This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like infinity, area, motion, and continuous change slowly evolved through solving problems and cultural exchange. I argue that bringing this history into the classroom helps students see calculus as more than a set of procedures: it becomes a story of human creativity and persistence. By revisiting the questions early mathematicians struggled with, students can better appreciate and better understand the core ideas behind the formulas they use today.
El abastecimiento de agua potable durante los años cuarenta en el estado de Veracruz, fue un proceso lento que reflejó la pausada mejora de la infraestructura urbana por parte de los gobiernos municipales. Para el caso xalapeño, en el primer lustro de esa década, ocurrieron una serie de cuestiones relacionadas con el líquido que denotaron la precaria gestión y el intento por mejorar la infraestructura hídrica. En este sentido, el presente artículo aborda la percepción del ayuntamiento xalapeño frente al proyecto de «modernidad nacional»,[1] a través del análisis del contenido de las peticiones municipales, específicamente a partir del servicio de agua potable para dar cuenta de sus acciones respecto a ello. Reflexionando así, desde una perspectiva de historia local que permite entender que los procesos urbanos no son unilaterales en ámbitos regionales.
La investigación sobre la infancia, adolescencia y familia en Latinoamérica tiene una larga tradición y, a la vez, una ardua tarea por delante. El libro que reseñamos es el resultado de un proyecto colectivo que indaga las jerarquías sociales en el siglo XX en Argentina, a partir de la infancia y la familia. La autoría está a cargo de investigadoras e investigadores con una sólida formación en historia y quienes desarrollan su trabajo en el marco del Grupo de Investigación Histórica Familias e Infancias en la Argentina Contemporánea, Instituto Interdisciplinario de Estudio de Género de la Facultad de Filosofía y Letras de la Universidad de Buenos Aires.
The Aryabhatta Research Institute of Observational Sciences (ARIES), a premier autonomous research institute under the Department of Science and Technology, Government of India has a legacy of about seven decades with contributions made in the field of observational sciences namely atmospheric and astrophysics. The Survey of India used a location at ARIES, determined with an accuracy of better than 10 meters on a world datum through institute participation in a global network of Earth artificial satellites imaging during late 1950. Taking advantage of its high-altitude location, ARIES, for the first time, provided valuable input for climate change studies by long term characterization of physical and chemical properties of aerosols and trace gases in the central Himalayan regions. In astrophysical sciences, the institute has contributed precise and sometime unique observations of the celestial bodies leading to a number of discoveries. With the installation of the 3.6 meter Devasthal optical telescope in the year 2015, India became the only Asian country to join those few nations of the world who are hosting 4 meter class optical telescopes. This telescope, having advantage of geographical location, is well-suited for multi-wavelength observations and for sub-arc-second resolution imaging of the celestial objects including follow-up of the GMRT, AstroSat and gravitational-wave sources.
El desarrollo histórico de la institucionalidad indígena en Costa Rica, en el periodo 1970-2000, tiende a olvidarse de los intereses culturales, sociales y económicos de las poblaciones indígenas, pero como respuesta, estas últimas se han encargado de dejar claro que las instituciones están fallando, por lo que procederán a deslegitimarlas. Pero existen algunas asociaciones de desarrollo que han sabido defender sus intereses, por encima del Estado o de personas ajenas a su etnia, y su resultado es que las comunidades den su aceptación y la legitimidad a la institución como gobierno local. En este texto se realiza un acercamiento a la legitimidad y aceptación que poseen los entes oficiales como la Comisión Nacional de Asuntos Indígenas, y las Asociaciones de Desarrollo Integral indígena dentro de los pueblos de Salitre y Cabagra en la zona sur del país. El análisis se realiza con base en diversas fuentes primarias, como prensa nacional, documentos jurídicos, y documentaciones localizadas en la Dirección Nacional de Desarrollo de la Comunidad, entre estas, cartas de miembros de la comunidad, informes de asambleas y denuncias.
María Carolina Zapiola estudia el proceso de transformación registrado en la infancia de los sectores populares en la ciudad de Buenos Aires. A partir del análisis de las instituciones de encierro de la capital argentina a fines del siglo XIX y comienzos del XX da cuenta de la exclusión de la niñez para su conversión en «menores» o sea una categoría en las que se les vincularía a la infracción penal.
