2026 (Current Year) Faculty Courses School of Computing Department of Mathematical and Computing Science Graduate major in Mathematical and Computing Science
Topological Data Analysis
- Academic unit or major
- Graduate major in Mathematical and Computing Science
- Instructor(s)
- Zin Arai / Shinya Nishibata / Masaaki Umehara / Sakie Suzuki / Shunsuke Tsuchioka
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MCS.M427
- Number of credits
- 200
- Course offered
- 2026
- Offered quarter
- 3Q
- Syllabus updated
- Mar 26, 2026
- Language
- Japanese
Syllabus
Course overview and goals
We give an introduction to topological data analysis, a method of data analysis that involves topology. As mathematical foundations, we also learn the basics of computational topology and computational geometry.
Course description and aims
The goal is to understand the fundamental concepts of computational topology/geometry and become proficient in applying them to practical topological data analysis.
Keywords
Computational Topology, Computational Geometry, Algorithms
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
A report assignment will be announced In the final class.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Overview |
Understand the contents of the lecture. |
| Class 2 | Voronoi and Delaunay Diagrams |
Understand the contents of the lecture. |
| Class 3 | Alpha Complexes and Simplicial Complexes |
Understand the contents of the lecture. |
| Class 4 | Topological Spaces and Homotopy |
Understand the contents of the lecture. |
| Class 5 | Homology |
Understand the contents of the lecture. |
| Class 6 | Computation of Homology Groups |
Understand the contents of the lecture. |
| Class 7 | Persistent Homology |
Understand the contents of the lecture. |
| Class 8 | Computation of Persistent Homology Groups |
Understand the contents of the lecture. |
| Class 9 | Stability of Persistent Homology |
Understand the contents of the lecture. |
| Class 10 | On Software for Computational Topology |
Understand the contents of the lecture. |
| Class 11 | Analysis of Persistent Diagrams |
Understand the contents of the lecture. |
| Class 12 | Mapper Algorithm |
Understand the contents of the lecture. |
| Class 13 | Advanced Topics 1 |
Understand the contents of the lecture. |
| Class 14 | Advanced Topics 2 |
Understand the contents of the lecture. |
| Class 15 | Advanced Topics 3 |
Understand the contents of the lecture. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Not specified.
Reference books, course materials, etc.
H. Edelsbrunner and J. L. Harer, Computational Topology, AMS, 2010
Evaluation methods and criteria
By reports.
Related courses
- MCS.T201 ： Set and Topology I
- MCS.T221 ： Set and Topology II
- MCS.T331 ： Discrete Mathematics
Prerequisites
None.