One year of algebra. Algebra II is recommended but not required.
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.
Monica Marinescu is a Ph.D. candidate in Columbia University’s Department of Mathematics. She holds a B.A. in mathematics from Princeton University and an M.A. in mathematics from Columbia. Monica is conducting research focused on algebraic geometry, under the supervision of Professor Johan de Jong. She has worked with other noted mathematicians, including Fields medalist Manjul Bhargava, who advised her on her undergraduate senior thesis. She has served as a teaching assistant for a number of Columbia undergraduate courses and will be teaching calculus in spring, 2018.