41.
Álgebra no ensino fundamental : produzindo significados para as operações básicas com expressões algébricas
- Bonadiman, Adriana
Nesta dissertação destacamos nossa preocupação com o ensino e aprendizagem da álgebra elementar, sempre muito presente em nossa prática docente. Nosso principal objetivo foi a elaboração, implementação e validação de uma proposta didática para o desenvolvimento de um ensino que promovesse a compreensão das operações básicas com expressões algébricas no Ensino Fundamental. De acordo com os referenciais teóricos utilizados buscamos construir uma proposta que contemplasse a produção de significados para a atividade algébrica em um ambiente de aprendizagem cooperativa, fazendo uso de representações múltiplas e de materiais manipulativos juntamente com a resolução de situações-problema. A implementação da proposta foi desenvolvida...
42.
O ensino de álgebra no Brasil e na França: estudosobre o ensino de equações do 1º grau à luz da teoriaantropológica do didático
- Abraão Juvencio de Araújo
Este estudo se insere na problemática da modelização de conhecimentos algébricos, cujoprincipal objetivo foi caracterizar e comparar as transposições didáticas realizadas na França eno Brasil sobre o ensino de resolução de equações do 1º grau com uma incógnita. Para tanto,apoiamo-nos na Teoria da Transposição Didática (CHEVALLARD, 1991), que ressalta opapel das instituições na relação com os objetos de saberes escolares, bem como na TeoriaAntropológica do Didático (CHEVALLARD, 1999), como um método de análise que permitereconstruir a organização matemática existente no interior de uma determinada instituição deensino. Como primeiro resultado da pesquisa, realizamos estudos teóricos e didáticos sobre oensino de resolução...
43.
1 HEYTING ALGEBRAS
- Heyting Algebras; Dutch Arend Heyting
algebraic structures that play in relation to intuitionistic logic (q.v.) a role analogous to that played by Boolean algebras (q.v) in relation to classical logic. They are most simply defined as a certain type of lattice. A lattice is a partially ordered set (L ≤) in which every pair of elements x, y has a least upper bound, or join, denoted by x ∨ y, and a greatest lower bound, or meet, denoted by x ∧ y. A top (bottom) element of a lattice L is an element, denoted by 1 (0) such that x ≤ 1 (0 ≤ x)...
44.
In 1965 James Hardy Wilkinson published his classic work on numerical linear algebra,
- The Algebraic Eigenvalue; In James; Hardy Wilkinson
results in computational savings. However, the theory of eigensystems is best treated in terms of complex matrices. Consequently, throughout this chapter: Unless otherwise stated A is a complex matrix of order n. 1 2 Chapter 1. Eigensystems 1. THE ALGEBRA OF EIGENSYSTEMS In this section we will develop the classical theory of eigenvalues, eigenvectors, and reduction by similarity transformations, with an emphasis on the reduction of a matrix by similarity transformations to a simpler form. We begin with basic definitions and their consequences. We then present Schur's reduction of a triangular matrix to triangular form by unitary similarity transformations ---...
45.
Semisimple Algebra -- from MathWorld
- Weisstein, Eric W.
An algebra with no nontrivial nilpotent ideals. In the 1890s, Cartan, Frobenius, and Molien independently proved that any finite-dimensional semisimple algebra over the real or complex numbers is a finite and unique direct sum of simple algebras. This result was then extended to algebras over arbitrary fields by Wedderburn in 1907 (Kleiner 1996). See also: Ideal, Nilpotent Element, Simple Algebra
46.
Nonstable K-Theory For Z-Stable C*-Algebras
- Xinhui Jiang; Algebra A
. Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state (cf. Jiang and Su [11]). Let A 6= 0 be a unital C -algebra with A = A\Omega Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants, namely, i (U(A)) = K i\Gamma1 (A) for all integer i 0. Furthermore, A has cancellation for full projections, and satisfies the comparability question for full projections. Analogous results hold for non-unital Z-stable C -algebras. 0. Introduction and summary of results Let Z denote the only simple limit...
47.
On finiteness of the number of
- N-dimensional Hopf C –algebras; Etienne Blanchard
Given an algebraically closed field k and an integer N, D. S¸tefan has proved that there exists only a finite number of Hopf k-algebras which are both semisimple and co-semi-simple. In the C ∗ –algebraic framework, we provide in this note explicit upper-bounds for the number of Hopf C ∗ –algebra structures on a given finite dimensional C ∗ –algebra.
