MEASURE-THEORETIC PROBABILITY
| Title | ΘΕΩΡΙΑ ΜΕΤΡΟΥ ΚΑΙ ΠΙΘΑΝΟΤΗΤΩΝ / MEASURE-THEORETIC PROBABILITY |
| Code | ΣΜΥ005 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Georgios Afendras |
| Common | Yes |
| Status | Active |
| Course ID | 600025940 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn Merikīs Foítīsīs (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| STATISTIKĪ, MONTELOPOIĪSĪ KAI YPOLOGISTIKES METHODOI | Elective Courses belonging to the selected specialization | Winter | - | 10 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| STATISTIKĪ, MONTELOPOIĪSĪ KAI YPOLOGISTIKES METHODOI | Elective Courses belonging to the selected specialization | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268397
|
Course Type 2021
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268397
- eLearning: https://elearning.auth.gr/course/view.php?id=9913
Language of Instruction
- Greek (Instruction, Examination)
Learning Outcomes
Upon successful completion of the course, the students:
1. will have acquired the knowledge of σ-algebras and probability measure spaces,
2. will have acquired the knowledge of Lebesque integral,
2. will be able to handle limit theorems (laws of large numbers, central limit theorems, 0-1 laws etc.),
3. will have acquired knowledge of the basic statistical functions as well as their asymptotic distribution,
4. will be able to use probability inequalities and martingales.
General Competences
- Apply knowledge in practice
- Make decisions
- Work autonomously
- Work in teams
- Work in an international context
- Work in an interdisciplinary team
- Generate new research ideas
Course Content (Syllabus)
In this course we study the foundations of modern Probability Theory in Probability-Measure level. We cover topics such as: independence, 0-1 laws, limit theorems, bounded mean, martingales, stochastic convergences, measure-concentration inequalities.
Educational Material Types
- Notes
- Interactive excersises
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ✓ | |||
| Fieldwork | 108 | ✓ | |||
| Reading Assigment | 150 | ✓ | |||
| Exams | 3 | ✓ | |||
| Total | 300 |
Student Assessment
Description
Homework/Presentation 60%
Final Examination 40%
Student Assessment methods
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
Bibliography
Additional bibliography for study
Billingsley, P. (1995). Probability and Measure, Wiley series in probability and mathematical statistics, 3rd edition. John Wiley, New York.
Feller, W. (1968). An introduction to probability theory and its applications. John Wiley, New York.
Feller, W. (1971). An introduction to probability theory and its applications, vol. II. John Wiley, New York.
Lo´eve, M. (1977). Graduate Texts in Mathematics, Probability Theory I. Springer-Verlag, New York.
Petrov, Valentin V. (1975). Limit theorems of probability theory: sequences of independent random variables. No.
04; QA273. 67, P4. Oxford, New York.
Serfling, R. (1980). Approximation Theorems of Mathematical Statistics. John Wiley, New York.
Last Update
02-12-2024
