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- FIU Digital Commons
- Washington, DC
- UNESP-DEPT MATHEMATICA
- Biblioteca Digital da Unicamp
- Instituto Politécnico do Porto. Instituto Superior de Contabilidade e Administração do Porto
- UNESP - Universidade Estadual Paulista, Pró-Reitoria de Pesquisa; Programa de Pós-Graduação em Educação Matemática
- Universidade de Lisboa
- Universidade Cornell
- Mais Publicadores...

## Effects of using manipulative materials to teach remedial algebra to community college students on achievement and attitudes towards mathematics

Fonte: FIU Digital Commons
Publicador: FIU Digital Commons

Tipo: Artigo de Revista Científica

Português

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This dissertation derived hypotheses from the theories of Piaget, Bruner and Dienes regarding the effects of using Algebra Tiles and other manipulative materials to teach remedial algebra to community college students. The dependent variables measured were achievement and attitude towards mathematics. The Piagetian cognitive level of the students in the study was measured and used as a concomitant factor in the study.^ The population for the study was comprised of remedial algebra students at a large urban community college. The sample for the study consisted of 253 students enrolled in 10 sections of remedial algebra at three of the six campuses of the college. Pretests included administration of an achievement pre-measure, Aiken's Mathematics Attitude Inventory (MAI), and the Group Assessment of Logical Thinking (GALT). Posttest measures included a course final exam and a second administration of the MAI.^ The results of the GALT test revealed that 161 students (63.6%) were concrete operational, 65 (25.7%) were transitional, and 27 (10.7%) were formal operational. For the purpose of analyzing the data, the transitional and formal operational students were grouped together.^ Univariate factorial analyses of covariance ($\alpha$ =.05) were performed on the posttest of achievement (covariate = achievement pretest) and the MAI posttest (covariate = MAI pretest). The factors used in the analysis were method of teaching (manipulative vs. traditional) and cognitive level (concrete operational vs. transitional/formal operational).^ The analyses for achievement revealed a significant difference in favor of the manipulatives groups in the computations by campus. Significant differences were not noted in the analysis by individual instructors.^ The results for attitude towards mathematics showed a significant difference in favor of the manipulatives groups for the college-wide analysis and for one campus. The analysis by individual instructor was not significant. In addition...

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## Vietnam : Reading and Mathematics Assessment Study, Volume 3

Fonte: Washington, DC
Publicador: Washington, DC

Tipo: Economic & Sector Work :: Other Education Study; Economic & Sector Work

Português

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#CLASS SIZE#CLASSROOMS#CURRICULUM#DISTANCE LEARNING#EDUCATIONAL ACHIEVEMENT#EDUCATIONAL DEVELOPMENT#EDUCATIONAL OUTCOMES#EDUCATIONAL SCIENCE#EDUCATIONAL SCIENCES#EFFECTIVE SCHOOLS#FEMALE TEACHERS

This paper contains three volumes
presenting the Vietnam Reading and Mathematics Assessment
Study conducted in 2001. The first volume sets the study in
its country context, describes its genesis, outlines the
methodology, and summarizes the results. The main purpose is
to show how the analysis of the study results points to
specific policy interventions. The strong link between a
teacher's subject knowledge, and the performance of her
pupils argues for teacher upgrade programs, while the high
variation of pupil performance between schools in the same
province calls for local programs that improve school
effectiveness. The first volume is followed by a second
volume detailing the study results, and a third providing a
full description of the study methodology.

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## Avaliação do Processo de Ensino e Aprendizagem em Matemática: contribuições da teoria histórico-cultural; Evaluation of the Teaching and Learning Process in Mathematics: contributions from historical-cultural theory

Fonte: UNESP-DEPT MATHEMATICA
Publicador: UNESP-DEPT MATHEMATICA

Tipo: Artigo de Revista Científica

Português

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#Activity Theory#Teaching Activity#Learning Activity#Teaching of Mathematics#Learning Evaluation#Education & Educational Research

This article presents the results of a study that investigated the meaning of evaluation in mathematics from the historical cultural perspective, focusing on activity theory. In order to develop the investigation, a collaborative group was formed from the Oficina Pedagogica de Matematica de Ribeirao Preto - Sao Paulo (Math Pedagogic Workshop of Ribeirao Preto - OPM/RP), constituted of pre-school teachers and early elementary school teachers, who were participants in this research. The main role of the collaborative group was to offer guided development to the teachers about the teaching of mathematics from the historical-cultural perspective, aiming at collecting data on the process of appropriation of mathematical knowledge by the teachers. The syntheses about the teachers' learning process have contributed to systematize the guiding elements of evaluation in mathematics from the historical-cultural perspective.

