Math 491: Non-research Independent Study
This course is an introduction to topological data analysis (TDA) for undergraduate students that have taken introductory courses on real analysis and abstract algebra.
Notes
Expository document: An introduction to TDA by Ryan Iki and Mark Rekutin
Recommended Texts
Readings and exercises will be taken from [1]. However, we will also refer to [2-7] for specific topics.
- Dey, T. & Wang, Y. (2022). Computational Topology for Data Analysis. Cambridge: Cambridge University Press. DOI: 10.1017/9781009099950.
- Hatcher, A. (2005). Notes on Introductory Point-set Topology. https://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf.
- Lee, J.M. (2003). Introduction to Smooth Manifolds. Springer Science & Business Media. DOI: 10.1007/978-1-4419-9982-5.
- Lee, J.M. (2012). Introduction to Topological Manifolds. Springer Science & Business Media. DOI: 10.1007/978-1-4419-7940-7.
- Morris, S. (2023). Topology Without Tears. https://www.topologywithouttears.net.
- Munkres, J.R. (1975). Topology: A First Course. Prentice-Hall Inc., Englewood Cliffs.
- Rabadan, R. & Blumberg, A. (2019). Topological Data Analysis for Genomics and Evolution: Topology in Biology. Cambridge University Press. DOI: 10.1017/9781316671665.
Resources
- An introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists by Chazal & Michel.
- A roadmap for the computation of persistence homology by Otter, Porter, Tillmann, Grindrod & Harrington.
- Topological Data Analysis Course – Henry Adams
- Topological Data Analysis – Peter Bubenik
- Topological Data Analysis – nLab
