**Section 1:** TR 11:00-12:15 AvH 119

**Instructor:** Mark Brittenham

**Office:** 317 Avery Hall, 472-7222

**Email:** mbritten at math dot unl dot edu

**Course web page:** Link:
http://www.math.unl.edu/~ mbritten/classwk/971s05/

**Office hours:**
*Tentatively*: My office hours will be
Tuesdays and Thursdays 9:30-10:30
(or by appointment) in Avery 317. The grader for Math 971,
Steve Haataja, will hold hold office hours Mondays
and Wednesdays 9:30-10:30 (or by appointment) in Avery 228.

** Prerequisite:**
Math 970, or consent of instructor.

**Course description:**
This course will give an overview of
algebraic topology. We'll begin with an overview/review
of several Math 970 topics, including quotient
topology and homotopy (fundamental groups and covering spaces).
We'll build on these, to develop methods to build
topological spaces as cell complexes, to compute
many fundamental groups with the Seifert-Van Kampen Theorem,
and to classify covering spaces (the "Galois correspondence").
Next we'll cover the basics of homology, including
using the Mayer-Vietoris Theorem to compute homology groups.
As time permits, we'll also discuss topics in
geometric/differential topology, in
particular the study of manifolds.

**Text:**
The textbook that we will primarily follow is
*Algebraic Topology* by Allen Hatcher; we'll cover
most of chapters 0-2 of that text. This book is
available electronically at the author's web site,
http://www.math.cornell.edu/~hatcher/AT/ATpage.html.
I recommend
that you purchase the paperback version.
The hardback version is on reserve in the math library
(QA612 .H42 2002).
I will supplement that text from time to time with
material from other texts Susan placed on reserve
in the math library:
*Topology*, Second Edition, by
James R. Munkres (QA611 .M82 2000)
includes material on homotopy in chapters 9-14, and
*Elements of Algebraic Topology* by James R. Munkres
(QA612 .M86 1984)
discusses homology theory in considerable depth.

**Requirements:**
Each two weeks or so I will be assigning
some homework problems; a subset of the
problems will be marked out to be handed in.
These will vary in difficulty from easy to
the size of a small project (expect a few of this size).
For those that are not handed in, I will
expect you to discuss answers in class.
You may work on the homework in groups if you wish,
although I recommend that you each try the problems
and proofs individually before talking them over with other
people. When it is written,
the homework must be written up
individually, even if the problems are solved
by a group of students - several identical copies of the same
solutions will not be accepted.
Late homework won't be accepted, but the two lowest
homework grades will be dropped.
The grade for the course will be
based completely on the homework.

**Notes:**
I'd like to encourage you to ask questions during lectures.
At the beginning of each class, if you have a question on the material we've
covered so far, or if you're thoroughly stuck on a homework problem,
please feel free to ask about it. If I say something confusing
during the class, also please let me know. I very much prefer
lectures to be interactive.

**Miscellaneous legal stuff:**
Students who believe their academic evaluation has been prejudiced
or capricious have recourse for appeals to (in order) the instructor,
the departmental chair, the
departmental appeals committee, and the college appeals committee.

Friday, January 21 is the last day to drop a course and not have
it appear on your transcript.
Friday, March 4 is the last day to change a course registration
to or from ``Pass/No Pass''.
Friday, April 8 is the last day to drop
a course with a grade of W
(withdrawal).

*M. Brittenham
*