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!