M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2015
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Wed 10:00–11:50 M3,01023
  • Timetable of Seminar Groups:
M7500/01: Wed 12:00–12:50 M3,01023, M. Bulant
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2013
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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 13:00–14:50 MS2,01022
  • Timetable of Seminar Groups:
M7500/01: Thu 15:00–15:50 MS2,01022, M. Bulant
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to further study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions Algebraic and transcendental numbers The Fundamental Theorem of Algebra
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and solutions of homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2012
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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 of Seminar Groups
M7500/01: No timetable has been entered into IS. M. Bulant
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Construction of number domains (an axiomatic development of real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to introduce some topics of algebra and field theory into the secondary-school education
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions Algebraic and transcendental numbers The Fundamental Theorem of Algebra Complex numbers in elementary geometry. Combinatorial game theory. Groups and Rubik's cube.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and solutions of homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2009
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 16:00–17:50 MS1,01016
  • Timetable of Seminar Groups:
M7500/01: Wed 18:00–18:50 MS1,01016, M. Bulant
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to further study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions Algebraic and transcendental numbers The Fundamental Theorem of Algebra
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and solutions of homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2008
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 14:00–15:50 MP2,01014a
  • Timetable of Seminar Groups:
M7500/01: Thu 16:00–16:50 MP2,01014a, M. Bulant
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to further study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions Algebraic and transcendental numbers The Fundamental Theorem of Algebra
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Assessment methods
lectures, class discussion, homeworks. final written and oral exam
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2006
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
Timetable
Fri 13:00–14:50 N41
  • Timetable of Seminar Groups:
M7500/01: Fri 15:00–15:50 N41
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers).
Syllabus (in Czech)
  • Vytvořující rozklady na algebraických strukturách - faktorgrupoidy, faktorgrupy, faktorokruhy
  • Obory přirozených, celých a racionálních čísel
  • Reálná a komplexní čísla
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Assessment methods (in Czech)
Výuka bude probíhat formou pravidelných přednášek a cvičení. Docházka na cvičení (max. 2 neúčasti) je nutným předpokladem úspěšného absolvování zkoušky. Zkouška bude písemná a ústní a bude probíhat jednorázově na konci semestru (tj. bez dalších průběžných požadavků).
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2005
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
Timetable
Tue 8:00–9:50 UP2
  • Timetable of Seminar Groups:
M7500/01: Tue 10:00–10:50 UP2, M. Bulant
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers).
Syllabus (in Czech)
  • Vytvořující rozklady na algebraických strukturách - faktorgrupoidy, faktorgrupy, faktorokruhy
  • Obory přirozených, celých a racionálních čísel
  • Reálná a komplexní čísla
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Assessment methods (in Czech)
Výuka bude probíhat formou pravidelných přednášek a cvičení. Docházka na cvičení (max. 2 neúčasti) je nutným předpokladem úspěšného absolvování zkoušky. Zkouška bude písemná a ústní a bude probíhat jednorázově na konci semestru (tj. bez dalších průběžných požadavků).
Language of instruction
Czech
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2004
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
Timetable
Tue 12:00–13:50 UM
  • Timetable of Seminar Groups:
M7500/01: Tue 14:00–14:50 UM, M. Bulant
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers).
Syllabus (in Czech)
  • Vytvořující rozklady na algebraických strukturách - faktorgrupoidy, fakrotgrupy, faktorokruhy
  • Obory přirozených, celých a racionálních čísel
  • Reálná a komplexní čísla
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Assessment methods (in Czech)
Výuka bude probíhat formou pravidelných přednášek a cvičení. Docházka na cvičení (max. 2 neúčasti) je nutným předpokladem úspěšného absolvování zkoušky. Zkouška bude písemná a ústní a bude probíhat jednorázově na konci semestru (tj. bez dalších průběžných požadavků).
Language of instruction
Czech
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2003
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
Timetable of Seminar Groups
M7500/01: No timetable has been entered into IS. M. Bulant
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers).
Syllabus (in Czech)
  • Vytvořující rozklady na algebraických strukturách - faktorgrupoidy, fakrotgrupy, faktorokruhy
  • Obory přirozených, celých a racionálních čísel
  • Reálná a komplexní čísla
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Assessment methods (in Czech)
Výuka bude probíhat formou pravidelných přednášek a cvičení. Docházka na cvičení (max. 2 neúčasti) je nutným předpokladem úspěšného absolvování zkoušky. Zkouška bude písemná a ústní a bude probíhat jednorázově na konci semestru (tj. bez dalších průběžných požadavků).
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2002
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
Timetable of Seminar Groups
M7500/01: No timetable has been entered into IS. M. Bulant
M7500/02: No timetable has been entered into IS. M. Bulant
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers).
Assessment methods (in Czech)
Výuka bude probíhat formou pravidelných přednášek a cvičení. Docházka na cvičení (max. 2 neúčasti) je nutným předpokladem úspěšného absolvování zkoušky. Zkouška bude písemná a ústní a bude probíhat jednorázově na konci semestru (tj. bez dalších průběžných požadavků).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-III/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra V

Faculty of Science
Autumn 2001
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
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
Divisibility in $\Bbb Z$: primes, unique prime factorization, greatest common divisor, least common multiple, Euclidean algorithm. Congruence, solutions of linear congruences in one variable, Chinease remainder theorem, Fermat and Euler theorems, primitive roots. Quadratic residues, Legendre symbol, quadratic reciprocity law. Linear diophantine equation, some elementary methods solving of special types of diophante equations. Decomposition and factorisation of algebraic structures. Construction of ${\bold N}$, ${\bold Z}$, ${\bold Q}$, ${\bold R}$ and ${\bold C}$.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra V

