TOPOLOGICAL DATA ANALYSIS
| Title | ΤΟΠΟΛΟΓΙΚΗ ΑΝΑΛΥΣΗ ΔΕΔΟΜΕΝΩΝ / TOPOLOGICAL DATA ANALYSIS |
| Code | Θ013 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Georgios Raptis |
| Common | No |
| Status | Active |
| Course ID | 600025893 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Spring | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Spring |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268419
|
Type Of Offer
- Disciplinary Course
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268419
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
Prerequisites
General Prerequisites
Basic knowledge of general topology and algebra at the undergraduate level
Learning Outcomes
Upon successful completion of the course, students will:
1. be familiar with concepts and methods of combinatorial and applied topology
2. acquire knowledge of the topology and homology theory of simplicial complexes
3. know the fundamental properties of persistent homology and its applications in data science
4. be able to compute barcodes of persistent homology and examine the topological characteristics of data sets
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Make decisions
- Work autonomously
- Work in teams
- Generate new research ideas
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Simplicial complexes. The Euler characteristic and simplicial homology. Relative homology. Persistent modules. Cech and Vietoris-Rips complexes. Persistent homology and Betti numbers. Barcodes. Interleaving distance. Stability of persistent homology. Clustering. Zigzag persistent homology. Discrete Morse theory. Applications.
Keywords
simplicial complex, Cech complex, Vietoris-Rips complex, persistence homology, barcode, interleaving distance
Educational Material Types
- Notes
- Multimedia
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Seminars | 20 | ||||
| Reading Assigment | 183 | ||||
| Project | 20 | ||||
| Written assigments | 35 | ||||
| Exams | 3 | ||||
| Total | 300 |
Student Assessment
Description
Written or oral exam, short presentation and written report (details will be explained at the beginning of the course).
Student Assessment methods
- Written Exam with Extended Answer Questions (Summative)
- Written Assignment (Formative)
- Oral Exams (Summative)
- Performance / Staging (Formative, Summative)
- Written Exam with Problem Solving (Summative)
- Report (Formative, Summative)
- Labortatory Assignment (Formative)
Bibliography
Additional bibliography for study
Αναλυτική βιβλιογραφία συγγραμμάτων, ερευνητικών άρθρων και οπτικοακουστικού υλικού θα δοθεί στην αρχή του μαθήματος (θα ανανεώνεται τακτικά δεδομένης της ραγδαίας και συνεχούς ανάπτυξης του πεδίου).
Last Update
11-05-2025