48.
Ore Algebra -- from MathWorld
- Weisstein, Eric W.
Ore algebra is an algebra of noncommutative polynomials representing linear operators for functional equations such as linear differential or difference equations. Ore polynomials satisfy particular commutation relations.
49.
Schur Algebra -- from MathWorld
- Weisstein, Eric W.
An Auslander algebra which connects the representation theories of the symmetric group of permutations and the general linear group {\it GL}(n,\mathbb{C}). Schur algebras are "quasihereditary."
50.
Field Algebras
- Bakalov, Bojko; Kac, Victor G.
A field algebra is a ``non-commutative'' generalization of a vertex algebra.
In this paper we develop foundations of the theory of field algebras.
51.
Image Algebra
Introduction
Since the field of image algebra is a recent development it will be instructive
to provide some background information. In the broad sense, image algebra is a
mathematical theory concerned with the transformation and analysis of images.
Although much emphasis is focused on the analysis and transformation of digital
images, the main goal is the establishment of a comprehensive and unifying theory
of image transformations, image analysis, and image understanding in the discrete
as well as the continuous domain [36].
The idea of establishing a unifying theory for the various concepts and
operations encountered in image and signal processing is not new. Over thirty
years ago, Unger proposed that...
52.
Process Algebra
- Rance Cleaveland; Scott A. Smolka
Process algebra represents a mathematically rigorous framework for modeling concurrent systems of interacting processes. The process-algebraic approach relies on equational and inequational reasoning as the basis for analyzing the behavior of such systems. This chapter surveys some of the key results obtained in the area within the setting of a particular process-algebraic notation, the Calculus of Communicating Systems (CCS) of Milner. In particular, the Structural Operational Semantics approach to defining operational behavior of languages is illustrated via CCS, and several operational equivalences and refinement orderings are discussed. Mechanisms are presented for deducing that systems are related by the equivalence relations...
53.
Division Algebra -- from MathWorld
- Weisstein, Eric W.
A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not necessarily commutative. Every field is therefore also a division algebra. In French, the term "corps non commutatif" is used to mean division algebra, while "corps" alone means field. Explicitly, a division algebra is a set together with two binary operators S(+,*) satisfying the following...
54.
Heyting Algebra -- from MathWorld
- Weisstein, Eric W.
An algebra which is a special case of a logos. See also: Logos, Topos
55.
Nilpotent Algebra -- from MathWorld
- Weisstein, Eric W.
An algebra, also called a nilalgebra, consisting only of nilpotent Elements. See also: Nilpotent Element
56.
Topological Algebra -- from MathWorld
- Weisstein, Eric W.
A topological algebra is a pair (\mathbb{A},\tau), where \mathbb{A}=\left(A,(f_i^{\mathbb{A}})_i\in I\right) is an algebra and each of the operations f_i^{\mathbb{A}} is continuous in the product topology. Examples of topological algebras include topological groups, topological vector spaces, and topological rings. See also: Topological Group, Topological Partial Algebra, Topological Ring, Topological Vector Space
57.
Ennea-algebras
- Leroux, Philippe
We propose a generalisation of a recent work of M. Aguiar and J.-L. Loday on
Quadri-algebras, called Ennea-algebras. In this second version, this paper has
been extended. We show that the augmented free Ennea-algebra is a connected
Hopf algebra and construct explicit formal deformations of dendriform
dialgebras, quari-algebras and ennea-algebras via Baxter operators.
58.
Linear Algebra -- from MathWorld
- Weisstein, Eric W.
Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many other problems in mathematics, physics, and engineering. Confusingly, linear algebra is not actually an algebra in the technical sense of the word "algebra" (i.e., a vector space V over a field...
59.
Baxter Algebras and Hopf Algebras
- Andrews, George E.; Guo, Li; Keigher, William; Ono, Ken
By applying a recent construction of free Baxter algebras, we obtain a new
class of Hopf algebras that generalizes the classical divided power Hopf
algebra. We also study conditions under which these Hopf algebras are
isomorphic.
60.
Local P-Algebra -- from MathWorld
- Weisstein, Eric W.
Let P be a class of (universal) algebras. Then an algebra \mathbb{A} is a local P-algebra provided that every finitely generated subalgebra \mathbb{F} of \mathbb{A} is a member of the class P. Note that classes P of algebras are identified with properties of algebras, so an algebra in the class P is said to be a P-algebra.
