当前概率学科中的研究机遇

Current and Emerging Research Opportunities in Probability

由美国国家自然科学基金委员会组织的有关“当前和显露出来的概率论学科中研究机遇”研讨会于2002年5月29—31日召开,以下报告概括介绍18位出席会议的概率学家(名单参见附注)的观点和建议,这些并不一定代表美国国家自然科学基金委员会的意见。 概率论既是观察世界的一种基本方法,也象几何、代数和分析一样是一门核心数学学科,最近几年,作为科学探索的一种独具特色的方法,概率推理的显著功效已经导致了概率理论在科学研究中的重要性的爆炸性增加,数十年来一直在统计学中起中心作用的,在物理学、遗传学和信息论中所常见的概率方法,最近已经在许多其他学科,包括金融、地球科学、神经学、人工智能和通讯网络中成为不可缺少的方法。概率论愈来愈大的影响以及人们对概率论愈来愈高的觉醒,为我们的学科带来了新的责任和机遇,尽管从事研究的性质已经发生变化,但我们大学和学院关于如何进行概率论教学并不总是有相应的变革。在许多地方,目前的课程设置与30年前没有多大差异。概率学界必须带头研究课程设置和其他教育工具以便适应不同背景的多方面人才的需要。 根据概率在科学界地位的变化和重要性的增加,我们提出下列5点建议: 1 大学必须探索出一种机制,以便协调当前校园内概率论教学分散的局面。 2

The Workshop on Current and Emerging Research Opportunities in Probability was held on May 29-31, 2002, at the National Science Foundation. The following report summarizes the observations and recommendations of the eighteen probabilists who participated in that workshop. The views and opinions expressed are not necessarily those of the National Science Foundation. Probability is both a fundamental way of viewing the world, and a core mathematical discipline, alongside geometry, algebra, and analysis. In recent years, the evident power and utility of probabilistic reasoning as a distinctive method of scientific inquiry has led to an explosive growth in the importance of probability theory in scientific research. Central to statistics and commonplace in physics, genetics, and information theory for many decades, the probabilistic approach to science has more recently become indispensable in many other disciplines, including finance, geosciences, neuroscience, artificial intelligence and communication networks. The increased influence and heightened awareness of probability carries new responsibilities and opportunities for our discipline. Although the nature of doing research has changed, there has not always been a corresponding evolution in how probability is taught in our colleges and universities. In many places, curricula today are not significantly different from those of thirty years ago. The probability community must take the lead in developing course offerings and other educational tools that accommodate widely varying audiences with diverse backgrounds. In response to the changing role and increasing importance of probability in the scientific enterprise, five recommendations are made in this paper.