Syllabus

Download a full course syllabus here.
A more detailed forecast of individual classes is available in this pdf calendar.

Course Description

This course presents mathematical methods that are useful in the physical sciences. While proofs and demonstrations are a core part of the course, we will put the primary emphasis on applications. In a wonderful article the theoretical physicist Eugene Wigner explored what he called the ``unreasonable effectiveness of mathematics in the physics sciences''. The article concludes

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

Our aim will be to explore some of the many branches that this miracle has already extended to: the ubiquitous appearance of oscillations, the geometry and physics of linear transformations, the utility of complex numbers in algebra and in wave physics, the description of unfolding processes through differential equations, and the explicative power of statistics. Not only are these methods of great utility in applications, but their practice in physics has also often led to new discoveries in mathematics!