数学实验与数学建模

继数学建模之后 ,一门新的课程——数学实验——引起不少教师的注意 ,本文根据作者的教学实践对数学实验课程的指导思想、内容和方法 ,以及与数学建模课的关系等问题提出一些看法 .     

数学概念与数学实验

讨论了通过讲透基本概念、引入数学实验、适当削减运算方法的讲授来改革高职、高专的高等数学课程.     

Mathematical induction,difference equations and divisibility

Many exercises in mathematical induction require the student to prove a divisibility property of a function of the integers. Such problems are generally presented as being independent of each other. However, many of these problems can be presented in terms of difference equations, and the theory of difference equations can be used to provide a uniform method for creating such divisibility problems. This article shows how a multitude of such problems can be created, and how standard problems from textbooks can be analysed in terms of difference equations.     

Mathematical elasticity,volume I: Three-dimensional elasticity

Book Review

Mathematical elasticity, volume I: Three-dimensional elasticityPhilippe G. Ciarlet: Studies in Mathematics and its Applications 20, North-Holland, Amsterdam, 1988, xlii + 452 pp     

Output Devices, Computation, and the Future of Mathematical Crafts

This paper argues that the advent of powerful,affordable output devices offers the potential for a vastly expanded landscape of computationally-enriched mathematical craft activities in education. While mathematical crafts have a venerable history in classrooms, they have also suffered from a reputation of being both intellectually marginal and technologically retrograde. Nonetheless, this paper argues that craft activities have both intellectual and emotional affordances that are relatively lacking in `traditional' computer-based education; and that the combination of crafts and computation (facilitated by novel output devices and materials) can render such activities still more valuable. As springboards for discussion, the paper describes three software applications geared toward computational crafts (HyperGami, HyperSpider, and MachineShop). Each of these systems highlights its own particular set of issues relevant to the development of output technologies. Using these three systems as objects-to-think-with, the paper describes a wide variety of possible craft activities that could be invented or pursued in the near future with the aid of appropriately designed output devices.This revised version was published online in September 2005 with corrections to the Cover Date.     

数学软件在数学建模中的应用

本文以 2 0 0 1年全国大学生数学竞赛 A题为例 ,介绍数学软件在数学建模中的应用 ,并通过例子揭示该竞赛题本身在数学表述上是有缺陷的 .