Libor Barto

HOME COCOSYM RESEARCH FOR STUDENTS

UNIVERSAL ALGEBRA (NMAG405)

Lecture: Wed 11:30 - 13:00 K12
Practicals run by M. Kompatscher: Tue 11:30 - 13:00 K8

Grading:

  • Practicals ("Z: Zapocet"): homeworks (60% from 4 best scores out of 5 homeworks)
  • Lecture ("Zk: Zkouska"): 15% homeworks, 85% written test + possible oral examination

Literature:

topicsrecommended reading homework
2.10.Motivation. Algebra (signature, type). Examples.
Ex.: Lattices vs. lattice ordered sets
Bergman 1.1, 1.2
9.10.Lattices, complete lattices, closure operators.
Ex.: Isomorphism
Bergman 2.1, 2.2, 2.3
16.10. Algebraic lattices and closure operators. Galois correspondences.
Ex.: Distributive and modular lattices. The lattice of equivalence relations.
Bergman 2.4, 2.5 Homework 1
due 29 Oct
23.10. Subalgebras, products, quotients.
Ex.: Complete lattices, closure operators, Galois correspondences.
Bergman 1.3, 1.4, 1.5
30.10. H,S,P operators, variety. Homomorphisms.
Ex.: Subalgebras, congruences.
Bergman 1.1, 1.3, 3.1, 3.5 Homework 2
due 12 Nov
6.11. Direct and subdirect decomposition
Ex.: Homomorphisms. Finite algebras generate locally finite varieties.
Bergman 3.2, 3.3
13.11. ---
Ex.: ---.
20.11. Subdirect decomoposition, SIs in congruence distributive vaieties
Ex.: Direct and subdirect decomposition.
Bergman 3.4, 3.5, (5.2) Homework 3
due 3 Dec
27.11. Terms, identities, free algebras.
Ex.: SIs in monnounary algebras.
Bergman 4.3, 4.4
4.12. The syntax-semantics Galois correspondence, Birkhoff's theorem.
Ex.: Free algebras.
Bergman 4.4, (4.6) Homework 4
due 17 Dec
11.12. Clones. Free algebras as clones of term operations.
Ex.: Equational bases.
Bergman 4.1
18.12. The operations-relations Galois correspondence.
Ex.: Clones.
Bergman 4.2 Homework 5
due 7 Jan
8.11. Mal'cev conditions: Mal'cev, majority.
Ex.: Algebraic and relational clones.
Bergman 4.7 (part)

 

 

INTRODUCTION TO COMPLEXITY OF CSP (NMAG563)

Run by Antoine Mottet: Thr 9:00 seminar room of the Department of Algebra

References:

  • short survey (Barto): here (see complexity column)
  • longer survey (Barto, Krokhin, Willard): here
  • Krokhin's tutorial: available here
  • Another Krokhin's tutorial, a bit different topics: available here
  • My tutorial: PDF
  • Paper Bulatov, Jeavons, Krokhin: Classifying the Complexity of Constraints Using Finite Algebras PDF

 

 

KAFKA (NMMB551)

Wed 15:40 seminar room of KA web

 

 

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