19 036: COMPUTATIONAL TOPOLOGY
| Instructors: | Herbert Edelsbrunner |
| announcements | schedule | references |
- April 15: our first class meeting.
- April 29 and 30: Dmitriy will teach material on surfaces.
| Date | Lecture Topic | Notes | Assignments |
| Apr 15 Tue | introduction | General information [pdf] | |
| I. GRAPHS | |||
| Apr 16 Wed | connected components | Lecture [pdf] | |
| Apr 22 Tue | curves | Lectures [pdf] [pdf] | |
| Apr 23 Wed | planar graphs | Lecture [pdf] | Homework [pdf] |
| II. SURFACES | |||
| Apr 29 Tue | two-dimensional manifolds | Lectures [pdf] [pdf] [pdf] | |
| Apr 30 Wed | surface simplification | Lecture [pdf] | Homework [pdf] |
| III. COMPLEXES | |||
| May 06 Tue | simplicial complexes | Lecture [pdf] | |
| May 07 Wed | convex set systems | Lecture [pdf] | |
| May 13 Tue | Delaunay complexes | Lecture [pdf] | |
| May 14 Wed | alpha complexes | Lecture [pdf] | Homework [pdf] |
| IV. HOMOLOGY | |||
| May 20 Tue | homology groups | Lecture [pdf] Problem [pdf] | |
| May 21 Wed | matrix reduction | Lecture [pdf] | |
| May 27 Tue | relative homology | Lecture [pdf] | |
| May 28 Wed | exact sequences | Lecture [pdf] | Homework [pdf] |
| VI. MORSE THEORY | |||
| Jun 03 Tue | generic smooth functions | Lecture [pdf] Problem [pdf] | |
| Jun 04 Wed | transversality | Lecture [pdf] | |
| Jun 10 Tue | piecewise linear functions | Lecture [pdf] | |
| Jun 11 Wed | Reeb graphs | Lecture [pdf] | Homework [pdf] |
| VII. PERSISTENCE | |||
| Jun 17 Tue | persistent homology | Lecture [pdf] | |
| Jun 18 Wed | time series | Lecture [pdf] | |
| Jun 24 Tue | bottleneck stability | Lecture [pdf] | |
| Jun 25 Wed | length of a curve | Lecture [pdf] | Homework |
[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.
| announcements | schedule | references |
Herbert Edelsbrunner (edels@cs.duke.edu) April 2008