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

宾夕法尼亚州立大学伊利的REU数学生物学课程将使本科生参与数学最丰富和发展最快的领域之一。 它为六名参与者提供了数学生物学的研究培训，并向他们介绍了当前感兴趣的几个领域：活性介质中的图案形成，电兴奋细胞的建模以及植物和树木的肢体生长。 唯一的先决条件是成功完成一门课程，在常微分方程和生物学的兴趣。 该计划的目标是双重的。 首先，学生将获得非线性动力系统的理论和方法的介绍，包括相平面分析和分叉理论。 然后，这些技术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，因为动力系统出现在许多领域，除了生物学，如物理学，工程学和化学。 在详细研究模型中获得的经验将在未来的课程中很好地为他们服务，无论他们选择追求的研究领域如何。 第二，学生接触到当前的数学生物学研究课题。 该计划中讨论的许多主题都处于发展的早期阶段，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，这是一种用于相平面和分叉分析的强大工具。 研讨会将在整个计划由教师和学生参与者沿着与讨论组在每天结束。

Penn State Erie's REU Program in Mathematical Biology will involve undergraduates in one of the richest and fastest growing fields of mathematics. It gives the six participants research training in mathematical biology and introduces them to several areas of current interest: pattern formation in active media, the modeling of electrically excitable cells, and limb growth of plants and trees. 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 of study 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 the 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 throughout the program by both faculty and student participants along with discussion groups at the end of each day.