Module Handbook

  • Dynamischer Default-Fachbereich geändert auf INF

Module INF-18-51-M-6

Computational Topology (M, 5.0 LP)

Module Identification

Module Number Module Name CP (Effort)
INF-18-51-M-6 Computational Topology 5.0 CP (150 h)

Basedata

CP, Effort 5.0 CP = 150 h
Position of the semester 1 Sem. in SuSe
Level [6] Master (General)
Language [DE/EN] German or English as required
Module Manager
Lecturers
Area of study [INF-VIS] Visualisation and Scientific Computing
Reference course of study [INF-88.79-SG] M.Sc. Computer Science
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+2U INF-18-51-K-6
Computational Topology
P 56 h 94 h
U-Schein
ja PL1 5.0 SuSe
  • About [INF-18-51-K-6]: Title: "Computational Topology"; Presence-Time: 56 h; Self-Study: 94 h
  • About [INF-18-51-K-6]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.
    • It is a prerequisite for the examination for PL1.

Examination achievement PL1

  • Form of examination: oral examination (20-60 Min.)
  • Examination Frequency: Examination only within the course
  • Examination number: 61851 ("Computational Topology")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • theoretical foundations
    • formal defintions
    • graph topology
    • simplicial complexes
  • topological Analysis of Fields
    • contour tree and Reeb graph
    • Morse-Smale complex
    • topology of dynamical systems
    • parameter- and time-dependent topology
  • topological analysis of unstructured data
    • alpha complex
    • topology of point sets
    • persistent homology
  • applications
    • scientific and medical visualization
    • topological techniques for large datasets

Competencies / intended learning achievements

After successfully completing the module, students will be able to
  • implement topological methods in data analysis and visualization,
  • apply topological techniques to specific problems, and
  • choose suitable topological techniques for particular applications.

Literature

  • H. Edelsbrunner: Computational Topology – An Introduction. American Mathematical Society, 2010, ISBN: 978-0-8218-4925-5
  • A. Zomorodian: Topology for Computing. Cambridge University Press, 2009. ISBN: 978-0521136099

Requirements for attendance of the module (informal)

Modules:

Requirements for attendance of the module (formal)

None

References to Module / Module Number [INF-18-51-M-6]

Course of Study Section Choice/Obligation
[INF-88.79-SG] M.Sc. Computer Science [Specialisation] Specialization 1 [WP] Compulsory Elective