As a student of applied mathematics, I have often found that many powerful ideas are first introduced through examples that are already too complicated for initial understanding. While finishing our book Applied Mathematics Toolkit: Modeling • Data • Algorithms, my advisor Nan Chen and I decided to explore a different approach in parallel by creating a short video series built around a simple principle: one concept • one example. Each video is 5–10 minutes long, focuses on a single idea, and uses deliberately simple examples to support first exposure, intuition building, and efficient review. So far, we have completed two modules (Statistical Toolkit and Machine Learning Toolkit), with three more in progress (Applied Analysis Toolkit, Dynamical Systems Toolkit, and Stochastic Toolkit). The series is intended primarily for upper-level undergraduates, early graduate students, and researchers seeking a clean conceptual entry point before engaging with more technical treatments. The videos are shared openly in the hope that they may be useful for learning, teaching, or quick conceptual review. The full collection is available on my YouTube and RedNote.
I am also a part of Dr. Nan Chen's team in putting together the MPE studio. It is an open educational platform that brings applied mathematics, data science, and Earth-system science together through interactive experiments, visual stories, short videos, and accessible scientific examples. It is designed to make mathematical ideas easier to enter and explore, especially when the underlying concepts are often introduced through examples that are already technically complicated. The Studio connects intuitive explanations with hands-on exploration, allowing students and researchers to experiment with ideas in prediction, uncertainty, inference, dynamical systems, machine learning, and related areas directly in the browser.