Math 242 - Topology of Surfaces

Overview: The three main topics covered in this undergraduate
mathematics course are: 

    *	Knot theory 
    *	Point set topology, or abstract spaces 
    *	Surfaces 

Knot theory is about loops of string in 3-dimensional space. We'll prove
that knots exist, define some of the modern polynomial invariants that
distinguish knots, and find ourselves at the frontiers of research
thinking about unanswered questions. 

Point set topology concerns local properties of spaces needed to discuss
such fundamental notions as continuity, connectedness and compactness.
This is foundational material for many branches of mathematics. 

Surface theory is about spheres, tori, Moebius bands, Klein bottles,
projective planes and more. We'll prove a classification theorem and
learn how to distinguish one surface from another. 

This course is highly recommended if you are mathematically talented and
if one of the following fits: 

    *	you are considering graduate work in mathematics 

    *	you are considering a research career in theoretical physics,
	chemistry or biology and want an introduction to some modern
	mathematical tools 

    *	you like geometric thinking and want to pursue that in a
	mathematically rigorous way 

    *	you are an engineering student and want to see a side of
	mathematics different from routine calculations 

Warning: This is a rigorous proof-based mathematics course. You will be
required to understand theorems and their proofs, and discover and write
proofs of your own. 

Prerequisites include a completion of our calculus sequence (preferably
MATH 175) and Linear Algebra (MATH 204). You should know the basics of
mathematical logic, sets, functions and proofs.