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Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Gadanidis, George; Silva, Ricardo Scucuglia Rodrigues da
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Artigo de Revista Científica Formato: 8-23
Português
Relevância na Pesquisa
45.41%
Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.; Pesquisas sobre as imagens de estudantes e professores sobre matemática e sobre matemáticosrevelam uma série de imagens estereotipadas, das quais muitas são negativas. Neste artigo, apresentamosuma visão geral de algumas dessas imagens e estereótipos e consideramos as seguintes questões: (1)Como a imagem da matemática e dos matemáticos pode ser um problema em educação matemática...

A New Elementary Mathematics Curriculum: Practice, Learning and Assessment - Some Classroom Episodes

Vale, Isabel; Fernandes, Domingos; Borralho, António
Fonte: The Mathematics Education into the 21st Century Project – MEC 21 Publicador: The Mathematics Education into the 21st Century Project – MEC 21
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.38%
The aim of this paper is to present the new and innovative mathematics curriculum for elementary levels that is being implemented in the Portuguese basic education system (students from 1st to 9th grade) through an overview of an ongoing study of implementation/experimentation of this curriculum. A specific mechanism was implemented in the field to provide scientific and pedagogical support to the development of the new elementary mathematics curriculum (NPMEB) implementation at all grade levels and all over the country. In particular, the NPMEB is being experimented by a set of teachers that teach in their own classes and that have been trained and accompanied along the experience by the different authors of the program. We will focus on some classroom practices, sharing innovative and creative ideas of teachers and students, grounded on some of the tasks used by the teachers. The preliminary results suggest that some improvements are already visible, namely regarding students’ attitudes and mathematical competences and teachers’ practice

Evaluation of the implementation process of a new mathematics curriculum for Grades 1-­‐9: A discussion of the main results

Vale, Isabel; Fernandes, Domingos; Borralho, António
Fonte: Universidade de Évora Publicador: Universidade de Évora
Tipo: Aula
Português
Relevância na Pesquisa
45.38%
Recently, a new Mathematics curriculum for basic education (Grades 1-9) has been introduced in the Portuguese educational system. This curriculum was designed to bring together some disperse curricular documents and to substitute the former one that was being used since the early 90s. But, above all, the new curriculum was aimed at providing a more sustained development of students’ mathematical learning based upon recent international recommendations for mathematics teaching and learning. The new curriculum implementation was strongly supported by a special designed programme aimed at providing scientific and pedagogical support to all teachers of Grades 1-9 throughout all the schools of the country. Before its generalization to all basic education schools of the country, the new curriculum had been put into practice by 40 teachers of the different grade levels for a three-year period. These teachers had the opportunity to attend a number of workshops and to share their experiences in a variety of contexts. In fact, they functioned as a true network, working in close collaboration. Besides they were also in touch with the authors of the new curriculum to insure that it was put into practice according to the authors’ proposal. At the same time the Ministry of Education appointed a team of three mathematics educators to conduct a three-year evaluation study of the whole process of implementation of the new curriculum. An overview of this evaluation study will be presented: Besides...

Groups, Wavelets, and Wavelet Sets

Olafsson, Gestur; Speegle, Darrin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/07/2003 Português
Relevância na Pesquisa
45.34%
Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and groups acting on $\mathbb{R}^n$. We also show how this action can give rise to wavelets, and in particular, MSF wavelets)in $L^2(\mathbb{R}^n)$.

Blaschke addition and convex polyhedra

Alexandrov, Victor; Kopteva, Natalia; Kutateladze, S. S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/02/2005 Português
Relevância na Pesquisa
45.34%
This is an extended version of a talk on October 4, 2004 at the research seminar ``Differential geometry and applications'' (headed by Academician A. T. Fomenko) at Moscow State University. The paper contains an overview of available (but far from well-known) results about the Blaschke addition of convex bodies, some new theorems on the monotonicity of the volume of convex bodies (in particular, convex polyhedra with parallel faces) as well as description of a software for visualization of polyhedra with prescribed outward normals and face areas.; Comment: 17 pages, 7 figures

Finite-dimensional algebras and quivers

Savage, Alistair
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/05/2005 Português
Relevância na Pesquisa
45.34%
This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of Lusztig and Nakajima.; Comment: 9 pages, 7 figures

The use of geometric and quantum group techniques for wild quivers

Reineke, Markus
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/04/2003 Português
Relevância na Pesquisa
45.36%
This overview paper reviews several results relating the representation theory of quivers to algebraic geometry and quantum group theory. (Potential) applications to the study of the representation theory of wild quivers are discussed. To appear in the Proceedings of the International Conference on Representations of Algebras and Related Topics ICRA X, The Fields Institute, July/August 2002.; Comment: 32 pages

Differential Isomorphism and Equivalence of Algebraic Varieties

Berest, Yuri; Wilson, George
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/04/2003 Português
Relevância na Pesquisa
45.36%
In this survey article we discuss the question: to what extent is an algebraic variety determined by its ring of differential operators? In the case of affine curves, this question leads to a variety of mathematical notions such as the Weyl algebra, Calogero-Moser spaces and the adelic Grassmannian. We give a fairly detailed overview of this material.; Comment: 22 pages, to appear in a volume dedicated to Graeme Segal's 60th birthday

