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

数学科学（21）生物科学（61）这个“概念验证”项目正在开发一个综合数学和生物学课程，在生物案例研究的背景下教授线性代数概念。这门课程是团队授课的初中生物学生和大二数学学生的混合物，旨在补充，而不是取代，目前的线性代数课程的数学专业和生态学专业的生物学专业的课程。该课程旨在加强生物学学生的数学技能，让数学学生接触生物学中使用的数学模型，教学生如何与受过不同科学学科训练的人合作，并教学生如何批判性地阅读研究论文。生物学和数学的学生一起工作的案例研究，小组项目和演示文稿形成了课程的广泛的一部分。这些案例研究是基于可访问的生物研究论文，其中包含数学模型，由数学和生物学教师共同撰写。课程的家庭作业和补充阅读材料也正在制作中。本课程的数学主题包括矩阵代数、基、本征向量、本征值、线性差分和微分方程系统以及病态矩阵。生物学的主题包括种群矩阵、弹性和敏感性、水生系统中的营养流、传染病的传播和遗传学。这些材料正在修改，以便分发给希望补充生态学、保护生物学或线性代数现有课程的学科教师，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.