Archive of posts with tag “abstract algebra”

Oct 10, 2024
Some understanding of Grassmann numbers out of intuition
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.
/math #quantum field theory #linear algebra #abstract algebra
Apr 13, 2020
Algebraic structure of chemicals
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 ( $\mathbb Z$ ), which is not a field, so the algebraic structure of chemicals is not linear space. They actually live in a free $\mathbb Z$ -module. See how I formalize this idea in mathematical language.
/chemistry #linear algebra #abstract algebra
Mar 27, 2020
The frequency assignment of musical notes
This article explores the concept which I call the frequency assignment, which is a mapping from $N$ (the set of notes) to $\mathbb R^+$ (the set of frequencies). Concepts such as octaves, intervals, and equal temperaments are introduced.
/music #music theory #number sequence #long paper #abstract algebra