Mathematical Sciences: Undergraduate Program in Mathematical Biology

宾夕法尼亚州立大学伊利分校的数学生物学REU项目将涉及数学中最丰富和发展最快的领域之一的本科生。它为六名参与者提供了在数学生物学的几个领域之一进行研究的机会：癌症建模，活性介质中的模式形成，以及电兴奋细胞的建模。唯一的先决条件是成功完成一门常微分方程课程并对生物学感兴趣。在整个为期四周的课程中，学生们将在数学生物学当前研究问题的不同方面进行团队合作。这个问题的生物学基础将在第一周详细讨论，并将激发后续的数学分析。课程中介绍的数学方法包括相平面分析和分岔理论。学生将有机会使用运行Linux操作系统的奔腾计算机，并将学习数学软件包XPP，这是一个用于相平面和分岔分析的强大工具。在整个项目中，教师和学生都将参加研讨会，最后每个团队将提交一份书面报告，并介绍他们的成果。参与将给学生带来许多好处。首先，通过亲身参与解决生物学研究问题，他们将看到数学的重要性和适用性。其次，通过团队合作，他们将学习合作的价值，以及与他人合作和沟通技术信息的能力。最后，这次经历将使参与者接触到科学研究中的兴奋和艰苦工作，并将为继续学习数学或科学提供动力。

Penn State Erie's REU Program in Mathematical Biology will involve undergraduates in one of the richest and fastest growing fields of mathematics. It affords the six participants the opportunity to pursue research in one of several areas of mathematical biology: cancer modeling, pattern formation in active media, and the modeling of electrically excitable cells. The only prerequisites are the successful completion of a course in ordinary differential equations and an interest in biology. Throughout the four-week period of the program students will work in teams on different aspects of a current research problem in mathematical biology. The biological underpinnings of the problem will be discussed in detail during the first week and will motivate the subsequent mathematical analysis. Mathematical methods introduced during the program will include phase plane analysis and bifurcation theory. Students will have access to Pentium computers running the Linux operating system and will learn the mathematical software package XPP, a powerful tool for phase plane and bifurcation analysis. Seminars will be given throughout the program by both faculty and student participants, and the program will culminate with a written report and presentation by each team on their results. Participation will result in many benefits to the students. First, they will see the importance and applicability of mathematics by participating, first hand, in the solution of a research problem from biology. Second, through team work they will learn the value of cooperation and the ability to work with, and communicate technical information to, others. Finally, the experience will give the participants exposure to the excitement and hard work involved in scientific research, and will provide motivation for continued study in mathematics or the sciences.