**Lattice Theory for Parallel Programming**
*Course diary 2024 for the lattice theory part*
# Ressources
The course material for the lattice theory part is available in this [shared folder](https://uniluxembourg-my.sharepoint.com/:f:/g/personal/bruno_teheux_uni_lu/EtN22uWEUjRNkC0JlL6ftB4Bfs_HOX17ewSzYFkUaxk14A?e=1flrfv).
The following introductory textbook can be consulted for further reference. An electronic version is available for free via [a-z.lu](https://www.a-z.lu).
[#1]: B. Davey and H.A. Priestley. *Introduction to lattice and order*. Second edition. Cambridge University Press, 2002.
# Week 1: Sepember 20, 2024
**Topics covered:** Order and poset. Constructions of partial orders. Mappings between orders. Special subsets in posets.
# Week 2: September 27, 2024.
**Topics covered:** Bounds, lattices, complete lattices: definitions and examples. Lattices as algebras: definition and correspondence with lattices as posets.
# Week 3: October 11, 2024.
**Topics Covered:** Maps between lattices: (bounded) homomorphisms, isomorphisms and link with monotone map. Sublattices. Homomorphic images. Class operators $\mathbb{H}$, $\mathbb{S}$ $\mathbb{P}$, terms, equations, equational classes and the $\mathbb{HSP}$ theorem.