Algebra I and geometry. Participants should be comfortable with math and logical reasoning.
“I have gained a greater understanding of mathematics and was exposed to challenging and interesting problems.” — From a program course evaluation
What do cryptography, game theory, artificial intelligence, and space-time have in common? They all benefit enormously from their shared backbone in mathematics. Mathematics, as a discipline, concerns itself with logic and the abstract, yet in doing so makes itself indispensable in a vast multitude of fields ranging from daily life to astrophysics.
In this course, which is intended for students who enjoy math and logical reasoning, participants develop a deeper appreciation for the richness of mathematics while further developing their thinking and problem-solving skills. The combination of subjects and methods in this course enables participants to experience math in a way traditional high schools are often unable to present it, approaching problems as open-ended opportunities for creativity, independent thinking, and intellectual excitement.
The course focuses on three overarching topics:
- Probability and Information: abstract counting (combinatorics), statistics (and how not to be fooled by them). Applications include cryptography, game theory, and machine learning: how can you beat your friends at your favorite games, and how can a machine do it (maybe even better!)?
- Logic: this sets the stage for further mathematical reasoning. What is mathematical logic, and how does one structure a proof (including basic techniques of mathematical proofs)? How can this framework be applied to philosophical thought and debate?
- Geometry: the notions of space, including how it changes when curvature is introduced; symmetry, and how it applies to modern physics; and how proofs can be tackled from a geometric perspective. Humans have a very particular way of visualizing the world around them: how can mathematics be used to peer into the realms of minuscule particles and strings, or gargantuan galaxies and black holes?
Students are introduced to some of the tools in the mathematician's kit, with an overarching theme of critical and creative thinking. After diving into various applications of mathematics, participants select and complete a personal project based upon their own interests within the field.
Constantijn Van der Poel is currently pursuing his PhD in theoretical physics under David Schwab at the City University of New York. Originally focused on high energy theory and mathematical physics (i.e. all things stringy), he is now working on artificial intelligence theory. He received a double bachelor's degree in mathematics and physics (with a minor in economics) at Utrecht University in the Netherlands, and his master's degree in physics at Northwestern University in the United States.