ERGODIC THEORY
| Title | ΕΡΓΟΔΙΚΗ ΘΕΩΡΙΑ / ERGODIC THEORY |
| Code | Θ025 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Andreas Koutsogiannis |
| Common | Yes |
| Status | Active |
| Course ID | 600025914 |
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 | 600268424
|
Course Type 2021
Specific Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268424
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
Learning Outcomes
Under the succesful completion of the course, the students will be able to study:
-Recurrence and ergodicity
-equidistribution of sequences
-polynomial recurrence
Also they will know how to use
-van der Corput's trick
-Furstenberg's correspondence principle
-Szemerédi's theorem
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Work autonomously
- Advance free, creative and causative thinking
Course Content (Syllabus)
The goal of the course is the study of the following topics:
• Measure preserving systems
• Recurrence and ergodicity
• Mean ergodic theorem
• Equidistribution of sequences
• van der Corput's trick
• Polynomial recurrence
• Mixing and weak mixing
• Compact functions
• Multiple recurrence and weakly mixing systems
• Multiple recurrence in compact systems
• Complementary notions of compactness and weak mixing
• Restricting recurrence in ergodic systems
• Disintegration of a measure in ergodic parts
• Furstenberg's correspondence pronciple
• Szemerédi's theorem
Keywords
recurrence, ergodicity, equidistribution
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ✓ | |||
| Reading Assigment | 258 | ✓ | |||
| Exams | 3 | ✓ | |||
| Total | 300 |
Student Assessment
Description
Exercises: During the talks various exercises are assigned. The students must submit them by the end of the course. These are counted positively towards the final grade. In particular, usually the students take up to 2/10 points from the exercises.
Exam: There is one final written exam at the end.
Final grade: The final grade is a combination of the exercises' grade and the final written exam.
Student Assessment methods
- Written Exam with Multiple Choice Questions (Formative, Summative)
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Performance / Staging (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
• M. Einsiedler and T. Ward. Ergodic theory with a view towards number theory, volume 259 of Graduate Texts in Mathematics. Springer-Verlag London, Ltd., London, 2011.
• H. Furstenberg. Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, 1981.
• P. Walters. An Introduction to Ergodic Theory, Springer-Verlag, 1982.
Last Update
03-12-2024
