Uma proposta de oficina sobre códigos para a contextualização do estudo de aritmética e matrizes no ensino médio

• Ano de defesa: 2015
• Autor(a) principal: Alves, Bruno Coelho
• Orientador(a): Souza, Mário José de
• Banca de defesa: Souza, Mário José de, Souza, Flávio Raimundo de, Lima, Lidiane dos Santos Monteiro
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Programa de Pós-graduação em PROFMAT (RG)
• Departamento: Instituto de Matemática e Estatística - IME (RG)
• País: Brasil
• Palavras-chave em Português: Códigos Corretores de Erros; O cina para ensino médio; Álgebra
• Palavras-chave em Inglês: Error-Correcting Codes; Algebra; Workshop for high school
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/4839

This work aims to present the content of Error-Correcting Codes to teachers, in a way to use this content in their classes. A code representing a particular word or symbol by another word or symbol. This study handle with the error correcting codes, especially that said linears. Thus, the concept of code is disclosed along two examples. The Linear Algebra and Algebra requirements are exposed, handling the concept of nite elds, the de nition of linear space and linear transformation. The error correcting codes, from alphabets de ned in nite elds, allow sending messages, even in noisy channels, they can be interpreted with a lower probability of error. This process is done in linear codes through linear transformations. Hamming codes and Reed-Solomon codes are exemples of linear codes which are showed in this work. After presented the theoretical basis of content, it is proposed a workshop that has as target students from the nal years of High School. This workshop explore some common feature codes, such as the use of check digits and the interpretation of texts by digital machines by zeros and ones. It is hoped that this work can assist the release of some current research topics among teachers and encourage the use of new methodologies for teaching content that is considered di cult and useless to several students of High School.