Libor Barto

DOMU VYZKUM PRO STUDENTY

UNIVERSAL ALGEBRA (NMAG405)

Lecture: Mon 10:40 - 12:10 K6
Practicals: Thu 10:40 - 12:10 Seminar room of KA

Grading:

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

Literature:

topicsrecommended reading homework
2.10.Motivation. Algebra (signature, type). Homomorphism, isomorphism.
Ex.: (semi)lattice vs. semi(lattice) ordered set. Homomorphisms.
Bergman 1.1, 1.2
9.10.Basic constructions - subalgebra, product.
Ex.: Homomorphisms, isomorphisms, products, subalgebras.
Bergman 1.3, 1.4
16.10. Quotients. HSP operators. Constructions and homomorphisms.
Ex.: Congruences of groups. Computing congruences and subalgebras.
Bergman 1.5, (3.1, 3.5) Homework 1
due 2 Nov 10:40
23.10. Isomorphism theorems. Complete lattices.
Ex.: Join of congruences.
Bergman 3.1, 2.3
30.10. Complete lattices, closure operators, Galois correspondeces.
Ex.: (Algebraic) complete lattices and (algebraic) closure operators
Bergman 2.4, 2.5 Homework 2
due 16 Nov 10:40
6.11. Examples of Galois correspondeces. Direct decomposition.
Ex.: Direct decomposition
Bergman 3.2
13.11. Subdirect decomposition.
Ex.: Subdirect decomposition
Bergman 3.3
20.11. Terms, free algebras.
Ex.: Free algebras
Bergman 4.3 Homework 3
due 7 Dec 10:40
27.11. Mod-Inv Galois correspondence, closed objects.
Ex.: Birkhoff's Theorem
Bergman 4.4, 4.6
4.12. Clones.
Ex.: Clones of term operations
Bergman 4.1 Homework 4
due 21 Dec 10:40

INTRODUCTION TO COMPLEXITY OF CSP (NMAG563)

Fri 9:00 Lab KA

Problems

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)

streda 15:40 seminarni mistnost KA stranka

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