Description
Elliptic
functions are a classical and most beautiful topic of
complex analysis which in fact was crucial in development of
the field. Their rich structure and applications are truly
remarkable.
In this project, we still study
- Weierstrass theory of
elliptic functions.
- Connections with
elliptic curves and elliptic
integrals:
(and why `elliptic' even though it has little to do with
ellipsis...)
- Further Topics (term2): Jacobi theory of
elliptic functions, connections to number
theory, physics
etc...
Group project
The group project will revolve around
learning basic concepts and results in the theory of
elliptic functions, in particular the first two topics
above. By the end of the group project we would have
learned about
- Weierstrass theory of elliptic functions
- Connections with elliptic functions and elliptic
integrals.
Mode of Operation
and Evidence of Learning for the group project
The project will revolve around learning through reading
with focus on the underlying theory, mathematical
rigour, and the development of deep conceptual
understanding. Students will demonstrate their
understanding by solving relevant problems, exploring
examples and theoretical applications of the material,
and clearly communicating it in both written and oral
formats.
Resources and Outline
There are many textbooks on the subject, but in term 1 we
will mainly study the lecture notes of a (discontinued) one
term course and its problem sheets covering the first two
topics above.
For term 2 we
will then also consult other resources depending on
interest.
Warning
I will be away on research leave in term 2, so the
supervision will happen remotely during that period.
Prerequisites
- Complex Analysis II
- Algebra II
- Interest in pure mathematics, demonstrated by taking
pure year III modules such NT III and/or
Analysis&Topology III
email: J Funke
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