Universal Algebra 1 - NMAG405

• Title: Universální algebra 1
• Guaranteed by: Department of Algebra (32-KA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2024
• Semester: winter
• E-Credits: 5
• Hours per week, examination: winter s.:2/2, C+Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English, Czech
• Teaching methods: full-time
• Additional information: https://www.karlin.mff.cuni.cz/~barto/students2223zima.html
• Guarantor: Dmitrii Zhuk, Ph.D.
• Teacher(s): Maximilian Hadek, B.Sc.; Dmitrii Zhuk, Ph.D.
• Class: M Mgr. MSTR; M Mgr. MSTR > Povinné
• Classification: Informatics > Theoretical Computer Science; Mathematics > Algebra
• Incompatibility : NALG103
• Interchangeability : NALG103
• Is interchangeable with: NALG103

Annotation

English

Basic course in universal algebra.

Last update: T_KA (09.05.2013)

Czech

Základní přednáška z univerzální algebry pro obor Matematické struktury.

Last update: T_KA (09.05.2013)

Course completion requirements

English

Practicals ("Z: Zapocet"): homeworks (60% from the sum of 4 best scores out of 5 homeworks)

Lecture ("Zk: Zkouska"): written test + oral examination

Last update: Hadek Maximilian, B.Sc. (02.10.2024)

Czech

Zápočet - řešení domácích úkolů.

Zkouška - písemný test.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.10.2019)

Literature

English

Clifford Bergman: Universal algebra: Fundamentals and selected topics. Chapman and Hall, 2011.

Stanley N. Burris, H. P. Sankappanavar: A course in universal algebra. Springer-Verlag, 1981.

Ralph McKenzie, George McNulty, Walter Taylor: Algebras, Lattices, Varieties, vol. 1. Wadsworth and Brooks/Cole, 1987.

Last update: Hadek Maximilian, B.Sc. (02.10.2024)

Czech

Clifford Bergman: Universal algebra: Fundamentals and selected topics. Chapman and Hall, 2011.

Stanley N. Burris, H. P. Sankappanavar: A course in universal algebra. Springer-Verlag, 1981.

Ralph McKenzie, George McNulty, Walter Taylor: Algebras, Lattices, Varieties, vol. 1. Wadsworth and Brooks/Cole, 1987.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (06.09.2013)

Requirements to the exam

English

Written test

Last update: Hadek Maximilian, B.Sc. (02.10.2024)

Czech

Zkouška je písemná a zahrnuje témata probraná na přednášce.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.10.2019)

Syllabus

English

Basic notions and constructions in nniversal algebra.

Lattices.

Isomorphism theorems.

Direct and subdirect decomposition.

Varieties and equational theories.

Algebraic and relation clones.

Malcev conditions.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (06.09.2013)

Czech

Základní pojmy a konstrukce v univerzální algebře.

Svazy.

Věty o izomorfismech.

Direktní a subdirektní rozklady.

Variety a rovnicové teorie.

Algebraické a relační klony.

Malcevské podmínky.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (06.09.2013)

Entry requirements

English

Basics of general algebra.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (17.05.2019)

Czech

Základy obecné algebry.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (17.05.2019)