The course is an introduction to analysis on fractals. This subject can
involve such diverse topics as analysis, probability, differential equations,
linear algebra, electrical networks etc. It gives a good opportunity to show
how different areas of mathematics are combined together to form a unified
theory. The exposition is going to be down to earth and require little
background beyond the basic courses. There will be a choice of projects of
various types and difficulty, which can be purely theoretical or involve
computers. The aim of the projects will be exploration of differential
equations and various operators on fractal domains.
The course itself will be organized to provide background for the chosen
projects. The exact format will be determined with the input of the
participants. When this course was offered before, the projects resulted in
three published papers with students as co-authors, see
http://www.math.uconn.edu/~teplyaev/fractals/
Besides being interesting, taking part in such research projects may be very
useful in the future (for instance, when applying to graduate schools). The
course satisfies departmental requirements for the math major and minor.
math.uconn.edu
