Lattice Theory

Lattices, and related ordered structures, are one of the more unifying concepts in mathematics. They play central roles in logic, algebra, analysis, topology, geometry, combinatorics, computer science, and category theory. The aim of this course is to give the student the basic concepts and tools of lattice theory, a feeling of the scope of the subject, as well as looks at some of the paths that tie the subject to language, logic, and information. Topics will include the basics of posets and lattices; distributive lattices, Boolean algebras, and Heyting algebras, algebraic treatments via varieties and universal algebra, Stone duality, modular and algebraic lattices, and completions.