Oct 10, 2024
I was briefly introduced to Grassmann numbers when I studied quantum field theory. I then had the natural question of how we can formally define them. In this article, I went with my intuition and tried to answer this question.
Apr 13, 2020
Regarding balancing chemical equations, actually we are trying to find a non-trivial linear combination of some chemicals to get zero. The interesting thing is that the coefficients can only be integers (Z), which is not a field, so the algebraic structure of chemicals is not linear space. They actually live in a free Z-module. See how I formalize this idea in mathematical language.
Mar 27, 2020
This article explores the concept which I call the frequency assignment, which is a mapping from N (the set of notes) to R+ (the set of frequencies). Concepts such as octaves, intervals, and equal temperaments are introduced.