As conjecturas como instrumentos de ensino de matemática

Detalhes bibliográficos
Ano de defesa: 2021
Autor(a) principal: Alves, David Barreto
Orientador(a): Dória, André Vinicius Santos
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Mestrado Profissional em Matemática
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Ensino de matemática
Conjectura de Beal
Conjectura de Collatz
Conjectura de Goldbach
Conjectura de Toeplitz
Palavras-chave em Inglês:
Mathematics teaching
Beal’s conjecture
Collatz’s conjecture
Goldbach’s conjecture
Toeplitz’s conjecture
Área do conhecimento CNPq:
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Link de acesso: https://ri.ufs.br/jspui/handle/riufs/21378
Resumo: Conjectures are fundamental in the development of Mathematics. Each result that we know, it arose initially from assumptions formulated by deducting of problem situations, and after much analysis, their statements were constructed then. However, there are several claims that mathematicians have still not been able to prove or to refute them, some of them are several centuries old. In this work we present some of thes conjectures, namely: Beal’s Conjecture, Collatz’s Conjecture, Goldbach’s Conjecture and Toeplitz’s Conjecture in which, although they have proved to be extremely complex to demonstrate or to refute them, they present simple comprehension statements and have properties that allow us to explore a few concepts that can be used in Elementary and High school Mathematics classes.
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spelling Alves, David BarretoDória, André Vinicius Santos2025-03-17T14:02:17Z2025-03-17T14:02:17Z2021-05-31ALVES, David Barreto. As conjecturas como instrumentos de ensino de matemática. 2021. 57 f. Dissertação (Mestrado Profissional em Matemática)- Universidade Federal de Sergipe, São Cristóvão, 2021.https://ri.ufs.br/jspui/handle/riufs/21378Conjectures are fundamental in the development of Mathematics. Each result that we know, it arose initially from assumptions formulated by deducting of problem situations, and after much analysis, their statements were constructed then. However, there are several claims that mathematicians have still not been able to prove or to refute them, some of them are several centuries old. In this work we present some of thes conjectures, namely: Beal’s Conjecture, Collatz’s Conjecture, Goldbach’s Conjecture and Toeplitz’s Conjecture in which, although they have proved to be extremely complex to demonstrate or to refute them, they present simple comprehension statements and have properties that allow us to explore a few concepts that can be used in Elementary and High school Mathematics classes.As conjecturas são fundamentais no desenvolvimento da Matemática. Cada resultado que conhecemos, inicialmente surgiu de suposições formuladas através da dedução de situações problemas, e após muita análise, eram construídas suas demonstrações. No entanto, há várias afirmações que até hoje os matemáticos ainda não conseguiram prová-las e nem refutá-las, algumas das quais com vários séculos de existência. Neste trabalho apresentamos algumas dessas conjecturas, a saber: a Conjectura de Beal, a Conjectura de Collatz, a Conjectura de Goldbach e a Conjectura de Toeplitz que, apesar de terem se mostrados extremamente complexas para demonstrá-las ou refutá-las, apresentam enunciados de simples compreensão e possuem propriedades que permitem explorar um pouco alguns conceitos que podem ser usados nas aulas de Matemática dos Ensinos Fundamental e Médio.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão CristóvãoporEnsino de matemáticaConjectura de BealConjectura de CollatzConjectura de GoldbachConjectura de ToeplitzMathematics teachingBeal’s conjectureCollatz’s conjectureGoldbach’s conjectureToeplitz’s conjectureCIENCIAS EXATAS E DA TERRA::MATEMATICAAs conjecturas como instrumentos de ensino de matemáticainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisMestrado Profissional em MatemáticaUniversidade Federal de Sergipe (UFS)reponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/21378/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALDAVID_BARRETO_ALVES.pdfDAVID_BARRETO_ALVES.pdfapplication/pdf2320865https://ri.ufs.br/jspui/bitstream/riufs/21378/2/DAVID_BARRETO_ALVES.pdff2ff26caf74acdf5166b2bf17e23caf1MD52TEXTDAVID_BARRETO_ALVES.pdf.txtDAVID_BARRETO_ALVES.pdf.txtExtracted texttext/plain72764https://ri.ufs.br/jspui/bitstream/riufs/21378/3/DAVID_BARRETO_ALVES.pdf.txt8e2d6db8b265b80397d3165fda564527MD53THUMBNAILDAVID_BARRETO_ALVES.pdf.jpgDAVID_BARRETO_ALVES.pdf.jpgGenerated Thumbnailimage/jpeg1464https://ri.ufs.br/jspui/bitstream/riufs/21378/4/DAVID_BARRETO_ALVES.pdf.jpgd6147e13917b38203a588754b45a1f7dMD54riufs/213782025-03-26 07:52:59.843oai:oai:ri.ufs.br:repo_01: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2025-03-26T10:52:59Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.pt_BR.fl_str_mv As conjecturas como instrumentos de ensino de matemática
title As conjecturas como instrumentos de ensino de matemática
spellingShingle As conjecturas como instrumentos de ensino de matemática
Alves, David Barreto
Ensino de matemática
Conjectura de Beal
Conjectura de Collatz
Conjectura de Goldbach
Conjectura de Toeplitz
Mathematics teaching
Beal’s conjecture
Collatz’s conjecture
Goldbach’s conjecture
Toeplitz’s conjecture
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short As conjecturas como instrumentos de ensino de matemática
title_full As conjecturas como instrumentos de ensino de matemática
title_fullStr As conjecturas como instrumentos de ensino de matemática
title_full_unstemmed As conjecturas como instrumentos de ensino de matemática
title_sort As conjecturas como instrumentos de ensino de matemática
author Alves, David Barreto
author_facet Alves, David Barreto
author_role author
dc.contributor.author.fl_str_mv Alves, David Barreto
dc.contributor.advisor1.fl_str_mv Dória, André Vinicius Santos
contributor_str_mv Dória, André Vinicius Santos
dc.subject.por.fl_str_mv Ensino de matemática
Conjectura de Beal
Conjectura de Collatz
Conjectura de Goldbach
Conjectura de Toeplitz
topic Ensino de matemática
Conjectura de Beal
Conjectura de Collatz
Conjectura de Goldbach
Conjectura de Toeplitz
Mathematics teaching
Beal’s conjecture
Collatz’s conjecture
Goldbach’s conjecture
Toeplitz’s conjecture
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Mathematics teaching
Beal’s conjecture
Collatz’s conjecture
Goldbach’s conjecture
Toeplitz’s conjecture
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description Conjectures are fundamental in the development of Mathematics. Each result that we know, it arose initially from assumptions formulated by deducting of problem situations, and after much analysis, their statements were constructed then. However, there are several claims that mathematicians have still not been able to prove or to refute them, some of them are several centuries old. In this work we present some of thes conjectures, namely: Beal’s Conjecture, Collatz’s Conjecture, Goldbach’s Conjecture and Toeplitz’s Conjecture in which, although they have proved to be extremely complex to demonstrate or to refute them, they present simple comprehension statements and have properties that allow us to explore a few concepts that can be used in Elementary and High school Mathematics classes.
publishDate 2021
dc.date.issued.fl_str_mv 2021-05-31
dc.date.accessioned.fl_str_mv 2025-03-17T14:02:17Z
dc.date.available.fl_str_mv 2025-03-17T14:02:17Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv ALVES, David Barreto. As conjecturas como instrumentos de ensino de matemática. 2021. 57 f. Dissertação (Mestrado Profissional em Matemática)- Universidade Federal de Sergipe, São Cristóvão, 2021.
dc.identifier.uri.fl_str_mv https://ri.ufs.br/jspui/handle/riufs/21378
identifier_str_mv ALVES, David Barreto. As conjecturas como instrumentos de ensino de matemática. 2021. 57 f. Dissertação (Mestrado Profissional em Matemática)- Universidade Federal de Sergipe, São Cristóvão, 2021.
url https://ri.ufs.br/jspui/handle/riufs/21378
dc.language.iso.fl_str_mv por
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dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.publisher.program.fl_str_mv Mestrado Profissional em Matemática
dc.publisher.initials.fl_str_mv Universidade Federal de Sergipe (UFS)
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