REU Program in Mathematical Biology: Penn State Erie, The Behrend College

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数学生物学方面的研究培训，并向他们介绍了当前感兴趣的几个领域：癌症建模、活性介质中的模式形成和电兴奋细胞的建模。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。该计划的目标是双重的。首先介绍非线性动力系统的理论和方法，包括相平面分析和分岔理论。这些技术随后被用来回答有关生物现象的数学模型的问题。这是非常有价值的，因为动力系统除了在生物学之外，还出现在许多领域，如物理、工程和化学。在详细研究模型中获得的经验将对他们未来的课程很有帮助，无论他们选择从事什么领域。其次，学生接触到数学生物学的最新研究课题。课程中讨论的许多主题都处于早期发展阶段，并为未来的研究提供了许多机会。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。在整个课程中，教师和学生参与者将举行研讨会，并在每天结束时举行讨论小组。

Penn State Erie's REU Program in Mathematical Biology will involve undergraduates in one of the richest and fastest growing fields in mathematics. It gives the six participants research training in mathematical biology and introduces them to several areas of current interest: 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. The goal of the program is two-fold. First the students receive an introduction to the theory and methods of nonlinear dynamical systems, including phase plane analysis and bifurcation theory. These techniques are then used to answer questions about mathematical models of biological phenomena. This is of great value since dynamical systems arise in many areas in addition to biology, such as physics, engineering, and chemistry. The experience gained in studying models in detail will serve them well in future courses regardless of the field they choose to pursue. Second, the students are exposed to current topics of research in mathematical biology. Many of the topics discussed during the program are at early stages of development, and offer many opportunities for future research. 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 throught the program by both faculty and student participants along with discussion groups at the end of each day.