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

每年都有数十万商业和公共管理（BPA）学位课程的学生参加必修的数学课程，因为他们需要学习如何有效地使用数学进行决策。然而，传统的必修课程往往不能满足这一需求。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档案，基于技术的案例研究（一个现实的场景，可以用来介绍数学内容）在数学决策。这些将需要几天到几周的时间来教授，可以用来代替或补充文本。每个案例研究将由来自数学和BPA的教师组成的团队开发，从全国各地选择。联合PI汤普森和Lamoureux，在大学的数学系和商业与公共管理学院之间的合作伙伴关系，已经产生了案例研究是否取消商业贷款或制定与债权人的安排，以及如何定价股票期权。Hughes Hallett与E.韦尔斯利学院的康纳利和哈佛大学肯尼迪政府学院的教师，对奥地利国家养老金制度进行了案例研究，利用美国人口普查数据和中央情报局世界手册的数据进行了人口预测，并利用美国地质调查局的数据对查尔斯河的水流进行了研究。

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.