Mathematical Sciences: Undergraduate Program in Mathematical Biology

宾夕法尼亚州立大学伊利数学生物学的REU项目将让本科生进入最丰富、增长最快的数学领域之一。它为六名参与者提供了在数学生物学的几个领域中的一个领域进行研究的机会：癌症建模、活性介质中的图案形成以及电可兴奋细胞的建模。唯一的先决条件是成功完成一门常微分方程式的课程，并对生物学感兴趣。在整个为期四周的课程期间，学生们将分组研究当前数学生物学研究问题的不同方面。这个问题的生物学基础将在第一周详细讨论，并将激励随后的数学分析。程序中引入的数学方法包括相平面分析和分叉理论。学生们将有机会接触到运行Linux操作系统的奔腾电脑，并将学习数学软件包XPP，这是一个用于相平面和分叉分析的强大工具。在整个项目中，教师和学生都将进行研讨会，项目的最终结果将是每个团队的书面报告和陈述。参与会给学生带来很多好处。首先，他们将通过第一手参与解决生物学中的研究问题来认识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交流技术信息的能力。最后，这一经历将使参与者接触到科学研究中的兴奋和辛勤工作，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.