Math 4570 Applied Algebraic Topology

This is an introductory course on topological data analysis, with a focus on persistent homology.

References: 

• Introduction to Applied Algebraic Topology by Tom Needham

• Linear Algebra by Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence

• Topology by James Munkres

• Algebraic Topology by Allen Hatcher

Topics: 

1. Linear Algebra

• Abstract Vector Space

• Basis and Dimention

• Linear Transformaion and Matrix Representation

• Subspace and Quotient space

2. Topology

• Metric Space

• Topological Space

• Continuous Function

3. Simplicial Complexes and Homology

4. Persistent Homology