Convex Analysis (MAE753): Διαφορά μεταξύ των αναθεωρήσεων
Γραμμή 108: | Γραμμή 108: | ||
=== Attached Bibliography === | === Attached Bibliography === | ||
See [https://service.eudoxus.gr/public/departments#20 Eudoxus]. Additionally: | See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Additionally: | ||
* R. J. Gardner, Geometric tomography. Second edition. | * R. J. Gardner, Geometric tomography. Second edition. | ||
* R. Tyrel Rockafellar, Convex Analysis. | * R. Tyrel Rockafellar, Convex Analysis. |
Αναθεώρηση της 13:05, 26 Ιουλίου 2022
Undergraduate Courses Outlines - Department of Mathematics
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑE817 |
Semester |
8 |
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) |
In the platform "E-course" of 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. Additionally:
- R. J. Gardner, Geometric tomography. Second edition.
- R. Tyrel Rockafellar, Convex Analysis.
- R. Schneider, Convex bodies: the Brunn-Minkowski theory. Second expanded edition.
- A. C. Thompson, Minkowski Geometry.
- R. Webster, Convexity.