Subjects

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Polynomial algebra - OB2310010

Title:	Polynomická algebra
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2022
Semester:	summer
E-Credits:	4
Examination process:	summer s.:
Hours per week, examination:	summer s.:1/2, MC [HT]
Capacity:	unknown / unknown (999)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Is provided by:	OPBM2M110A
Additional information:	http://class.pedf.cuni.cz/Jancarik/DesktopDefault.aspx?tabindex=5&tabid=27&portalsekce=2
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. doc. RNDr. Antonín Jančařík, Ph.D.
Class:	Matematika 1. cyklus - povinné
Classification:	Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Pre-requisite :	OB2310N009
Interchangeability :	OB2310201
Is pre-requisite for:	OB2310067, OB1310N004
Is interchangeable with:	OKB2310N10

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

The basic course focusing on polynomials. The gained knowledge and skills belong to the basic elements necessary for further mathematics courses.

Last update: Novotná Jarmila, prof. RNDr., CSc. (22.01.2022)

Aim of the course -

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.

Last update: Novotná Jarmila, prof. RNDr., CSc. (22.01.2022)

Descriptors - Czech

V případě přechodu na distanční výuku, bude kurz probíhat v době, kdy je v rozvrhu, na adrese

Join Zoom Meeting
https://cuni-cz.zoom.us/j/7534626575?pwd=RElKaUZSUDgvb1hzMTM1bnI1Q0VOZz09

Meeting ID: 753 462 6575
Passcode: f09ZYx

Last update: Novotná Jarmila, prof. RNDr., CSc. (22.01.2022)

Course completion requirements - Czech

Studentům budou průběžně zadávány seminární práce, jejichž řešení budou odevzdávat vyučující. Jejich úspěšné vyřešení uznané vyučující je jednou z podmínek k udělení zápočtu.

Zápočtový test; pro test jsou možné dva opravné pokusy

Last update: Novotná Jarmila, prof. RNDr., CSc. (22.01.2022)

Literature - Czech

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.

Last update: Novotná Jarmila, prof. RNDr., CSc. (22.01.2022)

Teaching methods -

Lecture & practice

Last update: Novotná Jarmila, prof. RNDr., CSc. (22.01.2022)

Syllabus -

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.

Last update: Novotná Jarmila, prof. RNDr., CSc. (22.01.2022)