This course is intended for students who already have a proficiency with math and are eager to further expand their mathematical toolboxes in preparation for serious future work in the natural sciences. Rich examples drawn from classical and quantum wave phenomena, statistical physics, astrophysics, cosmology, engineering physics, chaos and nonlinear dynamics are used to introduce and develop crucial mathematical concepts during the morning lectures. Afternoons are devoted to hands-on experiments and computer simulations to test the physics concepts presented. There will be a science-based New York City field trip as well as a visit to one of the Columbia research labs. This course is mainly math, but with plenty of physics mixed in, whereas Investigations in Theoretical and Experimental Physics focuses more on introductory physics material. Because there is significant overlap between the two courses, it is not recommended that students take both.

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