Unit ball in high dimensions

In this article, we compute the volume V _n of the unit ball in an n-dimensional space. For n = 1, 2, 3, the volumes are respectively 2, π 4π /3, which are the length of interval [−1,1], area of a unit circle and volume of the unit sphere. The numbers V _n ‘appear’ to increase. But in fact this not so. In fact V _n tends to zero as n tends to infinity! K B Athreya is a Visiting Professor at IMI, Mathematics Department, IISc, Bangalore. He is a professor in the Mathematics Department of the Iowa State University, USA. His research interests include mathematical analysis, probability theory and its applications and statistics. His spare time is spent listening to Indian classical music.     

Seven different proofs of the irrationality of √2

Atiyah (winner of Abel prize for 2004, jointly with Isador Singer) says “Any good theorem should have several proofs, more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalize in different directions — they are not just repetitions of each other”. Following this remark by a great mathematician, we have given in this article, seven proofs for the irrationality of square root of 2. V G Tikekar is a former professor of mathematics at IISc, Bangalore. His research interests are in mathematical programming, numerical mathematics, theoretical computer science, probability and statistics.     

George Andrews’ game

This is an expository article showing how Zeck-endorf’s Theorem (every positive integer can be represented in one and only one way as the sum of non-consecutive Fibonacci numbers) can be used to construct a number-guessing game invented by Professor George Andrews. Jerold Mathews is professor (emeritus) of mathematics at Iowa State University, Ames, Iowa, USA, where he served on the faculty from 1961–1995. His interests include research in point set topology, history of mathematics and writing textbooks. He enjoys reading, photography and helping international students learn English.     

The effect of scheduling format on long-term retention

This study examines the relationship between course intensity and long-term retention on graduate level counseling students enrolled in a research and statistics course. It confirms earlier findings of time and learning studies, which have primarily dealt with end-of-course outcomes, that there is no effect due to scheduling format. In this study, older students performed significantly higher on a six-month follow-up test than younger students. Students who had previous, related course work scored significantly higher in final course grades than students with no prior course work, however, differences were moderated and no longer significant at the time of follow-up. Implications from these findings are discussed.Rebecca LaFountain is an assistant professor in the Department of Counseling, Shippenburg University of Pennsylvania. She earned an Ed.D in Counseling from the College of William and Mary, an M.S. in Counseling from Iowa State University, and a B.A. in French from Grand Valley State University. She is a Licensed Psychologist and a Certified Clinical Mental Health Counselor. Her primary professional interests include the teaching of research and statistics so that it is not threatening; Adlerian psychology; and, Solution-Focused counseling.     

关于概念图在概率统计教学中应用的一些思考

概念图是用来组织与表征知识的工具,概念图在概率统计教学中的应用为概率统计教学提供了一条新的途径.概念图由3部分组成:节点、连线、连接语词.概率统计概念图的特征有:层次性、综合性和关联性.概率统计概念图的习得经过图式的获得以及图式的精制两个阶段.概率统计概念图的功能体现在以下几方面:概念图对输入刺激的解释功能;概念图对输入刺激的评判功能;概念图的迁移功能.     

在概率统计中引入数学实验的教学探讨

对概率论与数理统计教学的现状和不足进行了分析,并讨论了其改革中引人数学实验的必要性。结合具体实例,从三个方面阐述了数学实验在概率统计课程教学中的功能及其相应的措施。最后指出在概率论与数理统计教学中引入数学实验是其教学改革的一种很好的尝试。     

Beginnings of group cohomology

Cohomology theory is a powerful mathematical tool. This theory applied to topology is a part of algebraic topology, which associates algebraic invariants to topological spaces. In this article, we give a brief outline of group cohomology. R Sridharan has been an Adjunct Professor at the CMI, Chennai since retiring from TIFR, Bombay in 2000 where he was a senior professor. He is also an INSA senior scientist now. His scholarship permeates to literature (English and Sanskrit) and philosophy as well. Many of the algebraists in the country were his students. Dedicated to my teacher S Eilenberg     

The Bernoullis and the origin of probability theory: Looking back after 300 years

This paper describes the contribution of the four famous Bernoullis (Jacob, Johann, Daniel and Nicolaus) to the development of the theory of probability between 1670 and 1760. Their contributions are evaluated from a modern day position of probability theory and statistics. We argue that abstract formulation of problems and mathematical solution concepts for abstract problems and seemingly special questions have a long term impact on the diversification of science. In the appendix, reference is also given to the ongoing work of the Bernoulli Edition in Basel.     

