**Course outline:** Homotopy, fundamental group,
Van Kampen's theorem, fundamental theorem of algebra,
Jordan curve theorem, singular homology, homotopy invariance,
long exact sequence of a pair, excision, Mayer-Vietoris sequence,
Brouwer fixed point theorem, Jordan-Brouwer separation theorem,
invariance of domain, Euler characteristic, cell complexes,
projective spaces, Poincaré theorem.

**Instructor:**Dan Christensen**E-mail:****jdc@uwo.ca****Office:**Middlesex 103b.**Office Phone:**661-2111 x86530.**Office Hours:**to be determined.**Class times and location:**Mondays, 11 am to 12:20 pm, and Fridays, 1:30 pm to 2:50 pm. MC107.**Prerequisites:**Algebra I (group theory, Math 302a) and General Topology (Math 404a); or permission of instructor. (Students from other departments are welcome and should consult with me.)**Web page:**This page is available at http://jdc.math.uwo.ca/algtop/, where you should also check for course announcements.

**Text:** The text for the course is
*Algebraic Topology: A first course*, by Marvin J. Greenberg and
John R. Harper. Published by Perseus Books. Revised edition.
ISBN 0-8053-3557-9.
Here is a list of other reading material:
dvi, ps,
or pdf.
A few of these will be available at the bookstore, and most will
be on reserve in the library.

New addition: Alan Hatcher has a very nice book on algebraic topology.

**Homework:** Homework will be due every week
or two, in class. Doing problems and talking about the
material are both important ways to learn, so
you are encouraged to **discuss**
the problems with classmates and with me.
But you must write up the solutions on your own and must not
show your written work to others.
Your solutions should be clear and carefully written and
you should give credit to
those who helped you and to any references you used.
Late problem sets won't be accepted unless arranged in advance
for a good reason.

**Presentations:** In the second half of the semester,
each student will give a presentation on a topic related to the
course. The scheduling will be worked out later.

**Evaluation:** Evaluation will be based on homework
and the presentations. There will be no tests or quizzes.