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## O infinito de George Cantor : uma revolução paradigmatica no desenvolvimento da matematica; The George Cantor's infinite : a paradigmatic revolution in the development of mathematics

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 30/05/2008
Português

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Georg Cantor foi um dos mais importantes matemáticos do final do século XIX. A idealização de sua teoria de conjuntos representa um marco no desenvolvimento da matemática. De fato, o aparecimento e o desenvolvimento dessa teoria tiveram profundas conseqüências que não se limitaram ao círculo da matemática. O debate científico que se seguiu a certos resultados como, por exemplo, a apresentação dos números transfinitos, reavivou uma discussão que remonta a antigas disputas ontológicas da filosofia présocrática, exatamente àquelas discussões que se voltavam para a afirmação do Ser como infinito. Essa discussão nasce na Grécia antiga e perpassa toda a história do pensamento ocidental. Conhecemo-la por meio de nomes como Anaximandro, Pitágoras, Parmênides, Platão, Aristóteles. Atravessando os séculos, essas idéias povoaram a mente de personagens como Bruno, Galileu, Leibniz, Kant e muitos outros. Nos séculos XIX e XX, os trabalhos de Cantor reavivaram e deram novo impulso ao tema. Esforçamo-nos em mostrar que estes trabalhos são absolutamente revolucionários. Motivados pelo filósofo da ciência Thomas Kuhn, concluímos que o aparecimento da Teoria de Conjuntos de Cantor representa a revisão de um antigo paradigma filosófico-matemático. Paradigma este que teve sua primeira elaboração lógica e filosófica com Aristóteles e que se desenvolveu como a maneira dominante de pensar a idéia de infinito. Destacamos que alguns dos aspectos apontados por Kuhn como sintomáticos de uma revolução científica estão presentes no trabalho de Cantor e que há...

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## A matemática moderna e o Ginásio Estadual Vocacional Oswaldo Aranha : sobre caminhos e encontros; Modern mathematics and the Oswaldo Aranha State Vocational High School : on paths and encounters

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 25/02/2013
Português

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#Educação matematica - História#Matemática moderna#Ginasio vocacional#History of the education of mathematics#Modern mathematics#Vocational high schools

Este trabalho busca discutir os caminhos e encontros de dois grandes movimentos educacionais da década de 1960. São eles: a Matemática Moderna, movimento internacional de renovação do ensino da disciplina que, no Brasil, teve o Grupo de Estudos do Ensino da Matemática (GEEM) como principal difusor, e os Ginásios Vocacionais, experiência educacional nacional baseada nas Classes Experimentais, que por sua vez foram inspiradas nas Classes Nouvelles francesas. Os Ginásios Vocacionais foram considerados uma experiência diferenciada por propor uma formação não apenas teórica, mas integral do estudante, desenvolvedora de habilidades teóricas e práticas. A relação entre os movimentos dar-se-á através de um de seus integrantes, a professora Lucília Bechara Sanchez, educadora presente na lista de fundadores do GEEM e primeira docente de matemática do Ginásio Estadual Vocacional "Oswaldo Aranha", o GEVOA, sendo três anos mais tarde nomeada coordenadora da disciplina do Serviço de Ensino Vocacional (SEV), órgão gerenciador dos Ginásios Vocacionais de São Paulo. Para tanto situaremos no contexto deste período: o nascimento, atuação e esgotamento do GEEM na perspectiva dos jornais que veiculavam na época as ações do grupo...

