Subjects

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Polynomial algebra - OKB2310201

Title:	Polynomická algebra
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2019
Semester:	winter
E-Credits:	3
Examination process:	winter s.:
Hours per week, examination:	winter s.:0/0, MC [HS]
Extent per academic year:	12 [hours]
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:	combined
Teaching methods:	combined
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 :	OKB2310208
Is interchangeable with:	OKB2310N10

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

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

Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

Aim of the course -

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 training.

Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

Literature -

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: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

Teaching methods -

Lecture & practice, in some cases supported by the work on computers.

Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

Requirements to the exam - Czech

vypracování seminární práce

2 až 3 testy

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

Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

Syllabus -

Ring, integral domain, field.

Algebraic and functional definitions of a polynomial.

Divisibility of polynomials, reducible and irreducible polynomials.

Roots of polynomials.

Algebraic equation (in one variable).

Greatest common divisor and least common multiple of polynomials, Euclidean algorithm.

Derivative of a polynomial, multiplicity of roots.

Numerical methods for real roots.

Polynomial approximation of a function.

Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)