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Introduction to Algebraic Structures
This post is an experiment in explaining math concepts via colorful hand-drawn diagrams. At the recommendation of a few friends, I will likely add examples in the near future. If you find this post...
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Studying Symmetry
Group(oid) theory is the study of symmetry. When we are dealing with objects that appear symmetric, group theory assists with analysis of these objects. The label of “symmetric” is applied to anything...
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A Gentle Introduction to Tensors and Monoids
There are at least three distinct conceptual roles which vectors and vector spaces play in mathematics: A vector is a column of numbers. This is the way vector spaces appear in quantum mechanics,...
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Understanding the Lazard Ring
When I define a polynomial, I am simply handing you an indexed collection of coefficients. A polynomial with two variables, $x, y$ and coefficients $c$, is of the form: $F(x, y) = \sum\limits_{ij}...
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Group Law on the (Punctured) Affine Line
There are likely inaccuracies in this post, as I am just beginning to learn the basics of algebraic geometry. Constructive criticism is strongly encouraged. There once was a line… Let’s look at the...
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What is an elliptic curve?
There are many ways to define it. An elliptic curve is an equation of the form: $y^2$ = polynomial of degree $3$ in $x$ without a multiple root Sidenote: This is a bit misleading, for the elliptic...
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