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CSE 60973: Topological Data Analysis
Fall 2025
Course Policies and Syllabus
Class meeting time: MWF 12:30-1:40pm
Class location: 209 DeBartolo
Course Staff
- Instructor: Dr. Erin Chambers
Contact Info: echambe2 - at - nd.edu
Office: 180 Fitzpatrick
Office Hours: TBD, or by arrangement
Table of contents
Topological data analysis (TDA) is an emerging area at the intersection of topology, geometry, and algorithms, which
is aimed at providing tools to better understand the concept of the shape of a data set. Geometric data is seeing widespread
use in many settings, much of it coming from a high-dimensional space yet often containing lower dimensional patterns
and structures. As a result, there is an increasing need for statistically sound ways to cluster, classify, and
simplify such data in ways that allow for improved computational pipelines. This course will survey
algorithms and techniques from TDA, with an aim to both cover the theoretical foundations as well as the
practical tools which are seeing widespread use in a wide range of domains.
- Introduction to topology and data
- Homology, homotopy, and persistence
- Generators and other descriptors
- Topology inference for point clouds
- Reeb graphs and mapper graphs
- Discrete Morse theory and its applications
- Multiparameter persistences
- Machine learning with TDA
At the conclusion of this course, students should be able to:
- Explain and identify basic signatures from topology that are useful for analyzing data sets
- Master a subset of algorithms for computing, such as: Betti numbers, topological persistence, homology cycles, Reeb graphs, discrete Morse structures, multiparameter persistence
- Identify and explain likely techniques for problems in applications that deal with geometric data
- Understand and explain how the TDA pipeline is used in shape comparison and ML workflows
The material of the class will primarily come from the book Computational Topology for Data Analysis, by Tamal Dey and Yusu Wang, which is available freely online.
I will also pull material from the book Persistence Theory: From Quiver Representations to Data Analysis, by Steve Oudot, although this text may be more comfortable for students coming from a mathematical background.
In addition to these two references, there are several other freely available ones which may be helpful as a resource:
As this is a fast moving area, I'll also post papers where relevant, since many things are too new to be in a book!
In general, I won't be taking attendance in lectures. However, you will miss important material if you are not present, including homework discussion/hints as well as discussion about the final project. You are responsible for any material covered in class; this includes course material as well announcements changes in due dates, etc. I will do my best to also post these in the lecture notes on the schedule page, but that is a courtesy and not a requirement, so please plan accordingly! If you will miss a lecture, I'd suggest checking with a fellow student, since my tablet does occasionally fail. You're also welcome to check in with me with any questions.
- Homework and/or Programming Assignments (50%)
There will be a series of written/or and programming assignments which (in total)
will compromise half of your final grade.
- Final project (50%)
The remaining half of your grade is tied up in your final project. See the homework page for details, but at a high level, this is a proposal followed by a group project which will allow you to dive deeper into a theorietical problem or analysis, an experimental evaluation using tools from the class, a survey of a particular topic we cover, or a creative work (youtube videos, demos, or other contributions which are not traditional papers or code). About 10% of this score will be based on a project proposal; another 20% will be based on a presentation of your work in the final week of class; and the rest of the score (70%) will be based on the final project you submit.
Letter grades will be based on each students overall percentage of awarded points according to the following formula.
-
Student percentage above 93% will result in a grade of
A or better.
-
Student percentage above 90% will result in a grade of
A- or better.
-
Student percentage above 87% will result in a grade of
B+ or better.
-
Student percentage above 83% will result in a grade of
B or better.
-
Student percentage above 80% will result in a grade of
B- or better.
-
Student percentage above 77% will result in a grade of
C+ or better.
-
Student percentage above 73% will result in a grade of
C or better.
-
Student percentage above 70% will result in a grade of
C- or better.
-
Student percentage above 60% will result in a grade of
D or better.
-
Student percentage below 60% will result in a grade of
F.
Any modification to this scale at the end of the year will be in favor of the students. That is we may later decide to award an A to a student who is slightly below the cutoff, but we certainly will not deny an A from someone who is above the cutoff.
No matter what curve I impose, I maintain that the minimum passing grade for this class is a 50% - so if your average is lower than that, you will fail this class.
In general, extra credit will not be assigned in this class. The homework assignments and final project will be challenging enough for everyone, so I would like for students to focus on the assignments provided.
Homeworks will generally be due at 11:59pm on canvas.
I am happy to regrade any assignments which you think were unfair or incorrect. Please email me a written explanation of your question; you are also welcome and encouraged to come discuss it with me, as that can often be helpful in understanding the issue better.
In general, late assignments will not be accepted or graded. However, life does happen, and occasionally emergencies come up. So, once per semester, you are welcome to get a 3 day extension, with no questions asked or no details needed, on any homework assignment. Please email myself and the TAs before 11;59pm on the due date, if you choose to exercise this.
Note that this policy does *not* apply to Persusall readings. I will drop your lowest three persusall readings, so that if you miss one or two due to travel or illnes, it will not hurt that portion of your grade.
