WSE
187, Spring 2008 Curves and Surfaces Moira Chas and Katherine Poirier moira@math.sunysb.edu kpoirier@gc.cuny.edu 

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


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 onedimensional space, a piece of string living in a surface. We will make a first approximation to the concept of dimension.Math Arxiv 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. 


