https://repositorio.ufu.br/handle/123456789/5473 2026-07-30T04:42:32Z https://repositorio.ufu.br/handle/123456789/48968 Title: Matemática financeira: despertando a consciência financeira em crianças e adolescentes Abstract: Financial Mathematics plays a fundamental role in students’ education, as its concepts are directly related to everyday situations involving consumption, planning, and financial decision-making. However, its approach in Basic Education still faces challenges, particularly with regard to the contextualization of content and the availability of pedagogical materials that support teachers’ classroom practices. In this context, this study aims to develop didactic games and teaching sequences for the instruction of Financial Mathematics at different stages of Basic Education, with a focus on supporting teaching practice. The research has a propositional nature and adopts a qualitative approach, centered on the development of educational products applicable to the school context. Three original didactic games were developed — Mercadinho da Matemática, Família emEquilíbrio, and Simulador de Investimentos — each accompanied by structured tea ching sequences designed to guide their use in the classroom. The application of two of these games in a school setting had a pedagogical and formative character, enabling the analysis of the contributions of the materials to the mobilization of Financial Mathematics concepts, decision-making processes, and student learning. The results indicate that the games and teaching sequences constitute viable and relevant pedagogical resources, contributing to the contextualization of Financial Mathematics teaching and to the support of teachers’ work in Basic Education. 2026-02-24T00:00:00Z https://repositorio.ufu.br/handle/123456789/48926 Title: Área máxima de um triângulo equilátero circunscrito a um triângulo qualquer Abstract: This work explores a classic optimization problem in Plane Euclidean Geometry: determining the equilateral triangle with the largest area that circumscribes any given triangle. The approach adopted relattes tools from Geometry and Differential Calculus, allowing the modeling of geometric quantities through real functions and the analysis of their maximum values using analytical techniques. A proof of this classic problem is presented, accompanied by a geometric construction using ruler and compass. As an applied development, a didactic sequence aimed at elementary and secondary education is proposed, as well as a report of its application in the classroom. 2026-03-19T00:00:00Z https://repositorio.ufu.br/handle/123456789/48916 Title: O teorema da fibração de Milnor para singularidades reais Abstract: The main objective of this work is to present and prove the classic Milnor Fibration Theorem for Real Singularities. To provide a foundation for understanding this result, we first establish the study of differentiable manifolds, including the case of manifolds with boundary. Next, we review essential concepts of algebraic topology, such as contractible spaces, homology, cohomology, CW complexes, and homotopy groups. We present a review of algebraic sets and, as a fundamental tool for the main proof, we demonstrate the Curve Selection Lemma. We introduce the notions of fiber bundles and fibrations, also discussing Ehresmann’s Fibration Theorem for both manifolds without boundary and manifolds with boundary. Finally, we prove the Milnor Fibration Theorem for the real case and analyze the topology of the resulting fibers. 2026-02-26T00:00:00Z https://repositorio.ufu.br/handle/123456789/48906 Title: Existência de elementos primitivos k-normais em corpos finitos Abstract: This dissertation investigates conditions for the existence of elements that are simultaneously primitive and k normal in finite field extensions. The study of the existence of such elements is a central problem in modern Algebra, with direct implications on the efficiency of cryptographic systems and the construction of error-correcting codes. To approach this problem, we employ a theoretical framework that combines combinatorial and analytical methods. The primary tools utilized are the Euler totient function (ϕ) and the Möbius function (µ). Within the scope of Linear Algebra over finite fields, we explore the properties of linearized polynomials, which allow the characterization of the linear independence of an element’s conjugates under the action of Frobenius automorphisms. To prove the main results, we use tools such as additive and multiplicative characters, a particular type of homomorphism, integrating them with the study of Gaussian sums, which provide the estimates for exponential sums needed to guarantee that the number of desired elements is strictly positive. 2026-02-27T00:00:00Z