Computational topology is a relatively new, but lively field
somewhere between computer science and mathematics. On the mathematical
side it is closely connected to topology. Topology is a somewhat loose
form of geometry, where sizes, distances, angles and other numerical
measures are not really important. Instead, objects are described using
qualitative measures like the number of connected pieces, the number of
holes of different shapes and of tunnels. Because of this, topological
methods have turned out as useful in several problems where too high
precision is unnecessary or even bad. Topological approaches and methods
are used for example for analyzing big data sets, for modelling
networks, reconstructing objects from samples, in robot motion planning,
distributing tasks among processors, and so on.

The course will
have a strong emphasis on student projects. Several typical problems
suitable for a topological approach will be described. Through solving
these problems, the basic topological concepts, structures and
algorithms will be introduced, and tested on real data.To successfully pass this course, the student has to complete 3 homework assignments (deadlines at the ends of months March, April, and May), one group project (in May), and pass a theoretical exam at the end of the semester.