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.
MATE5165 Ramsey Theory 5 op
Organised by
Person in charge
Matematiikan ja tilastotieteen laitos, Juhani Karhumäki

Learning outcomes

To learn Ramsey theory.


The course considers a few "jewels" of combinatorics. The results proved are similar showing "unavoidable regularities" or "impossibility of complete disorder". More intuitively the above means that "Any large enough structure contains some (still large) regular substructure". The following result is an example of theorems considered Ramsey's Theorem; any large enough vertex coloured graph contains a large monochromatic subgraph.

Teaching methods

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

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


Numeric 0-5.

Study materials

Lecture notes


R.L. Graham, B.L. Rothschild, J.H. Spencer, Ramsey Theory, John Wiley & Sons, 1990.

L. Lovasz, Combinatorial Problems and Exercises, American Mathematical Society, 2007.

Belongs to following study modules

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