从投掷问题到概率论的创立

点数问题的解决是概率论创立的标志.该问题最终由帕斯卡和费马圆满解决,正是这些新思想奠定了概率论基础.惠更斯的<论赌博中的计算>第一次把概率论建立在公理、命题和问题上而构成较完整的理论体系.     

摸奖与概率

“概率”是现行高中数学新教材必修课新增加的内容.概率最早起源于赌博问题的研究,17世纪帕斯卡、费尔玛、惠更斯等数学家对“合理分配赌注”问题进行了深入的研究,并作了系统的归纳与总结,从而产生了概率论.     

非齐次树指标马氏双链转移矩阵的一个强极限性质

强极限定理是概率论中的重要问题之一.通过引入广义赌博系统的概念,研究给出了关于非齐次树指标马氏双链转移矩阵的一个强极限定理.     

概率论产生源于赌博

概率论是研究大量随机现象统计规律的数学分科.但直接导致概率论产生的却是赌博.1651年,赌徒梅尔与保罗赌钱.他们事先每人拿出6枚金币,然后玩骰子,约定谁先胜3局     

布尔代数及其应用简介(Ⅰ)

第一章 两个元素的布尔代数 引言“布尔代数”最初产生于对思维规律的研究.在逻辑学中常常要考虑命题的“真”和“假”,这“真”和“假”可看作是两个值或两个元素.在电子技术中,往往在开关网络中出现有两种可能的情形:有电与无电、灯亮与灯灭、导通与截止、高电压与低电压等,总之是“两种状态”,这“两种状态”也同样地可看作是两个值或两个元素.并且在这些实际问题中,往往要考虑一些量之间的关系,其中出现的每一个量所取的值为“两种状态”、两     

常用一元分布间的关系

1.引子 在概率论的初级教程中,学生通常是学习常用的一元分布,而大多数概率论入门教程都是在若干部分孤立地讨论每一个分布.这种教程造成的障碍之一就是学生不能抓住各个分布的全部的相互关系.这篇文章即是通过绘出并讨论一个图示来克服这种不足. 2.讨论 图中表示出常用一元分布间的一些关系,这些分布也许是一本概率论人问教程所能够提到的.共有9个离散型分布,表示在图的上方部分.还有19个连续型分布.每一个框的第一行是分布的名称,第二行为分布的定义区间,最后一行是分布的参数.这些参数必须满足下列条件:n是整数;0相似文献   

概率中5个比较著名的问题

概率是中学数学的新增内容 ,对学生解决问题的能力提出了更高的要求 .下面介绍概率中 5个比较著名的问题 ,供大家了解和理解概率及其在生活中的应用 .1　赌徒分金币问题概率论的产生 ,还有段名声不好的故事 .1 7世纪的一天 ,保罗与著名的赌徒梅尔赌钱 ,每人拿出 6枚金币 ,然后玩骰子 ,约定谁先胜三局谁就得到 1 2枚金币 .比赛开始后 ,保罗胜了一局 ,梅尔胜了两局 ,这时一件意外的事中断了他们的赌博 .于是 ,他们商量这1 2枚金币应怎样分配才合理 ?保罗认为 ,根据胜的局数 ,他应得总数的13,即 4枚金币 ,梅尔得总数的 23,即 8枚金币 ;但精通赌…     

曹雪芹懂概率吗?

概率论产生于对机会游戏和赌博的研究.凡是机会游戏和赌博的问题,都可以计算各种事件出现的概率.同时,也可以通过事件出现的概率对事件的真伪作出合理的推断. 在《红楼梦》原著第63回、电视连续剧第24集“怡红院群芳开在宴”中,写到宝玉过生日,晚上请来了林黛玉、史湘云、薛宝钗、李纨、贾探春、薛宝琴等在怡红院玩掷骰子抽签的游戏.大家围成一圈,按照掷出骰子的点数数到谁,谁就从签筒中抽出一签,并按照签上所写的要求,或罚做诗,或罚喝酒.按照电视连续剧编剧周雷的考证,其座位顺序和掷骰子结果见右图和下表: 开始时,由晴霎第一个摇装有四个…     

关于概率论中的分段函数问题

分段函数在概率论中有着广泛的应用.通过对几个概率问题的研究,探讨针对分段函数如何合理分段或分区域进行积分问题,体现分段函数在概率论中的重要性.     

从“彩票没有概率”说起—关于彩票概率的讨论

历史上 ,概率论是从博弈问题的讨论发展起来的 ,现在概率在许多领域都有广泛的应用 ,其中包括彩票的问题 ,这是很显然的 .本文想从概率论的角度对“中国体育彩票”概率问题作一点简单的分析 ,以澄清当前社会上彩票热中出现的各种说法 ,端正心态 ,防止彩票过热可能出现的弊病 ,并且让具有高中数学知识的读者重温代数中排列组合的应用 .为了方便阅读 ,首先对中国体育彩票设计的中奖办法作一简要的说明 .中国体育彩票设计的中奖办法是从 1至 36这个 36个数码中任选 7个不重复的数码 ,组成一注彩票 (每注 2元 ) ,每一注有一次中奖机会 ,只可领取…     

Mathematics in the time of the pharaohs: By Richard J. Gillings. Cambridge,Mass. (M.I.T. Press), 1972. 297 p. US $25

