FI:MA009 Algebra II - Course Information
MA009 Algebra II
Faculty of InformaticsSpring 2018
- 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
- Fri 8:00–9:50 A320
- Timetable of Seminar Groups:
- 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
- Applied Informatics (programme FI, N-AP)
- Information Technology Security (eng.) (programme FI, N-IN)
- Information Technology Security (programme FI, N-IN)
- Bioinformatics (programme FI, N-AP)
- Information Systems (programme FI, N-IN)
- Mathematical Informatics (programme FI, B-IN)
- Parallel and Distributed Systems (programme FI, N-IN)
- Computer Graphics (programme FI, N-IN)
- Computer Networks and Communication (programme FI, N-IN)
- Computer Systems (programme FI, N-IN)
- Embedded Systems (eng.) (programme FI, N-IN)
- Embedded Systems (programme FI, N-IN)
- Service Science, Management and Engineering (eng.) (programme FI, N-AP)
- Service Science, Management and Engineering (programme FI, N-AP)
- Social Informatics (programme FI, B-AP)
- Theoretical Informatics (programme FI, N-IN)
- Upper Secondary School Teacher Training in Informatics (programme FI, N-SS) (2)
- Artificial Intelligence and Natural Language Processing (programme FI, N-IN)
- Image Processing (programme FI, N-AP)
- 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.
- 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.
- 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.
- Enrolment Statistics (Spring 2018, recent)
- Permalink: https://is.muni.cz/course/fi/spring2018/MA009