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Infinitary Combinatorics with Applications to Mathematical Analysis - NMMA625
Title:
Nekonečná kombinatorika s aplikacemi v matematické analýze
Guaranteed by:
Institute of Mathematics CAS (32-MUAV)
Faculty:
Faculty of Mathematics and Physics
Actual:
from 2016
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:
taught
Language:
English
Teaching methods:
full-time
Teaching methods:
full-time
Note:
course can be enrolled in outside the study plan
Guarantor:
prof. Wieslaw Kubiš
Class:
DS, matematická analýza
Classification:
Mathematics > Mathematics , Algebra , Differential Equations, Potential Theory , Didactics of Mathematics , Discrete Mathematics , Math. Econ. and Econometrics , External Subjects , Financial and Insurance Math. , Functional Analysis , Geometry , General Subjects , Real and Complex Analysis , Mathematics General , Mathematical Modeling in Physics , Numerical Analysis , Optimization , Probability and Statistics , Topology and Category
Interchangeability :
NMAT094
Annotation -
--- Czech English
Last update: G_M (08.05.2014)
The aim of the course is to present the main results and ideas of
infinite combinatorics, mainly
partition problems and dichotomies, with selected applications in
mathematical analysis.
Last update: G_M (08.05.2014)
Cílem přednášky je prezentace hlavních výsledků a ideí nekonečné kombinatoriky, zejména problémy dělení a
dichotomie, s vybranými aplikacemi v matematické analýze.
Last update: G_M (08.05.2014)
1. R.L. Graham, B.L. Rothschild, J.H. Spencer, Ramsey Theory, Wiley 1990
2. N. Hindman, D. Strauss, Algebra in the Stone-Cech Compactification, de Gruyter 1998
3. I. Protasov, Combinatorics of Numbers, VNTL Publishers, Lviv 1997
Syllabus -
--- Czech English
Last update: G_M (08.05.2014)
Syllabus:
1. Ramsey Theorem and its uncountable versions
2. Van der Warden and Hindman Theorems; tools from topological dynamics
3. Galvin-Prikry Theorem and its application to Banach spaces
4. Ramsey property in various categories
5. Selected applications in analysis
Last update: G_M (08.05.2014)
Sylabus:
1. Ramseyova věta a její nespočtené verze
2. Van der Wardenova a Hindmanova věta, nástroje z topologick dynamiky
3. Galvin-Prikryova věta a její aplikace v Banachových prostorech
4. Ramseyova vlastnost v různých kategoriích
5. Vybrané aplikace v analýze
