M3150 Algebra II

Faculty of Science
Autumn 2024
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M2150 Algebra I || MUC32 Algebra
Zvládnutí základů matematiky a kurzu 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
Course objectives
The aim of this course is to give students the necessary algebraic background, which is assumed in some advanced courses.
Learning outcomes
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, field theory, and lattice theory;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Groups (normal subgroups, quotient groups, group actions, center of a group and inner automorphisms, Sylow's theorems).
  • Rings and polynomials (ideals, quotient rings, fields, localization, field of quotients, field extensions, finite fields, rudiments of Galois theory).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.

M3150 Algebra II

Faculty of Science
Autumn 2023
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 M2,01021
  • Timetable of Seminar Groups:
M3150/01: Thu 8:00–9:50 M4,01024, P. Francírek
Prerequisites (in Czech)
M2150 Algebra I || MUC32 Algebra
Zvládnutí základů matematiky a kurzu 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
Course objectives
The aim of this course is to give students the necessary algebraic background, which is assumed in some advanced courses.
Learning outcomes
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, field theory, and lattice theory;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Groups (normal subgroups, quotient groups, group actions, center of a group and inner automorphisms, Sylow's theorems).
  • Rings and polynomials (ideals, quotient rings, fields, localization, field of quotients, field extensions, finite fields, rudiments of Galois theory).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2022
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M3150/01: Wed 16:00–17:50 M2,01021, P. Francírek
Prerequisites (in Czech)
M2150 Algebra I || MUC32 Algebra
Zvládnutí základů matematiky a kurzu 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
Course objectives
The aim of this course is to give students the necessary algebraic background, which is assumed in some advanced courses.
Learning outcomes
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, field theory, and lattice theory;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Groups (normal subgroups, quotient groups, group actions, center of a group and inner automorphisms, Sylow's theorems).
  • Rings and polynomials (ideals, quotient rings, fields, localization, field of quotients, field extensions, finite fields, rudiments of Galois theory).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
autumn 2021
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M3150/01: Wed 10:00–11:50 M4,01024, P. Francírek
Prerequisites (in Czech)
M2150 Algebra I || MUC32 Algebra
Zvládnutí základů matematiky a kurzu 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
Course objectives
The aim of this course is to give students the necessary algebraic background, which is assumed in some advanced courses.
Learning outcomes
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, field theory, and lattice theory;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Groups (normal subgroups, quotient groups, group actions, center of a group and inner automorphisms, Sylow's theorems).
  • Rings and polynomials (ideals, quotient rings, fields, localization, field of quotients, field extensions, finite fields, rudiments of Galois theory).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2020
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught partially online.
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M2,01021
  • Timetable of Seminar Groups:
M3150/01: Mon 18:00–19:50 M6,01011, P. Francírek
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The aim of this course is to give students the necessary algebraic background, which is assumed in some advanced courses.
Learning outcomes
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, field theory, and lattice theory;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Groups (normal subgroups, quotient groups, group actions, center of a group and inner automorphisms, Sylow's theorems).
  • Rings and polynomials (ideals, quotient rings, fields, field of quotients, field extensions, finite fields, rudiments of Galois theory).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. 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 to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2019
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M3150/01: Thu 14:00–15:50 M4,01024, P. Francírek
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The aim of this course is to give students the necessary algebraic background, which is assumed in some advanced courses.
Learning outcomes
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, field theory, lattice theory, and universal algebra;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Rings and polynomials (ideals, factorrings, fields, field of quotients, extensions, finite fields, symmetric polynomials).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2018
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 17. 9. to Fri 14. 12. Wed 10:00–11:50 M6,01011
  • Timetable of Seminar Groups:
M3150/01: Mon 17. 9. to Fri 14. 12. Thu 8:00–9:50 M6,01011, R. Kučera
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The aim is to finish the basic two-semester course of algebra.
Learning outcomes
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, lattice theory, and universal algebra;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Rings and polynomials (ideals, factorrings, fields, field of quotients, extensions, finite fields, symmetric polynomials).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
autumn 2017
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 9. to Fri 15. 12. Thu 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M3150/01: Mon 18. 9. to Fri 15. 12. Thu 12:00–13:50 M1,01017, P. Francírek
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, lattice theory, and universal algebra;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Rings and polynomials (ideals, factorrings, fields, field of quotients, extensions, finite fields, symmetric polynomials).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2016
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 9. to Sun 18. 12. Wed 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M3150/01: Mon 19. 9. to Sun 18. 12. Thu 16:00–17:50 M5,01013, R. Kučera
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, lattice theory, and universal algebra;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, field of quotients, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2015
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M3150/01: Fri 8:00–9:50 M6,01011, R. Kučera
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, lattice theory, and universal algebra;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, field of quotients, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2014
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Bc. Jaromír Kuben (assistant)
doc. Mgr. Ondřej Klíma, Ph.D. (alternate examiner)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M3150/01: Thu 8:00–9:50 M6,01011, R. Kučera
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu Algebra I.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, lattice theory, and universal algebra;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, field of quotients, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2013
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
doc. Mgr. Michal Kunc, Ph.D. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (assistant)
Mgr. Bc. Jaromír Kuben (assistant)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M5,01013
  • Timetable of Seminar Groups:
M3150/01: Fri 10:00–11:50 M5,01013, R. Kučera
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu Algebra I.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, lattice theory, and universal algebra;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, field of quotients, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
Assessment methods
Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2012
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M2,01021
  • Timetable of Seminar Groups:
M3150/01: Thu 16:00–17:50 M5,01013, R. Kučera
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
* understand rudiments of group theory, ring theory and lattice theory;
* understand rudiments of universal algebra;
* explain basic notions and relations among them.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homeworks.
Assessment methods
Examination consists of two parts: written test and oral examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2011
