Text:
Knote: All the above
materials are available on-line. If you want to purchase Hatcher's Book
you can and the ZIP proof can also be found in Jeffrey R. Weeks'
Shape of Space .
X-Session: The X-sessions will play a crucial role in this
course. At each X-session we will meet and students will be randomly
asked to describe their attempts at a solution to a selected homework
problem.
Grade: Your grade will be determined as follows:
a
midterm exam (30% of your grade), homework (30% of your grade), and a
final exam (the remaining 40% of your grade).
Class Log:
The homework assignments and exam due dates will be posted in the class
log.
Honor Principle: On the exams,
no help is to be given or received.
On the homework, collaboration is
permitted and encouraged.
Students with disabilities: I
encourage students with
disabilities, including "invisible" disabilities
like chronic diseases
and learning disabilities, to discuss with me any
appropriate accommodations that might be helpful.
PRELIMINARY
Syllabus:
This class will cover several topics in combinatorial,
algebraic and geometric topology.
In particular, we will cover various
topics in Knot Theory (see the Knots Knotes for details), we will classify
surfaces (see the ZIP proof) and we will classify the covering spaces of
a nice topological space (see chapter one of Hatcher). To accomplish
these goals, we will need to carefully develop the notion of
the fundamental group of topological space.