Topology

Topology of Euclidean spaces, winding number and applications, knot theory, fundamental group and covering spaces. Eulercharacteristic, simplicial complexes, classification of two-dimensional manifolds, vector fields, the Poincaré-Hopf theorem, andintroduction to three-dimensional topology. Prerequisites: Abstract Algebra (Math 1530) and Real Analysis (Math 1010 or Math 1630).