▶Japanese
Post to SNS
- Home
- > School of Computing
- > Graduate major in Mathematical and Computing Science
- > Topological Data Analysis
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematical and Computing Science
- Instructor(s)
- Arai Zin Nishibata Shinya Umehara Masaaki Murofushi Toshiaki Suzuki Sakie Tsuchioka Shunsuke
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue5-6(W8E-306(W832)) Fri5-6(W8E-306(W832))
- Group
- -
- Course number
- MCS.M427
- Credits
- 2
- Academic year
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
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.
Student learning outcomes
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 that will be developed
| ✔ 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/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Overview | Understand the contents of the lecture. |
| Class 2 | Voronoi and Delaunay Diagrams | Understand the contents of the lecture. |
| Class 3 | Weighted Diagrams | Understand the contents of the lecture. |
| Class 4 | Diagrams in 3D | Understand the contents of the lecture. |
| Class 5 | Alpha Complexes | Understand the contents of the lecture. |
| Class 6 | Holes in Spaces | Understand the contents of the lecture. |
| Class 7 | Area Formulas | Understand the contents of the lecture. |
| Class 8 | Topological Spaces | Understand the contents of the lecture. |
| Class 9 | Homology Groups | Understand the contents of the lecture. |
| Class 10 | Complex Construction | Understand the contents of the lecture. |
| Class 11 | Filtrations | Understand the contents of the lecture. |
| Class 12 | PL Functions | Understand the contents of the lecture. |
| Class 13 | Matrix Reduction | Understand the contents of the lecture. |
| Class 14 | Softwares and Applications 1 | Understand the contents of the lecture. |
| Class 15 | Softwares and Applications 2 | Understand the contents of the lecture. |
Out-of-Class Study Time (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.
Herbert Edelsbrunner, A Short Course in Computational Geometry and Topology, Springer, 2014
Assessment criteria and methods
By reports.
Related courses
- MCS.T201 ： Set and Topology I
- MCS.T221 ： Set and Topology II
- MCS.T331 ： Discrete Mathematics
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None.
