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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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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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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.
1. Knowledge Describe and understand comprehensively principles and methods in topological methods in computer science.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral exam
Completing the assignments. Passing the 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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