For any student raising children, I understand that minor illnesses and unforeseen disruptions in childcare often put parents in the position of having to chose between missing class to stay home with a child and leaving him or her with someone you or the child does not feel comfortable with. While this is not meant to be a long-term childcare solution, occasionally bringing a child to class in order to cover gaps in care is perfectly acceptable. (You are likely to meet mine at some point this semester!)
All exclusively breastfeeding babies are welcome in class as often as is necessary to support the breastfeeding relationship. Because not all women can pump sufficient milk, and not all babies will take a bottle reliably, I never want students to feel like they have to choose between feeding their baby and continuing their education. You and your nursing baby are welcome in class anytime.
I ask that all students work with me to create a welcoming environment that is respectful of all forms of diversity, including diversity in parenting status. In all cases where babies and children come to class, I ask that you sit close to the door so that if your little one needs special attention and is disrupting learning for other students, you may step outside until their need has been met. Non-parents in the class, please reserve seats near the door for your parenting classmates. (Policy adapted from Dr. Melissa Cheyney)
As I'm sure you are all aware, Notre Dame students are expected to abide by Academic Code of Honor Pledge. “As a member of the Notre Dame community, I acknowledge that it is my responsibility to learn and abide by principles of intellectual honesty and academic integrity, and therefore I will not participate in or tolerate academic dishonesty."
In addition:
“All students must familiarize themselves with the Honor Code on the University’s website and pledge to observe its provisions in all written and oral work, including oral presentations, quizzes and exams, and drafts and final versions of essays.”
When in doubt about whether something is allowable, don’t assume that you are right – ask me first.
In the context of this course, I encourage students to discuss general course
material, which includes working on homework or practice problems, or discussing projects and sharing ideas.
You are also
allowed to turn in homework assignments in pairs. I also encourage you to discuss
problems with other students, but please be careful to write up all solutions
separately in your own group, and do not copy any material from another student.
As a good rule of thumb, make sure to write your solutions without using any notes
or papers written while talking to anyone other than your partner.
You are allowed to use outside sources of information in this class, including
textbooks and webpages. If the complete and correct answer is on page 263 of the
textbook, the best solution you can submit is "See page 263 of the text." Period.
However, if you find a solution from any other source, such as a web page, a
journal paper, a different algorithms textbook, or your mom, you must rewrite
the solution in your own words, and you must properly cite your sources. Assume
the graders have access to all the official course material, but nothing else.
While we strongly encourge you to use any outside source at your disposal, please
remember that the homework is supposed to demonstrate that you understand of the
material, not just how to use Google. In particular, verbatim copying is worth
NOTHING, and will be considered a violation of the academic integrity policy.
(Note that I'm also pretty good with google as well as ChatGPT, so I wouldn't recommend copying!)
We strongly encourage you to use any printed, online, or living resource at your disposal to help you solve homework problems, but you must cite your sources.
- If you use an idea from a book, cite the book.
- If you use an idea from a paper, cite the paper.
- If you use an idea from Wikipedia, cite Wikipedia.
- If you use an idea from CS StackExchange, cite CS StackExchange.
- If you use an idea from last semester's homework solutions, cite last semester's homework solutions.
- If you use an idea from the class slack channel, cite the class slack channel.
- If you use an idea from another student, cite that student.
- If you use an idea from Chegg, cite Chegg.
- If you use an idea from ChatGPT, cite ChatGPT.
- If you use an idea from the bathroom graffiti at Fiddler's Hearth, cite the bathroom graffiti at Fiddler's Hearth.
This is not an exhaustive list!
In general, just remember that submitting someone else's work without giving them proper credit is plagiarism, even if you have the other person's explicit permission. Submitting someone else's work without giving them proper credit is plagiarism, even if that “someone else” is a computer program. Citing your sources will not lower your homework grade.
Allowing someone else to use your ideas without giving you credit is also an academic integrity violation.
Students who violate academic integrity policies will be reported to the department, particularly in cases where relevant sources are not cited or in cases of direct copying of another student's work. First time
offenses on homework will result in a minimum of a failing grade on the assignment in question, with
egregious or repeated offenses resulting in failure in the course.
It is the policy and practice of The University of Notre Dame to provide reasonable accommodations for students with properly documented disabilities. Students who have questions about Sara Bea Accessibility Services or who have, or think they may have, a disability are invited to contact Sara Bea Accessibility Services for a confidential discussion by emailing at sarabeacenter@nd.edu or by phone at 574-631-7157. Because the University’s Academic Accommodations Processes generally require students to request accommodations well in advance of the dates when they are needed, students who believe they may need an accommodation for this course are encouraged to contact Sara Bea Accessibility Services at their earliest opportunity. Additional information about Sara Bea Accessibility Services and to learn more about the student process for requesting accommodations, please visits Accessibility Support. As an instructor, I encourage you to utilize these services, and feel free to reach out if you'd like to discuss how this might help in the context of this specific class.
The University of Notre Dame is committed to a safe and excellent education for all student enrolled, regardless of background. I share that commitment and strive to maintain a positive learning environment based on open communication, mutual respect, and non-discrimination. In this class we will not discriminate on the basis of race, sex, age, economic class, disability, veteran status, religion, sexual orientation, color or national origin. Any suggestions as to how to further such a positive and open environment will be appreciated and given serious consideration.