MA009 Algebra II

Faculty of Informatics
Spring 2016
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. Mgr. Michal Kunc, Ph.D. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Wed 14:00–15:50 B204
  • Timetable of Seminar Groups:
MA009/01: Wed 16:00–17:50 B204, M. Kunc
Prerequisites (in Czech)
( MB008 Algebra I || MV008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))
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
there are 20 fields of study the course is directly associated with, display
Course objectives
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.
Syllabus
  • 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.
Literature
  • BURRIS, Stanley N. 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
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim of understanding basic concepts and theorems.
Assessment methods
Examination written (pass mark 50%) and oral.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
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 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2024.
  • Enrolment Statistics (Spring 2016, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2016/MA009