CONVEX ANALYSIS
| Title | ΚΥΡΤΗ ΑΝΑΛΥΣΗ / CONVEX ANALYSIS |
| Code | Θ019 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Romanos diogenis Malikiosis |
| Common | No |
| Status | Active |
| Course ID | 600025908 |
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 | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268388
|
Course Type 2021
Specific Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268388
- eLearning: https://elearning.auth.gr/course/view.php?id=9904
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Good knowledge of basic concepts from Analysis and Geometry: Measure Theory, Real Analysis, basic geometric concepts, and possibly some elements of Differential Geometry. Excellent knowledge of Linear Algebra and Matrix Theory is also needed
Learning Outcomes
Upon successful completion of the course, students will have learned the modern extensions of Convex Analysis regarding:
1) analytical concepts, about the space of convex bodies in terms of the Hausdorff or Banach-Mazur metric
2) geometric concepts, e.g. mixed volumes, and their applications to isoperimetric problems
3) concepts from combinatorial geometry, such as Karatheodoris, Radon, Helly Theorems, and the geometry of polytopes
General Competences
- Generate new research ideas
- Advance free, creative and causative thinking
Course Content (Syllabus)
1) Basic convexity theorems (Caratheodory, Radon, Helly)
2) Support and separation
3) Polytopes and polyhedra
4) The space of convex bodies in terms of the Hausdorff distance
5) Mixed volumes and isoperimetric problems
6) Ellipsoids. John and Loewner ellipsoids
Keywords
Convex bodies, Polytopes, Hausdorff distance, Mixed volumes, Ellipsoids, John and Loewner ellipsoids
Educational Material Types
- Notes
- Video lectures
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
Description
Video lessons from the pandemic
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Reading Assigment | 150 | ||||
| Written assigments | 108 | ||||
| Exams | 3 | ||||
| Total | 300 |
Student Assessment
Description
1) Solutions to the homework exercises assigned by the instructor (4 assignments): 40%
2) Final exam: 60%
Student Assessment methods
- Written Assignment (Summative)
- Oral Exams (Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
1) Peter M. Gruber, Convex and Discrete Geometry, Springer Berlin Heidelberg, 2007.
2) Απόστολος Γιαννόπουλος, Πρόχειρες σημειώσεις Κυρτής Γεωμετρικής Ανάλυσης.
3) Martin Henk, Convex Geometry I & Convex Geometry II. (Σημειώσεις από μεταπτυχιακό μάθημα)
Last Update
30-11-2024
