Elementos of geometry and trigonometry : from the works of A.M. Legendre, adapted to the course of mathematical instruction in the United State

UANL

The psychology of exclusivity

L’amitié et l’amour romantique sont, de par leur nature, des relations exclusives. Cet article suggère que l’on peut mieux comprendre la nature de l’exclusivité dont il est question en comprenant l’erreur au coeur de la vision du raisonnement pratique que je nomme « le point de vue englobant » . Selon le PVE, pour que le raisonnement pratique soit rationnel, il doit s’agir d’un processus ayant pour but de choisir la meilleure alternative possible à partir d’une perspective qui est aussi détachée et objective que possible. Quoique cette vision cherche à être neutre à l’égard des porteurs de valeurs, elle incorpore en fait un biais contre les porteurs de valeurs qui ne peuvent être appréciés qu’à partir d’une perspective qui n’est pas détachée - qui ne peuvent être appréciés, par exemple, que par les agents qui sont engagés à long terme envers les valeurs en question. Dans le contexte des relations personnelles, de tels engagements tendent à donner naissance à la sorte d’exclusivité qui caractérise l’amitié et l’amour romantique ; ils empêchent l’agent d’être impartial entre les besoins, les intérêts, etc. de la personne qui lui est chère, d’une part, et ceux des autres, d’autre part. Je suggère que dans de tels contextes les besoins et les revendications des autres personnes peuvent être réduites au silence, de la même manière que, comme le suggère John McDowell, les tentations de l’immoralité sont, pour l’agent vertueux, réduites au silence.

Décisions et perspectives : de la théorie de l'utilité à la philosophie de la volonté.

Les implications philosophiques de la Théorie de la Perspective de 1979, notamment celles qui concernent l’introduction d’une fonction de valeur sur les résultats et d’un coefficient de pondération sur les probabilités, n’ont à ce jour jamais été explorées. Le but de ce travail est de construire une théorie philosophique de la volonté à partir des résultats de la Théorie de la Perspective. Afin de comprendre comment cette théorie a pu être élaborée il faut étudier la Théorie de l’Utilité Attendue dont elle est l’aboutissement critique majeur, c’est-à-dire les axiomatisations de la décision de Ramsey (1926), von Neumann et Morgenstern (1947), et enfin Savage (1954), qui constituent les fondements de la théorie classique de la décision. C’est entre autres la critique – par l’économie et la psychologie cognitive – du principe d’indépendance, des axiomes d’ordonnancement et de transitivité qui a permis de faire émerger les éléments représentationnels subjectifs à partir desquels la Théorie de la Perspective a pu être élaborée. Ces critiques ont été menées par Allais (1953), Edwards (1954), Ellsberg (1961), et enfin Slovic et Lichtenstein (1968), l’étude de ces articles permet de comprendre comment s’est opéré le passage de la Théorie de l’Utilité Attendue, à la Théorie de la Perspective. À l’issue de ces analyses et de celle de la Théorie de la Perspective est introduite la notion de Système de Référence Décisionnel, qui est la généralisation naturelle des concepts de fonction de valeur et de coefficient de pondération issus de la Théorie de la Perspective. Ce système, dont le fonctionnement est parfois heuristique, sert à modéliser la prise de décision dans l’élément de la représentation, il s’articule autour de trois phases : la visée, l’édition et l’évaluation. À partir de cette structure est proposée une nouvelle typologie des décisions et une explication inédite des phénomènes d’akrasie et de procrastination fondée sur les concepts d’aversion au risque et de surévaluation du présent, tous deux issus de la Théorie de la Perspective.

Lien entre l'activité pariéto-occipitale enregistrée pendant une tâche de mémoire à court terme visuelle et les habiletés mathématiques : une étude en magnétoencéphalographie

