Math 310 - Topology
[Top]
[Home]
Instructor:
Alex Degtyarev
Office:
SA 130
Phone:
x2135
Mail:
no spam
Monday
15:40-17:30
Thursday
15:40-16:30 Office hours:
Monday
14:40-15:30
Thursday
14:40-15:30
Midterm I
Midterm II
[
2010
]
Final
[
2010
]
Class syllabus
Homeworks
[NEW]
Triangulation of a torus
[NEW]
Detailed weekly schedule
Topics causing problems
Exam rules and terms
Class roster
Textbook:
Sue E. Goodman,
Beginning Topology.
(Brooks/Cole, 2005)
Supplementary:
D. B. Fuks, V. A. Rokhlin,
Beginner's Course in Topology.
(Springer-Verlag, 1984)
Tentative course contents
Introduction. Metric spaces, topological spaces, continuous maps. Topological constructions.
Connectedness and compactness. Other topological properties.
Surfaces: definition, properties, models. Orientability. The classification theorem.
Cellular and simplicial complexes. The Euler characteristic. The genus of a surface.
Maps and graphs. Embeddings, colorings, etc.
Vector fields and Poincaré theorem.
Homotopy and homotopy equivalence. The fundamental group. Covering spaces. Seifert-van Kampen theorem. Applications.
Introduction to knots. Definition, knot diagrams, other ways to represent knots. Simple invariants. The knot group. Knot polynomials.
[Top]
[Home]
Midterm I
(25%) TBA See
important remarks
[Top]
[Home]
Midterm II
(30%) TBA See
important remarks
[Top]
[Home]
Final
(35%) TBA See
important remarks
*
All previous material is fully included!
[Top]
[Home]
Homeworks
(10%) Approximately weekly
[Top]
[Home]
Remarks
During the exams please keep in mind the following:
Calculators are
not
allowed
Identical solutions (especially identically wrong ones) will
not
get credit. I reserve the right to decide what "identical" means. You still have the right to complain
Do not argue about the distribution of the credits among different parts of a problem. I only accept complaints concerning my misunderstanding/misreadung your solution
Show all your work. Correct answers without sufficient explanation might
not
get full credit
Indicate clearly and unambiguously your final result. In proofs, state explicitly each claim
Do not misread the questions or skip parts thereof. If you did, do not complain
If you believe that a problem is misstated, do not try to solve it; explain your point of view instead
Each problem has a reasonably short solution. If your calculation goes completely out of hands, something must be wrong
Grading policy
I will take off a few (2-3) points for arithmetical mistakes. However,
a lot
of points will be taken off for `obvious' mistakes, i.e., either those that you can easily avoid or those showing a deep misunderstanding of the subject.
[Top]
[Home]