MA009 Algebra II

Faculty of Informatics
Spring 2026
Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
In-person direct teaching
Teacher(s)
doc. Mgr. Michal Kunc, Ph.D. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (assistant)
Guaranteed by
doc. Mgr. Michal Kunc, Ph.D.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 16. 2. to Mon 11. 5. Mon 10:00–11:50 A220
  • Timetable of Seminar Groups:
MA009/01: Wed 18. 2. to Wed 13. 5. Wed 10:00–11:50 B204, M. Kunc
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Abstract
The aim of the course is to become acquainted with basic notions of universal algebra employed in computer science, namely lattice-ordered sets and equational logic.
Learning outcomes
After passing the course, students will be able to: use the basic notions of the theory of lattices and universal algebra; define and understand basic properties of lattices and complete lattices; verify simple algebraic statements; apply theoretical results to algorithmic calculations with operations and terms.
Key topics
  • Lattice theory: semilattices, lattices, lattice homomorphisms, modular and distributive lattices, Boolean algebras, complete lattices, fixed point theorems, closure operators, completion of partially ordered sets, Galois connections, algebraic lattices.
  • Universal algebra: algebras, subalgebras, homomorphisms, term algebras, congruences, quotient algebras, direct products, subdirect products, identities, varieties, free algebras, presentations, Birkhoff's theorem, completeness theorem for equational logic, algebraic specifications, rewriting systems.
Study resources and literature
  • BURRIS, Stanley and H. P. SANKAPPANAVAR. A course in universal algebra. New York: Springer-Verlag, 1981, 276 s. ISBN 0387905782. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
Approaches, practices, and methods used in teaching
Lectures: theoretical explanation. Exercises: solving problems with the aim of understanding basic concepts and theorems.
Method of verifying learning outcomes and course completion requirements
Examination written (pass mark 50%) and oral, colloquium only oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/spring2026/MA009