Modern Biology, Modern Mathematics, and Modern Solutions: Moving Biomathematics Education Beyond Calculus

数学科学（21）本项目解决了对展示现代离散数学和代数统计在分子生物学紧迫问题中的应用的教育材料的未满足需求。该项目由两个成功的课程、课程和实验室改进（CCLI）项目（DUE-0126740和DUE-0340930）发展而来，为微积分以外的本科数学课程提供8-10个20页的模块，包括有限数学、离散结构、离散动力系统、线性代数、抽象代数、图论、概率论、生物统计学和数学建模。智力价值：反映了这些领域在生物数学研究中日益重要的当前趋势，这些材料在整个数学课程中弥合了理论和应用之间的现有鸿沟。通过借鉴相关教师的研究领域，弗吉尼亚理工大学生物信息学研究所正在进行的研究，以及生物学和数学计算方法的最新进展，这些模块解决了培养学生超越微积分的数学-生物学界面的关键国家需求。学生们使用开源计算代数软件来学习这些新的综合方法。更广泛的影响：这些模块在Sweet Briar学院（一所选择性的四年制女子文理学院）和西密歇根大学（一所大型卡内基研究中心地区州立大学）开发并随后进行了测试，旨在用于微积分以外的各种课程。这些独立的模块可以很容易地被广泛的本科院校采用，用于从通识教育数学到教师准备再到高级本科课程的课程。此外，这些模块是灵活的：希望在单个课程小时内进行练习的教师可以选择模块的一部分，而愿意在这些生物数学应用上投入更多课堂时间的教师可以更广泛地使用这些模块。这些模块通过国家科学数字图书馆（NSDL）在全国范围内提供，促进了更广泛的教师发展和更大的学生影响。最重要的是，通过为整个数学课程提供最新的、基于研究的应用程序，该项目进一步提高了学生在分子生物学和数学的关键联系方面的参与度和专业知识。

Mathematical Sciences (21)This project addresses an unmet need for educational materials demonstrating applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. Growing out of two successful Course, Curriculum, and Laboratory Improvement (CCLI) projects (DUE-0126740 and DUE-0340930), this project is producing a collection of 8-10 twenty-page modules for undergraduate mathematics courses beyond calculus, including finite mathematics, discrete structures, discrete dynamical systems, linear algebra, abstract algebra, graph theory, probability, biostatistics, and mathematical modeling.Intellectual Merit: Reflecting the current trend of increased importance of these fields in biomathematics research, the materials bridge the existing divide between theory and applications in courses throughout the mathematics curriculum. By drawing from the research areas of the faculty involved, ongoing research at the Virginia Tech Bioinformatics Institute, and recent advances in computational methods in biology and mathematics, these modules address a crucial national need to train students at the math-biology interface beyond calculus. Students employ open-source computational algebra software to learn these new integrated approaches. Broader Impact: Being developed and subsequently tested at Sweet Briar College (a selective four-year liberal arts college for women) and Western Michigan University (a large Carnegie Research I regional state university), the modules are designed for use in a wide variety of courses beyond calculus. The self-contained modules can be easily adopted by a broad spectrum of undergraduate institutions for use in courses ranging from general education mathematics to teacher preparation to advanced undergraduate courses. Moreover, the modules are flexible: faculty looking for an exercise for a single course hour may choose part of a module, while faculty willing to commit more class time to these biomathematical applications can use the modules more extensively. The modules are being made available nationwide through the National Sciences Digital Library (NSDL), facilitating broader faculty development and greater student impact. Most importantly, by providing current, research-based applications for use throughout the mathematics curriculum, this project is further increasing student engagement and expertise at the critical nexus of molecular biology and mathematics.