Intersection of Population Biology and Mathematics

使用微积分和统计学处理数学模型的扎实背景已经成为生物学教育的必要组成部分，特别是在生态学和进化的子领域。然而，数学概念对生物学的重要性很难传达给那些更习惯于定性的“自然历史”方法的初学者。大多数数学课程和生物学课程都是相互独立教授的，即使其中一门课程是另一门课程的先决条件，这极大地加剧了理解数学对生物学的必要性的问题。这些困难在教授这些科目时尤其严重，因为在市中心的环境中，学生往往缺乏定量分析能力，接触科学的机会也有限。为了解决这个问题，我们开发了两门协调的本科课程，一门是生态学与进化论，另一门是数学建模，这两门课程被设计成放在一起。主题流的设计是为了相互加强。数学课程阐明微积分和统计学模型的基本原理，而生物学课程则为它们的应用提供了一个背景。我们正在使用电子表格程序Excel开发计算机模拟和练习，所有学生都可以随时使用。《生命科学数学建模》的新教材正在制作中，我们正在把课堂笔记、实验练习和模拟放到网上。我们已经组建了一个外部顾问团队，帮助我们评估材料，并制定了评估计划。

A solid background in working with mathematical models using calculus and statistics has become a necessary component of education in Biology, particularly in the sub-fields of Ecology and Evolution. However, the importance of mathematical concepts to Biology is extremely difficult to convey to beginning students who are more comfortable with qualitative, "natural history" approaches. The problem in understanding the necessity of math to biology is greatly exacerbated by the fact that most Math courses and Biology courses are taught independently of each other, even when one course is a prerequisite to another. These difficulties are particularly acute in teaching these subjects in inner city environments where the students tend to have poor quantitative skills and limited exposure to science. We are addressing this difficulty by developing two coordinated undergraduate courses, one in Ecology and Evolution and one in Mathematical Modeling, that are designed to be taken together. The flow of topics is designed to reinforce each other. The Math course clarifies underlying principles of models of calculus and statistics and the Biology course provides a context for their application. We are developing computer simulations and exercises using the spreadsheet program Excel, which is readily available to all students. A new textbook in Mathematical Modeling for the Life Sciences is being produced, and we are making our lecture notes, laboratory exercises and simulations available on line. We have assembled a team of outside advisors helping us to evaluate our materials, and have constructed an assessment plan.