MA009 Algebra II

Faculty of Informatics
Spring 2024
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
there are 20 fields of study the course is directly associated with, display
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.
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.

MA009 Algebra II

Faculty of Informatics
Spring 2022
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
Wed 16. 2. to Wed 18. 5. Wed 12:00–13:50 B204
  • Timetable of Seminar Groups:
MA009/01: Wed 16. 2. to Wed 18. 5. Wed 14:00–15:50 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
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.
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 2024.

MA009 Algebra II

Faculty of Informatics
Spring 2020
Extent and Intensity
2/2. 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: Faculty of Science
Timetable
Mon 17. 2. to Fri 15. 5. Mon 12:00–13:50 B204
  • Timetable of Seminar Groups:
MA009/01: Mon 17. 2. to Fri 15. 5. Mon 14:00–15:50 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.
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.
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 2022, Spring 2024.

MA009 Algebra II

Faculty of Informatics
Spring 2019
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 12:00–13:50 B204
  • Timetable of Seminar Groups:
MA009/01: Wed 14:00–15:50 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.
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.
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 2020, Spring 2022, Spring 2024.

MA009 Algebra II

Faculty of Informatics
Spring 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:
MA009/01: Fri 10:00–11:50 A320, 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.
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.
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 2019, Spring 2020, Spring 2022, Spring 2024.

MA009 Algebra II

Faculty of Informatics
Spring 2017
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
Mon 14:00–15:50 A320
  • Timetable of Seminar Groups:
MA009/01: Mon 16:00–17:50 A320, 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 2016, Spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2024.

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.

MA009 Algebra II

Faculty of Informatics
Spring 2015
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 14:00–15:50 B411
Prerequisites
( MB008 Algebra I || MV008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))
Prerequisites: MV008 Algebra I.
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 19 fields of study the course is directly associated with, display
Course objectives
At the end of the course students should be able to work with ordered sets and abstract algebraic structures including applications. They will gain a serious formal basis for all areas of theoretical computer science.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and quotient algebras, products, terms, varieties, free algebras, Birkhoff's theorem, rewriting).
Literature
  • 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
Once a week a standard lecture with a stress on motivation and examples.
Assessment methods
A written exam has three parts: a completion of a text concerning (on advance) given theoretical issues, a completing a proof a new statement, and 3 tests problems where the students show the understanding the basics. It takes two hours. One half of possible points is needed for a success.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
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 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2024.

MA009 Algebra II

Faculty of Informatics
Spring 2014
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 14:00–15:50 B410
Prerequisites
( MB008 Algebra I || MV008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))
Prerequisites: MV008 Algebra I.
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 19 fields of study the course is directly associated with, display
Course objectives
At the end of the course students should be able to work with ordered sets and abstract algebraic structures including applications. They will gain a serious formal basis for all areas of theoretical computer science.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and quotient algebras, products, terms, varieties, free algebras, Birkhoff's theorem, rewriting).
Literature
  • 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
Once a week a standard lecture with a stress on motivation and examples.
Assessment methods
A written exam has three parts: a completion of a text concerning (on advance) given theoretical issues, a completing a proof a new statement, and 3 tests problems where the students show the understanding the basics. It takes two hours. One half of possible points is needed for a success.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
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 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2024.

MA009 Algebra II

Faculty of Informatics
Spring 2013
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Michal Kunc, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 14:00–15:50 B410
Prerequisites
( MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))
Prerequisites: MB008 Algebra I.
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 19 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and quotient algebras, products, terms, varieties, free algebras, Birkhoff's theorem, rewriting).
Literature
  • 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
Once a week a standard lecture with a stress on motivation and examples.
Assessment methods
A written exam has three parts: a completion of a text concerning (on advance) given theoretical issues, a completing a proof a new statement, and 3 tests problems where the students show the understanding the basics.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
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 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2024.

MA009 Algebra II

Faculty of Informatics
Spring 2012
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Fri 14:00–15:50 B410
Prerequisites
( MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))
Prerequisites: MB008 Algebra I.
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 19 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and quotient algebras, products, terms, varieties, free algebras, Birkhoff's theorem, rewriting).
Literature
  • 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
Once a week a standard lecture with a stress on motivation and examples.
Assessment methods
A written exam has three parts: a completion of a text concerning (on advance) given theoretical issues, a completing a proof a new statement, and 3 tests problems where the students show the understanding the basics.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
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 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2024.

