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Lecturer(s)
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Krupka Michal, doc. RNDr. Ph.D.
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Course content
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Advanced topics of general topology, basic topics of algebraic topology. Applications in Computer Science. General topology. Introduction to homotopy theory. Algebraic topology: singular homology, basics of homological algebra. Computation of homologies: Mayer-Vietoris sequence. Simplicial homology, computation of homologies of simplicial complexes as a discrete problem, simplicial structures for MV-algebras. Algebraic topology of finite spaces. Topology in data analysis. Topology and distributed computing.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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The students become familiar with basic concepts of general and algebraic topology and their applications in selected areas of Computer Science.
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Prerequisites
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unspecified
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Assessment methods and criteria
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unspecified
Active participation in class. Completion of assigned homeworks. Passing the oral (or written) exam.
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Recommended literature
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A.J. Zomorodian. (2009). Topology for Computing. Cambridge University Press.
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J.A. Bermak. (2011). Algebraic Topology of Finite Topological Spaces and Applications. Springer.
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J.R. Munkers. (2000). Topology.. Pearson.
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M. Herlihy, N. Shavit. (1999). The Topological Structure of Asynchronous Computability.
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