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 8:00–9:50 M5,01013
  • Timetable of Seminar Groups:
M3150/01: Wed 14:00–15:50 M6,01011, L. Vokřínek
M3150/02: Tue 10:00–11:50 M6,01011, R. Kučera
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
* understand rudiments of group theory, ring theory and lattice theory;
* understand rudiments of universal algebra;
* explain basic notions and relations among them.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homeworks.
Assessment methods
Examination consists of two parts: written test and oral examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2010
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
prof. RNDr. Radan Kučera, DSc. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 M2,01021
  • Timetable of Seminar Groups:
M3150/01: Tue 16:00–17:50 M5,01013
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
* understand rudiments of group theory, ring theory and lattice theory;
* understand rudiments of universal algebra;
* explain basic notions and relations among them.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homeworks.
Assessment methods
Examination consists of two parts: written test and oral examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2009
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Jan Herman (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 M2,01021
  • Timetable of Seminar Groups:
M3150/01: Wed 16:00–17:50 M3,01023, J. Herman
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
* understand rudiments of group theory, ring theory and lattice theory;
* understand rudiments of universal algebra;
* explain basic notions and relations among them.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homeworks.
Assessment methods
Examination consists of two parts: written test and oral examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2008
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Jan Herman (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 M1,01017
  • Timetable of Seminar Groups:
M3150/01: Mon 18:00–19:50 M5,01013, J. Herman
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
understand rudiments of group theory, ring theory and lattice theory;
understand rudiments of universal algebra;
explain basic notions and relations among them.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Assessment methods
Lecture with a seminar. Examination consists of two parts: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2007
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Jan Herman (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 12:00–13:50 N41
  • Timetable of Seminar Groups:
M3150/01: Thu 14:00–15:50 U1, J. Herman
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The second term of algebra being a continuation of Algebra I. The knowledge about fields is deepened, lattices and basics of universal algebra are studied.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials). Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras). Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Assessment methods (in Czech)
Standardní přednáška se cvičením. Zkouška písemná i ústní.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2006
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Jan Herman (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc.
Timetable
Thu 8:00–9:50 N41
  • Timetable of Seminar Groups:
M3150/01: Thu 18:00–19:50 N21, J. Herman
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The second term of algebra being a continuation of Algebra I. The knowledge about fields is deepened, lattices and basics of universal algebra are studied.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials). Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices, representation of finite distributive and Boolean lattices). Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Assessment methods (in Czech)
Standardní přednáška se cvičením. Zkouška písemná i ústní.
Language of instruction
Czech
Further Comments
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2005
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc.
Timetable
Mon 8:00–9:50 N21
  • Timetable of Seminar Groups:
M3150/01: Mon 14:00–15:50 UM, O. Klíma
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The second term of algebra being a continuation of Algebra I. The knowledge about fields is deepened, lattices and basics of universal algebra are studied.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials). Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices, representation of finite distributive and Boolean lattices). Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994, 140 s. ISBN 802100990X. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Assessment methods (in Czech)
Standardní přednáška se cvičením. Zkouška písemná i ústní.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2004
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc.
Timetable
Mon 10:00–11:50 N21
  • Timetable of Seminar Groups:
M3150/01: Mon 15:00–16:50 UP1, M. Kunc
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The second term of algebra being a continuation of Algebra I. The knowledge about fields is deepened, lattices and basics of universal algebra are studied. Numerous applications in informatics are presented.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials). Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices, representation of finite distributive and Boolean lattices). Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, subdirect products and corresponding decomposition, terms, varieties, free algebras, Birkhoff's theorem, word problems, heterogeneous algebras and coalgebras, applications in theoretical informatcs).
Literature
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994, 140 s. ISBN 802100990X. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Assessment methods (in Czech)
Standardní přednáška se cvičením. Písemná zkouška.
Language of instruction
Czech
Further Comments
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~polak
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2003
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Jan Pavlík, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc.
Timetable of Seminar Groups
M3150/01: No timetable has been entered into IS. J. Pavlík
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The second term of algebra being a continuation of Algebra I. The knowledge about fields is deepened, lattices and basics of universal algebra are studied. Numerous applications in informatics are presented.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials). Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices, representation of finite distributive and Boolean lattices). Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, subdirect products and corresponding decomposition, terms, varieties, free algebras, Birkhoff's theorem, word problems, heterogeneous algebras and coalgebras, applications in theoretical informatcs).
Literature
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994, 140 s. ISBN 802100990X. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Assessment methods (in Czech)
Standardní přednáška se cvičením. Písemná zkouška.
Language of instruction
Czech
Further Comments
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~polak
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Spring 2003
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). 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
Contact Person: doc. RNDr. Libor Polák, CSc.
Timetable of Seminar Groups
M3150/01: No timetable has been entered into IS. L. Polák
M3150/02: No timetable has been entered into IS. O. Klíma
M3150/03: No timetable has been entered into IS. O. Klíma
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The second term of algebra being a continuation of Algebra I. The knowledge about fields is deepened, lattices and basics of universal algebra are studied. Numerous applications in informatics are presented.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials). Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices, representation of finite distributive and Boolean lattices). Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, subdirect products and corresponding decomposition, terms, varieties, free algebras, Birkhoff's theorem, word problems, heterogeneous algebras and coalgebras, applications in theoretical informatcs).
Literature
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994, 140 s. ISBN 802100990X. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Assessment methods (in Czech)
Standardní přednáška se cvičením. Písemná zkouška.
Language of instruction
Czech
Further Comments
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~polak
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Mathematical Seminar

