WSE 187, Spring 2009
Curves and Surfaces
Moira Chas and Katherine Poirier

moira at math.sunysb.edu
kpoirier at gc.cuny.edu

Meeting at Math Tower, P131
Mondays and Fridays 12:50 to 2:10pm
Session 1, Section 2

• January 30, February 2, 6, 9, 13, 16, 20, 23

We will start by  exploring surfaces and curves from a topological point of view. Topology is "rubber sheet geometry", in which objects are equal if they can be deformed one into each other by stretching or compressing.

A surface is a space of two dimensions: length and width. A curve is a one-dimensional space, a piece of string living in a surface. We will make a first approximation to the concept of dimension.

By making concrete constructions with paper and scissors we will study properties of surfaces such as orientability, genus and number of boundary components. We will see how words in certain alphabets can be used to encode properties of surfaces and curves. We may also investigate how surfaces appear in the "real world" as the configuration spaces of certain machines.

If time permits, we will explore another amazing mathematical object, the hyperbolic plane, and the role this object plays in the understanding of surfaces.

• Notes of the course

• Applications of topology