Suchergebnisse

В статията са представени идеи за връзка между класическа и геометрична вероятност, които биха могли да подпомогнат преподавателите при операционализирането на учебната програма за общообразователна подготовка в ХІ клас. Най-общо казано, стохастично явление с безкрайно (неизброимо) много равновъзможни изходи се разлага на крайно обединение от равновероятни изходи. За това обединение е приложим моделът на класическата вероятност. Предимствата на такава методика са в по-добрата мотивация за въвеждане на новото понятие геометрична вероятност. Засегнати са и философски проблеми относно връзката между континуум и дискретна структура, които за целевата група носят мирогледно послание. Включени са примери от състезателните теми на турнира "Черноризец Храбър".

Positive effects have been reported when graphic calculator (GC) is used in Mathematics classrooms as it influences the way Mathematics is taught and learned. This study aims to examine the effects of GC instructional approach on students' Probability performance, particularly for students with different levels of Mathematics performance. Two groups of students were involved in this study; Group A adopted the GC instructional approach while group B used the conventional teaching approach. Students from different Mathematics performance levels, particularly the low-performing students, gained benefits when the GC instructional approach was adopted in learning Probability.

AbstractThe purpose of this paper is to discuss the role of financial practice in the development of mathematics as applied in human judgement. The basis of the paper is in historical research from the 1990s that argues that the monetisation of western commerce, which abstracted value into quantified price, was synthesised with scholastic analysis resulting in a "mathematical mechanistic world picture" that led to the widespread use of mathematics in science from the seventeenth century. An aspect of this process was the quantification of chance that led to the development of mathematical probability, the branch of mathematics most relevant to judgement and the focus of this paper. Ideas from this historical research are related to the fundamental theorem of asset pricing (FTAP), the foundational theory of contemporary financial mathematics. The paper observes that vestiges of medieval scholastic attitudes to financial ethics can be discerned in the FTAP, offering a novel interpretation of the mathematical theorem. The paper then considers the Dutch book argument (DBA), the most popular justification for subjective probability. The paper's main contribution is in describing the significance of financial practice in validating the DBA and the paper explains how the FTAP addresses some criticisms of how the DBA represents beliefs. The conclusions emphasise the distinction between pure and practical reasoning and that this should be mirrored in a distinction between the mathematics ofphysicaandpractica. This point is important as mathematics is becoming more widespread in modelling, and directing, social systems.

Book reviewed in this article: De organisatie van de kwaliteitszorg, J. H. Enters, H. E. Stenfert Kroese N.V. Statistiek voor Medici. Korte inleiding, Chr. L. Rumke, C. van Eeden, uitgeverij L. Stafleu en ZoonDe bloemisterij in Nederland Characteristic Functions, E. Lukacs, Griffins Statistical Monographs and Courses no. 5 Charles Griffin and Cy. Ltd. Portfolio Selection, Efficient Diversification of Investments, H. M. Markowitz, Cowles Foundation Monograph 16 Finite Markov Chains, J. G. Kemeny en J. L. Snell, University Series in Undergraduate Mathematics, Van Nostrand, Princeton, New Jersey Operations Research and Systems Engineering, onder redactie van Charles D. Flagle, William H. Hugginsen Robert H. Roy Tables of the Hypergeometric Probability Distribution, G. L. Lieberman and D. B. Owen, Stanford Studies in Mathematics and Statistics III Probability with statistical applications, Frederick Mosteller, Robert E. K. Rourke, George B. Thomas, Jr. Probability: a First Course, F. Mosteller, R. E. K. Rourke, G. B. Thomas, Jr.

AbstractFor a young science and even for most old ones, the intensity and variety of activities involved in computer science are unsurpassed. In an effort to provide the extremely varied training needed in the field, curriculum planners have tended to slight probability and statistics. Rarely has it been a requisite and only occasionally a desired electiveHowever, not only is an adequate foundation in probability and statistics necessary for such external computer applications as tracking and other data reduction, Monte Carlo techniques, gaming, operations research, traffic analyses, etc., but it also plays an important role in internal applications to computer science and technologyThis effort in Rand's continuing study of computational mathematics and its applications offers a number of examples in various areas of computational mathematics and computing machine arithmetic‐to say nothing of computer design, time sharing, and the like‐to support the thesis that probability and statistics should be a requisite, not simply an elective or, even worse, ignored, at any institution offering a program in computer science. Further more, a potentially profitable source of research problems can be found in the interface between probability and statistics and computer science.

AbstractAyache presents a view of markets and mathematics that attempts to conform to the philosophies of Alain Badiou and Quentin Meillassoux. However, this attempt is unsuccessful because Ayache adopts a view of probability rooted in nineteenth-century conceptions that cannot accommodate the radical uncertainty of the markets. This is unfortunate as it is reasonable to believe that the ideas of Badiou and Meillassoux, when synthesised with contemporary ideas of probability, could offer interesting insights. Roffe presents a better argued synthesis of Deleuze and markets, however he makes similar assumptions about contemporary probability that undermine his conclusions.

"Ostrowski inequality is one of the celebrated inequalities in Mathematics.
The main purpose of our study is to generalize the result of Ostrowski-Gruss
type inequality for first differentiable mappings and apply it to probability density
functions, composite quadrature rules and special means."