将计算挑战融入随机过程的多学科课程
Incorporating Computational Challenges into a Multidisciplinary Course on Stochastic Processes
摘要：
定量方法和数学建模在各个学科中发挥着越来越重要的作用。因此，跨学科的数学课程越来越受欢迎。然而，在高级水平上教授这些课程可能具有挑战性。学生们通常有不同的数学背景，不同的兴趣，以及想要学习材料的不同原因。在这里，我们描述了一门关于生物学中随机过程的课程，该课程于2020年9月至12月期间向数学家和生物学家的混合受众提供。除了传统的讲座和家庭作业，我们还将一系列每周的计算挑战纳入课程。这些挑战有助于学生熟悉主要的建模概念，并为他们提供如何在类似研究的环境中实施这些概念的介绍。为了考虑到学生们不同的学术背景，他们在小组中进行挑战，并在每周的专门讨论课上展示他们的结果和代码。我们讨论我们的经验，设计和实施的应用数学课程，通过计算的挑战，以问题为基础的学习的元素。我们还讨论了学生的反馈，并描述了课程中提出的挑战的内容。我们提供所有材料，以及一些挑战的示例代码。
英文摘要：
Quantitative methods and mathematical modeling are playing an increasingly important role across disciplines. As a result, interdisciplinary mathematics courses are increasing in popularity. However, teaching such courses at an advanced level can be challenging. Students often arrive with different mathematical backgrounds, different interests, and divergent reasons for wanting to learn the material. Here we describe a course on stochastic processes in biology, delivered between September and December 2020 to a mixed audience of mathematicians and biologists. In addition to traditional lectures and homeworks, we incorporated a series of weekly computational challenges into the course. These challenges served to familiarize students with the main modeling concepts, and provide them with an introduction on how to implement them in a research-like setting. In order to account for the different academic backgrounds of the students, they worked on the challenges in small groups, and presented their results and code in a dedicated discussion class each week. We discuss our experience designing and implementing an element of problem-based learning in an applied mathematics course through computational challenges. We also discuss feedback from students, and describe the content of the challenges presented in the course. We provide all materials, along with example code for a number of challenges.
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