La mémoire à court terme visuelle (MCTv) est un système qui permet le maintien temporaire de l’information visuelle en mémoire. La capacité en mémoire à court terme se définit par le nombre d’items qu’un individu peut maintenir en mémoire sur une courte période de temps et est limitée à environ quatre items. Il a été démontré que la capacité en MCTv et les habiletés mathématiques sont étroitement liées. La MCTv est utile dans beaucoup de composantes liées aux mathématiques, comme la résolution de problèmes, la visualisation mentale et l’arithmétique. En outre, la MCTv et le raisonnement mathématique font appel à des régions similaires du cerveau, notamment dans le cortex pariétal. Le sillon intrapariétal (SIP) semble être particulièrement important, autant dans la réalisation de tâches liées à la MCTv qu’aux habiletés mathématiques. Nous avons créé une tâche de MCTv que 15 participants adultes en santé ont réalisée pendant que nous enregistrions leur activité cérébrale à l’aide de la magnétoencéphalographie (MEG). Nous nous sommes intéressés principalement à la composante SPCM. Une évaluation neuropsychologique a également été administrée aux participants. Nous souhaitions tester l’hypothèse selon laquelle l’activité cérébrale aux capteurs pariéto-occipitaux pendant la tâche de MCTv en MEG sera liée à la performance en mathématiques. Les résultats indiquent que l’amplitude de l’activité pariéto-occipitale pendant la tâche de MCTv permet de prédire les habiletés mathématiques ainsi que la performance dans une tâche de raisonnement perceptif. Ces résultats permettent de confirmer le lien existant entre les habiletés mathématiques et le fonctionnement sous-jacent à la MCTv.

Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Investment analysis of chemical projects and development of standerdised mathematical co-relation for cost estimation of pressure vessels in chemical industry

The present study is intended to provide a new scientific approach to the solution of the worlds cost engineering problems encountered in the chemical industries in our nation. The problem is that of cost estimation of equipments especially of pressure vessels when setting up chemical industries .The present study attempts to develop a model for such cost estimation. This in turn is hoped would go a long way to solve this and related problems in forecasting the cost of setting up chemical plants.

Mathematical Morphology on Hypergraphs Using Vertex-Hyperedge Correspondence

The focus of this paper is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyperedge set of a hypergraph , by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of . This paper also studies the concept of morphological adjunction on hypergraphs for which both the input and the output are hypergraphs

Mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Elterliche Geschlechtsstereotype und deren Einfluss auf das mathematische Selbstkonzept von Grundschulkindern

Ausgangspunkt dieser Dissertation ist die Überlegung, warum Mädchen und Frauen in mathematisch-naturwissenschaftlichen Fächern und Berufen unterrepräsentiert sind. Irrtümlicherweise werden als Erklärung hierfür häufig Geschlechterdifferenzen in der Mathematikleistung herangezogen. Diese bieten jedoch aufgrund nicht einheitlicher Forschungsbefunde keinen zufriedenstellenden Erklärungsansatz. Naheliegender ist es, das mangelnde Selbstvertrauen von Mädchen in Mathematik (als mathematisches Selbstkonzept bezeichnet) als Ursache heranzuziehen, denn verschiedene Studien kamen zu dem Ergebnis, dass Mädchen, auch bei vergleichbarer Leistung, ein geringeres mathematisches Selbstkonzept aufweisen als Jungen (Dickhäuser & Stiensmeier-Pelster, 2003; Frome & Eccles, 1998; Rustemeyer & Jubel, 1996; Skaalvik & Skaalvik, 2004). Die Rolle der Eltern als primäre Sozialisationsinstanz wird als bedeutsamer Einflussfaktor auf das mathematische Selbstkonzept von Kindern beschrieben. Besonders für den Bereich Mathematik besteht die Gefahr, dass Eltern durch geschlechtsstereotype Einstellungen und Erwartungen ihre Tochter ungünstig beeinflussen (Jacobs, 1991; Tiedemann, 2000). In dieser Arbeit wird untersucht, inwiefern Eltern Geschlechtsstereotype zuungunsten der Mädchen in Mathematik äußern und inwiefern sich diese – schon zur Grundschulzeit – in den elterlichen Einschätzungen (elterliche Leistungs- und Fähigkeitseinschätzungen sowie elterliche Ursachenerklärungen) des eigenen Kindes widerspiegeln. Es wird angenommen, dass Mädchen entsprechend dem klassischen Geschlechtsstereotyp weniger talentiert und weniger leistungsstark in Mathematik eingeschätzt werden als Jungen. Für die Einschätzungen des eigenen Kindes wird erwartet, dass diese geschlechtsspezifische Verzerrungen zuungunsten der Mädchen aufweisen. Anhand von Pfadmodellen wird in dieser Arbeit der Einfluss elterlicher Geschlechtsstereotype und Einschätzungen, unter Kontrolle der vorangegangenen Mathematikleistung und des vorangegangenen mathematischen Selbstkonzeptes des Kindes, auf das aktuelle mathematische Selbstkonzept des Kindes am Ende des dritten Schuljahres analysiert. Als Grundlage dienen Daten von circa 900 Schülern und 400 Eltern aus dem Projekt Persönlichkeits- und Lernentwicklung von Grundschulkindern (PERLE). Die Befunde der vorliegenden Arbeit können bisherige Forschungsbefunde aus dem Sekundarbereich für den Grundschulbereich replizieren und weitere erstmalige Befunde ergänzen. Zusammenfassend kann festgehalten werden, dass knapp zwei Drittel der Eltern Geschlechtsstereotype zuungunsten der Mädchen in Mathematik äußern. Die Pfadanalysen ergeben, dass nicht das Geschlecht des Kindes, sondern Wechselwirkungen zwischen Geschlecht und elterlichen Geschlechtsstereotypen die elterlichen Einschätzungen des eigenen Kindes beeinflussen. Wenn Eltern Geschlechtsstereotype vertreten, schätzen sie eine Tochter ungünstiger ein als einen Sohn (unabhängig von der tatsächlichen Mathematikleistung des Kindes). Die elterlichen Einschätzungen haben wiederum einen signifikanten Einfluss auf das mathematische Selbstkonzept des Kindes. Die Ergebnisse dieser Arbeit werden abschließend diskutiert und Ansätze für Interventionen aufgezeigt.

