stochastic processes is the mathematical theory dealing with random dynamics. The objective of this course is to introduce the key concepts and mathematical tools in stochastic processes to lead the student to be able to analyze the solutions of stochastic processes, the evolution in time of the probabilities to be in a given state, the stationary behaviors, absorption probability and many other fun properties!

The Poisson process – picture credit: Wikipedia (public image)

Multiple realizations of the brownian motion.

Math 121a: Mathematics for Natural Sciences
Fall 2019

In the modern world, mathematics are a key tool to describe natural or social phenomena. Interactions between mathematics and other sciences date back several centuries, developed hand in hand, each science nurturing the other. And many of the current technological advances rely on mathematics, from the algorithms processing information in our phones to the coding and decoding videos on our computer, routing information through the web and delivery scheduling, to cite a few. This class covers a part of key mathematical methodologies useful in applications, introducing the students to the “hardware store” of applied mathematical tools and enable them to feel comfortable using these tools to solve real-life problems. Topics include complex numbers, functions of complex numbers, infinite series, power series and expansions of functions, asymptotic analysis and calculus of variations.