Capstone Courses and Projects in Applied Mathematics and Statistics

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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.