Math Concepts Guide
Does the world need more math?
I say yes. That’s why I’m announcing a new open source project to develop a guide to basic mathematical concepts—sets, tuples, relations, and functions.
We live in a world where people often struggle to communicate ideas with clarity and precision. Many times in the business world people have a meeting, collaborate on something, and come to an agreement on what should be done. Everyone leaves the meeting believing they’re on the same page with everyone else. Then later on, when things are well in motion, they find out that they actually had very different ideas about what they thought they agreed on.
This is, at least in part, a failure to write down precise unambiguous expressions of concepts, methods, and decisions. Mathematical concepts and notation can help with this. It need not involve advanced topics like differential equations and non-Euclidean geometry. Simple intuitive concepts like sets, relations, and functions can help tremendously with the clarity of expression for many ideas.
We also live in a world where people working in a field, such as software development, have much diversity in formal education. Some people have technical degrees, possibly advanced, other people have non-technical degrees, and still other people have a high school education. People working together may have been educated in different countries with different educational systems.
Today everyone learns new things as needed using online resources. This project will produce such an online learning resource.
I want to start using more math myself in my own work and I’m expecting that some people may recoil a bit when they see something like \( A = \left\{ x \mid x \in \mathbb{R}, x^3 < \pi \right\} \). I want to have a document that I can point to and say—go here to see what a set is, go here to understand the difference between a real number and an integer, and so on. The Guide to Basic Mathematical Concepts will fill that need.
This guide will not be a standard math textbook with proofs and exercises. It will be aimed at the practitioner looking to express an idea clearly, not the budding mathematician looking for proof techniques. It will be short and crisp—lay out clear definitions, straightforward examples, and be limited to basic concepts like sets and functions.
The project is hosted here on github, check it out: https://github.com/jlenthe/math-concepts-guide. There’s already an extensive draft and see the CONTRIBUTING.md file for how you can help.
Acknowledgements
ChatGPT was used in the preparation of this article for light proofreading and stylistic suggestions.