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ARCHIV 20/21 zimni semestr

[Zpet]

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:

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 readinglecture 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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