AMAT 583, Sections 7 and 8: Topological Data Analysis I

Spring 2024, Class #'s 8430, 8431

Section 8: Monday,Wednesday 10:10-11:30 Biology 152

Section 7: Monday,Wednesday 1:10-2:30 Massry 362

Instructor: Michael Lesnick
mlesnick [at] albany [dot] [the usual thing]
Office: CK 385 (Catskill Building)
Office Hours: T, Th 1:30-2:30, and by appointment.
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Exam Dates :
Midterm 1: Wednesday, February 28
Midterm 2: Wednesday, April 3
Final: TBD

About this Course:
This is the first course in a three-semester sequence on Topological Data Analysis (TDA), aimed primarily at students in Albany's Data Science MS program. No prior knowledge of topology is assumed. The first two semesters of the sequence will emphasize mathematical foundations and conceptual understanding. The third course in the sequence is a practicum focusing on hands-on work with real data.

Topics to be covered (in this course and in TDA II) may include:

sets and functions
graphs
metric spaces
clustering (with an emphasis on topological approaches)
complexity of algorithms
algorithms for graphs and clustering
Mapper
simplicial complexes
persistent homology
linear and non-linear dimensionality reduction
multiparameter persistence

Course Materials:
Course materials will be hosted on Brightspace.

The primary course reference is a set of typed course notes.

Additional resources:

Matthew Wright's animated introduction to Persistent Homology
Magnus Botnan's TDA course notes
Robert Ghrist's textbook "Elementary Applied Topology"
Edelsbrunner and Harer's textbook "Computational Topology." A (free) online version with much of the same content as the published version is here
Dey and Wang's textbook "Computational Topology for Data Analysis"
Steve Oudot's textbook "Persistence Theory: From Quiver Representations to Data Analysis", by
Boissonat, Chazal, and Yvinec's textbook "Geometric and Topological Inference"
Carlsson and Vejdemo-Johansson's textbook "Topological Data Analysis with Applications"
Vidit Nanda's Computational Algebraic Topology Course Notes and Videos
Gunnar Carlsson's survey "Topology and Data"
Otter et al.'s survey "A Roadmap for the Computation of Persistent Homology"
For point-set topology, good resources include "Introduction to Topology: Pure and Applied" by Adams and Franzosa, and "Topology" by Munkres.
For the abstract linear algebra that is needed to define homology, a nice text is Axler's "Linear Algebra Done Right."

Homework:
Homework will be assigned semi-regularly. All homeworks will be weighted equally. Homework handed in at most one day late may be accepted with a 30% penalty, or at most two days late with a 50% penalty. You may discuss homework with your classmates, but homework must be written up on your own. Quizzes:
We will occasionally have short quizzes at the start of class, based on the previous lecture. These will not be announced in advance.

Grading:
The class will use the university's A-E grading scheme.

10%: Homework
5%: Homework
25%: Midterm 1
25%: Midterm 2
35%: Final

The lowest HW score will be dropped.
NOTE: The midterm and final may be curved, but not downward.

Academic Regulations:
Naturally, the University's Standards of Academic Integrity apply to this course, and students are expected to be familiar with these.

There will be no leeway on missed exams or last-minute exam rescheduling, except as noted in the regulations. If you anticipate an issue with the timing of an exam, please let me know as soon as possible.