Date | Topics | Lecture notes | Exercises | Homework |
---|---|---|---|---|
24/02 | Equational theories, fully invariant congruences; completeness theorem for equational logic. | Section 1.1 | 1.1-1.3 | |
02/03 | Convergent term rewriting systems | Section 1.2 | ||
09/03 | Critical pairs, Knuth-Bendix algorithm; Affine algebras | Section 1.2, 1.3 Section 2.1 | 1.4, 1.8,1.9 | 1.5,1.6,1.7 due on 24/03 |
16/03 | Abelian algebras Herrmann's fundamental theorem | Section 2.1, 2.2 | 2.1-2.9; in particular 2.2, 2.6 | |
23/03 | Centralizer relation and commutator Example: groups | Section 2.3 | 2.11, 2.12 | 2.10, 2.13, 2.14 due on 07/04 |
30/03 | Properties of the commutator Characterization of CD varieties | Section 2.3, 2.4 | 2.15-2.20; in particular 2.18,2.19 | |
06/04 | Nilpotent algebras and open questions | Section 2.5 | Section 2.5 | |
20/04 | Birkhoff's theorem on Id_n(A) Example of a non-finitely based algebra | Chapter 3 | 3.1-3.4 | |
27/04 | McKenzies DPC theorem | Section 3.1 | 3.5-3.8 | |
04/05 | CSPs, pp-definable relations Pol-Inv | Section 4.1 | 4.1-4.5 | 3.5,3.6,4.3 due on 19/05 |
11/05 | Clone and minion homomorphisms | Section 4.2 | 4.6-4.8 | |
18/05 | Taylor operations the CSP dichotomy conjecture/theorem | Section 4.3 | 4.9-4.11 | 4.6,4.7,4.8 until your exam |
Date | Topics | Recommended reading | Exercises | Homework |
---|---|---|---|---|
28/02 | Abelian and affine algebras, Fundamental theorem. | Bergman 7.3 | Ex. 1 | |
07/03 | Checking identities, Relational description of Abelianness; Centralizer relation (in general and in groups) | Bergman 7.4 | ||
14/03 | Properties of the commutator Characterization of CD varieties | Bergman 7.4 | Ex. 2 | HW 1 due 28/03 |
21/03 | Equational theories, fully invariant congruences; completeness theorem for equational logic. | Bergman 4.6 Jezek 13 | ||
28/03 | Reduction order, critical pairs Knuth-Bendix algorithm | Jezek 13 | Ex. 3 | |
04/04 | Examples of finitely based and non finitely based algebras | Bergman 5.4 | HW 2 due 25/04 |
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11/04 | McKenzie's result on definable principal congruences | Bergman 5.5 | Ex. 4 | |
18/04 | Constraint satisfaction problems over finite templates Pol-Inv revisited | BKW | ||
25/04 | (h1-)clone homomorphisms Taylor terms | BKW | Ex. 5 | HW 3 due 09/05 |
02/05 | Taylor's theorem | Bergman 8.4. | ||
09/05 | Smooth digraphs, algebraic length 1,absorption | BK | ||
16/05 | Absorption, transitive terms | BK | Ex. 6 | HW 4 |
23/05 | Absorption theorem, LLL (loop lemma 'light', for linked digraphs) | BK |