## Archive of posts with tag “abstract algebra”

### 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.

- Categories: math
- Tags: quantum field theory, linear algebra, abstract algebra

### 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.

- Categories: chemistry
- Tags: linear algebra, abstract algebra

### 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.

- Categories: music
- Tags: music theory, number sequence, long paper, abstract algebra