Integrating Mathematics and Biology: A Case Studies Approach to Linear Algebra

数学科学(21)生物科学(61)这个“概念证明”项目正在开发一门综合的数学和生物课程，在生物案例研究的背景下教授线性代数概念。本课程面向生物专业三年级学生和数学二年级学生进行分组授课，旨在补充，而不是取代数学专业的线性代数课程和生物专业的生态课程。该课程旨在加强生物学学生的数学技能，让数学学生接触到生物中使用的数学模型，教会学生如何与在不同科学学科接受培训的人合作，并教会学生如何批判性地阅读研究论文。生物和数学专业的学生在案例研究、小组项目和报告方面共同工作，构成了这门课程的广泛部分。这些案例研究基于可访问的包含数学模型的生物学研究论文，由数学和生物学教师联合撰写。本课程的家庭作业和补充阅读材料也在编写中。本课程的数学主题包括矩阵代数、基、特征向量、特征值、线性差分方程组和微分方程组，以及病态矩阵。生物学主题包括种群矩阵、弹性和敏感性、水生系统中的营养物质流动、传染病的传播和遗传学。正在修改这些材料，以便分发给希望补充现有生态学、保护生物学或线性代数课程的学科教员，以及希望设计类似综合课程的机构。

Mathematical Sciences (21) Biological Sciences (61)This "Proof of Concept" project is developing an integrated mathematics and biology course that teaches linear algebra concepts in the context of biological case studies. This course is being team-taught to a mixture of junior biology students and sophomore mathematics students and is intended to supplement, not replace, current courses in linear algebra for the mathematics majors and current courses in ecology for the biology majors. The course is designed to strengthen the mathematical skills of biology students, expose mathematics students to mathematical models used in biology, teach students how to collaborate with people trained in different scientific disciplines, and teach students how to critically read research papers. Biology and mathematics students working together on case studies, group projects, and presentations form an extensive part of the course. The case studies, based on accessible biological research papers that incorporate mathematical models, are being written jointly by mathematics and biology faculty. Homework assignments and supplemental reading material for the course are also being created. The mathematical topics in the course include matrix algebra, bases, eigenvectors, eigenvalues, systems of linear difference and differential equations, and ill-conditioned matrices. The biological topics include population matrices, elasticity and sensitivity, nutrient flow in aquatic systems, spread of infectious diseases, and genetics. These materials are being modified for dissemination to disciplinary faculty who wish to supplement existing courses in ecology, conservation biology, or linear algebra and for institutions who wish to design a similar integrated course.