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Um estudo sobre índices de campos de vetores
(Universidade Federal de São Carlos, 2023-04-03)
One of the main goals of this project is to study the index of vector fields in compact
surfaces and present the Poincar´e-Hopf Theorem, remarking that such a result connects
topological elements to geometric objects.
Aspectos históricos e matemáticos da resolução de equações de 3o., 4o. e 5o. graus
(Universidade Federal de São Carlos, 2023-09-06)
During the years from 1530 to 1576, there were great mathematical advances in Europe, one of the greatest being the great duel of the resolution of the cubic equations, fought between Niccolò Tartaglia and Gerolamo Cardano, ...
A construção dos números reais desenvolvida por Richard Dedekind
(Universidade Federal de São Carlos, 2021-04-25)
In this work, we will study the emergence of incommensurability during classical antiquity and understand how this discovery was important for the development of real number theory during the arithmetic movement of analysis. ...
O grau de uma aplicação: uma abordagem via aplicação diferencial
(Universidade Federal de São Carlos, 2023-09-01)
In this work, we study the concepts of degree and local degree for maps between manifolds.
Furthermore, we define the Poincaré-Hopf index and study some relevant proprieties of this index
such as the famous Poincaré-Hopf ...
O homem que calculava: uma abordagem recreativa para o ensino de matemática e suas dramatizações em sala de aula
(Universidade Federal de São Carlos, 2022-09-30)
The motivation and unfolding of this monograph is to address 4 problems from the book The Man Who Counted, analyzing and characterizing the conceptions that the author had in his time and that persist until today, for ...
Ladrilhamentos regulares e semirregulares do plano
(Universidade Federal de São Carlos, 2021-11-24)
The tiling technique consists of filling the plane with geometric figures without overlapping or empty spaces. Although this technique is quite old, the science is recent and contains aspects that have not yet been developed ...
Criptografia RSA: aspectos históricos e matemáticos
(Universidade Federal de São Carlos, 2021-06-24)
This work studies aspects of RSA public key cryptography and its relationship with number theory, in particular with the properties of prime numbers. The methodology is based on bibliographical research. The study is based ...
A representação decimal fracionária de números reais: aspectos teóricos e históricos
(Universidade Federal de São Carlos, 2021-06-21)
In this work we carry out a study on the history and concepts of development of the decimal representation of real numbers, which probably started with works by Simon Stevin in La Theinde (The tenth) in 1585 (STEVIN, 1997), ...
Utilização do modelo pictórico da Matemática de Singapura em resoluções de problemas para os 5o e 6o anos do ensino fundamental, dentro da proposta curricular do estado de São Paulo
(Universidade Federal de São Carlos, 2021-11-25)
Teaching mathematics is a challenge for both educators and students. It is usual to notice the lack of interest of students in Mathematics, especially when it is associated with letters and symbols, missing its real meaning. ...
Superfícies de Weingarten no Espaço Hiperbólico
(Universidade Federal de São Carlos, 2020-06-26)
Desde o surgimento da definição de superfícies parametrizadas, foi questionado sobre suas propriedades que independem da parametrização. Propriedades essas que caracterizam objetivamente a geometria dessa família facilitando ...