Convex Analysis (MAE753)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
ΜΑE753 |
| Semester |
7 |
| Course Title |
Convex Analysis |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students |
Yes (in English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The course aims to an introduction to convex analysis at undergraduate level. It is desired for students to understand convex sets with respect to some of their qualitative (from a geometric/combinatorial point of view) and quantitative (e.g. volume, surface area) properties together with the study of the corresponding convex functions. |
|---|---|
| General Competences |
|
Syllabus
Basic notions. Convex functions and convex sets. Polytopes. Gauge functions and support functions. The Caratheodory. Radon's and Helly's theorems. Minkowski's First theorem. The Brunn-Minkowski inequality. Mixed volumes. Inequalities of isoperimetric type (e.g. the classical isoperimetric inequality and the Blaschke-Santalo inequality). F. John's Theorem. The reverse isoperimetric inequality.
Teaching and Learning Methods - Evaluation
| Delivery |
Lectures/ Class presentations | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | Use of the platform “E-course” of the University of Ioannina | ||||||||||
| Teaching Methods |
| ||||||||||
| Student Performance Evaluation |
Students' evaluation by the following:
Evaluation criteria and all steps of the evaluation procedure will be accessible to students through the platform "E-course" of the University of Ioannina. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- R. J. Gardner, Geometric tomography. Second edition. Cambridge University Press, 2006.
- R. Tyrel Rockafellar, Convex Analysis. Princeton University Press, 1970.
- R. Schneider, Convex bodies: the Brunn-Minkowski theory. Second expanded edition. Cambridge University Press, 2014.
- A. C. Thompson, Minkowski Geometry. Cambridge University Press, 1996.
- R. Webster, Convexity. Oxford University Press, 1970.