Topics in Algebra

(3 Credit Hours) · Undergraduate

This course will provide an introduction to partially ordered sets ("posets") and lattices, which are mathematical notions based on the idea of an "ordering" of a collection of objects, and which have both broad relevance in mathematics and many applications to other fields including computer science, social science, sports and games, philosophy and logic. The first part of the course will discuss basic properties, examples and special types of posets and lattices, their special elements and subsets, their visualization by Hasse diagrams, constructions involving them, and special types of functions between them. The second part of the course will treat a variety of special topics from amongst formal concept analysis, Galois connections, representations of lattices, congruences and quotient lattices, and fixed point theory. The course will use the text "Introduction to lattices and order" by Davey and Priestly. Formal prerequisites for the course are Math 20630 (Introduction to mathematical reasoning) or 10850 (Honors Calculus I) or consent of the instructor. Students, especially non-math majors, who are potentially interested in the course but who lack its formal prerequisites are encouraged to contact the instructor to determine if taking it would be reasonable in their case.