Ideas of Math

This course, if successful, will help students explore what mathematics really is. At its best, mathematics contains all of the following: creativity, beauty and, of course, precision. A masterpiece in mathematics could be compared to a great drawing or a classic novel. As an example, Martin Hairer’s regularity structure is compared to Lord of the Rings on Quanta Magazine.
We will start with the basic language of modern mathematics, logic and set theory. Then, depending on the interests of students, we will talk about some (but not limited to) of the following topics: infinity, number theory, combinatorics, probability, game theory, linear algebra, discrete and/or differential dynamical systems. Along the way, we will find real world applications of the above subjects.