FI:MA009 Algebra II - Course Information

MA009 Algebra II

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).

Teacher(s)

doc. Mgr. Michal Kunc, Ph.D. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (assistant)

Guaranteed by

doc. RNDr. Martin Čadek, CSc.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science

Timetable

Thu 12:00–13:50 B204

• Timetable of Seminar Groups:

MA009/01: Thu 14:00–15:50 B204, M. Kunc

Prerequisites (in Czech)

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

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.

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, colloquium only oral.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught once in two years.

• Enrolment Statistics (recent)
  
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