Applied and Computational Topology
Math 689-001 (Spring 2025)
This web page will be updated regularly and always contain the latest information on the course.
| Instructor: | Thomas Wanner |
| Office: | Exploratory Hall 4404 |
| E-mail: | twanner@gmu.edu |
| Web Page: | https://math.cos.gmu.edu/~wanner |
| Office Hours: | MW 1-2pm, and by appointment |
| Lectures: | MW 5:55-7:10pm, Exploratory Hall 4106 |
| Prerequisites: | This course is open to all graduate students in Mathematics. |
| Textbook: | There is no required textbook for the course, I will post handwritten lecture notes on Canvas after every class. |
| While I will draw the material from a variety of sources, the following text can be used for supplementary reading: | |
| 📘 Herbert Edelsbrunner, John Harer: Computational Topology, AMS, 2010. |
Important Links
- Detailed syllabus (including recommended books)
- Relevant official GMU policies, and required university-wide policies (or as pdf file)
Detailed lecture notes, reading assignments, and additional materials can be found on the Canvas site for this course. Homework assignments can be found on Gradescope, which is linked through Canvas as well. Please make sure to check there regularly!
Overview & Learning Outcomes
Topological data analysis is an active field that has seen tremendous growth over the last decade, with a variety of important applications. This course serves as an introduction to this area. We will cover a combination of topics from geometry and topology, such as graphs, surfaces, triangulations, complexes, homology, Morse theory, persistent homology, and stability. In addition, we will study combinatorial topological dynamics, and demonstrate how it can be used to obtain qualitative information about classical dynamics. All necessary mathematical background material will be introduced in detail, and students will obtain access to software to put the theory into action. A more detailed syllabus can be found here. It will be updated weekly.
Homework Assignments
Homework problems will be assigned once a week and posted on Gradescope. Some of these assignments will be graded and count towards your homework score. While the remaining ones do not have to be handed in, I do advise everyone strongly to study them and write out the solutions properly. I will go through many of the homework problems in the following class and you will not benefit from this if you have not made a serious attempt at solving them.
Grading Policy
Your final grade in the course will be determined from your performance in the homework assignments, a final project/presentation, and your attendance and class participation. Weights for these items will be distributed approximately according to the following schedule:
| Homework | Final Project/Presentation | Participation | |
|---|---|---|---|
| 60% | 30% | 10% |
These percentages might change, and any changes will be announced in class.
Course Logistics
Content distribution: The course uses Canvas for distributing lecture materials and links to the homework assignemnts. The latter will be submitted and graded via Gradescope. Canvas can be accessed by visiting https://canvas.gmu.edu and logging in with your MasonID and password, and there is a link to Gradescope from within the course site.
Communication: I will use Canvas announcements to distribute class updates, and Mason e-mail to communicate with students. You may address me as Tom or Dr. Wanner in email and verbally. Communication over email is largely preferred, and I will respond to student emails promptly within 24 hours.
Course Technology Requirements
Software and Hardware: This course uses Canvas as a learning management system available at https://canvas.gmu.edu. Students are required to have regular, reliable access to a computer with an updated operating system (recommended: Windows 10 or Mac OS X 10.15 or higher).
Course-Specific Software: This course will mostly use Julia, which is available freely from https://julialang.org. An introduction to this language will be given. The course makes use of the free add-on package ConleyDynamics.jl, which was developed by the instructor.
Technical Help: If you have difficulty with accessing Canvas, please contact the ITS Support Center at (703) 993-8870 or support@gmu.edu. If you have trouble with using the features in Canvas, email courses@gmu.edu.