Problema de otimização envolvendo a matemática do ensino médio

• Ano de defesa: 2013
• Autor(a) principal: Rocha, Alan Martins
• Orientador(a): Chaves, Rogério de Queiroz
• Banca de defesa: Chaves, Rogério de Queiroz, Souza, Flávio Raimundo de, Mizukoshi, Marina Tuyako
• 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 Matemática (IME)
• Departamento: Instituto de Matemática e Estatística - IME (RG)
• País: Brasil
• Palavras-chave em Português: Otimização; Resolução de problemas; Matemática no Ensino Médio.
• Palavras-chave em Inglês: Optimization; Problem Solving; Mathematics in secondary education
• Área do conhecimento CNPq: MATEMATICA::MATEMATICA APLICADA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tde/2955

Applied Mathematics is the branch of mathematics which deals with the application of mathematical knowledge to solving problems in other areas and, in the current curricula for secondary education in Brazil, it has not been as adequately explored as it could be. Optimization, for instance, is one type of mathematical applications which allows solving problems related to economy, management, engineering, transport and logistics, among others and can be introduced, at a basic level, in secondary school. With that in view, this work aims to present a few algebraic tools, accessible to the secondary school student, that allow solving some interesting elementary optimization problems. These tools include optimization of quadratic functions, discrete functions, some continuous functions, as well as some applications of the inequality between arithmetic and geometric means. The use of these methods is illustrated through several examples, chosen in a way that shows the rich variety of problems that can be solved with the seemingly basic tools presented. With this we aim at presenting these topics, accessible to secondary education, in a novel and interesting way that is attractive to students and, once assimilated, they can become powerful tools for solving several problems, whether they come from the daily experience, from mathematical olympics, or from exams.