## 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!