Applied Topology



Lecture 1:  Introduction to topology and the Euler-Poincare characteristic.
Lecture 2:  The Euler-Poincare characteristic and image recognition
Lecture 3:  Cluster analysis
Lecture 4:  Cluster analysis continued
Lecture 5:  Introduction to chain complexes, Betti numbers and homology
Lecture 6 :  Examples of Betti numbers
Lecture 7 :  Homology maps and persistence
Lecture 8 :  Natural Image Statistics
Lecture 9 :  Categories, functors and simplicial homology
Lecture 10 :  Simplicial approximation and singular homology
Lecture 11 :  Lefschetz fixed-point theorem
Lecture 12 :  Homotopy
Lecture 13 :  (We omitted this lecture on exact sequences)
Lecture 14 :  (We omitted this lecture on Smith Normal Form)
Lecture 15 :  Dynamical systems


Homework Exercises :  This kind of question could arise on the end of semester 3-hour exam!


I plan to (slowly) convert the above lectures into a booklet. The current version of this is available here and is best viewed in "presentation mode". Comments and corrections very welcome!