Projects and Assignments in Pure Mathematics
Fractal Geometry
This could develop in several directions:
(i) Study of Hausdorff dimension and sets of fractional
dimension.
(ii) Iteration of complex functions, Julia sets, Fatou sets, Mandelbrot
set.
(iii) Applications in Number Theory (continued fracions, Diophantine
approximation etc.).
(i) and (iii) are more sutibale at 4MM level, while (ii) would work
at 3MM or 4MM level.
Books
K. Falconer, Fractal geometry, mathematical foundations and applications.
Pure projects homepage