Presented as part of Thesis (Ph. D.)--University of Wisconsin--Madison, 1931. / Collective title from added t.p. Part 1 reprinted from Quarterly journal of economics, vol. XLVII (Nov. 1932), p. 36-62 -- Part 2 reprinted from Journal of the American Statistical Association, Mar. 1931, p. [36]-40 -- Part 3 reprinted from The economic journal : the quarterly journal of the Royal Economic Society, vol. XLII, no. 165 (Mar. 1932), p. [17]-26 -- Part 4 reprinted from Journal of the American Statistical Association, vol. 31 (June 1936), p. 258-272. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Made available in DSpace on 2014-06-11T19:25:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-09-25Bitstream added on 2014-06-13T19:33:05Z : No. of bitstreams: 1 rodrigues_rvr_me_prud.pdf: 1982108 bytes, checksum: 5cd99583a59b533223f322970e160062 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Esta pesquisa, referente à linha de pesquisa Tecnologias de Informação e Comunicação e Educação, consiste na construção de um Objeto de Aprendizagem (OA) fundamentado sob a perspectiva lógico-histórica e, em decorrência de sua utilização em sala de aula, na análise das potencialidades formadoras do conceito números inteiros. Proporcionar o conhecimento da constituição e extensão de um conceito matemático deve ser um desafio à implementação de qualquer recurso de natureza tecnológica no ensino da Matemática, do contrário esta ferramenta corre o risco de reproduzir técnicas esvaziadas de sentido. Para enfrentar esse desafio, o aporte teórico oferecido por Kopnin (1978), Caraça (1984), Lanner de Moura (et al 2003), Sousa (2004) e Dias (2007) mostrou o movimento histórico e intelectual de criação de conceitos como forma de pensamento e perspectiva didática na produção do conhecimento. O percurso desta investigação, concebido como um estudo de caso qualitativo dividiu-se em duas etapas. A partir dos trabalhos de Lizcano (1993/2006), Schubring (2000/2001), Lima & Moisés (1998), Prado & Moura (2007a/2007b) e Prado (2008), na primeira etapa denominada por caráter bibliográfico/laboratorial, os aspectos substanciais e simbólicos, apreendidos do desenvolvimento lógico-histórico do conceito números inteiros, aliados aos efeitos comunicacionais das novas tecnologias (BELLONI, 2000/2001)... / This research is connected to the research line Information and Communication Technologies and Education. The present paper is about the development of a Learning Object (LO) that is based on logical-historical approach and, due to it is applied to the classroom, on forming potentiality of whole numbers concepts. Providing knowledge about a mathematical concept constitution and extension might be a challenge for implementing any technological resource to Mathematics instruction. On the contrary, this toll may reproduce techniques with no meaning. In order to face such challenge, this paper is based on theoretical approaches offered by Kopnin (1978), Caraça (1984), Lanner de Moura (et al 2003), Sousa (2004) e Dias (2007) who point out the historical and intellectual movement of creating concepts as a way to think and a didactic perspective to produce knowledge. This investigation is a qualitative case study that was divided in two steps. The first one was based on Lizcano (1993/2006), Schubring (2000/2001), Lima & Moisés (1998), Prado & Moura (2007a/2007b) e Prado (2008) works. It had a bibliographical/laboratorial character. At this stage, theoretical and methodological processes of the LO “The Universe and its Opposites” production were outlined by substantial and symbolic aspects, apprehend from logical-historical development of whole numbers concept, joined to communicative effects of new technologies (BELLONI, 2000/2001)... (Complete abstract click electronic access below)

A remarkable inequality among integer numbers is given. Easily deduced from Fermat's Last Theorem, it would be nevertheless very difficult to establish through other means.

This thesis presents a series of theorems along with proofs to establish a theory of congruences.

No description available.

<p> This thesis gives new finite and asymptotic estimates of the Ramsey numbers using certain number-theoretical considerations; it also contains a brief historical survey on determination of Ramsey numbers and related number-theoretical problems.</p> / Thesis / Master of Science (MSc)

No description available.

