AMAT 584, Section 1: Topological Data Analysis II
Spring 2020, Class #8917
MWF 11:30-12:45, BB 221
Instructor: Michael Lesnick
mlesnick [at] albany [dot] [the usual thing]
Office: Earth Sciences 120D
Office Hours: Monday, Wednesday 4:10-5:10, and by appointment
Lecture Notes
Homework
Exam Dates :
Midterm 1: Monday March 9 (tentative).
Final: Thurs. May 7, 3:30 - 5:30.
About this Course:
This is the second course in a three-semester sequence on Topological Data
Analysis (TDA), aimed primarily at students in Albany's Data Science
MS program.
The course picks up where TDA I (as taught in Fall 2019) left off.
Topics will include:
- simplicial complexes,
- abstract linear algebra and quotient spaces,
- homology (with field coefficients),
- persistent homology,
- Reeb graphs and Mapper.
Prequisites:
Students are formally required to have either taken TDA I (AMAT 583)
or to have
permission of the instructor.
In addition, all students are expected to be familiar with the following
concepts, which were covered in TDA I in Fall 2019:
- metric spaces and topological spaces,
- homeomorphism,
- homotopy equivalence,
- path connectednesss,
- equivalence relations,
- single linkage clustering,
- graphs: connected components and cycles.
These topics will not reviewed minimally or not at all. If you are
unfamiliar with some of these concepts, you may wish to consider waiting to taking TDA II with Boris Goldfarb when he next
teaches it.
Course Materials:
I plan to post copies of my (handwritten) lecture notes after each
class, usually on the same day as the lecture. These notes will be the
main reference for the course.
Other recommended reading:
- The text "Computational Topology" by Edelsbrunner
and Harer offers a computationally-flavored introduction to persistent
homolgoy and related topics. It is a good resource. A (free) online
version with much of the same content as the published version is
here.
- For some of the abstract linear algebra that we will be covering, a
nice text is Axler's "Linear Algebra Done Right."
- For students wishing to brush up on basic point-set topology, a readable resource
is "Introduction to Topology: Pure and Applied" by Adams
and Franzosa. Another popular text covering point-set topology in more detail is
"Topology" by Munkres.
Additional resources include:
Homework and Quizzes:
Homework will be assigned (semi-)regularly. In addition, we may
occasionally have quizzes. Homeworks and quizzes will be weighted
equally. The lowest two scores among the homework
and quizzes will be dropped. Homework is to be handed in at the beginning
of class on the day it is due, and this rule will be enforced
strictly.
Homeworks more than 5 minutes late will be penalized by 25%
of the total score. Once I deliver the homeworks to the grader, no
late homework will be accepted.
Collaboration on homework is permitted. However, you must write up
the homework yourself.
Grading:
The class will use the university's A-E grading scheme.
40%: Homework and quizzes.
25%: Midterm
30%: Takehome final
5%: Attendance
2% (bonus): Class participation / engagement.
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.