II - July 21–August 7, 2020
One year of algebra. Algebra II is recommended but not required.
“[I gained] a better understanding of math in the real world and how I can build a career out of it.” – Preethi S. | Bangalore, India
In this course intended for students who enjoy mathematics and logical reasoning, participants explore innovative ways in which math is used in the real world, in fields such as economics, computer science, media, and the physical sciences. By engaging with challenging practical problems, students hone their independent thinking and problem-solving skills.
Areas covered include the following:
- Graph theory, a topic heavily developed by both mathematicians and computer scientists. We explore algorithmic ways to compute, for example, the optimal path between two points on a map (minimizing cost, time, or another parameter). Another application is minimizing the cost of an electrical network which has to provide power to all residents in a new neighborhood.
- Probability and its numerous applications. We look at how probabilities are applied in economics and in popular media, and examine how they can sometimes be counter-intuitive or even deceptive.
- Various counting methods, combinatorics, and examples of Nash equilibria. We study applications of these techniques in economics (the prisoner's dilemma), computer science (assessing the complexity of an algorithm), finance (loans and investments), and biology (population growth).
Students work individually and in groups to find creative solutions to given problems. Each student also works on a project of his or her own choosing, on a topic about which he or she is passionate.
Luke Peilen holds a B.S. and an M.S. in mathematics from Yale University, where he also served as a tutor and grader for several courses. He is currently working towards a Ph.D. in mathematics at New York University's Courant Institute. His research focuses generally on analysis and partial differential equations, particularly as they relate to mathematical questions in statistical mechanics. Luke has a strong interest in helping students see how math can be used to solve real-world problems.
Evan Toler is a Ph.D. student in mathematics at the Courant Institute of Mathematical Sciences at New York University. His research interests are in computational science and finding numerical solutions to partial differential equations. He earned his B.A. in statistics and computational and applied mathematics from Rice University, where he taught courses in coding for data science and engineering applications.