TA:
Laura Fredrickson,
Office: RLMXX.XXX
Email: lfredrickson@math.utexas.edu

** Textbook:** *Differential Topology*,
by Guillemin and Pollack. Another useful reference is Spivak's
*Calculus on Manifolds*. Of course, not everything in lecture will
be from a text, and not everything in Guillemin and Pollack
will appear in the lectures.

**Homework:** There will be weekly problem sets, due on Fridays.
You are *encouraged* to discuss your homework with other
students. (Not that anything I could say would stop you, anyway.)
However, in the end, the paper you turn in should reflect your own individual
understanding.

**Exams:** There will be two prelim-style in-class exams,
one shortly before Spring Break and one on the last day of class.

**Term paper:** One of the course requirements is to write
a term paper, either alone or in collaboration with up to three others.
Pick a theorem of differential topology and discuss it. You can explain its
history, the ideas behind it, applications of it, different approaches
to it, an elementary way of viewing it, or whatever you like. Just
say something interesting. The paper should be between 3+N and
4+2N TeX pages, where N is the number of people in the
collaboration. The term paper is due one week **before** the end of
classes. You should pick a topic and discuss it with me by spring
break at the latest.

**Grading:** Your grade will be based 30% on homework, 20% on
the term paper, 20% on the first exam and 30% on the second exam. Qualitatively,
an A means you're probably ready to pass the prelim exam this summer,
a B means that with some hard work you have a good shot to pass it, and a
C means that passing the exam just isn't in the cards. You can
do the obvious adjustments
for plus and minus grades. My hope (and this is **not** a promise) is not
to give any grades lower than a B-.

**Syllabus:** We'll be covering all of Guillemin and Pollack and
a little bit more. At the beginning of the course we'll do the
inverse function theorem and the implicit function theorem a bit more
deeply than Guillemin and Pollack do, (reference: Spivak) and at the
end of the term, time permitting, we'll do some de Rham cohomology theory.
We will also consistently work with abstract manifolds, rather than just
manifolds embedded in R^n.