I'm an experienced programmer, but my higher-level math skills have always been weak. I've tried working through traditional math books, but I lose motivation when I can't see an immediate practical use for what I'm learning. I'm looking for books, websites, or programming project ideas that could help me learn trigonometry and topics beyond it by applying the concepts in code.
4 Answers
You could build your own vector and matrix library, then use it for a physics simulation. A project like that gives linear algebra a clear purpose: vectors represent positions and forces, matrices handle transformations, and calculus concepts can be explored through motion, acceleration, and numerical integration.
A simple starting project would be a physics-based platformer or a projectile simulator. For example, making a character jump along a gravity-accurate parabolic arc forces you to work with velocity, acceleration, time, and equations of motion. In practice, the programming usually implements math you’ve learned, so it helps to study the concepts alongside the project rather than expecting the code alone to teach everything.
A useful book is *From Mathematics to Generic Programming* by Alexander Stepanov and Daniel Rose. It starts with foundational math, explains where the formulas come from, and then turns the ideas into C++ algorithms. The examples should be reasonably straightforward to adapt to C or another language.
Try using computer graphics as a practical path into the subject. Projects involving curves, camera transforms, depth buffering, anti-aliasing, and basic computer vision can naturally teach trigonometry, geometry, and linear algebra because you’ll immediately see how the math affects the output.
*Hacker’s Delight* is another worthwhile option once you’re interested in lower-level mathematics. Despite the title, it’s about clever programming techniques and the math behind bit manipulation and machine-level operations.