Libor Barto Studenti

Libor Barto

DOMU COCOSYM VYZKUM PRO STUDENTY

ARCHIV 17/18 letni semestr

UNIVERSAL ALGEBRA 2 (NMAG450)

Lecture: Wed 9:00 - 10:30 Seminar room of KA
Practicals (Alexandr Kazda): Mon 12:20 - 13:50 Seminar room of KA (only odd semester weeks = even calendar weeks)

Grading:

Practicals ("Z: Zapocet"): homeworks (60% from 3 best scores out of 4 homeworks)
Lecture ("Zk: Zkouska"): written test + possible oral examination; contact me by email

Available for the exam: now - 31 May; 25-29 June; July-August (some weeks), 10-28 September

Literature:

Clifford Bergman: Universal Algebra: Fundamentals and Selected Topics - our library has a few copies!
Jaroslav Jezek: Universal Algebra
(BKW) Barto, Krokhin, Willard: Polymorphisms, and how to use them .
(BK) Barto, Kozik: Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem
Burris, Sankappanavar: A Course in Universal Algebra (an alternative source of examples and exercises)

topics recommended reading homework

28.2. Abelian and affine algebras, fundamental theorem. Bergman 7.3

7.3. Relational desciption of Abelian algebras. Centralizing relation in UA vs. group theory.
Ex. 5.3.: Abelian and non-Abelian algebras. Bergman 7.4

14.3. Equational theories, completness theorem for equational logic. Jezek 13 Homework 1
due 4 Apr 9:00

21.3. Reduction order, critical pairs, Knuth-Bendix algorithm.
Ex. 19.3.: Basics of term rewriting systems Jezek 13

28.3. Finitely based varieties. Non-finitely based example.
Ex. 26.3.: Critical pairs, Knuth-Bendix Bergman 5.4.

4.4. McKenzie's DPC (definable principal congruences) result. Bergman 5.5. Homework 2
due 18 Apr 9:00

11.4. Constraint satisfaction problems over fixed templates. BKW

18.4. (h1-) clone homomorphisms, Taylor clones.
Ex. 16.4.: DPC, CSP BKW

25.4. Taylor's theorem. Bergman 8.4. Homework 3
due 9 May 9:00

2.5. Algebraic length 1, absorption and connectivity
Ex. 30.4.: Taylor algebras BK

9.5. Transitive operations BK

16.5. -----
Ex. 14.5.: Absorption and walking

23.5. Absorption theorem, Baby Loop Lemma, rare-area operation, CSP of smooth digraphs BK Homework 4
due 11 June 9:00

KAFKA (NMMB551)

Wed 15:40 seminar room of KA web

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