Introduction to Computational Topology - NMMB464
Title: Úvod do výpočetní topologie
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2025
Semester: summer
E-Credits: 4
Hours per week, examination: summer s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: 6
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Guarantor: RNDr. Zuzana Patáková, Ph.D.
Teacher(s): RNDr. Pavel Paták, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
Classification: Mathematics > Algebra
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Annotation -
The lecture introduces basic notions of computational topology.
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (14.05.2020)
Literature -

H. Edelsbrunner, J. Harer: Computational Topology: An Introduction

J.R. Munkres: Elements of algebraic topology

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (14.05.2020)
Syllabus -
  • basic topological notions: topological space, continuous map, homeomorphism

  • simplicial complexes and complexes on data: Čech, Delaunay, Vietoris-Rips

  • homotopy, homotopy equivalence, fundamental groups

  • homology, homology groups, Betti numbers, relative homology

  • persistent homology, filtrations, persistent algorithm, persistent diagram, stability

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (29.12.2020)
Entry requirements -

Basics of general algebra.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (14.05.2020)