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

    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.
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