The author's treatment of many problems and some of his hypotheses are original and elegant. He does not limit himself to describing the content of his sources but tries to reveal the paths followed by the Egyptians as well as their ideas and methods. This leads him to interesting and on the whole covinncing reconstructions and results. For example, the author concludes that there must have existed extensive addition tables that have not survived.Although the materials available today seem insufficient to explain how the Egyptians happened to use the qlumsy binary method mu multiplication and division, Gillings' discussion throws light on the problem and poses questions for further research. Careful analysis of special tables and solutions of problems and the comparison of sources enable the author in large measure to reveal the methods and ideas of Egyptian mathematicians. How the Egyptians constructed their tables still remains an unsolved problem. Because divisions sometimes began by dividing by 3, Gillings concludes that tables for 3 must have existed and his reconstruction of such a table has great interstt. His Rule G for sums and differences of fractions is original and ingenious. He strsses the importance of EMLR. He argues that the Egyptians used the concepts of arithmetic and harmonic means. He gives an interesting explanation for the origin of the Egyptian formulas for squaring the circle, though its simplicity is clear only after the result is known.Although answers are not given to all questions, the book leads the reader to search for answers, to formulate new reconstructions, and to make new hypotheses. This is its greatest merit.     

Mathematics Reform: Looking for Insights from Nineteenth Century Events

In the nineteenth century, Warren Colburn defended understanding as the avenue to learning arithmetic and questioned the memorization method in use since the seventeenth century. Colburn's work was appreciated by educators in the common school era, and his book is still considered an important one in the history of mathematics education. Many criticisms of Colburn's ideas, however, emerged during his time, and teaching for understanding never fully reached nineteenth century mathematics classrooms. This episode in the history ofmathematics education raises questions about the success of contemporary attempts to reform school mathematics.     

Recent development of Faith conjecture

Is a semiprimary right self-injective ring a quasi-Frobenius ring? Almost half century has passed since Faith raised this problem. He first conjectured “No” in his book Algebra II. Ring Theory in 1976, but changing his mind, he conjectured “Yes” in his article “When self-injective rings are QF: a report on a problem” in 1990. In this paper, we describe recent studies of this problem based on authors works and raise related problems.     

Teiji Takagi, Founder of the Japanese School of Modern Mathematics

This article is a brief historical report on Teiji Takagi which was prepared at the commencement of ‘Takagi Lectures’ of The Mathematical Society of Japan. The first of its two purposes is to give some informations on the circumstances of education and research of mathematics in Japan surrounding Takagi who could finally established himself as the founder of the Japanese school of modern mathematics. The other is a brief overview on Takagi’s works of mathematics some of which are still attractive to and influential on especially ambitious students of mathematics. The author hopes that careful readers may find some hints for the questions how and why Takagi was able to establish his class field theory. At the end of this article the readers will find an English translation of the preface of his book Algebraic theory of numbers (in Japanese) which is the only thing that he left for us to see his total view over class field theory after the establishment of Artin’s reciprocity law.     

Plane Fundamental Domains with Minimal Perimeters

Periodica Mathematica Hungarica - In his paper Á. G. Horváth posed two isoperimetric type questions for extremal polyhedra with respect to a given lattice L. He solved the problems in the...     

Embedding discrete flows on R in a continuous flow

The problem of determining when a given discrete flow on a topological space is embeddable in some continuous flow was mentioned by G. R. Sell (“Topological Dynamics and Ordinary Differential Equations,” Van Nostrand, New York, 1971) in his book on topological dynamics. In this book, the theory of generalized dynamical systems is exploited in the qualitative study of differential equations. Even more complicated is the problem of simultaneously embedding two or more discrete flows in a single continuous flow. We examine both of these problems when the underlying topological space is the space R of the real numbers.     

The approach to consistency in the analytic hierarchy process

In his first book on the Analytic Hierarchy Process, T. L. Saaty left open several mathematical questions about the structure of the set of positive reciprocal matrices. In this paper we consider three of these questions: Given an eigenvector and all matrices which give rise to it, can one go from one of them to any order by making small perturbations in the entries? Given two positive column vectors v and w is there a perturbation which carries the set of all positive reciprocal matrices with principal right eigenvector v to the set of positive reciprocal matrices with principal right eigenvector w? Does the set of positive reciprocal n×n matrices whose left and right principal eigenvectors are reciprocals coincide with the set of consistent matrices for n⩾4?     

Invariant holomorphic extension in several complex variables

Two fundamental problems on the invariant holomorphic extensions have been posed, which are naturally arose from our solution of the extended future tube conjecture and closely and deeply related to the general theory of Stein manifolds due to Cartan-Serre. In this paper, the relationship is presented between the two problems, the motivation of considering the problems, and the methods to approach the problems. We have also posed some questions and conjectures related to this two problems. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

A sum theorem for (FPV) operators and normal cones

In his 2008 book “From Hahn-Banach to Monotonicity”, S. Simons mentions that the proof of Lemma 41.3, which was presented in the previous edition of his book “Minimax and Monotonicity” in 1998, is incorrect, and one does not know if this lemma and its consequences are true. The aim of this short note is not only to give a proof to the mentioned lemma but also to improve upon it by relaxing one of its assumptions.     

Some general methods for constructing the theory of shells

The aim of the present short review is the exposition of the fundamental results obtained by Academician I. N. Vekua (1907–1977) in the theory of shells. The review deals with questions of constructing different versions of shell theory, questions of the infinitesimal bending of a surface of positive curvature and equilibrium membrane states of stress of a convex shell, and also the statically determinable problems and questions of existence of a neutral surface of the shell, i.e. the questions which Vekua investigated in different periods of his versatile scientific actively. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 51, Differential Equations and Their Applications, 2008.