On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

The methodology of knowledge layers for inducing descriptions of sequentially ordered events /

"UILU-ENG 80 1719"--Cover.

The Initial Stage of Teaching Proof in Mathematics Course

This article discusses techniques for organization of propaedeutic stage of teaching proof in mathematics course. It identifies types of tasks that allow students of 5–6 classes to form the ability to carry out simple proofs. This article describes each type of tasks features, it gives some examples.

The Methodology of the Subsistence Minimum Calculation for Developing Countries and its Computation on the Georgian Example

This article shows the social importance of subsistence minimum in Georgia. The methodology of its calculation is also shown. We propose ways of improving the calculation of subsistence minimum in Georgia and how to extend it for other developing countries. The weights of food and non-food expenditures in the subsistence minimum baskets are essential in these calculations. Daily consumption value of the minimum food basket has been calculated too. The average consumer expenditures on food supply and the other expenditures to the share are considered in dynamics. Our methodology of the subsistence minimum calculation is applied for the case of Georgia. However, it can be used for similar purposes based on data from other developing countries, where social stability is achieved, and social inequalities are to be actualized. ACM Computing Classification System (1998): H.5.3, J.1, J.4, G.3.

Rangsorolás páros összehasonlításokkal. Kiegészítések a felvételizői preferencia-sorrendek módszertanához (Paired comparisons ranking. A supplement to the methodology of application-based preference ordering)

A Közgazdasági Szemle márciusi számában Telcs és szerzőtársai [2013] a felvételizők preferenciái alapján új megközelítést javasolt a felsőoktatási intézmények rangsorolására. Az alábbi írás új szempontokat biztosít ezen alapötlet gyakorlati megvalósításához. Megmutatja, hogy az alkalmazott modell ekvivalens az alternatívák egy aggregált páros összehasonlítási mátrix révén végzett rangsorolásával, ami rávilágít a szerzők kiinduló hipotéziseinek vitatható pontjaira. A szerző röviden áttekinti a hasonló feladatok megoldására javasolt módszereket, különös tekintettel azok axiomatikus megalapozására, majd megvizsgálja a Telcs és szerzőtársai [2013] által alkalmazott eljárásokat. Végül említést tesz egy hasonló megközelítéssel élő cikkről, és megfogalmaz néhány, a vizsgálat továbbfejlesztésére vonatkozó javaslatot. _____ In the March issue of Közgazdasági Szemle, Telcs et al. suggested a new approach to university ranking through preference ordering of applicants. The paper proposes new aspects to the implementation of this idea. It is shown that the model of these is equivalent to the ranking of alternatives based on paired comparisons, which reveals the debatable points in their hypotheses. The author reviews briefly the methods proposed in the literature, focusing on their axiomatic properties, and thoroughly examines the procedures of Telcs et al. [2013]. The paper presents an article which applied a similar approach and suggests some improvements to it.

Methodology of a nationwide cross-sectional survey of prevalence and epidemiological patterns of hepatitis A, B and C infection in Brazil

Um inquérito de base populacional foi conduzido na população urbana de todas as capitais e do Distrito Federal no Brasil para fornecer informações sobre a prevalência de hepatites virais e fatores de risco, entre 2005 e 2009. Este artigo descreve o delineamento e a metodologia do estudo que envolveu a população com idade entre 5 e 19 anos para hepatite A e 10 a 69 anos para hepatite B e C. As entrevistas e amostras de sangue foram obtidas através de visitas domiciliares e a amostra selecionada a partir de uma amostragem estratificada em múltiplos estágios (por conglomerado) com igual probabilidade para cada domínio de estudo (região e faixa etária). Nacionalmente, 19.280 residências e ~31.000 indivíduos foram selecionados. O tamanho da amostra foi suficiente para detectar uma prevalência em torno de 0,1% e para avaliar os fatores de risco por região. A metodologia apresentou-se viável para distinguir entre diferentes padrões epidemiológicos da hepatite A, B e C. Estes dados serão de valia para a avaliação das políticas de vacinação e para o desenho de estratégias de controle.

Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

Multifocalité du carcinome épidermoïde sur les voies digestive supérieure et respiratoire distale : technicité du diagnostic endoscopique [Multiple squamous cell carcinoma of the upper digestive and lower respiratory tracts : methodology of endoscopic screening]

L'étude porte sur 951 porteurs d'un cancer primaire bucco-pharyngo-laryngé, et révèle un taux de multifocalité du carcinome épidermoïde sur les voies digestive supérieure (bouche-pharynx-oesophage) et aérienne distale (larynx-trachée-bronches) s'élevant à 14,5 %. Les secondes localisations peuvent être simultanées (6,4 %) ou successives (8,1 %) à la découverte du premier cancer: dès la deuxième année du follow-up leur incidence dépasse celle des récidives. Elles se localisent tant au niveau ORL (8,5 %) qu'oesophagien (3 %) ou bronchique (3 %). Le cancer du voile présente un taux de multifocalité particulièrement élevé (51 %). Les auteurs décrivent un type d'endoscopie de dépistage (bucco-pharyngo-oesophago-laryngo-trachéobronchoscopie) dont la fiabilité repose sur une technicité spécifique d'une part, et sur la connaissance des caractéristiques propres aux secondes localisations d'autre part. Ce dépistage systématique permet de détecter les tumeurs secondaires à un stade le plus souvent précoce et encore asymptomatique.

Implementation methodology of practices based on scientific evidence for assistance in natural delivery: a pilot study

AbstractOBJECTIVEPresenting methodology for transferring knowledge to improve maternal outcomes in natural delivery based on scientific evidence.METHOD: An intervention study conducted in the maternity hospital of Itapecerica da Serra, SP, with 50 puerperal women and 102 medical records from July to November 2014. The PACES tool from Joanna Briggs Institute, consisting of pre-clinical audit (phase 1), implementation of best practice (phase 2) and Follow-up Clinical Audit (phase 3) was used. Data were analyzed by comparing results of phases 1 and 3 with Fisher's exact test and a significance level of 5%.RESULTSThe vertical position was adopted by the majority of puerperal women with statistical difference between phases 1 and 3. A significant increase in bathing/showering, walking and massages for pain relief was found from the medical records. No statistical difference was found in other practices and outcomes. Barriers and difficulties in the implementation of evidence-based practices have been identified. Variables were refined, techniques and data collection instruments were verified, and an intervention proposal was made.CONCLUSIONThe study found possibilities for implementing a methodology of practices based on scientific evidence for assistance in natural delivery.

Traitement de la dépression résistante par l'association citalopram-lithium. Méthodologie d'une étude multicentrique en double aveugle et résultats préliminaires [Treatment of resistant depression with the citalopram-lithium combination. Methodology of a double-blind multicenter study and preliminary results].

