The pedagogical approach presented here draws heavily from two teachers whose influence shaped our understanding of engineering education. Professor Peter Hansbo taught us the art of making complex material accessible without sacrificing rigor, demonstrating through his finite element courses how mathematical precision and pedagogical clarity can coexist. His ability to present advanced topics in an approachable manner, integrating physical intuition with mathematical formalism, serves as the model we strive to follow in this work. Bertil Nilsson introduced us to computational thinking and computer-based mathematics [1], emphasizing that mathematical modeling and interpretation are the engineer’s core competencies, while routine computation should be delegated to computers. This philosophy: that humans should focus on what they do best (conceptualizing and interpreting) while computers handle what they excel at (calculating), pervades the entire approach. We wholeheartedly embrace this approach, which has repeatedly demonstrated its effectiveness in increasing student engagement through work on authentic applications, leading to improved knowledge retention.

The ideas presented here originated over several years of teaching mechanics, solid mechanics, optimization, and finite element method courses at various levels within the school of engineering. The work has been shaped by interactions with students as well as discussions with other professionals in the field.

Our approach aligns closely with Conrad Wolfram’s vision for mathematics education. In The Math(s) Fix [2], he argues that computers can and should handle routine computations and symbolic manipulations, allowing humans to focus on higher-level problem-solving. He emphasizes the importance of computational thinking—breaking down complex problems, formulating them in a way that a computer can process, and interpreting computational results to gain deeper insights.

Visualization is central to this work. Beyond illustrating concepts, we actively encourage students to use visualization as a tool for verifying and refining their models. This emphasis on visual thinking is inspired by Grant Sanderson of 3Blue1Brown, Welch Labs, 2swap, and many other creators who share their love for mathematics through beautiful visualizations.

This site is inspired by the Computational Thinking course at MIT and the Underactuated Robotics course. We embrace this format, combining traditional exposition with interactive computational notebooks that allow readers to explore concepts dynamically while engaging with the theory.

The technical implementation uses Python with the marimo editor for interactive computational work. The site is built with Quarto, integrating Jupyter Notebooks developed in VS Code. We are grateful for the outstanding tools the open-source community has created.