Libor Barto
 HOME POCOCOP RESEARCH FOR STUDENTS

UNIVERSAL ALGEBRA (NMAG405)

Lecture: Mon 12:20 - 13:50 K5
Practicals run by Michael Kompatscher: Fri 12:20 - 13:50 K2

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

Literature:

 topics (future topics may change) recommended reading lecture notes homework 2.10. Motivation. Algebra (signature, type). Examples. Pr.: Lattices vs. lattice ordered sets Bergman 1.1, 1.2 lecture 1 practical 1 9.10. Lattices, complete lattices, closure operators. Pr.: Distributive and modular lattices. Bergman 2.1, 2.2, 2.3 lecture 2 practical 2 16.10. Algebraic lattices and closure operators. Galois correspondences. Pr.: Complete lattices, closure operators, Galois correspondences. Bergman 2.4, 2.5 lecture 3 practical 3 Homework 1 due 3.11. 12:20 23.10. Subalgebras, products, quotients. Pr.: Subalgebras, congruences. Bergman 1.3, 1.4, 1.5 lecture 4 practical 4 corrected (lower quality) 30.10. H,S,P operators, variety. Homomorphisms. Pr.: HSP, homomorphisms. Bergman 1.1, 1.3, 3.1, 3.5 lecture 5 practical 5 Homework 2 due 24.11. 12:20 6.11. Direct and subdirect decomposition Pr.: Direct and subdirect decomposition. Bergman 3.2, 3.3 lecture 6 practical 6 13.11. Subdirect decomoposition, SIs in congruence distributive vaieties Pr.: --- Bergman 3.4, 3.5, (5.2) lecture 7 20.11. Terms, identities, free algebras. Pr.: Free algebras. Bergman 4.3, 4.4 lecture 8 practical 7 Homework 3 due 8.12. 12:20 27.11. The syntax-semantics Galois correspondence, Birkhoff's theorem. Pr.: Equational bases. Bergman 4.4, (4.6) lecture 9 practical 8 4.12. Clones. Free algebras as clones of term operations. Pr.: Clones. Bergman 4.1 lecture 10 practical 9 Homework 4 due 22.12. 12:20 11.12. The operations-relations Galois correspondence. Pr.: Algebraic and relational clones. Bergman 4.2 lecture 11 practical 10 18.12. Mal'cev conditions: Mal'cev, majority. Pr.: canceled Bergman 4.7 (part) lecture 12 Homework 5 due 5.1. 12:20 1.1. --- Pr.: Mal'cev conditions practical 11 8.1. Tame Congruence Theory Pr.: Tame Congruence Theory TCT exercises

ARCHIV