Faculty of Science
Autumn 2000
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
RNDr. Pavel Šišma, Dr. (seminar tutor)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
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
Divisibility in $\Bbb Z$: primes, unique prime factorization, greatest common divisor, least common multiple, Euclidean algorithm. Congruence, solutions of linear congruences in one variable, Chinease remainder theorem, Fermat and Euler theorems, primitive roots. Quadratic residues, Legendre symbol, quadratic reciprocity law. Linear diophantine equation, some elementary methods solving of special types of diophante equations. Decomposition and factorisation of algebraic structures. Construction of ${\bold N}$, ${\bold Z}$, ${\bold Q}$, ${\bold R}$ and ${\bold C}$.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Theoretical Arithmetics

Faculty of Science
Autumn 1999
Extent and Intensity
2/0/0. 3 credit(s). 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
Contact Person: prof. RNDr. Radan Kučera, DSc.
Prerequisites (in Czech)
M3510 Algebra III
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
  • Divisibility in $\Bbb Z$: primes, unique prime factorization, greatest common divisor, least common multiple, Euclidean algorithm. Congruence, solutions of linear congruences in one variable, Chinease remainder theorem, Fermat and Euler theorems, primitive roots. Quadratic residues, Legendre symbol, quadratic reciprocity law. Linear diophantine equation, some elementary methods solving of special types of diophante equations. Decomposition and factorisation of algebraic structures. Construction of ${\bold N}$, ${\bold Z}$, ${\bold Q}$, ${\bold R}$ and ${\bold C}$.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2025

The course is not taught in Spring 2025

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2024

The course is not taught in Spring 2024

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2023

The course is not taught in Spring 2023

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2022

The course is not taught in Spring 2022

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2021

The course is not taught in Spring 2021

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2020

The course is not taught in Spring 2020

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2019

The course is not taught in Spring 2019

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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 of Seminar Groups
M7500/01: No timetable has been entered into IS. M. Bulant
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
spring 2018

The course is not taught in spring 2018

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2017

The course is not taught in Spring 2017

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2016

The course is not taught in Spring 2016

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
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
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
Spring 2014

The course is not taught in Spring 2014

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions. Algebraic and transcendental numbers. The Fundamental Theorem of Algebra.
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples. Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homework. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2010

The course is not taught in Autumn 2010

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to further study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions Algebraic and transcendental numbers The Fundamental Theorem of Algebra
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and solutions of homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2007

The course is not taught in Autumn 2007

Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 UP2
  • Timetable of Seminar Groups:
M7500/01: Tue 12:00–12:50 UP2, M. Bulant
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers).
Syllabus (in Czech)
  • Vytvořující rozklady na algebraických strukturách - faktorgrupoidy, faktorgrupy, faktorokruhy
  • Obory přirozených, celých a racionálních čísel
  • Reálná a komplexní čísla
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Assessment methods (in Czech)
Výuka bude probíhat formou pravidelných přednášek a cvičení. Docházka na cvičení (max. 2 neúčasti) je nutným předpokladem úspěšného absolvování zkoušky. Zkouška bude písemná a ústní a bude probíhat jednorázově na konci semestru (tj. bez dalších průběžných požadavků).
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebraic Seminar for teachers

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (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
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to further study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions Algebraic and transcendental numbers The Fundamental Theorem of Algebra
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and solutions of homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Radan Kučera, DSc.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers).
Syllabus (in Czech)
  • Vytvořující rozklady na algebraických strukturách - faktorgrupoidy, faktorgrupy, faktorokruhy
  • Obory přirozených, celých a racionálních čísel
  • Reálná a komplexní čísla
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Assessment methods (in Czech)
Výuka bude probíhat formou pravidelných přednášek a cvičení. Docházka na cvičení (max. 2 neúčasti) je nutným předpokladem úspěšného absolvování zkoušky. Zkouška bude písemná a ústní a bude probíhat jednorázově na konci semestru (tj. bez dalších průběžných požadavků).
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2011 - acreditation

The course is not taught in Autumn 2011 - acreditation

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

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to further study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions Algebraic and transcendental numbers The Fundamental Theorem of Algebra
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and solutions of homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.

M7500 Algebra 3

Faculty of Science
Autumn 2010 - only for the accreditation

The course is not taught in Autumn 2010 - only for the accreditation

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Knowledge of basic algebra
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main topics of the course are: - Factorization of grupoids, groups and rings, field extensions. - Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). At the end of this course, students should understand the construction of the basic numbers and be able to further study further topics of algebra and field theory.
Syllabus
  • Construction of number domains (an axiomatic development of natural numbers, integers, and the fields of rational, real, and complex numbers). Quotient groups and fields, field extensions, ruler and compass constructions Algebraic and transcendental numbers The Fundamental Theorem of Algebra
Literature
  • KUČERA, Radan and Ladislav SKULA. Číselné obory. 1st ed. Brno: Masarykova univerzita, 1998, 95 pp. ISBN 80-210-1965-4. info
  • CAMERON, Peter J. Introduction to Algebra. Oxford University Press, 2001, 295 pp. ISBN 0-19-850194. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. info
  • SKULA, Ladislav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 117 s. info
Teaching methods
Lectures: theoretical explanation with practical examples Seminars: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Oral and writtent student presentation of the theme chosen after the negotiation with the lecturer.
Assessment methods
Final written and oral exam (80%). Into the consideration will be also taken work during the term - especially oral presentations and solutions of homework (20%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-3/
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015.
  • Enrolment Statistics (recent)