**Duration:**

**Number of lectures per week:** 3

**Assessment:**

**End-of-year Examination:** One 3-hour examination

**Description: **
The course will begin by introducing concepts of convergence
and continuity, first in the contexts of subsets of Euclidean spaces,
then in the context of metric spaces, and finally in the context of
topological spaces. Topological properties such as compactness and
connectedness will be investigated. The course will conclude with
a study of winding numbers and the exponential map, with applications
to the topology of the plane (including the Fundamental Theorem of
Algebra and the two-dimensional case of Brouwer's Fixed Point Theorem),
and an introduction to the concept of homotopy.

Feb 28, 2002

File translated from T

On 28 Feb 2002, 15:40.