Simultaneous Linear Inequalities: Yesterday and Today

Kutateladze, S. S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.34%
This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.; Comment: A talk at the International Conference "Order Analysis and Related Problems of Mathematical Modeling," Vladikavkaz, July 19--24, 2010, dedicated to the 10th anniversary of the Vladikavkaz Scientific Center of the Russian Academy of Sciences

Theory and Applications of N-Fold Integer Programming

Onn, Shmuel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.36%
We overview our recently introduced theory of n-fold integer programming which enables the polynomial time solution of fundamental linear and nonlinear integer programming problems in variable dimension. We demonstrate its power by obtaining the first polynomial time algorithms in several application areas including multicommodity flows and privacy in statistical databases.; Comment: IMA Volume on Mixed Integer Nonlinear Programming, Frontier Series, Springer, to appear

Barrier methods for critical exponent problems in geometric analysis and mathematical physics

Erway, Jennifer; Holst, Michael
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/07/2011 Português
Relevância na Pesquisa
45.36%
We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. This class of problems includes the Yamabe problem and the Einstein constraint equations, which simultaneously contain several challenging features: high spatial dimension n >= 3, varying (potentially non-smooth) coefficients, critical (even super-critical) nonlinearity, non-monotone nonlinearity (arising from a non-convex energy), and spatial domains that are typically Riemannian manifolds rather than simply open sets in Rn. These problems may exhibit multiple solutions, although only positive solutions typically have meaning. This creates additional complexities in both the theory and numerical treatment of such problems, as this feature introduces both non-uniqueness as well as the need to incorporate an inequality constraint into the formulation. In this work, we consider numerical methods based on Galerkin-type discretization, covering any standard bases construction (finite element, spectral, or wavelet), and the combination of a barrier method for nonconvex optimization and global inexact Newton-type methods for dealing with nonconvexity and the presence of inequality constraints. We first give an overview of barrier methods in non-convex optimization...

Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an overview

Terwilliger, Paul
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/07/2003 Português
Relevância na Pesquisa
45.41%
Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider an ordered pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy conditions (i), (ii) below. (i) There exists a basis for $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal. (ii) There exists a basis for $V$ with respect to which the matrix representing $A$ is diagonal and the matrix representing $A^*$ is irreducible tridiagonal. We call such a pair a Leonard pair on $V$. We give an overview of the theory of Leonard pairs.; Comment: 14 pages, 1 figure

Metric spaces: The definition, and some examples

Semmes, Stephen
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/12/2010 Português
Relevância na Pesquisa
45.34%
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.; Comment: 10 pages

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Komodakis, Nikos; Pesquet, Jean-Christophe
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.36%
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness.

Transport and Concentration Problems with Interaction Effects

Santambrogio, Filippo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/08/2005 Português
Relevância na Pesquisa
45.34%
After presenting an overview about variational problems on probability measures for functionals involving transport costs and extra terms encouraging or discouraging concentration, we look for optimality conditions, regularity properties and explicit computations in the case where Wasserstein distances and interaction energies are considered.; Comment: 12 pages

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Bioucas-Dias, José M.; Plaza, Antonio; Dobigeon, Nicolas; Parente, Mario; Du, Qian; Gader, Paul; Chanussot, Jocelyn
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.36%
Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace...

Root systems and generalized associahedra

Fomin, Sergey; Reading, Nathan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.36%
These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of root systems, generalized associahedra, and the combinatorics of clusters. Lectures 1-2 cover classical material: root systems, finite reflection groups, and the Cartan-Killing classification. Lectures 3-4 provide an introduction to cluster algebras from a combinatorial perspective. Lecture 5 is devoted to related topics in enumerative combinatorics.; Comment: 69 pages, many figures. Version 3 is the final version appearing in the PCMI Lecture Series volume.

Jordan structures in mathematics and physics

Iordanescu, Radu
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/06/2011 Português
Relevância na Pesquisa
45.39%
The aim of this paper is to offer an overview of the most important applications of Jordan structures inside mathematics and also to physics, up-dated references being included. For a more detailed treatment of this topic see - especially - the recent book Iordanescu [364w], where sugestions for further developments are given through many open problems, comments and remarks pointed out throughout the text. Nowadays, mathematics becomes more and more nonassociative and my prediction is that in few years nonassociativity will govern mathematics and applied sciences. Keywords: Jordan algebra, Jordan triple system, Jordan pair, JB-, JB*-, JBW-, JBW*-, JH*-algebra, Ricatti equation, Riemann space, symmetric space, R-space, octonion plane, projective plane, Barbilian space, Tzitzeica equation, quantum group, B\"acklund-Darboux transformation, Hopf algebra, Yang-Baxter equation, KP equation, Sato Grassmann manifold, genetic algebra, random quadratic form.

Nonstandard Models and Optimization

Kutateladze, S. S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/05/2008 Português
Relevância na Pesquisa
45.38%
This is an overview of a few possibilities that are open by model theory in applied mathematics. Most attention is paid to the present state and frontiers of the Cauchy method of majorants, approximation of operator equations with finite-dimensional analogs, and the Lagrange multiplier principle in multiobjective decision making.; Comment: An extended version of a talk prepared for the International Conference "Methods of Logic in Mathematics V," June 1--6, 2008, St. Petersburg

Homogenization problems in the Calculus of Variations: an overview

Matias, José; Morandotti, Marco
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/03/2015 Português
Relevância na Pesquisa
45.42%
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems.; Comment: 11 pages