Faculty of Science
Autumn 1999
Extent and Intensity
0/2/0. 3 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Vítězslav Veselý, CSc. (lecturer)
Guaranteed by
doc. RNDr. Vítězslav Veselý, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Vítězslav Veselý, CSc.
Prerequisites (in Czech)
M2142 Computer Science II
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
Syllabus
  • System MATLAB: basic philosophy of MATLAB and the syntax of its programming language, basic operators and commands, writing procedures (script and function M-files), graphics (1D and 2D plots), commands related to some more advanced topics from matrix and polynomial algebra.
  • Solving practical exercises and problems with MATLAB.
  • Note: The seminar courses utilize the computer projection screen. Practical training is with MATLAB for UNIX.
  • See http://www.math.muni.cz/~vesely/educ/mssylle.ps for more details.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~vesely/educ_cz.html#mat_semin
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
prof. RNDr. Radan Kučera, DSc. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
* understand rudiments of group theory, ring theory and lattice theory;
* understand rudiments of universal algebra;
* explain basic notions and relations among them.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homeworks.
Assessment methods
Examination consists of two parts: written test and oral examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
prof. RNDr. Radan Kučera, DSc. (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
At the end of this course, students should be able to:
* understand rudiments of group theory, ring theory and lattice theory;
* understand rudiments of universal algebra;
* explain basic notions and relations among them.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homeworks.
Assessment methods
Examination consists of two parts: written test and oral examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.

M3150 Algebra II

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Jan Herman (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc.
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu 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
Course objectives
The second term of algebra being a continuation of Algebra I. The knowledge about fields is deepened, lattices and basics of universal algebra are studied.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials). Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras). Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Assessment methods (in Czech)
Standardní přednáška se cvičením. Zkouška písemná i ústní.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (recent)