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
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MATE5103 Ordered Sets 10 op
Organised by
Mathematics
Person in charge
Department of Mathematics and Statistics, Tero Harju
Preceding studies
Recommended:
Combinatorics is recommended. Some algebra is useful.

General description

The course treats ordered general ordered structures mostly in discrete mathematics.
The main notion is that of a partially ordered set, or poset, a transitive and reflexive
operation on a given set. Partially ordered sets have their origin in the works of Boole,
Peirce and Schroeder in the context of Boolean algebras. Modern theory of posets
covers close connections to lattice theory and universal algebra.

Learning outcomes

The theory of partially ordered sets belongs to discrete mathematics.
The course offers an overview of ordered structures in mathematics.

Contents

1. Posets including Moebius functions
2. Lattices including congruences and ideals
3. Special Lattices:
Distributive and modular lattices
Algebraic lattices
Complemented lattices
Moebius function for lattices

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

Evaluation

Numeric 0-5.

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