SYMMETRIC POLYNOMIALS AS ENRICHMENT OF HIGH SCHOOL MATHEMATICS
TEACHING.

D 2019

SYMMETRIC POLYNOMIALS AS ENRICHMENT OF HIGH SCHOOL MATHEMATICS TEACHING.

VYSOKÁ, Jana

Basic information

Original name

SYMMETRIC POLYNOMIALS AS ENRICHMENT OF HIGH SCHOOL MATHEMATICS TEACHING.

Name in Czech

SYMETRICKÉ POLYNOMY - OBOHACENÍ VÝUKY NA STŘEDNÍ ŠKOLE

Authors

VYSOKÁ, Jana (203 Czech Republic, guarantor, belonging to the institution)

Edition

Depósito Legal: V-1702-2019. LAURI VOLPI 6, VALENICA, BURJASSOT 46100, doi: 10.21125/edulearn.2019.1554, p. 6502-6505, 4 pp. 2019

Publisher

IATED-INT ASSOC TECHNOLOGY EDUCATION & DEVELOPMENT, LAURI VOLPI 6, VALENICA, BURJASSOT 46100, SPAIN

Other information

Language

English

Type of outcome

Proceedings paper

Field of Study

10100 1.1 Mathematics

Country of publisher

Spain

Confidentiality degree

is not subject to a state or trade secret

Publication form

printed version "print"

RIV identification code

RIV/75081431:_____/19:00001785

Organization unit

Institute of Technology and Business in České Budějovice

ISBN

978-84-09-12031-4

ISSN

UT WoS

000553304901011

Keywords (in Czech)

Symetrické polynomy; Vietovy vztahy; Newtonovy vzorce; Heronovy vzorce

Keywords in English

Symmetric polynomials; Vieta´s formulas; Newton´s formulas; Heron´s formula

Abstract

ORIG CZ

V originále

This paper presents an example of solutions of elementary mathematical problems designed for high school students. The focus was on simple tasks of algebraic and geometrical kind, whose solving may lead to systems of nonlinear equations, in which variables are bound by special conditions. Symmetric polynomials are not a part of curriculum of high school mathematics, but students can already encounter Viete's formulas at this level in the connection with the study of quadratic equations. From Vieta's formulas there is only a small step to the definition of symmetric polynomials and the derivation of Newton's formulas. A wide variety of examples can be solved by Newton's formulas together with Vieta's formulas very easily and elegantly. New topics can bring the enrichment for high school mathematics mostly at schools with an extended teaching mathematics.

In Czech

Tato práce představuje příklad řešení základních matematických problémů určených pro studenty středních škol. Důraz byl kladen na jednoduché úkoly algebraického a geometrického druhu, jejichž řešení může vést k systémům nelineárních rovnic, ve kterých jsou proměnné vázány zvláštními podmínkami. Symetrické polynomy nejsou součástí učebních osnov středoškolské matematiky, ale studenti se již mohou na této úrovni setkat s Vieteovými vztahy v souvislosti se studiem kvadratických rovnic. Z Vietových vzorců vede již jen malý krok k definici symetrických polynomů a odvození Newtonových vzorců. S pomocí Newtonových formulí spolu s Vietovými vztahy lze snadno a elegantně vyřešit celou řadu příkladů. Nová témata mohou obohatit středoškolskou matematiku většinou na školách s rozšířenou výukou matematiky.

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Cite

VYSOKÁ, Jana. SYMMETRIC POLYNOMIALS AS ENRICHMENT OF HIGH SCHOOL MATHEMATICS TEACHING. In "L. Gómez Chova, A. López Martínez, I. Candel Torres IATED Academy". doi: 10.21125/edulearn.2019.1554. Depósito Legal: V-1702-2019. LAURI VOLPI 6, VALENICA, BURJASSOT 46100: IATED-INT ASSOC TECHNOLOGY EDUCATION & DEVELOPMENT, LAURI VOLPI 6, VALENICA, BURJASSOT 46100, SPAIN, 2019, p. 6502-6505. ISBN 978-84-09-12031-4.

@inproceedings{54861,
   author = {Vysoká, Jana},
   address = {LAURI VOLPI 6, VALENICA, BURJASSOT 46100},
   booktitle = {doi: 10.21125/edulearn.2019.1554},
   edition = {Depósito Legal: V-1702-2019},
   editor = {"L. Gómez Chova, A. López Martínez, I. Candel Torres IATED Academy"},
   keywords = {Symmetric polynomials; Vieta´s formulas; Newton´s formulas; Heron´s formula},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {LAURI VOLPI 6, VALENICA, BURJASSOT 46100},
   isbn = {978-84-09-12031-4},
   pages = {6502-6505},
   publisher = {IATED-INT ASSOC TECHNOLOGY EDUCATION & DEVELOPMENT, LAURI VOLPI 6, VALENICA, BURJASSOT 46100, SPAIN},
   title = {SYMMETRIC POLYNOMIALS AS ENRICHMENT OF HIGH SCHOOL MATHEMATICS TEACHING.},
   year = {2019}
}

TY  - CONF
ID  - 54861
AU  - Vysoká, Jana
PY  - 2019
TI  - SYMMETRIC POLYNOMIALS AS ENRICHMENT OF HIGH SCHOOL MATHEMATICS TEACHING.
PB  - IATED-INT ASSOC TECHNOLOGY EDUCATION & DEVELOPMENT, LAURI VOLPI 6, VALENICA, BURJASSOT 46100, SPAIN
CY  - LAURI VOLPI 6, VALENICA, BURJASSOT 46100
SN  - 9788409120314
KW  - Symmetric polynomials
KW  - Vieta´s formulas
KW  - Newton´s formulas
KW  - Heron´s formula
N2  - This paper presents an example of solutions of elementary mathematical problems designed for high school students. The focus was on simple tasks of algebraic and geometrical kind, whose solving may lead to systems of nonlinear equations, in which variables are bound by special conditions. Symmetric polynomials are not a part of curriculum of high school mathematics, but students can already encounter Viete's formulas at this level in the connection with the study of quadratic equations. From Vieta's formulas there is only a small step to the definition of symmetric polynomials and the derivation of Newton's formulas. A wide variety of examples can be solved by Newton's formulas together with Vieta's formulas very easily and elegantly. New topics can bring the enrichment for high school mathematics mostly at schools with an extended teaching mathematics.
ER  -

VYSOKÁ, Jana. SYMMETRIC POLYNOMIALS AS ENRICHMENT OF HIGH SCHOOL MATHEMATICS TEACHING. In ''L. Gómez Chova, A. López Martínez, I. Candel Torres IATED Academy''. \textit{doi: 10.21125/edulearn.2019.1554}. Depósito Legal: V-1702-2019. LAURI VOLPI 6, VALENICA, BURJASSOT 46100: IATED-INT ASSOC TECHNOLOGY EDUCATION \&{} DEVELOPMENT, LAURI VOLPI 6, VALENICA, BURJASSOT 46100, SPAIN, 2019, p.~6502-6505. ISBN~978-84-09-12031-4.

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