论文标题
代数生物学的案例：从研究到教育
The case for algebraic biology: from research to education
论文作者
论文摘要
尽管不用说线性代数是数学生物学的基础，但多项式代数不太明显。在本文中，我们将简要介绍四种不同的生物学问题，其中多元多项式发挥了核心作用 - 有时被称为“代数生物学”的子场。也就是说，这些主题包括生化反应网络，基因调节网络的布尔模型，代数统计和基因组学以及神经科学中的位置领域。之后，我们将总结数学生物学中离散和代数结构的历史，从1960年代后期到当天的早期出现。最后，我们将讨论代数生物学在现代课堂和课程中的作用，包括文献中的资源和相关软件。我们的目标是使这篇文章变得更加易于访问，并吸引了不知道代数的数学生物学家，不知道生物学的代数主义者，尤其是对这两个看似无关的领域之间的协同作用感到好奇的有兴趣的学生。
Though it goes without saying that linear algebra is fundamental to mathematical biology, polynomial algebra is less visible. In this article, we will give a brief tour of four diverse biological problems where multivariate polynomials play a central role -- a subfield that is sometimes called "algebraic biology." Namely, these topics include biochemical reaction networks, Boolean models of gene regulatory networks, algebraic statistics and genomics, and place fields in neuroscience. After that, we will summarize the history of discrete and algebraic structures in mathematical biology, from their early appearances in the late 1960s to the current day. Finally, we will discuss the role of algebraic biology in the modern classroom and curriculum, including resources in the literature and relevant software. Our goal is to make this article widely accessible, reaching the mathematical biologist who knows no algebra, the algebraist who knows no biology, and especially the interested student who is curious about the synergy between these two seemingly unrelated fields.
