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ARCHIV 20/21 zimni semestr

UNIVERSAL ALGEBRA (NMAG405)

Lecture: Thr 9:00 - 10:30 zoom
Practicals run by William DeMeo: Thr 10:40 - 12:10 zoom (the link contains material for/from practicals)

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
Burris, Sankappanavar: A Course in Universal Algebra (an alternative source of examples and exercises)
Stanovsky: Exercises in algebra (in Czech) - chapter V

Link to material only for NMAG405 students" (e.g. lecture recordings). The username and password was sent to you by email.

Homework

Please prepare in PDF format. Latex or handwritting+Adobe Scan highly recommended.
Submit your homeworks to your GitLab repository. Follow the instructions here.
We will add comments to the PDF and record your mark to SIS

topics (future topics may change) recommended reading lecture notes homework

8.10. Motivation. Algebra (signature, type). Examples.
Pr.: Lattices vs. lattice ordered sets Bergman 1.1, 1.2 lecture 1

15.10. Lattices, complete lattices, closure operators.
Pr.: Distributive and modular lattices. The lattice of equivalence relations. Bergman 2.1, 2.2, 2.3 lecture 2

22.10. Algebraic lattices and closure operators. Galois correspondences.
Pr.: Complete lattices, closure operators, Galois correspondences. Bergman 2.4, 2.5 lecture 3 Homework 1
due 5 Nov

29.10. Subalgebras, products, quotients.
Pr.: Subalgebras, congruences. Bergman 1.3, 1.4, 1.5 lecture 4
corrected (lower quality)

5.11. H,S,P operators, variety. Homomorphisms.
Pr.: Homomorphisms. Finite algebras generate locally finite varieties. Bergman 1.1, 1.3, 3.1, 3.5 lecture 5 Homework 2

due 19 Nov

12.11. Direct and subdirect decomposition
Pr.: Direct and subdirect decomposition. Bergman 3.2, 3.3 lecture 6

19.11. Subdirect decomoposition, SIs in congruence distributive vaieties
Pr.: SIs in monounary algebras. Bergman 3.4, 3.5, (5.2) lecture 7 Homework 3
due 3 Dec

26.11. Terms, identities, free algebras.
Pr.: Free algebras. Bergman 4.3, 4.4 lecture 8

3.12. The syntax-semantics Galois correspondence, Birkhoff's theorem.
Pr.: Equational bases. Bergman 4.4, (4.6) lecture 9 Homework 4
due 17 Dec

10.12. Clones. Free algebras as clones of term operations.
Pr.: Clones. Bergman 4.1 lecture 10
17.12. The operations-relations Galois correspondence.
Pr.: Algebraic and relational clones. Bergman 4.2 lecture 11 Homework 5
due 7 Jan

7.1. Mal'cev conditions: Mal'cev, majority.
Mal'cev conditions Bergman 4.7 (part) lecture 12

INTRODUCTION TO COMPLEXITY OF CSP (NMAG563)

Run by Antoine Mottet: Fri 9:00 Zoom

KAFKA (NMMB551)

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