Survey of Modern Mathematics

Level: Open to students entering grades 11 or 12 or freshman year of college in fall 2016.
Session: I, June 27–July 15, 2016
Days & Time: Monday–Friday, 10:10 a.m.–12:00 p.m. and 2:10–4:00 p.m.
Sebastian Garcia-Saenz,

Thorough knowledge of high school mathematics, up to and including first-year calculus. Students are selected on the basis of their aptitude for mathematics.

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Students interested in this course might also be interested in Mathematical Boot Camp for Budding String Theorists.

Course Description

This course is designed to acquaint high school students with some of the exciting developments in modern mathematics, including differential geometry, differential equations, chaos and fractals, and computational geometry.

Students meet for a two-hour lecture in the morning, and participate in a supervised computer laboratory session in the afternoon. Each student is assigned to a computer terminal for completion of laboratory exercises designed to expand upon the focus of the morning lecture. The exercises employ the special Mathematica packages and graphics that have recently become available for the advanced topics mentioned above. An additional benefit of the course is that students become proficient in the use of Mathematica.


Sebastian Garcia-Saenz

Sebastian Garcia-Saenz is a graduate research assistant in the Department of Physics at Columbia University. He holds a bachelor’s degree in astronomy from P. Universidad Catolica in Chile and an M.S. and M.Phil. in physics from Columbia. He is currently completing his Ph.D. with the Columbia theoretical physics group, where he pursues research on the subjects of field theory, gravitation, and cosmology. Sebastian has worked as a teaching assistant for both introductory and advanced courses in physics at the college level. He is an instructor in Columbia’s Science Honors Program, in which he teaches modern cosmology to advanced high school students.

Specific course information, such as hours and instructors, are subject to change at the discretion of the University.