Mathematics Computer Laboratory

数学计算机实验室

• 批准号: 9851196
• 负责人: Sheldon Axler
• 金额: $ 3.13万
• 依托单位: San Francisco State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-10-15 至 2001-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9851196&HistoricalAwards=false
• 关键词: Mathematics; Computer; Laboratory

The goal of this project is to improve the calculus sequence at San Francisco State University by making modern symbolic and numeric calculation an integral part of the course. Our Mathematics Department is committed to including mathematical computing as part of calculus. We propose to revamp our calculus sequence so that student use of Mathematica becomes a key part of the course. However, the present computing facilities of the Mathematics Department are not capable of supporting most modern mathematical software. Thus we propose to re-equip our computing facility with new computers that can run Mathematica. Our philosophy for using Mathematica in calculus is that the existence of such software changes what and how we teach. For example, knowing how to integrate a rational function by using the partial fraction decomposition is no longer a marketable skill because Mathematica can perform the calculation with ease. However, understanding what an integral is and knowing which integration to perform is more important than ever now that huge computational power is available. Thus we envision shifting the calculus course away from algorithmic skills and toward more problem solving, more applications, and a deeper understanding of the objects being manipulated. Mathematica will allow us to drop some training in computations that are better performed by machines than by people. With the time freed by dropping a few such topics, we expect to spend more time emphasizing the key ideas and applications of calculus. Thus the use of Mathematica will make our calculus course more demanding, not easier. In return, we expect to produce students who can use their calculus (and Mathematica) skills in other courses and in their professional lives.

这个项目的目标是通过使现代符号和数值计算成为课程的一个组成部分来改进旧金山弗朗西斯科州立大学的微积分序列。 我们的数学系致力于将数学计算作为微积分的一部分。我们建议修改我们的微积分序列，使学生使用Mathematica成为课程的关键部分。 然而，数学系目前的计算设施无法支持大多数现代数学软件。因此，我们建议重新装备我们的计算设施与新的计算机，可以运行Mathematica。 我们在微积分中使用Mathematica的理念是，这种软件的存在改变了我们的教学内容和教学方式。例如，知道如何通过使用部分分式分解来积分有理函数不再是一种有市场的技能，因为Mathematica可以轻松地执行计算。然而，理解什么是积分以及知道执行哪种积分比以往任何时候都更重要，因为现在可以使用巨大的计算能力。因此，我们设想将微积分课程从算法技能转向更多的问题解决，更多的应用，以及对被操纵对象的更深入理解。 Mathematica将允许我们放弃一些计算训练，这些计算由机器执行比由人执行更好。由于放弃了一些这样的主题，我们希望花更多的时间来强调微积分的关键思想和应用。因此，Mathematica的使用将使我们的微积分课程更苛刻，而不是更容易。作为回报，我们希望培养出能够在其他课程和职业生活中使用微积分（和Mathematica）技能的学生。