The history of Lapland : containing a geographical description, and a natural history of that country; with an account of the inhabitants, their original, religion, customs, habits, marriages, conjurations, employments, &c. Written by John Scheffer, ... Translated from the last edition in Latin, and illustrated with many curious copper-cutts. To which are added, the travels of the King of Sweden's mathematicians into Lapland: the history of Livonia, and the wars there: also a journey into Lapland, Finland, &c. Written by Dr. Olof Rudbeck in the year 1701

Added engraved title page: The history of Lapland.

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

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.

Of men and numbers; the story of the great mathematicians

Mode of access: Internet.

Transactions of the ... Conference of Army Mathematicians.

Mode of access: Internet.

Miscellanea mathematica: consisting of a large collection of curious mathematical problems, and their solutions. Together with many other important disquisitions in various branches of the mathematics. Being the literary correspondence of several eminent mathematicians.

Includes tables and diagrams.

Numerical Uncertainty and Its Implications

Copyright © 2014 António F. Rodrigues, Nuno O. Martins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accordance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual property António F. Rodrigues, Nuno O. Martins. All Copyright © 2014 are guarded by law and by SCIRP as a guardian.

José Anastácio da Cunha e o projeto MAT² : no trilho de uma história extraordinária

A ideia de que as Matemáticas de Portugal (e de Espanha) atravessaram, depois de um período áureo nos Descobrimentos, um longo deserto onde não foi possível florescerem Mestres, nem escolas, nem cultura científica, nem investigação de relevo foi, durante muito tempo, reiteradamente veiculada, inclusivé através de alguns dos nossos mais referenciados historiadores da Matemática, como é o caso de Gomes Teixeira ou de Rey Pastor. Mas a verdade é que o estudo da História das Matemáticas em Portugal tem, na última década, vivido um interesse crescente onde sobressaem, em particular, uma leitura menos enviesada sobre, por exemplo, o papel educativo dos Jesuítas ou a publicação das obras completas de Pedro Nunes. Está-se assim a contribuir para uma compreensão mais completa da História geral de Portugal, de que a História da Ciência e da Cultura faz parte. José Anastácio da Cunha (1744-1787) foi figura de proa no século XVIII português. Sabíamo-lo matemático que, sem nunca ter saído de Portugal, havia sido capaz de antecipar, em mais de 50 anos, os esforços de matemáticos franceses e alemães para fundar a Matemática com rigor. Sabíamo-lo também autor de uma vasta e diversificada obra de inegável importância matemática mas, igualmente, autor de textos poéticos. Agora, com o projecto que denominámos de MAT2, centramo-nos em José Anastácio da Cunha e pretendemos, se possível, ir ainda mais além. Partimos de uma descoberta, árdua mas com final feliz, em um Arquivo de família: o da Casa de Mateus. Sentimo-nos, com esta “sorte”, privilegiados e gratos por nos ter sido gentilmente concedido o acesso a um vasto conjunto de documentos únicos (diários de viagens, notas de aulas e correspondência) que incluem memórias autógrafas e inéditas de Anastácio da Cunha. Organizámo-nos, cientes do trabalho árduo que temos pela frente, multi e interdisciplinarmente englobando a Matemática (nas suas múltiplas especializações) e a História (incluindo a da Matemática) mas também contando com a Física, a Informática, os estudos militares ou a Arquivística e as Humanidades; reunimos académicos, mais e menos veteranos, com investigadores jovens e juntámos valências nacionais e estrangeiras. No presente artigo daremos conta do percurso trilhado, até agora, pelo projecto MAT2.

Las reformas de las universidades ibéricas en la segunda mitad del siglo XVIII

Bajo los auspicios reformadores del Marqués de Pombal, los nuevos estatutos de la Universidad de Coimbra, ratificados por el rey José I en junio de 1772, representaron una importante revisión de los principales estudios en Portugal. Hacia un largo tiempo que los Estatutos de la Universidad de Coimbra no fueron revisados, y la revisión de los Estatutos de 1559 (rey Sebastián), 1591 (el rey Felipe I de Portugal, II de Castilla) y 1653 (rey João IV), se observa que, en comparación con más de dos siglos de vigencia del mismo modelo con modificaciones más o menos limitados, los Estatutos de 1772 traen un nuevo pensamiento y un nuevo impulso mediante la promoción, en particular, de la educación y el desarrollo de las Ciencias exactas y naturales y la valoración del método experimental. Al mismo tiempo, en España, el rey Carlos III, renuncia a imponer un único modelo de estudios de todas las universidades. En ambos casos, el portugués y el español, la urgencia de las reformas es mas aguda pues que los jesuitas fueron expulsados de los territorios en 1759 y 1767, respectivamente; y tanto precursores como mentores quieren estas reformas para abrir las universidades a la ciencia moderna y el humanismo de la Ilustración. La renovación de los contenidos y métodos de enseñanza en Coimbra fue notoria, con la preocupación notable con la investigación, lo que no era muy común en la época. Había también una preocupación con las necesidades de la sociedad en una forma muy práctica (habiendo sido en la época construido el Observatorio Astronómico, el Laboratorio de Física, etc.). Al mismo tempo, la universidad de Coimbra tuvo como profesores dos matemáticos notables, José Anastácio da Cunha y José Monteiro da Rocha. En España también fueron importantes los ensayos de renovación de los métodos, de apertura a la ciencia de la época, de conexión con las realidades de la sociedad española, de coordinación de esfuerzos para conformar una «comunidad universitaria española». En esta comunicación se hace una discusión de comparación entre las dos reformas ibéricas.

Sistema de apoio à aprendizagem na área da discalculia em menores

Dissertação de mestrado integrado em Engenharia Biomédica (área de especialização em Informática Médica)

Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil

Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.

Geometry and physics of catenanes applied to the study of DNA replication.

The concept of ideal geometric configurations was recently applied to the classification and characterization of various knots. Different knots in their ideal form (i.e., the one requiring the shortest length of a constant-diameter tube to form a given knot) were shown to have an overall compactness proportional to the time-averaged compactness of thermally agitated knotted polymers forming corresponding knots. This was useful for predicting the relative speed of electrophoretic migration of different DNA knots. Here we characterize the ideal geometric configurations of catenanes (called links by mathematicians), i.e., closed curves in space that are topologically linked to each other. We demonstrate that the ideal configurations of different catenanes show interrelations very similar to those observed in the ideal configurations of knots. By analyzing literature data on electrophoretic separations of the torus-type of DNA catenanes with increasing complexity, we observed that their electrophoretic migration is roughly proportional to the overall compactness of ideal representations of the corresponding catenanes. This correlation does not apply, however, to electrophoretic migration of certain replication intermediates, believed up to now to represent the simplest torus-type catenanes. We propose, therefore, that freshly replicated circular DNA molecules, in addition to forming regular catenanes, may also form hemicatenanes.

Pasquale del Pezzo, Duke of Caianello, Neapolitan mathematician

This article is dedicated to a reconstruction of some events and achievements, both personal and scientific, in the life of the Neapolitan mathematician Pasquale del Pezzo, Duke of Caianello.