然森的学习型社会理论及其启示

英国伯明翰大学教育学院的斯第沃特.然森(Stewart Ranson)教授,在多年研究的基础上,提出了他的学习型社会理论,其内容包括前提假设、指导原则、主要目的和建设条件等。这一理论的突出特点是:从应对人类社会变化和转型的需要出发,特别重视重建社会道德和政治秩序,倡导双重公民身份和学习型民主,并试图以民主的学习和教育来实现整个社会的价值转换。他的理论对于我国的学习型社会建设具有重要的参考价值。     

网络环境下《概率论与数理统计》教学的思考

在当前应用计算机网络教育功能时,如何在网络环境下进行《概率论与数理统计》教学设计是大学中所关心的重大问题.在本文中,论述了《概率论与数理统计》网络教学是时代的需要,能激发学生的学习兴趣和创新能力,能因材施教、发展个性,弊端明显,不容忽视,网络教学实践所带来的思考等五个方面的问题.     

哲学与文化视角下概率统计课的育人功能

概率论与数理统计是认识和理解随机世界的一把钥匙。从哲学、文化视角来看，概率论与数理统计具有无价的文化内涵和育人功能，它是进行唯物辩证法教育的好素材；具有辩证唯物主义认识论教育功能；在培养人的科学品质方面具有得天独厚的功能。在概率论与数理统计教学中注重挖掘这些因素，对实施素质教育有着十分重要的意义。     

Curious consequences of simple sequences

Simple sequences and series of natural numbers, their reciprocals, integer powers of natural numbers and their reciprocals are considered. Some interesting physical and mathematical consequences of these are discussed. A K Mallik is a professor at IIT, Kanpur. His research interests are mechanical vibration, vibration control, nonlinear vibration and chaos in mechanical systems, kinematics and dynamics of machinery.     

独立同分布中心极限定理的应用

中心极限定理在概率论与数理统计教学中占有重要的地位,本文阐述了独立同分布中心极限定理的两个特例,并给出其在实际问题和统计分析中的有关应用.     

大数定律应用问题分析与概率直觉思维培养

为指导人们正确地认识随机事件,引导人们适当抑制盲目应对随机事件的冲动。该文选取一个独特的视角,讨论概率统计中的小概率事件,拆解概率理论,分析中奖概率,并就概率论联系实际,培养统计思维,提高学生的应用能力等方面,探讨了通过生活中的数学问题增强对实际事物中随机性的敏感,培养学生概率直觉思维,提高学生的应用能力,培养创新人才的途径。     

嵌入式自控系统软件抗干扰技术

利用基于概率统计和信息编码理论设计的一种自动控制嵌入式系统数学模型,可合理高效的进行嵌入式系统软件抗干扰的设计,提高系统的可靠性．     

数学思想方法在教学中的渗透

概率论与数理统计这门课程是理工科类一门重要的课程,它与其他的数学课程有着明显的不同,学生在学习和理解上有些困难,鉴于这一点,从数学思想方法的角度谈谈这门课程的教学。     

民族经管类专业概率论与数理统计教学方法探讨

本文分析了少数民族经管类专业学生的特点,结合概率论与数理统计课程的现状,基于工作实践,对概率论与数理统计教学过程中,如何运用好的教学方法与教学手段提高教学效果进行探讨并提出自己的几点心得和建议。     

概率统计在信息社会中的教育价值

基于对信息化社会中概率统计教育重要性的认识,重点从四个方面论述了概率统计的教育价值：（1）概率统计的随机观念有助于人们认识和理解随机现象;（2）概率统计的学习有助于学生对数学的整体理解;（3）概率统计的数学方法有助于提高公民处理信息的能力;（4）概率统计的思想方法有助于培养学生的科学观念.     

新课程理念下高师概率统计教学改革的探索

在新课程理念的指导下,从“大统计学”角度去整合和优化高师概率统计有关的教学内容,提出高师概率统计的教学内容应为三大模块,即概率论与数理统计、现代统计分析方法与应用、中学概率统计教学与研究．教学内容的确定要符合基础性、师范性、先进性和实践性等原则．教学方法和手段多样化,讲授、操作和实践相结合,注重思想方法的教学,采用类比法教学和案例教学,以及情境体验与建模的教学,注重现代信息技术与课程的整合．考试形式多样化,开卷与闭卷、笔试与口试相结合;成绩评定灵活化,充分调动学生学习的积极性．     

Demarches de resolution et de simulation face au probleme de la ruine d'un joueur

Prior to large experimentations on the teaching of probability theory, it appeared useful to observe some students working for a fairly long time. This observation should make more precise the difficulties of an important aspect when solving probability problems: the modelling aspect. Does systematic use of simulation produce miracles as it is sometimes said? Are the students naturally sensitive to a frequentist approach of probability theory? This paper contains some results on these questions, for example we pointed out for some students an obstacle to the frequentist approach. The results permit to conceive how using simulation for teaching could contribute to an improvement of students' approach to probability.