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MATH 8200 UGA, Spring 2003 |
 knot by brad shelton group <a,b ; a3b5> |
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MATH 8200 UGA, Spring 2003 |
knot by brad shelton group <a,b ; a3b5> |
Instructor
Professor Clint
McCrory
Office: 402 Boyd Graduate Studies Research Center, (706) 542-2576
Home: 245 Oglethorpe Avenue, Athens 30606, (706) 353-6517
Email: clint at math dot uga dot edu
Fax: (706) 542-5907
Class meetings
Second period (9:30 - 10:45) Tuesday and
Thursday
Boyd GSRC, room 326
Office hours
Monday 12:20 - 2:15
Tuesday 1:00 - 2:00
Wednesday 12:20 - 2:15
Thursday (no office hours)
Friday 1:25 - 2:15
- or by appointment -
Syllabus
The textbook is A Basic Course in Algebraic Topology, by William S. Massey. It is available at the UGA bookstore.
One goal of this course is to prepare Ph.D. candidates for the written qualifying exam in topology. We'll cover the first nine chapters of Massey's book: surfaces, the fundamental group, free products, van Kampen's theorem, covering spaces, homology groups, applications of homology, CW complexes.
The background required for this course is point set topology (MATH 4200/6200, a formal course prerequisite) and basic group theory (as in MATH 4010/6010).
Notes from class
Clasification
of surfaces with boundary
Exisistence
of covering spaces
Homology
of the projective plane,
figure
Cell
structure on complex projective space
Homology
of real projective space
Homework and exams
Homework will be assigned every week, and it will be graded. There will be a midterm exam (Tuesday, March 4) and a final exam (7:00 - 10:00 pm, Thursday, May 8).
Problem
set 1
Problem
set 2
Problem
set 3
Problem
set 4
Problem
set 5
Problem
set 6
Problem
set 7
Problem
set 8
Problem
set 9
Problem
set 10
Useful links and references
Algebraic Topology, by Allen Hatcher, Cambridge University Press, 2001. We will cover the topics in chapters 0, 1, and 2.
Categories for the Working Mathematician, by S. MacLane, second edition, Springer-Verlag, 1998.
Combinatorial Group Theory, by W. Magnus, A. Karrass, and D. Solitar, second edition, Dover Publications, 1976.
The Shape of Space, by Jeff Weeks, second edition, Marcel Dekker, New York, 2002.
Galois' Dream: Group Theory and Differential Equations, by Michio Kuga, Birkhauser, Boston, 1993.
Elements of Algebraic Topology, by James Munkres, Addison-Wesley 1984.
Foundations of Algebraic Topology, by Samuel Eilenberg and Norman Steenrod, Princeton University Press, 1952.
The Poincare conjecture, history, news
This page was created on December 16, 2002. It was last modified on April 24, 2003.