Libor Barto
 DOMU COCOSYM VYZKUM PRO STUDENTY

UNIVERSAL ALGEBRA (NMAG405)

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

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

Literature:

 topics recommended 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 11.12. Pol-Inv Galois correspondence, closures of algebras. Ex.: Pol, Inv Bergman 4.2 18.12. Relational clones. Ex.: Pol-Inv Homework 5 due 8 Jan 10:40 1.1. --------- Ex.: Compact clones, Boolean clones 8.1. Mal'tsev conditions. Ex.: Mal'tsev conditions Bergman 4.7

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

streda 15:40 seminarni mistnost KA stranka

ARCHIV