SubjectsSubjects(version: 850)
Course, academic year 2019/2020
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Polynomic algebra - OPBM2M110A
Title in English: Polynomická algebra
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2018
Semester: summer
E-Credits: 3
Examination process: summer s.:
Hours per week, examination: summer s.:1/2 C [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: prof. RNDr. Jarmila Novotná, CSc.
Pre-requisite : OPBM2M101A
Annotation -
Last update: prof. RNDr. Jarmila Novotná, CSc. (28.01.2019)
The basic course focusing on polynomials. The gained knowledge and skills belong to the basic elements necessary for further mathematics courses.
Aim of the course -
Last update: prof. RNDr. Jarmila Novotná, CSc. (28.01.2019)
Poslední úprava: NOVOTNAJ/PEDF.CUNI.CZ (31.08.2008)

Subject aiming to acquaint students with these basic parts of algebra and theoretical arithmetic on which school mathematics is based and which serve as tools for other mathematical disciplines in teacher education.

 

 

 

Literature - Czech
Last update: prof. RNDr. Jarmila Novotná, CSc. (28.01.2019)

BLAŽEK, J. a kol.: Algebra a teoretická aritmetika 1. Praha: SPN, 1983.

KATRIŇÁK, T. a kol.: Algebra a teoretická aritmetika 1. Bratislava, Praha: ALFA, SNTL, 1985.

NOVOTNÁ, J., TRCH, M.: Algebra a teoretická aritmetika, Sbírka příkladů část 2, Polynomická algebra. 2. vyd. Praha: Karolinum, 2000.

DEMLOVÁ, M., NAGY, J.: Algebra. Praha: SNTL, 1985.

 
Teaching methods -
Last update: prof. RNDr. Jarmila Novotná, CSc. (28.01.2019)

lecture & practice, supported by individual work (seminar work)

Syllabus -
Last update: prof. RNDr. Jarmila Novotná, CSc. (28.01.2019)

Ring, integral domain, field.

Algebraic and functional definitions of a polynomial.

Divisibility of polynomials, reducible and irreducible plynomials.

Substituting into a polynomial, roots, decomposition into prime factors.

Algebraic equation (with one unknown), solutions and solvability.

Greatest common divisor of polynomials, Euclidean algorithm.

Derivative of a polynomial, simple and multiple roots.

Special types of algebraic equations.

Symmetric polynomials.

Course completion requirements - Czech
Last update: prof. RNDr. Jarmila Novotná, CSc. (28.01.2019)

Vypracování seminární práce

1 až 2 testy (při neúspěchu možno dvakrát opakovat)

minimálně 80% účast na cvičeních či adekvátní náhrada řešenými úlohami v případě odůvodněné neúčasti

aktivita ve cvičeních během celého semestru

 
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