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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 2023 to 2023
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
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

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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.