Verbal proficiency as fitness indicator: Experimental and comparative research on the evolutionary psychology of language and verbal displays

Summary: Recent research on the evolution of language and verbal displays (e.g., Miller, 1999, 2000a, 2000b, 2002) indicated that language is not only the result of natural selection but serves as a sexually-selected fitness indicator that is an adaptation showing an individual’s suitability as a reproductive mate. Thus, language could be placed within the framework of concepts such as the handicap principle (Zahavi, 1975). There are several reasons for this position: Many linguistic traits are highly heritable (Stromswold, 2001, 2005), while naturally-selected traits are only marginally heritable (Miller, 2000a); men are more prone to verbal displays than women, who in turn judge the displays (Dunbar, 1996; Locke & Bogin, 2006; Lange, in press; Miller, 2000a; Rosenberg & Tunney, 2008); verbal proficiency universally raises especially male status (Brown, 1991); many linguistic features are handicaps (Miller, 2000a) in the Zahavian sense; most literature is produced by men at reproduction-relevant age (Miller, 1999). However, neither an experimental study investigating the causal relation between verbal proficiency and attractiveness, nor a study showing a correlation between markers of literary and mating success existed. In the current studies, it was aimed to fill these gaps. In the first one, I conducted a laboratory experiment. Videos in which an actor and an actress performed verbal self-presentations were the stimuli for counter-sex participants. Content was always alike, but the videos differed on three levels of verbal proficiency. Predictions were, among others, that (1) verbal proficiency increases mate value, but that (2) this applies more to male than to female mate value due to assumed past sex-different selection pressures causing women to be very demanding in mate choice (Trivers, 1972). After running a two-factorial analysis of variance with the variables sex and verbal proficiency as factors, the first hypothesis was supported with high effect size. For the second hypothesis, there was only a trend going in the predicted direction. Furthermore, it became evident that verbal proficiency affects long-term more than short-term mate value. In the second study, verbal proficiency as a menstrual cycle-dependent mate choice criterion was investigated. Basically the same materials as in the former study were used with only marginal changes in the used questionnaire. The hypothesis was that fertile women rate high verbal proficiency in men higher than non-fertile women because of verbal proficiency being a potential indicator of “good genes”. However, no significant result could be obtained in support of the hypothesis in the current study. In the third study, the hypotheses were: (1) most literature is produced by men at reproduction-relevant age. (2) The more works of high literary quality a male writer produces, the more mates and children he has. (3) Lyricists have higher mating success than non-lyric writers because of poetic language being a larger handicap than other forms of language. (4) Writing literature increases a man’s status insofar that his offspring shows a significantly higher male-to-female sex ratio than in the general population, as the Trivers-Willard hypothesis (Trivers & Willard, 1973) applied to literature predicts. In order to test these hypotheses, two famous literary canons were chosen. Extensive biographical research was conducted on the writers’ mating successes. The first hypothesis was confirmed; the second one, controlling for life age, only for number of mates but not entirely regarding number of children. The latter finding was discussed with respect to, among others, the availability of effective contraception especially in the 20th century. The third hypothesis was not satisfactorily supported. The fourth hypothesis was partially supported. For the 20th century part of the German list, the secondary sex ratio differed with high statistical significance from the ratio assumed to be valid for a general population.