Uusi opinto-opas (sisältäen myös opetusohjelmat) lukuvuodelle 2018-2019 sijaitsee osoitteessa https://opas.peppi.utu.fi . Tältä sivustolta löytyvät enää vanhat opinto-oppaat ja opetusohjelmat.

The new study guide (incl. teaching schedules) for academic year 2018-2019 can be found at https://studyguide.utu.fi. This site contains only previous years' guides.

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Arkistoitu opetussuunnitelma 2016–2018
Selaamasi opetussuunnitelma ei ole enää voimassa. Tarkista tiedot voimassa olevasta opetussuunnitelmasta.
MATE5148 Tilings and Patterns 10 op
Organised by
Mathematics
Person in charge
Department of Mathematics and Statistics, Jarkko Kari
Planned organizing times
Period(s) I II III IV
2017–2018 X X
Preceding studies
Recommended: Basic group theory, e.g. "Algebran peruskurssi I", understanding of elementary concepts of geometry. Automata theory.

Learning outcomes

To learn the lecture material; to be able to apply the studied concepts and methods to prove new facts concerning tilings and patterns; to be able to identify symmetry groups of patterns; to understand the concept of algorithmic undecidability.

Contents

Symmetries of tilings and patterns, rosette, frieze and wallpaper groups, tilings by regular polygons, archimedean tilings, Wang tiles and their relation to Turing machines, the undecidability of the tiling problem, aperiodicity, quasiperiodicity, Penrose's kite and dart.

Teaching methods

Teaching method Contact Online
Lectures 56 h 0 h
Exercises 26 h 0 h

Teaching language

English

Modes of study

Option 1
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
Exercises Exercise(s)
  • In English
Written exam
  • In English
Option 2
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
Exercises Exercise(s)
  • In English
Midterm examination Written exam
  • In English

Evaluation

Numeric 0-5.

Study materials

Lecture Notes

Belongs to following study modules

Matematiikan ja tilastotieteen laitos
2016–2017
Teaching
Archived Teaching Schedule. Please refer to current Teaching Shedule.
Implementation details are unavailable.
Matematiikan ja tilastotieteen laitos
MDP in Information Security and Cryptography
Opintokokonaisuudet