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## O Colegio Tecnico de Limeira e o Movimento da Matematica Moderna : uma paisagem; The Limeira Technical School and the Modern Mathematics Movement : a view

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 29/01/2010
Português

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#Ensino tecnico#Matematica moderna#Historia oral#Limeira Technical School#Technical education#Modern mathematics#Oral history

O Colégio Técnico de Limeira (Cotil), da Universidade Estadual de Campinas, foi instalado em 1967, na cidade Limeira - SP, então grande pólo industrial na área de mecânica e metalurgia. Nesse mesmo período, de vigência do projeto político-econômico desenvolvimentista do regime militar e dos acordos MECUSAID, temos em nosso país o fortalecimento de um movimento internacional para introdução de projetos inovadores do ensino de Matemática denominado "Movimento da Matemática Moderna". Este trabalho tem como objetivo analisar como um grupo de professores que lecionaram no COTIL, nos primeiros vinte anos de seu funcionamento, percebeu os processos de transformação da instituição e se posicionou em relação ao Movimento de Matemática Moderna. Utilizando a História Oral como metodologia central da investigação, constituímos documentos escritos, a partir dos relatos orais, que foram complementados por outros documentos, tais como: atas de reuniões, diários de professores, planos de disciplina, livros didáticos, legislações educacionais, fotografias.; The Technical College of Limeira (Cotil) as part of State University of Campinas started the activities in 1967 in Limeira -SP , at the time one of the greatest industrial areas for Mechanics and Metallurgy industry. At the same period that the country was under political and economic military regime bringing the incentives for strengthening of international movement for introduction of innovative projects in Mathematics teaching denominated as "Movement of Modern Mathematics". This work has the objective to describe how a group of math teachers realized the transformation process at Cotil during the primary years and how these teachers had positioned themselves into the Movement of Modern Mathematics. To perform the analyzes...

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## Teaching and learning mathematics using moodle

Fonte: Instituto Politécnico do Porto. Instituto Superior de Contabilidade e Administração do Porto
Publicador: Instituto Politécnico do Porto. Instituto Superior de Contabilidade e Administração do Porto

Tipo: Artigo de Revista Científica

Publicado em //2008
Português

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This paper summarizes a project that is contributing to a change in the way of teaching and learning
Mathematics.
Mathematics is a subject of the Accounting and Administration course. In this subject we teach:
Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply
them in other issues, when possible, establishing a bridge between the issues that they have studied
and their application in Accounting.
As from this year, the Accounting course falls under in Bologna Process. The teacher and the student
roles have changed. The time for theoretical and practical classes has been reduced, so it was
necessary to modify the way of teaching and learning.
In the theoretical classes we use systems of multimedia projection to present the concepts, and in the
practical classes we solve exercises. We also use the Excel and the mathematical open source
software wxMaxima.
To supplement our theoretical and practical classes we have developed a project called MatActiva
based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project).
With the creation of this new project we wanted to take advantage already obtained results with the
previous experiences, giving to the students opportunities to complement their study in Mathematics.
One of the great objectives is to motivate students...

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## Symmetry and rotation skills of prospective elementary mathematics teachers

Fonte: UNESP - Universidade Estadual Paulista, Pró-Reitoria de Pesquisa; Programa de Pós-Graduação em Educação Matemática
Publicador: UNESP - Universidade Estadual Paulista, Pró-Reitoria de Pesquisa; Programa de Pós-Graduação em Educação Matemática

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/04/2014
Português

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The aim of this study was to investigate the skills and deficiencies of senior university students enrolled in a mathematics education program with the concepts of symmetry and rotation of geometric figures. The study was conducted with 32 prospective teachers in the Department of Education at a public university located in Western Turkey. This descriptive study was designed with a case study. A structured interview technique was used for data collection. A measurement tool consisting of 12 drawing problems testing symmetry (5 problems) and rotation (7 problems) ability was used in the study. Descriptive statistical methods were used for data analysis. The drawings were analyzed individually, and the students' mistakes and deficiencies were categorized. According to the results of the study, prospective elementary mathematics teachers did not have difficulty in drawing the symmetry of an object or in determining the symmetry axis. However, while they could rotate the figure when a rotation axis was provided, they failed to rotate it in the absence of an axis. In addition, prospective elementary mathematics teachers generally failed to find the center of the given rotated figures. The results of the present study were consistent with results in the literature.

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## Students' views and attitudes towards mathematics teaching and learning: A case study of a curriculum experience

Fonte: Universidade de Lisboa
Publicador: Universidade de Lisboa

Tipo: Conferência ou Objeto de Conferência

Publicado em //1992
Português

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This paper describes a qualitative case study dealing with the views about mathematics teaching and learning held by students of a school involved in a experience of new curricula, stressing active methodologies and groupwork. At grade 7, the students noticed important differences in the mathematics classes and welcomed them. At grade 10, students had a general positive attitude towards mathematics but did not perceive major chnages. However, they were very concerned with the implications of this experience for their academic progression.

