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One of the important proof techniques in discrete mathematics
is the application of theorems from algebraic topology.
The course covers the necessary topological preliminaries
and establishes several combinatorial and geometric results
by topological methods, mainly using the Borsuk-Ulam theorem.
Last update: T_KAM (07.05.2001)
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For getting the credit from tutorials, the students are required to get at least 20 points from homework. However, it is also necessary to get at least 2.5 points from at least four series of the homeworks out of five possible series. The total number of available points will be at least 80. There is no provision for repeated attempts for the credit. Credit from tutorials is a necessary condition for an attempt to pass an exam.
Last update: Tancer Martin, doc. RNDr., Ph.D. (26.02.2024)
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J. Matousek, Using the Borsuk-Ulam Theorem V. V. Prasolov, Elements of Combinatorial and Differential Topology J. R. Munkres, Elements of Algebraic Topology Last update: Hladík Milan, prof. Mgr., Ph.D. (06.05.2014)
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The exam will be oral based on the contents of the lectures. Extra points gained by students by solving problems for tutorials will be considered in favor of the students. Last update: Kynčl Jan, doc. Mgr., Ph.D. (23.05.2019)
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Simplicial complexes, connectedness of a space.
Borsuk-Elam theorem, equivalent versions.
Ham-sandwich theorem, Necklace theorem.
Theorems on non-embeddability and colorings (chromatic number of Kneser graphs, Radon theorem).
Additional (possible) topics: homology, degree of a map, colorful Tverberg theorem, Z_2 index. Last update: Tancer Martin, doc. RNDr., Ph.D. (25.10.2018)
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