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Course, academic year 2022/2023
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Convex Bodies - NMAG262
Title: Konvexní tělesa
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Jan Rataj, CSc.
Class: M Bc. OM
M Bc. OM > Doporučené volitelné
M Bc. OM > 2. ročník
Classification: Mathematics > Geometry
Incompatibility : NMAT092
Interchangeability : NMAT092
Annotation -
Last update: G_M (09.05.2014)
An elective course for bachelor's students of General Mathematics. Introduction to convex geometry in Euclidean spaces with orientation to integral-geometric relations.
Literature - Czech
Last update: JUDr. Dana Macharová (30.09.2014)

F.A. Valentine: Convex Sets. McGraw-Hill, New York, 1964

A. Barvinok: A Course in Convexity. Amer. Math. Soc., Providence, R.I., 2002

R. Schneider: Convex Bodies: The Brunn-Minkowski Theory. Cambridge Univ. Press, Cambridge, 1993

Syllabus -
Last update: G_M (09.05.2014)
  • Convex bodies in Rn , Minkovski operations, support function, Hausdorff metric on the space of convex bodies.
  • Intrinsic volumes of a convex body, mixed volumes, basic integral-geometric relations.
  • Symmetrization, isoperimetric and isodiametric inequalities.
  • Hadwiger's characterization theorem.

 
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