A la luz del análisis de las coyunturas de auge y crisis de la caficultura nacional, entre 1980 y 2008, se desarrolla un estudio de caso en el cantón de Naranjo, Alajuela, con el propósito de valorar el impacto de dichos procesos socioeconómicos en las continuidades y rupturas en las tradiciones ocupacionales y su incidencia en las experiencias y constitución de las identidades de las y los jóvenes de la zona. Para tales efectos, se ejecuta una estrategia metodológica que propone el estudio de la historia del presente, por medio de la valoración de tres generaciones coexistentes en la zona, para la comprensión de sus encuentros y conflictividades. Producto de este ejercicio comparativo se esbozarán recomendaciones para la ejecución de políticas públicas inclusivas para las y los jóvenes, que estimulen la activa participación ciudadana, el empoderamiento y la búsqueda de soluciones a las problemáticas que afectan a este segmento en particular de la población.
We continue our efforts to understand, within the framework of the quantum mechanics of the universe as a whole, the quasiclassical realm of familiar experience as a feature emergent from the Hamiltonian of the elementary particles and the initial condition of the universe. Quantum mechanics assigns probabilities to exhaustive sets of alternative decoherent histories of the universe. We introduce and define the notion of strong decoherence. We replace the notion of maximal sets of alternative decohering histories by defining the more useful concept of "full" sets of alternative strongly decohering histories. These full sets fall into equivalence classes each of which is characterized by a basis in Hilbert space. Finally we describe our continuing efforts to find measures of classicality --- measures that could be applied to such full sets of alternative strongly decohering so as to characterize a quasiclassical realm.
Gene duplication is a major mechanism through which new genetic material is generated. Although numerous methods have been developed to differentiate the ortholog and paralogs, very few differentiate the "Parent-Daughter" relationship among paralogous pairs. As coined by the Mira et al, we refer the "Parent" copy as the paralogous copy that stays at the original genomic position of the "original copy" before the duplication event, while the "Daughter" copy occupies a new genomic locus. Here we present a novel method which combines the phylogenetic reconstruction of duplications at different evolutionary periods and the synteny evidence collected from the preserved homologous gene orders. We reconstructed for the first time a deep evolutionary history of "Parent-Daughter" relationships among genes that were descendants from 2 rounds of whole genome duplications (2R WGDs) at early vertebrates and were further duplicated in later ceancestors like early Mammalia and early Primates. Our analysis reveals that the "Parent" copy has significantly fewer accumulated mutations compared with the "Daughter" copy since their divergence after the duplication event. More strikingly, we found that the "Parent" copy in a duplication event continues to be the "Parent" of the younger successive duplication events which lead to "grand-daughters".
La proclamación de Fernando VII en la ciudad de Guatemala legó, de la pluma de Antonio Juarros, unos de los más completos ejemplares del género literario de la relación de fiestas. Guatemala por Fernando Sétimo el día 12 de diciembre de 1808, es tanto una síntesis de los complejos acontecimientos políticos que enfrentó el imperio español a raíz de la invasión francesa de la península ibérica como una muestra de las transformaciones que experimentó la retórica de la lealtad que había operado durante el período barroco a ambos lados del Atlántico.
The amount of information available to the mathematics teacher is so enormous that the selection of desirable content is gradually becoming a huge task in itself. With respect to the inclusion of elements of history of mathematics in mathematics instruction, the era of Big Data introduces a high likelihood of Recency Bias, a hitherto unconnected challenge for stakeholders in mathematics education. This tendency to choose recent information at the expense of relevant older, composite, historical facts stands to defeat the aims and objectives of the epistemological and cultural approach to mathematics instructional delivery. This study is a didactic discourse with focus on this threat to the history and pedagogy of mathematics, particularly as it affects mathematics education in Nigeria. The implications for mathematics curriculum developers, teacher-training programmes, teacher lesson preparation, and publication of mathematics instructional materials were also deeply considered.
