This course will focus on one topic typically covered in
a second course in complex analysis: Elliptic function theory.
Elliptic functions-as developed by Jacobi, Weierstrass,
Eisenstein, Dedekind, and others-are one of the crowning
achievements of 19th century mathematics and are widely
applied in physics and engineering. Their study
is the natural continuation of the analysis of polynomial,
exponential, and trigonometric functions of a complex variable.
In the 20th century, the analysis of the beautiful transformation
properties of elliptic functions
developed into the theory of elliptic curves and modular forms,
a central topic of algebraic geometry and number theory.
Recently, elliptic functions have played an important role in
the 21st century mathematics inspired by theoretical physics. For
example, the Dedekind eta function
Here are some specific topics we may explore:
References: I have ordered the following textbook from the bookstore:
Assessment: Problems will be assigned regularly. Each problem is due the second Monday after it is assigned (i.e., the first homework is due September 9). This will account for 60% of the final grade. There will be a take-home, closed-book final exam which will account for the remaining 40% of the grade.
Herman Brown 422