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Course, academic year 2019/2020
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Infinitary Combinatorics with Applications to Mathematical Analysis - NMMA625
Title in English: Nekonečná kombinatorika s aplikacemi v matematické analýze
Guaranteed by: Matematický ústav AV ČR, v.v.i. (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 [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
Guarantor: 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 -
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.
Literature - Czech
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 -
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

 
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