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 | Attendance | |
|---|---|---|---|
| 60% | 30% | 10% |
These percentages might change, and any changes will be announced in class.
Important Notice
This course will be hosted on Canvas for the Spring 2025 semester. Please ensure you are familiar with accessing and navigating this platform. Resources and support are available at https://lms.gmu.edu/getting-started-students/ to help you get started. If you have any questions, do not hesitate to reach out to me or contact the ITS Support Center for assistance.