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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Archived Curricula Guide 2014–2016
Curricula Guide is archieved. Please refer to current Curricula Guides
MATE5038 Combinatorial Enumeration 5 ECTS
Organised by
Person in charge
Matematiikan ja tilastotieteen laitos, Tero Harju
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

Not lectured 2014-2016

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

Department of Mathematics and Statistics
Archived Teaching Schedule. Please refer to current Teaching Shedule.
Implementation details are unavailable.
Department of Mathematics and Statistics
DP in Mathematics and Statistics
DP in Mathematics
Finnish Study Modules
DP in Statistics