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## Recursion and Combinatorial Mathematics in Chandashaastra

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Contribution of Indian Mathematics since Vedic Period has been recognised by
the Historians. Pingala (200 BC) in his book on 'Chandashaastra', a text
related to the description and analysis of meters in poetic work, describes
algorithms which deal with the Combinatorial Mathematics. These algorithms
essentially deal with the conversion of Binary numbers to Decimal numbers and
vice versa, finding the value of 'n choose r', evaluating 2^n, etc. All these
algorithms are recursive in nature. There are also evidences of making use of
stack variables to stack the intermediate results for later use. Interestingly
later work by Kedar Bhatt (around 800 AD) has only iterative algorithms for the
same problems. We describe both the recursive as well as iterative algorithms
in this paper.; Comment: 25 pages

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## On the transition period of implementing new mathematics curriculum for Foundation Engineering students

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/03/2015
Português

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An overview on several mathematics modules in the transition period of
introducing a new curriculum for the Foundation programme in Engineering at the
University of Nottingham Malaysia Campus is discussed in this paper. In order
to progress to Undergraduate programmes in Engineering, previously the students
must complete three mathematics modules of 40 credit points in total, for which
one of them was a year-long module with 20 credit points. Currently under the
new curriculum, the students are required to complete five mathematics modules
with 10 credit points each. The new curriculum gives positive impacts for both
the lecturers and the students in terms of material organization, fully
utilizing textbooks and a new arrangement for tutorial sessions. The new
curriculum also provides the students with stronger mathematical background in
critical thinking and problem solving skills to equip them to embark the
Undergraduate programmes in Engineering.; Comment: 17 pages

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## Mathematics and language

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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This essay considers the special character of mathematical reasoning, and
draws on observations from interactive theorem proving and the history of
mathematics to clarify the nature of formal and informal mathematical language.
It proposes that we view mathematics as a system of conventions and norms that
is designed to help us make sense of the world and reason efficiently. Like any
designed system, it can perform well or poorly, and the philosophy of
mathematics has a role to play in helping us understand the general principles
by which it serves its purposes well.

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## Application of multivariate splines to discrete mathematics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Combinatorics#Mathematics - Functional Analysis#Mathematics - Numerical Analysis#05A15

Using methods developed in multivariate splines, we present an explicit
formula for discrete truncated powers, which are defined as the number of
non-negative integer solutions of linear Diophantine equations. We further use
the formula to study some classical problems in discrete mathematics as
follows. First, we extend the partition function of integers in number theory.
Second, we exploit the relation between the relative volume of convex polytopes
and multivariate truncated powers and give a simple proof for the volume
formula for the Pitman-Stanley polytope. Third, an explicit formula for the
Ehrhart quasi-polynomial is presented.; Comment: Box splines; Number of integer points in polytopes; Pitman-Stanley
polytope

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## Hypothesis of the Functional Semantic Constructions and Mathematics in the Functional Semantic Aspect

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/06/2002
Português

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This essay contains three parts. The first part of essay focuses on the
hypothesis of the functional semantic constructions (FSC-Hypothesis). This
hypothesis explains that a language, a number, a money are the functional
semantic constructions. In the second part the author considers the Mathematics
with respect to the FSC-Hypothesis. Author turns in the solution for the
following problems: Ontology of Mathematics, Objects of Mathematics, Number,
Classification of the numbers. Last part contains the critical remarks to the
axiomatic allocation of the real numbers to the linear point continuum and to
the countability / uncountability of the set of rational and of the set of real
numbers.

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## Topical Bias in Generalist Mathematics Journals

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Generalist mathematics journals exhibit bias toward the branches of
mathematics by publishing articles about some subjects in quantities far
disproportionate to the production of papers in those areas within all of
mathematics.; Comment: 8 pages, 3 figures

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## Klein's double discontinuity revisited: what use is university mathematics to high school calculus?