The super Catalan numbers T(m,n) = (2m)!(2n)!=2m!n!(m+n)! are integers which generalize the Catalan numbers. Since 1874, when Eugene Catalan discovered these numbers, many mathematicians have tried to find their combinatorial interpretation. This dissertation is dedicated to this open problem. In Chapter 1 we review known results on T (m,n) and their q-analog polynomials. In Chapter 2 we give a weighted interpretation for T(m,n) in terms of 2-Motzkin paths of length m+n2 and a reformulation of this interpretation in terms of Dyck paths. We then convert our weighted interpretation into a conventional combinatorial interpretation for m = 1,2. At the beginning of Chapter 2, we prove our weighted interpretation for T(m,n) by induction. In the final section of Chapter 2 we present a constructive combinatorial proof of this result based on rooted plane trees. In Chapter 3 we introduce two q-analog super Catalan numbers. We also define the q-Ballot number and provide its combinatorial interpretation. Using our q-Ballot number, we give an identity for one of the q-analog super Catalan numbers and use it to interpret a q-analog super Catalan number in the case m= 2. In Chapter 4 we review problems left open and discuss their difficulties. This includes the unimodality of some of the q-analog polynomials and the conventional combinatorial interpretation of the super Catalan numbers and their q-analogs for higher values of m.

Orientador: Jose Plinio de Oliveira Santos / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-14T08:31:50Z (GMT). No. of bitstreams: 1 Reis_JacksonMartins_M.pdf: 998765 bytes, checksum: ea7248e69be4c892e184263be7050375 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho foram abordados tópicos de Teoria dos Números e alguns testes de primalidade. Mostramos propriedades dos números inteiros, bem como alguns critérios de divisibilidade. Apresentamos também, além das propriedades do Máximo Divisor Comum e Mínimo Múltiplo Comum, interpretações geométricas dos mesmos. Foram estudados Tópicos da Teoria de Congruências e por fim trabalhamos alguns Testes de Primalidade, com respectivos exemplos. / Abstract: In this work were discussed topics of the theory of numbers and some primality tests. We show properties of whole numbers, and some criteria for divisibility. We also present, beyond the properties of the Common Dividing Maximum and Minimum Common Multiple, geometric interpretations of the same ones. They had been study topics of theory of congruences and finally we work some of primality tests, whith respective applications. / Mestrado / Teoria dos Numeros / Mestre em Matemática

Orientador: José Plínio de Oliveira Santos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T01:08:23Z (GMT). No. of bitstreams: 1 Silva_KeniaCristinaPereira_D.pdf: 1388554 bytes, checksum: 5bb3b8622c46807f58b3ebf6cb458fca (MD5) Previous issue date: 2014 / Resumo: Neste trabalho apresentamos novas interpretações combinatórias para sequências que incluem os números de Fibonacci, os números de Pell e os números de Jacobsthal, em termos de partição. Na primeira parte listamos as identidades, definições e resultados que foram utilizados durante o trabalho. Na segunda parte introduzimos o método de Andrews para encontrar as relações de recorrência usadas nas interpretações combinatórias e exemplos de como estas interpretações foram feitas. Os capítulos seguintes estão dedicados a novas interpretações para as sequências de Fibonacci, Pell, Jacobsthal, entre outras. No último capítulo encontramos identidades entre as sequências, algumas provadas bijetivamente, através das interpretações combinatórias estabelecidas nos capítulos anteriores / Abstract: We have presented in this work new combinatorial interpretations for sequences including Fibonacci numbers, Pell numbers and Jacobsthal numbers, in terms of partitions. At the first moment we have listed the identities, definitions and results that we used in this work. Next we have introduced the Andrews method to find out the recurrence relations used at combinatorial interpretations and examples that them had been done. The next chapters are dedicated to new interpretations to Fibonacci, Pell and Jacobsthal sequences, and others. Lastly we have found identities among the sequences, some of them proved bijectively, through combinatorial interpretations setted up on previous chapters / Doutorado / Matematica Aplicada / Doutora em Matemática Aplicada