Prof.Dr.Hc. Klaus Denecke, Institut fur Mathematik, Universitat Potsdam, Germany		Prof. Dr. Jorg Koppitz, Institut fur Mathematik, Universitat Potsdam, Germany
kdenecke@rz.uni-potsdam.de		koppitz@rz.uni-potsdam.de
Tel:	+49-(0)331/977-1415	Tel:	+49-(0)331/977-1060

SERBIA, NIS	SERBIA, NOVI SAD
Dejan Mancev	Nenad Moraca
Elena Stevanovic	Srdjan Skrbic
Mima Stojic	Luka Aleksic
	Dragana Cuk
MACEDONIA, SKOPJE	BULGARIA, PLOVDIV
Natasa Ilievska	Elena Asyova
Aleksandar Blazevski	Elena Mihaylova
Simona Samardziska	Stefan Djukelov
BOSNIA and HERZEGOVINA, SRAJEVO	BULGARIA, BLAGOEVGRAD
Almir Huskanovic	Ilinka Dimitrova
Hermina Alajbegovic	Dimitrina Tzvetkova
	Strahil Shorgov
	Irena Atanasova
	Elena Karashtranova
BULGARIA, SOFIA
Lasko Laskov

I. State-based systems

1. Black boxes.
2. Functional programming.
3. Data types.
4. Automata and Languages.
5. Object-oriented programs.
6. Non-deterministic systems.
7. The concept of a coalgebra.

II. Basic concepts from category theory

1. The concept of a category.
2. Special morphisms.
3. Terminal objects, sums, pushouts.
4. The category Set.
5. Functors.
6. Natural transformations.

III. Coalgebras

1. Substructures.
2. Homomorphic images, factorizations.
3. Colimits in setF.
4. Bisimulation.
5. Epis and Monos in SetF.
6. Congruences.
7. Covarieties

IV. Terminal Coalgebras

1. Terminal automata.
2. Existence of terminal coalgebras.
3. Weakly terminal coalgebras.
4. Restricted functors.
5. Cofree coalgebras.
6. Pattern-defined classes as covarieties.
7. Programming with terminal coalgebras.
8. Proofs by coinduction.

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Objectives

The main goal and target of the Intensive course "Application of Algebra and Discrete Mathematics in Computer Science" is to give an opportunity for students, postdocs or young researchers from the partner universities in the South Eastern Europe to create good relationships and to help them in their research. Next goal of the course is to demonstrate the flexibility to application in Computer Science of a traditional field of mathematics as algebra and discrete mathematics.

Our countries could benefit a lot, if we can continue the cooperation between these young people, started with this course.

The programme of the course provide many examples for application of some classical topics of algebra in computer science as:

• Category Theory;
• Coalgebras
• State-based Systems

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Links

South-West University, Blagoevgrad

Institut fur Mathematik, Universitat Potsdam

Bulgarian Academy of Sciences

IMI of BAS

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last change 09 November 2005

shtrakov@aix.swu.bg