Date  Topics  Lecture notes  Exercises  Homework 

24/02  Equational theories, fully invariant congruences; completeness theorem for equational logic.  Section 1.1  1.11.3  
02/03  Convergent term rewriting systems  Section 1.2  
09/03  Critical pairs, KnuthBendix 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  2.12.9; 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  2.152.20; 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 nonfinitely based algebra  Chapter 3  3.13.4  
27/04  McKenzies DPC theorem  Section 3.1  3.53.8  
04/05  CSPs, ppdefinable relations PolInv  Section 4.1  4.14.5  3.5,3.6,4.3 due on 19/05 
11/05  Clone and minion homomorphisms  Section 4.2  4.64.8  
18/05  Taylor operations the CSP dichotomy conjecture/theorem  Section 4.3  4.94.11  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 KnuthBendix algorithm  Jezek 13  Ex. 3  
04/04  Examples of finitely based and non finitely based algebras  Bergman 5.4  HW 2 due 25/04 

11/04  McKenzie's result on definable principal congruences  Bergman 5.5  Ex. 4  
18/04  Constraint satisfaction problems over finite templates PolInv 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 