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School of Science
Department of Mathematics
|Level of Studies||
|Independent Teaching Activities||
Lectures (Weekly Teaching Hours: 3, Credits: 6)
|Language of Instruction and Examinations||
|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.|
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.
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
Lectures/ Class presentations
|Use of Information and Communications Technology||Use of the platform “E-course” of the University of Ioannina|
|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.
- 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.