Citalopram, a new bicyclic antidepressant, is the most selective serotonin reuptake inhibitor. In a number of double-blind controlled studies, citalopram was compared to placebo and to known tricyclic antidepressants. These studies have shown their efficacy and good safety. The inefficacy of a psychotropic treatment in at least 20% of depressives has led a number of authors to propose original drug combinations and associations, like antidepressant/lithium (Li), antidepressant/sleep deprivation (agrypnia), antidepressant/ECT, or antidepressant/LT3. The aim of this investigation is to evaluate the clinical effectiveness and safety of a combined citalopram/lithium treatment in therapy-resistant patients, taking account of serotonergic functions, as tested by the fenfluramine/prolactin test, and of drug pharmacokinetics and pharmacogenetics of metabolism. DESIGN OF THE STUDY: A washout period of 3 days before initiating the treatment is included. After an open treatment phase of 28 days (D) with citalopram (20 mg D1-D3; 40 mg D4-D14; 40 or 60 mg D15-D28; concomitant medication allowed: chloral, chlorazepate), the nonresponding patients [less than 50% improvement in the total score on the 21 item-Hamilton Depression Rating Scale (HDRS)] are selected and treated with or without Li (randomized in double-blind conditions: citalopram/Li or citalopram/placebo) during the treatment (D29-D35). Thereafter, all patients included in the double-blind phase subsequently receive an open treatment with citalopram/Li for 7 days (D36-D42). The hypothesis of a relationship between serotoninergic functions in patients using the fenfluramine/prolactin test (D1) and the clinical response to citalopram (and Li) is assessed. Moreover, it is evaluated whether the pharmacogenetic status of the patients, as determined by the mephenytoin/dextromethorphan test (D0-D28), is related to the metabolism of fenfluramine and citalopram, and also to the clinical response. CLINICAL ASSESSMENT: Patients with a diagnosis of major depressive disorders according to DSM III are submitted to a clinical assessment of D1, D7, D14, D28, D35, D42: HDRS, CGI (clinical global impression), VAS (visual analog scales for self-rating of depression), HDRS (Hamilton depression rating scale, 21 items), UKU (side effects scale), and to clinical laboratory examens, as well as ECG, control of weight, pulse, blood pressure at D1, D28, D35. Fenfluramine/prolactin test: A butterfly needle is inserted in a forearm vein at 7 h 45 and is kept patent with liquemine. Samples for plasma prolactin, and d- and l-fenfluramine determinations are drawn at 8 h 15 (base line). Patients are given 60 mg fenfluramine (as a racemate) at 8 h 30. Kinetic points are determined at 9 h 30, 10 h 30, 11 h 30, 12 h 30, 13 h 30. Plasma levels of d- and l-fenfluramine are determined by gas chromatography and prolactin by IRNA. Mephenytoin/dextromethorphan test: Patients empty their bladders before the test; they are then given 25 mg dextropethorphan and 100 mg mephenytoin (as a racemate) at 8 h 00. They collect all urines during the following 8 hours. The metabolic ratio is determined by gas chromatography (metabolic ratio dextromethorphan/dextrorphan greater than 0.3 = PM (poor metabolizer); mephenytoin/4-OH-mephenytoin greater than 5.6, or mephenytoin S/R greater than 0.8 = PM). Citalopram plasma levels: Plasma levels of citalopram, desmethylcitalopram and didesmethylcitalopram are determined by gas chromatography--mass spectrometry. RESULTS OF THE PILOT STUDY. The investigation has been preceded by a pilot study including 14 patients, using the abovementioned protocol, except that all nonresponders were medicated with citalopram/Li on D28 to D42. The mean total score (n = 14) on the 21 item Hamilton scale was significantly reduced after the treatment, ie from 26.93 +/- 5.80 on D1 to 8.57 +/- 6.90 on D35 (p less than 0.001). A similar patCitalopram, a new bicyclic antidepressant, is the most selective serotonin reu

Design and methodology of the Swiss Transplant Cohort Study (STCS): a comprehensive prospective nationwide long-term follow-up cohort.

In Switzerland, organ procurement is well organized at the national-level but transplant outcomes have not been systematically monitored so far. Therefore, a novel project, the Swiss Transplant Cohort Study (STCS), was established. The STCS is a prospective multicentre study, designed as a dynamic cohort, which enrolls all solid organ recipients at the national level. The features of the STCS are a flexible patient-case system that allows capturing all transplant scenarios and collection of patient-specific and allograft-specific data. Beyond comprehensive clinical data, specific focus is directed at psychosocial and behavioral factors, infectious disease development, and bio-banking. Between May 2008 and end of 2011, the six Swiss transplant centers recruited 1,677 patients involving 1,721 transplantations, and a total of 1,800 organs implanted in 15 different transplantation scenarios. 10 % of all patients underwent re-transplantation and 3% had a second transplantation, either in the past or during follow-up. 34% of all kidney allografts originated from living donation. Until the end of 2011 we observed 4,385 infection episodes in our patient population. The STCS showed operative capabilities to collect high-quality data and to adequately reflect the complexity of the post-transplantation process. The STCS represents a promising novel project for comparative effectiveness research in transplantation medicine.

Un análisis optimista de la educación matemática en la formación de maestros de educación infantil = An optimistic analysis of mathematics education in training pre-school teachers

This article offers a panorama of mathematics training for future teachers at pre-school level in Spain. With this goal in mind, this article is structured infour sections: where we come from, where we are, where we’re going and where we want to go. It offers, in short, a brief analysis that shows the efforts made to ensure there is sufficient academic and scientific rigour in teachers’ studies at pre-school in general and students’ mathematics education in particular. Together with a description of the progress made in recent years, it also raises some questions for all those involved in training future teachers for this educational stage

HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

Conceptions of mathematics teacher education : thoughts among teacher educators in Tanzania

This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.