The present discussion concerning certain fundamental physical theories (such as string theory and multiverse cosmology) has reopened the demarcation problem between science and non-science. While parts of the physics community see the situation as a beginning epistemic shift in what defines science, others deny that the traditional criterion of empirical testability can or should be changed. As demonstrated by the history of physics, it is not the first time that drastic revisions of theory assessment have been proposed. Although historical reflection has little to offer modern physicists in a technical sense, it does offer a broader and more nuanced perspective on the present debate. This paper suggests that history of science is of some indirect value to modern physicists and philosophers dealing with string theory, multiverse scenarios, and related theoretical ideas.
The genesis of the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) after German re-unification as described here, shows that the history of the founding of the institute is not as simplistic as claimed e.g., in the presentation by the institute.Quite a few people and institutions have been involved.The institute now seems to be one of the largest institution for research in gravity, worldwide.
This is a partial account of the fascinating history of Distance Geometry. We make no claim to completeness, but we do promise a dazzling display of beautiful, elementary mathematics. We prove Heron's formula, Cauchy's theorem on the rigidity of polyhedra, Cayley's generalization of Heron's formula to higher dimensions, Menger's characterization of abstract semi-metric spaces, a result of Goedel on metric spaces on the sphere, and Schoenberg's equivalence of distance and positive semidefinite matrices, which is at the basis of Multidimensional Scaling.
The increasing complexity of deep learning architectures is resulting in training time requiring weeks or even months. This slow training is due in part to vanishing gradients, in which the gradients used by back-propagation are extremely large for weights connecting deep layers (layers near the output layer), and extremely small for shallow layers (near the input layer); this results in slow learning in the shallow layers. Additionally, it has also been shown that in highly non-convex problems, such as deep neural networks, there is a proliferation of high-error low curvature saddle points, which slows down learning dramatically. In this paper, we attempt to overcome the two above problems by proposing an optimization method for training deep neural networks which uses learning rates which are both specific to each layer in the network and adaptive to the curvature of the function, increasing the learning rate at low curvature points. This enables us to speed up learning in the shallow layers of the network and quickly escape high-error low curvature saddle points. We test our method on standard image classification datasets such as MNIST, CIFAR10 and ImageNet, and demonstrate that our method increases accuracy as well as reduces the required training time over standard algorithms.
A sentence from Carl Boyer's A History of Mathematics can be interpreted so that the full brothers Nicolaus II (02/06/1695 - 07/31/1726) and Daniel Bernoulli (02/08/1700 - 03/17/1782) are the authors of the St. Petersburg paradox. The paradox was formulated by their cousin Nicolaus I Bernoulli (10/21/1687 - 11/29/1759). The author did not find evidences that Nicolaus II and Daniel Bernoulli discussed the paradox. The key articles on the topic and its history from Karl Menger and Paul Samuelson, and recent papers presenting the time resolution miss Alexandr Khinchin's resolution of the paradox in his paper "On Petersburg game." Matematicheskii sbornik, Volume 32, No 2, 1925, pp. 330 - 341. The C++ program khinchin.cpp simulates conditions of two Khinchin's theorems and confirms his results providing concrete empirical dependencies of the frequencies corresponding to geometric and arithmetic mean payments on the number of Petersburg games.
In this first paper, we briefly retrace some historical pathways of modern physics of 20th Century. In particular, we have considered some moments of cosmic ray physics and, above all, the early theoretical and experimental bases which will lead to the first exact measurements of the anomalous magnetic moment of the muon, one of the main high precision tests of QED.
El propósito de las siguientes líneas es traer a colación, entre tantos recuerdos de aquellos años de mi ingreso a la Universidad de Costa Rica, los cambios de los que fui testigo y partícipe. Era la época de la irrupción en las aulas universitarias de los numerosos jóvenes nacidos durante el Baby Boom de los años cincuenta y de la postguerra. […] Por esos años comencé a tomar cursos con Ciro F. S. Cardoso, recientementenllegado al país y quien se iniciaba como profesor en la Escuela de Historia y Geografía de la Universidad de Costa Rica, proponiendo nuevos enfoques sobre el quehacer histórico. Entre los cursos que impartió el profesor Cardoso estaba “Métodos de investigación”. […]