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Profile of the programme
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The course “Sobre polinómios: desde as operações básicas à Teoria de Operadores” gives Mathematical knowledge on a very well-known class of functions studied not only in the syllabus of the high school Portuguese education system, within the “3º Ciclo de Ensino Básico” and “Ensino Secundário”, but also in several curricular units of Mathematics from university courses in Sciences and Engineering. This course is focused in the study of polynomials. We shall start by analysing the main properties of these functions by studying the elementary operations between polynomials and results on zeros. Then, these properties shall be used to study derivatives within an approach in the framework of divided-difference operators.
In general terms, the course aims to improve the knowledge on polynomial functions, by exploring the inter-relation between several topics in Mathematics that are usually studied in several cycles of studies.
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Key learning outcomes
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At the end of the course, the student should:
- know how to operate with polynomials;
- have general knowledge on polynomial equations (concerning its historical context, and also on the solutions – exact and approximate solution, as well as the techniques on solving polynomial equations);
- know how to solve the polynomial equations of degree less than or equal to four;
- know several methods to deduce the equation of the tangent to a polynomial curve;
- know how to introduce the concept of derivative using the tools from the algebra of polynomials;
- know how to analyse the derivative within the framework of the divided-difference operators;
- know how to construct a hierarchy of operators, doing the corresponding geometric interpretation.
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Occupational profiles of graduates
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The course “Sobre polinómios: desde as operações básicas à Teoria de Operadores” is a “curso de formação – Ação de Formação Contínua –“ in Mathematics (subject area A152, according to the Portuguese label system). Primarily, it is intended to be attended by High School teachers, namely the Math teachers in the Portuguese levels “3º ciclo do Ensino Básico” and “Ensino Secundário”. Furthermore, it is also intended to the ones that have a Bachelor degree, a Master, or a PhD degree in Mathematics or related courses (e.g., in teaching Mathematics or Sciences) or in any Science or Engineering course. |
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Learning facilities
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The course “Sobre polinómios: desde as operações básicas à Teoria de Operadores” will be run in the University of Beira Interior, so the students will have access to the usual places and commodities at UBI, namely, teaching labs, the UBI library, and study rooms. |