Term: Fall 2006
Time: Mo We 4:25pm - 5:40pm
Location: LSRC D106
Instructors: Herbert Edelsbrunner
TA: Amit Patel, Tu W F from 1 to 2pm in D214

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]
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]
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]
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]
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]
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

Herbert Edelsbrunner (edels@cs.duke.edu) August 2006