The Mathematics of Decision Making: A Model for Collaboration Between Mathematics and Other Fields

每年，成千上万的商业和公共管理（BPA）学位课程的准学生参加必修的数学课程，因为他们需要学习有效地使用数学来做决策。然而，传统的必修课程往往不能满足这种需求。该项目的主要目标是制作材料，使学生相信数学和现代计算机技术是解决现实问题的宝贵工具，并教他们有效地利用这些工具。我们计划开发，现场测试，并在全国范围内传播大量的，基于技术的案例研究档案（可用于介绍数学内容的现实场景）。这些课程需要几天到几周的教学时间，可以用来代替课文，也可以作为课文的补充。每个案例研究将由从全国各地挑选的数学和BPA教师组成的团队进行开发。Thompson和Lamoureux是哈佛大学数学系和商业与公共管理学院的合作伙伴，他们对是否取消商业贷款的抵押品赎回权或与债权人达成协议，以及如何为股票期权定价等问题进行了案例研究。休斯·哈雷特与韦尔斯利学院的E.康纳利和哈佛大学肯尼迪政府学院的教员合作，对奥地利国家养老金制度、使用美国人口普查数据和中央情报局世界手册的数据进行人口预测、使用美国地质调查局的数据进行查尔斯河的水流进行了案例研究。

Each year, hundreds of thousands of prospective students in business and public administration (BPA) degree programs take required mathematics courses because they need to learn to use mathematics effectively in making decisions. However, this need is often not addressed by the traditionally required courses. The main goal of this project is to produce materials that convince students that mathematics and modern computer technology are valuable tools in solving realistic problems and to teach them to utilize these tools effectively. We plan to develop, site-test, and nationally disseminate an archive of substantial, technology-based case studies (a realistic scenario which can be used to introduce the mathematical content) in the mathematics of decision-making. These will take between a few days and a few weeks to teach, and can be used instead of or in addition to a text. Each case study will be developed by teams consisting of faculty from mathematics and BPA, to be chosen from around the county. The co-PIs Thompson and Lamoureux, in a partnership between the University's Department of Mathematics and the College of Business and Public Administration, have produced case studies on whether to foreclose a commercial loan or work out an arrangement with the creditor, and on how to price a stock option. Hughes Hallett, in collaboration with E. Connally of Wellesley College and faculty at Harvard University's Kennedy School of Government, has produced case studies on the Austrian state pension system, population projection using US census data and data from the CIA World-book, and water flow in the Charles River using data from the US Geological Survey.