MATH142 PO

Calculus in one variable is usually divided into two parts: the Differential Calculus, which focuses on derivates; and the Integral Calculus, which focuses on integration. Motivated by the question "what is the logarithm of (-1)?", this course explores the properties of Riemann Surfaces. The first half of the course focuses on Differentiation, where we discuss meromorphic functions, differential forms, the RIemann-Roch Theorem, and the concept of genus. The second half of the course focuses on Integration, where we discuss exterior derivatives, de Rham cohomology, the Generalized Stokes Theorem, and the Gauss-Bonnet Theorem. Along the way, we define and classify Riemann Surfaces using the Uniformization Theorem. This course emphasizes applications to physics and geometry; it is intended for physicists and mathematicians alike.

PO Area 5 Requirement, Mathematics