MA009 Algebra II

Faculty of Informatics
Spring 2011
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Faculty of Informatics
Timetable
Tue 14:00–15:50 B204
Prerequisites
( MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))
Prerequisites: MB008 Algebra I.
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 19 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and quotient algebras, products, terms, varieties, free algebras, Birkhoff's theorem, rewriting).
Literature
  • 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
Once a week a standard lecture with a stress on motivation and examples.
Assessment methods
A written exam has three parts: a completion of a text concerning (on advance) given theoretical issues, a completing a proof a new statement, and 3 tests problems where the students show the understanding the basics.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
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 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2024.

MA009 Algebra II

Faculty of Informatics
Spring 2010
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 B003
Prerequisites
( MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))
Prerequisites: MB008 Algebra I.
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 22 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and quotient algebras, products, terms, varieties, free algebras, Birkhoff's theorem, rewriting).
Literature
  • 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
Once a week a standard lecture with a stress on motivation and examples.
Assessment methods
A written exam has three parts: a completion of a text concerning (on advance) given theoretical issues, a completing a proof a new statement, and 3 tests problems where the students show the understanding the basics.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2024.

MA009 Algebra II

Faculty of Informatics
Spring 2009
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor), Mgr. David Kruml, Ph.D. (deputy)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 B011
Prerequisites
( MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))
Prerequisites: MB008 Algebra I.
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 16 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • 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
Assessment methods
Written exam.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, 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.

MA009 Algebra II

Faculty of Informatics
Spring 2008
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 13:00–14:50 B003
Prerequisites
( MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))
Prerequisites: MB008 Algebra I.
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 19 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • 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
Assessment methods (in Czech)
Zkouška je písemná.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, 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.

MA009 Algebra II

Faculty of Informatics
Spring 2007
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 12:00–13:50 B003
Prerequisites
( M008 Algebra I || MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))&&! M009 Algebra II
Prerequisites: MB008 Algebra I.
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 6 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • 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
Assessment methods (in Czech)
Zkouška je písemná.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2005, Spring 2006, 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.

MA009 Algebra II

Faculty of Informatics
Spring 2006
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 B011
Prerequisites
( M008 Algebra I || MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))&&! M009 Algebra II
Prerequisites: MB008 Algebra I.
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 6 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • 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
Assessment methods (in Czech)
Zkouška je písemná.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2005, 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.

MA009 Algebra II

Faculty of Informatics
Spring 2005
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
Timetable
Fri 11:00–12:50 B011
Prerequisites
( M008 Algebra I || MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))&&! M009 Algebra II
Prerequisites: MB008 Algebra I.
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 6 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • 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
Assessment methods (in Czech)
Zkouška je písemná; důraz je kladen na pochopení problematiky.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
The course is also listed under the following terms Spring 2003, Spring 2004, 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.

MA009 Algebra II

Faculty of Informatics
Spring 2004
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
Timetable
Fri 13:00–14:50 B204
Prerequisites
( M008 Algebra I || MB008 Algebra I ||PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS))&&! M009 Algebra II
Prerequisites: MB008 Algebra I.
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 6 fields of study the course is directly associated with, display
Course objectives
This course is a continuation of Algebra I. We focus on fields, lattice theory and universal algebra with applications in computer science.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • 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
Assessment methods (in Czech)
Zkouška je písemná.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/algebra-II.html
The course is also listed under the following terms Spring 2003, 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.

MA009 Algebra II

Faculty of Informatics
Spring 2003
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Faculty of Informatics
Contact Person: prof. RNDr. Radan Kučera, DSc.
Timetable
Fri 11:00–12:50 D2
Prerequisites
( M008 Algebra I || MB008 Algebra I )&&! M009 Algebra II
Prerequisites: M005 Foundations of mathematics and M008 Algebra I.
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 7 fields of study the course is directly associated with, display
Course objectives (in Czech)
Jedná se o pokračování kurzu Algebra I. Pozornost je věnována polynomům, teorii svazů a teorii univerzálních algeber.
Syllabus
  • Rings and polynomials II (extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • 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
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms 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.

MA009 Algebra II

Faculty of Informatics
Spring 2025

The course is not taught in Spring 2025

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. RNDr. Martin Čadek, CSc.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
PROGRAM(N-IN)||PROGRAM(N-AP)||PROGRAM(N-SS)
Course Enrolment Limitations
The course is offered to students of any study field.
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)
The course is taught once in two years.
The course is taught: every week.
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.

MA009 Algebra II

Faculty of Informatics
Spring 2023

The course is not taught in Spring 2023

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
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
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.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
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.

MA009 Algebra II

Faculty of Informatics
Spring 2021

The course is not taught in Spring 2021

Extent and Intensity
2/2. 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: Faculty of Science
Timetable of Seminar Groups
MA009/01: No timetable has been entered into IS. 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.
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 using videos for offline study. Exercises (online): 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 (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)