BIRKHOFF MACLANE ALGEBRA MODERNA PDF

We began this construction observing the international plan, trying to understand, on the one hand, some contexts that helped to give a configuration to the current programs and menus of the disciplines and, on the other hand, how was the incorporation of the themes of the LA in the first foreign didactic books. First, we describe the motivations of the research as well as the type of historical source used to develop it. In a second moment, we made a survey of the first signs of its emergence and of some contexts that helped to establish LA as a discipline in other countries, and then we did an analysis about how its contents were being incorporated into the first textbooks. We conclude that initially AL was present in textbooks of Modern Algebra AM and that, gradually, there was a movement of detachment, generating independent LA texts, although still today, in many texts, this pattern persists. In addition, since its inception, AL has always been frequented by several types of professionals, thus generating a direction for applications, both in research in this area and in its teaching, detaching itself from the algebraic character that is oriented in a structuralist tendency. Keywords: Modern Algebra.

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We began this construction observing the international plan, trying to understand, on the one hand, some contexts that helped to give a configuration to the current programs and menus of the disciplines and, on the other hand, how was the incorporation of the themes of the LA in the first foreign didactic books.

First, we describe the motivations of the research as well as the type of historical source used to develop it. In a second moment, we made a survey of the first signs of its emergence and of some contexts that helped to establish LA as a discipline in other countries, and then we did an analysis about how its contents were being incorporated into the first textbooks.

We conclude that initially AL was present in textbooks of Modern Algebra AM and that, gradually, there was a movement of detachment, generating independent LA texts, although still today, in many texts, this pattern persists. In addition, since its inception, AL has always been frequented by several types of professionals, thus generating a direction for applications, both in research in this area and in its teaching, detaching itself from the algebraic character that is oriented in a structuralist tendency.

Keywords: Modern Algebra. Didatic books. Academic discipline. Linear Algebra. E-mail: edugonsan gmail. Interessante notar o papel do livro de Bartel van der Waerden, Moderne Algebra, nesse processo. Esse tipo de atividade ainda era pouco frequente Dorier, Aydin, , p. Between these two orientations, there exist a continuum of teaching designs, in which each pole is more or less dominant. In one approach, computational techniques appear before abstract ideas computation-to- abstraction approach.

The other approach is the reverse: abstract ideas appear before computational techniques abstraction-to-computation approach Frequently, the former approach is used by elementary textbooks, whereas the latter approach is used by the more advanced textbooks. These faculties expect linear algebra course to play its proper roles in their curriculum; Education faculties expect it to contributing the abstract thinking of their teacher candidates. Engineering faculties expect it to make emphasis on physical science applications and computer experiences.

Maybe some programs intend to teach linear algebra at the secondary level. Tomei, , p. Some have a large population of engineering students, with an emphasis on physical science applications, notably differential equations and signal processing.

At other schools a large proportion of the linear algebra students are mathematics majors, many of whom intend to teach at the secondary level.

Some colleges teach linear algebra as a subset of a differential equations course. The concepts taught within these courses lend themselves to the understanding of more advanced mathematics courses. This further extends to the maximization of these theories as transferable knowledge to courses in engineering, economics, physical and chemical sciences, and statistics.

A mastery of finite vector spaces, linear transformations, and their extensions to function spaces is essential. Tucker, , p. Linear algebra gives a formal structure to analytic geometry and solutions to 2 X 2 and 3x3 systems of linear equations learned in high school. Unlike groups and fields, one can draw insightful pictures of elements in vector spaces.

Linear transformations on finite-dimensional vector spaces also have concrete descriptions with matrices. Birkhoff, , p. This book would introduce a generation of American students to linear algebra, polynomial algebra, and the theory of elementary divisors. Halmos, , p.

Matrizes, IV. Linear Forms. Matrices, Modules with Respect to a Skew Field. Linear Equations, Modules in Euclidean Rings. Elementary Divisors, The Fundamental Theorem of Abelian Groups, Representations and Representation Modules, Normal Forms of a Matrix in a Commutative Field, Elementary Divisors and Characteristic Function, Quadratic and Hermitian Forms.

The book was translated into many languages, being widely used in universities all around the world. The success of Moderne Algebra was responsible for the widespread absorption of the idea of "algebraic structure. An examination of the contents of Moderne Algebra in the present section will give us a better understanding of the meaning of its "structural" character. Van Der Waerden, , p. Section was influenced by Otto Schreier in Hamburg, who was a specialist in linear algebra and theory of groups.

We had tried out our somewhat differing ideas of how this should be done in a course at Harvard for three successive years, before reorganizing and presenting them in textbook form. Foi produzido um conjunto de notas para o curso.

Mais adiante, "[ Em , A. Moore, , p. In A. Albert published his textbook, Modern Higher Algebra, in which he too began with groups and rings. He introduced what he called a "linear set," i.

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