Modern Mathematical Methods in Informatics
MID Acad. year 2012/2013 Summer semester
Language of instruction
Subject specific learning outcomes and competences
Generic learning outcomes and competences
Prerequisite kwnowledge and skills
- G. Grätzer, Lattice Theory, Birkhäuser, 2003
- K.Denecke and S.L.Wismath, Universal Algebra and Applications in Theoretical Computer Science, Chapman & Hall, 2002
- S. Roman, Lattices and Ordered Sets, Springer, 2008
- J.L. Kelley, general Topology, Van Nostrand, 1955.
- G. Grätzer, Universal Algebra, Springer, 2008
- B.A. Davey, H.A. Pristley, Introduction to Lattices ad Order, Cambridge University Press, 1990
- P.T. Johnstone, Stone Spaces, Cambridge University Press, 1982
- S. Willard, General Topology, Dover Publications, Inc., 1970
- N.M. Martin and S. Pollard, Closure Spaces and Logic, Kluwer, 1996
- T. Y. Kong, Digital topology; in L. S. Davis (ed.), Foundations of Image Understanding, pp. 73-93. Kluwer, 2001
Syllabus of lectures
- Partially ordered sets, Axiom of choice and its equivalents.
- Well ordered sets, ordinal and cardinal numbetrs.
- Semilattices, lattices and complete lattices.
- Meet structures and closure operators.
- Lattice homomorphisms.
- Ideals and filters.
- Galois correspondence and Dedekind-McNeille completion.
- Partially ordered sets with suprema of directed sets (DCPO) and their applications in informatics
- Scott information systems and domains, category of domains
- Closure operators, their basic properties and applications (in logic)
- Basics og topology: topological spaces and continuous maps, separation axioms
- Connectedness and compactness in topological spaces
- Special topologies in informatics: Scott and Lawson topologies
- Basics of digital topology, Khalimsky topology
Course inclusion in study plans