Libor Barto Studenti

Libor Barto

HOME COCOSYM RESEARCH FOR STUDENTS

ARCHIV 19/20 zimni semestr

[Zpet]

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:

Clifford Bergman: Universal Algebra: Fundamentals and Selected Topics - our library has a few copies!
Burris, Sankappanavar: A Course in Universal Algebra (an alternative source of examples and exercises)
Stanovsky: Exercises in algebra (in Czech) - chapter V

topics recommended 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

ARCHIV