# 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.
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Midterm I     (25%)   TBA     See   important remarks

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Midterm II     (30%)   TBA     See   important remarks

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Final     (35%)   TBA     See   important remarks

All previous material is fully included!
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Homeworks     (10%)   Approximately weekly
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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