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Survey of Modern Mathematics

Level: Open to students entering grades 11 or 12 or freshman year of college in fall 2013.

Session: I, June 24-July 12, 2013

Days & Time: Monday-Friday, 10:00 AM-12:00 PM and 2:00-4:00 PM

Instructor(s): Burton Budick, Ali Masoumi,

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

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

"The instructor was always so eager to help us... he allowed us to work at an individual pace, taking care not to leave anyone behind but also push us to succeed to the best of our abilities."

- From a 2012 Student Program Evaluation

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.

Instructor(s)

Burton Budick

Burton Budick earned a B.A. from Harvard College and was awarded a Ph.D. from the University of California, Berkeley. A specialist in experimental atomic and nuclear physics, Dr. Budick first came to Columbia University in 1962 as a research physicist and lecturer. He has taught at Columbia as a lecturer for the past decade and he is a full professor of physics at New York University.

Ali Masoumi

Ali Masoumi is a Ph.D. student of theoretical physics and cosmology at Columbia University. He got his B.A. in 2006 in mathematics and physics from Sharif University, Tehran, Iran. He started graduate school in 2006 at Columbia and got his M.A. and M.Phil. in 2008 and 2009. He taught in Columbia's science honors program for high school students in 2010 and 2011 and won the Alan Scahs teaching award as a T.A. at Columbia. He is studying early and late universe cosmology and topological solutions in field theory.

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