Instructor: László Fehér
Text: McCluskey and McMaster, handouts
Prerequisite: Calculus
Course description: We start with point set topology, which is an essential part of modern analysis, to be ready for algebraic topology, which is one of the most dramatic topic of modern geometry. Level depends on the background of the class.

Topics:
Experiments in Topology: Untie knots, Set yourself free, Spinning plates and why did Dirac got the Nobel price, The chess problem the computer couldn’t solve …
 The notion of continuity
 Metric spaces and continuous functions
 Open and closed sets
 Equivalent metrics: the notion of topological space
 Examples and constructions
 Translating the experiments into mathematics
 Separation axioms: the zoo
 Compactness
 Surfaces and other manifolds
How to distinguish them? Euler characteristic, brushing the hedgehog, the coloring problem.
 The curve which fills the square. Why dimension is a topological notion?
 Connectivity
 Homotopy and the fundamental group
 Fundamental group of the circle and the sphere
 Applications, back to the experiments
 Prospects