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Much effort and research has been invested into understanding and bridging
the gaps which many students experience in terms of contents and expectations
as they begin university studies with a heavy component of mathematics,
typically in the form of calculus courses. We have several studies of bridging
measures, success rates and many other aspects of these entrance transition
problems. In this paper, we consider the inverse transition, experienced by
university students as they revisit core parts of high school mathematics (in
particular, calculus) after completing the mandatory undergraduate mathematics
courses. To what extent does the advanced experience enable them to approach
the high school calculus in a deeper and more autonomous way? To what extent
can capstone courses support such an approach? How could it be hindered by
deficiencies in the students' advanced experience? In this paper, we present a
theoretical framework for an analysis of these questions, as well as a number
of critical observations and reflections on how they appear in our own
institutional context.; Comment: Will appear in "Recherches en Didactique des Math\'ematiques" vol. 34
no. 1

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## Responses to ``Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics'', by A. Jaffe and F. Quinn

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/03/1994
Português

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This article is a collection of letters solicited by the editors of the
Bulletin in response to a previous article by Jaffe and Quinn
[math.HO/9307227]. The authors discuss the role of rigor in mathematics and the
relation between mathematics and theoretical physics.; Comment: 30 pages. Abstract added in migration.

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## Reforms of the university mathematics education for non-mathematical specialties

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/04/2003
Português

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This article is a part of the report for the research project ``Reform of the
Course System and Teaching Content of Higher Mathematics (For Non-Mathematical
Specialties)'' in 1995, supported by the National Ministry of Education. There
are thirteen universities participated in this project. The Report not only
reflects results of our participants, but also includes valuable opinions of
many colleagues in the mathematical education circles. In this article, after a
brief description on the history and reform situation of the higher mathematics
education in China, attention concentrates to three aspects. They are: main
problems in this field existing; the functions of mathematics accomplishment
for college students; these concern course system, teaching and learning
philosophy, such as overemphasized specialty education, overlooking to arouse
rational thinking and aesthetic conceptions, etc. The last aspect contains a
discussion on several important relationships, such as: knowledge impartment
and quality cultivation, inherence and modernization of the mathematical
knowledge, teacher's guidance and students' initiative, mathematical basic
training and mathematical application consciousness and ability cultivation,
etc.

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## The strength of the tree theorem for pairs in reverse mathematics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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No natural principle is currently known to be strictly between the arithmetic
comprehension axiom (ACA) and Ramsey's theorem for pairs (RT^2_2) in reverse
mathematics. The tree theorem for pairs (TT^2_2) is however a good candidate.
The tree theorem states that for every finite coloring over tuples of
comparable nodes in the full binary tree, there is a monochromatic subtree
isomorphic to the full tree. The principle TT^2_2 is known to lie between ACA
and RT^2_2 over RCA, but its exact strength remains open. In this paper, we
prove that RT^2_2 together with weak K\"onig's lemma (WKL) does not imply
TT^2_2, thereby answering a question of Montalban. This separation is a case in
point of the method of Lerman, Solomon and Towsner for designing a
computability-theoretic property which discriminates between two statements in
reverse mathematics. We therefore put the emphasis on the different steps
leading to this separation in order to serve as a tutorial for separating
principles in reverse mathematics.; Comment: 16 pages

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## Nonlocal Mathematics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/08/2000
Português

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This is a research announcement on what is best termed `nonlocal' methods in
mathematics. (This is not to be confused with global analysis.) The nonlocal
formulation of physics in \cite{principia} points to a fresh viewpoint in
mathematics: Nonlocal viewpoint. It involves analyzing objects of geometry and
analysis using nonlocal methods, as opposed to the classical local methods,
e.g., Newton's calculus. It also involves analyzing new nonlocal geometries and
nonlocal analytical objects, i.e. nonlocal fields. In geometry, we introduce
and study (nonlocal) forms, differentials, integrals, connections, curvatures,
holonomy, G-structures, etc. In analysis, we analyze local fields using
nonlocal methods (semilocal analysis); nonlocal fields nonlocally (of course);
and the connection between nonlocal linear analysis and local nonlinear
analysis. Analysis and geometry are next synthesized to yield nonlocal (hence
noncommutative) homology, cohomology, de Rham theory, Hodge theory, Chern-Weil
theory, K-theory (called N-theory) and index theory. Applications include
theorems such as nonlocal-noncommutative Riemann-Roch, Gauss-Bonnet, Hirzebruch
signature, etc. The nonlocal viewpoint is also investigated in algebraic
geometry, analytic geometry...

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