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.
MATE5038 Combinatorial Enumeration 5 op
Organised by
Person in charge
Matematiikan ja tilastotieteen laitos, Tero Harju
Planned organizing times
Period(s) I II III IV
2016–2017 X
Preceding studies
Basics of Algebra I or II is useful but not necessary.

Learning outcomes

The special interest in the course is in counting objects according to given problem settings. In many instances it is not sufficient just to count the objects satisfying certain properties. Instead, one is required to count the types of these objects when a classification or criterion is given for objects to be similar. Such restrictions refer to symmetry, and the methods for counting often use elementary group theory.


The course covers various general methods for counting of objects including permutations, generating functions, sieve methods, Moebius inversion, group theoretic methods and the Polya-Redfield Theorem.

Teaching methods

Teaching method Contact Online
Lectures 28 h 0 h
Exercises 12 h 0 h

Teaching language


Modes of study

Option 1
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
  • In English
Written exam
  • In English


Numeric 0-5.

Study materials

lecture notes

Belongs to following study modules

Matematiikan ja tilastotieteen laitos
Archived Teaching Schedule. Please refer to current Teaching Shedule.
Matematiikan ja tilastotieteen laitos
MDP in Information Security and Cryptography