635 research outputs found
A Friendly Introduction to "Knowledge in Pieces": Modeling Types of Knowledge and Their Roles in Learning
Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
Many historians of the calculus deny significant continuity between
infinitesimal calculus of the 17th century and 20th century developments such
as Robinson's theory. Robinson's hyperreals, while providing a consistent
theory of infinitesimals, require the resources of modern logic; thus many
commentators are comfortable denying a historical continuity. A notable
exception is Robinson himself, whose identification with the Leibnizian
tradition inspired Lakatos, Laugwitz, and others to consider the history of the
infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies,
Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly
demonstrating the inconsistency of reasoning with historical infinitesimal
magnitudes. We argue that Robinson, among others, overestimates the force of
Berkeley's criticisms, by underestimating the mathematical and philosophical
resources available to Leibniz. Leibniz's infinitesimals are fictions, not
logical fictions, as Ishiguro proposed, but rather pure fictions, like
imaginaries, which are not eliminable by some syncategorematic paraphrase. We
argue that Leibniz's defense of infinitesimals is more firmly grounded than
Berkeley's criticism thereof. We show, moreover, that Leibniz's system for
differential calculus was free of logical fallacies. Our argument strengthens
the conception of modern infinitesimals as a development of Leibniz's strategy
of relating inassignable to assignable quantities by means of his
transcendental law of homogeneity.Comment: 69 pages, 3 figure
Stevin numbers and reality
We explore the potential of Simon Stevin's numbers, obscured by shifting
foundational biases and by 19th century developments in the arithmetisation of
analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420
HIV infection and severe malnutrition: a clinical and epidemiological study in Burkina Faso.
OBJECTIVE: To define a clinical profile indicative of HIV infection in a population of severely malnourished children in Burkina Faso. A total of 433 children (average age, 19 months) were recruited at the Sanou Souro National Hospital, Bobo Dioulasso, Burkina Faso.
RESULTS: Sixty-three per cent presented with marasmus, 13% with kwashiorkor and 24% with both forms of malnutrition. The prevalence of HIV infection in children aged over 12 months was 13.8%, with a marked predominance of HIV-1 (95.8%). Mother-to-child transmission was proven in 77% of the cases; in 10% of the observed paediatric AIDS cases, transmission may have occurred through multi-injections with contaminated equipment. Marasmus was the form of malnutrition most frequently associated with HIV (P < 0.001); its severity was exacerbated by HIV infection. Adenopathy (P < 0.0001), oral candidiasis (P < 0.0006), skin disorders (P < 0.01) and hepatomegaly (P = 0.01) appeared to be significantly related to HIV infection. Discriminant analysis revealed that the presence of adenopathies was the strongest indicator symptom of HIV infection. Multivariate analysis revealed that a clinical profile of marasmus, adenopathies and oral candidiasis (specificity, 82%) was indicative of HIV infection in this population. The short-term clinical prognosis was poor and usually led to the death of the child when seropositive (P < 0.001).
CONCLUSIONS: Among children exhibiting severe malnutrition, HIV-positive children are distinguished by a high horizontal transmission rate, a high specific clinical profile and a very poor prognosis
Genome sequence of an Enterobacter helveticus strain, 1159/04 (= LMG 23733), isolated from fruit powder
We report the draft genome sequence of Enterobacter helveticus strain LMG 23733, isolated from fruit powder. The draft genome assembly for E. helveticus strain LMG 23733 has a size of 4,635,476 bp and a G+C content of 55.9%
Estudio sobre las praxeologías que se proponen estudiaren un curso universitario de cálculo
En este trabajo se analizan las organizaciones que se proponen estudiar en un curso de cálculo universitario relativas a las nociones de límite y continuidad funcional. Desde la Teoría Antropológica de lo Didáctico se analizó el material editado por lo profesores destinado a estudiantes universitarios. Los principales resultados indican que se propone el estudio de tareas aisladas, que no conducen a la elaboración y validación de elementos tecnológicos. De esta manera, se evidencia la organización de los saberes en dos niveles: uno teórico y otro práctico, donde este último no tiene incidencia para la conformación del primero. Esto genera una inadecuada interpretación del conocimiento científico, reduciendo su estudio a organizaciones matemáticas desarticuladas
Teaching and Learning of Calculus
This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions
Ten Misconceptions from the History of Analysis and Their Debunking
The widespread idea that infinitesimals were "eliminated" by the "great
triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an
uninterrupted chain of work on infinitesimal-enriched number systems. The
elimination claim is an oversimplification created by triumvirate followers,
who tend to view the history of analysis as a pre-ordained march toward the
radiant future of Weierstrassian epsilontics. In the present text, we document
distortions of the history of analysis stemming from the triumvirate ideology
of ontological minimalism, which identified the continuum with a single number
system. Such anachronistic distortions characterize the received interpretation
of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note:
text overlap with arXiv:1108.2885 and arXiv:1110.545
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