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.

中文翻译：

---

代数生物学案例：从研究到教育

虽然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，我们将简要介绍四个不同的生物学问题，其中多元多项式起着核心作用 - 有时称为代数生物学的子领域。也就是说，这些主题包括生化反应网络、基因调控网络的布尔模型、代数统计和基因组学，以及神经科学中的领域。之后，我们将总结数学生物学中离散和代数结构的历史，从它们在 1960 年代后期的早期出现到现在。最后，我们将讨论代数生物学在现代课堂和课程中的作用，包括文献资源和相关软件。