CPS296.1: COMPUTATIONAL TOPOLOGY | |
Term:
Fall 2006
| |
Time: Mo We 4:25pm - 5:40pm | |
Location: LSRC D106 | |
Instructors: | Herbert Edelsbrunner |
announcements | schedule | projects | references |
Date | Lecture Topic | Notes | Assignments |
Aug 28 Mon | introduction | General information [pdf] | |
I. GRAPHS | |||
Aug 30 We | connected components | Lecture [pdf] | |
Sep 01 Fr | curves and knots | Lecture [pdf] | |
Sep 11 Mo | planar graphs | Lecture [pdf] Problem [pdf] | HW#1 out [pdf] |
II. SURFACES | |||
Sep 13 We | two-dimensional manifolds | Lecture [pdf] | |
Sep 15 Fr | fundamental group | Lecture [pdf] | |
Sep 18 Mo | self-intersections | Lecture [pdf] Problem [pdf] | HW#1 due |
Sep 20 We | surface simplification | Lecture [pdf] | HW#2 out [pdf] |
III. COMPLEXES | |||
Sep 25 Mo | simplicial complexes | Lecture [pdf] | |
Sep 27 We | convex set systems | Lecture [pdf] | |
Oct 11 We | Delaunay complexes | Lecture [pdf] Problem [pdf] | HW#2 due |
Oct 16 Mo | alpha complexes | Lecture [pdf] | HW#3 out [pdf] |
IV. HOMOLOGY | |||
Oct 18 We | homology groups | Lecture [pdf] | |
Oct 23 Mo | matrix reduction | Lecture [pdf] | |
Oct 25 We | cohomology | Lecture [pdf] | HW#3 due |
Oct 30 Mo | Practice Hour | HW#4 out [pdf] | |
VI. PERSISTENCE | |||
Nov 01 We | persistent homology | Lecture [pdf] | |
Nov 06 Mo | stability | Lecture [pdf] | |
Nov 08 We | an application to curves | Lecture [pdf] | HW#4 due |
Nov 13 Mo | extended persistence | Lecture [pdf] | HW#5 out [pdf] |
V. MORSE FUNCTIONS | |||
Nov 15 We | generic smooth functions | Lecture [pdf] | |
Nov 20 Mo | transversality condition | Lecture [pdf] | |
Nov 27 Mo | piecewise linear functions | Lecture [pdf] | HW#5 due |
Nov 29 We | Reeb graphs | Lecture [pdf] | HW#6 out [pdf] |
Dec 07 Th | due at 4:25pm on Dec 8 | take-home exam | |
Dec 13 We | due at 4:25pm | project report |
[1] P. S. Alexandroff. Elementary Concepts in Topology. translated by A. E. Farley, Dover, New York, 1961. [2] H. Edelsbrunner. Geometry and Topology for Mesh Generation. Cambridge Univ. Press, England, 2001. [3] P. J. Giblin. Graphs, Surfaces and Homology. 2nd edition, Chapman and Hall, London, 1977. [4] Y. Matsumoto. An Introduction to Morse Theory. Amer. Math. Soc., Providence, Rhode Island, 2002. [5] J. W. Milnor. Topology from the Differential Viewpoint. Princeton Univ. Press, New Jersey, 1965. [6] J. R. Munkres. Topology. A First Course. Prentice-Hall, Englewood Cliffs, New Jersey, 1975. [7] J. R. Munkres. Elements of Algebraic Topology. Perseus, Cambridge, Massachusetts, 1984. [8] R. E. Tarjan. Data Structures and Network Algorithms. SIAM, Philadelphia, Pennsylvania, 1983.
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announcements | schedule | projects | references |