Libor Barto

HOME COCOSYM RESEARCH FOR STUDENTS

 

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 4 best scores out of 5 homeworks)
  • Lecture ("Zk: Zkouska"): written test + possible oral examination

Literature:

topics (future topics may change)recommended readinglecture 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
13.10. Algebraic lattices and closure operators. Galois correspondences.
Pr.: Complete lattices, closure operators, Galois correspondences.
Bergman 2.4, 2.5 lecture 3 Homework 1
due ?
20.10. Subalgebras, products, quotients.
Pr.: Subalgebras, congruences.
Bergman 1.3, 1.4, 1.5 lecture 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 Homework 2
due ?
3.11. Direct and subdirect decomposition
Pr.: Direct and subdirect decomposition.
Bergman 3.2, 3.3 lecture 6
10.11. Subdirect decomoposition, SIs in congruence distributive vaieties
Pr.: SIs in monounary algebras.
Bergman 3.4, 3.5, (5.2) lecture 7 Homework 3
due ?
17.11. ---
---
24.11. Terms, identities, free algebras.
Pr.: Free algebras.
Bergman 4.3, 4.4 lecture 8
1.12. The syntax-semantics Galois correspondence, Birkhoff's theorem.
Pr.: Equational bases.
Bergman 4.4, (4.6) lecture 9 Homework 4
due ?
8.12. Clones. Free algebras as clones of term operations.
Pr.: Clones.
Bergman 4.1 lecture 10
15.12. The operations-relations Galois correspondence.
Pr.: Algebraic and relational clones.
Bergman 4.2 lecture 11 Homework 5
due ?
22.12. Mal'cev conditions: Mal'cev, majority.
Mal'cev conditions
Bergman 4.7 (part) lecture 12
5.1. ???
???

 

 

INTRODUCTION TO COMPLEXITY OF CSP (NMAG563)

TBD

 

 

ARCHIV

[Archiv 2021/22 letni semestr]
[Archiv 2021/22 zimni semestr]
[Archiv 2020/21 letni semestr]
[Archiv 2020/21 zimni semestr]
[Archiv 2019/20 zimni semestr]
[Archiv 2018/19 letni semestr]
[Archiv 2018/19 zimni semestr]
[Archiv 2017/18 letni semestr]
[Archiv 2017/18 zimni semestr]
[Archiv 2016/17 letni semestr]
[Archiv 2016/17 zimni semestr]
[Archiv 2015/16 letni semestr]
[Archiv 2015/16 zimni semestr]
[Archiv 2014/15 letni semestr]
[Archiv 2014/15 zimni semestr]
[Archiv 2013/14 letni semestr]
[Archiv 2013/14 zimni semestr]
[Archiv 2012/13 letni semestr]
[Archiv 2012/13 zimni semestr]
[Archiv McMaster]
[Archiv 2009/10 letni semestr]
[Archiv 2009/10 zimni semestr]
[Archiv 2008/09 letni semestr]
[Archiv 2008/09 zimni semestr]
[Archiv 2007/08 letni semestr]
[Archiv 2007/08 zimni semestr]
[Archiv 2006/07 letni semestr]
[Archiv 2006/07 zimni semestr]
[Archiv 2005/06 letni semestr]