Capstone Courses and Projects in Applied Mathematics and Statistics

该项目涉及在数学系建立一个本科生计算实验室，该实验室还包括进行简单物理实验的设施。该实验室用于开发和实施本科应用数学和统计专业的顶峰课程和项目。这些课程和项目帮助学生学习将实验方法、数学和统计建模技术、数学分析和计算技能相结合来研究物理问题和过程。该项目为学生提供了整合不同教育领域的经验，以培养当今工作场所所需的技术和批判性思维技能。这些课程，一门是应用数学，一门是统计学，通过讲座、物理实验、数据收集和计算机实验室课程来实施。第一学期使用的是案例研究。这门课程之后是第二学期由教师指导的学生研究项目。学生通过实施可用的计算算法并对其进行必要的修改，学习如何对真实世界的流程进行建模和分析。他们还被要求口头和书面传达项目结果。本科生实验室是现有教职员工和研究生计算机实验室的延伸，允许研究生担任本科生的导师。为该课程开发的案例研究和学生项目可以提供给表示对该项目感兴趣的其他大学(通过万维网)，并可在适当的会议上提出。顶峰课程和项目可以通过提高学生的批判性思维、分析和综合技能，以及通过更好地为学生进入工业、政府或研究生研究环境做好准备，来显著加强本科数学课程。

This project addresses the establishment of an undergraduate computational laboratory, which also contains facilities for performing simple physical experiments, in the mathematics department. The laboratory is used in the development and implementation of capstone courses and projects for undergraduate applied mathematics and statistics majors. These courses and projects help students learn to combine experimental methods, mathematical and statistical modeling techniques, mathematical analysis, and computational skills to study physical problems and processes. The project provides students the experience of integrating different areas of their education in order to develop the technological and critical-thinking skills necessary in today's workplace. The courses, one in Applied Mathematics and one in Statistics, are implemented using lectures, physical experimentation, data collection, and computer laboratory sessions. Case studies are used during the first semester. This course is followed by a second semester of faculty-guided student research projects. The students learn to model real-world processes and to analyze the models by implementing available computational algorithms and making necessary modifications to them. They are also required to communicate project results orally and in writing. The undergraduate lab is administered as an extension of an existing faculty and graduate student computer lab, which allows graduate students to serve as mentors for undergraduates. The case studies and student projects developed for the course can be made available to other universities (via the World Wide Web) that have expressed interest in the project and can be presented at appropriate conferences. The capstone courses and projects can significantly strengthen the undergraduate mathematics program by improving students' critical thinking, analysis, and synthesis skills and by better preparing students to enter industrial, government, or graduate research environments.