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UNIVERSAL ALGEBRA (NMAG405)
Lecture: Thr 15:40 - 17:10 K5
Practicals run by Filippo Spaggiari: Thr 17:20 - 18:50 K5
Grading:
- Practicals ("Z: Zapocet"): homeworks (60% from the sum of 4 best scores out of 5 homeworks)
- Lecture ("Zk: Zkouska"): written test + possible oral examination
Literature:
| topics (future topics may change) | recommended reading | lecture notes | homework |
29.9. | Motivation. Algebra (signature, type). Examples.
Pr.: Lattices vs. lattice ordered sets |
Bergman 1.1, 1.2 |
lecture 1
practicals 1 |
|
6.10. | Lattices, complete lattices, closure operators.
Pr.: Distributive and modular lattices. The lattice of equivalence relations.
|
Bergman 2.1, 2.2, 2.3 | lecture 2
practicals 2 | |
13.10. | Algebraic lattices and closure operators. Galois correspondences.
Pr.: Complete lattices, closure operators, Galois correspondences. |
Bergman 2.4, 2.5 | lecture 3 practicals 3 |
Homework 1 due 27.10. 17:20 |
20.10. | Subalgebras, products, quotients.
Pr.: Subalgebras, congruences. |
Bergman 1.3, 1.4, 1.5 |
lecture 4 practicals 4 corrected (lower quality) |
|
27.10. | 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 practicals 5 |
Homework 2 due 10.11. 17:20 |
3.11. | Direct and subdirect decomposition
Pr.: Direct and subdirect decomposition. |
Bergman 3.2, 3.3 | lecture 6 practicals 6 | |
10.11. | Subdirect decomoposition, SIs in congruence distributive vaieties
Pr.: SIs in monounary algebras. |
Bergman 3.4, 3.5, (5.2) | lecture 7 practicals 7 | Homework 3 due 24.11. 17:20 |
17.11. | ---
--- |
| | |
24.11. | Terms, identities, free algebras.
Pr.: Free algebras. |
Bergman 4.3, 4.4 | lecture 8 practicals 8 | |
1.12. | The syntax-semantics Galois correspondence, Birkhoff's theorem.
Pr.: Equational bases. |
Bergman 4.4, (4.6) | lecture 9 practicals 9 | Homework 4 due 15.12. 17:20 |
8.12. | Clones. Free algebras as clones of term operations.
Pr.: Clones. |
Bergman 4.1 | lecture 10 practicals 10 | |
15.12. | The operations-relations Galois correspondence.
Pr.: Algebraic and relational clones. |
Bergman 4.2 | lecture 11 practicals 11 | Homework 5 due 5.1. 17:20 |
22.12. | Mal'cev conditions: Mal'cev, majority.
Pr.: Mal'cev conditions |
Bergman 4.7 (part) | lecture 12 practicals 12 | |
5.1. | Tame Congruence Theory
Pr.: Tame Congruence Theory |
| practicals 13 | |
 
 
INTRODUCTION TO COMPLEXITY OF CSP (NMAG563)
Fri 10:40 K12
Problems
References (contain a lot of spoilers):
- survey (Barto, Krokhin, Willard): here
- shorter survey (Barto): here (see the complexity column)
- 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
 
 
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