SubjectsSubjects(version: 861)
Course, academic year 2019/2020
Polynomial algebra - ORMA10201
Title: Polynomická algebra
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2019
Semester: summer
E-Credits: 4
Examination process: summer s.:
Hours per week, examination: summer s.:0/0 MC [hours/semester]
Extent per academic year: 12 [hours]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Additional information:
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
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (09.06.2010)
The basic course focusing on polynomials and their properties. The gained knowledge and skills belong to the basic elements necessary for further mathematics courses.
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (09.06.2010)

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.

Literature -
Last update: NOVOTNAJ/PEDF.CUNI.CZ (02.02.2016)

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: JANCARIK/PEDF.CUNI.CZ (09.06.2010)

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

Requirements to the exam - Czech
Last update: NOVOTNAJ/PEDF.CUNI.CZ (02.02.2016)

- vypracování seminární práce
- 1 až 2 testy
- minimálně 80% účast na cvičeních či adekvátní náhrada řešenými úlohami v případě odůvodněné neúčasti

Syllabus -
Last update: JANCARIK/PEDF.CUNI.CZ (09.06.2010)

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.

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