We continue the discussion from the previous post in the series.
Tag: Studies
Categories
Motivation for Analytic Number Theory
In this post, we try to tease out more motivation and a better systematization of analytic number theory, which traditionally has been viewed more as a collection of ad-hoc concepts. This may end up including new concepts that aren’t yet part of the standard literature, and hopefully these can yield more fruit in the subject.
Both model theory and category theory formalize the idea of “structure” in some way. Is this purely different formal interpretations of an informal idea, or is there more of a formal relationship beyond this between these two subjects?
Earlier, on August 6, 2021, I had tried to formalize a mathematical concept that would generalize the idea of a “basis,” as seen in the theory of vector spaces or the Fundamental Theorem of Arithmetic. I discuss in this post what I tried and what I learned.
In this post, we attempt to better understand the questions posed in this post and its follow-up by formalizing them generally in the language of universal algebra.
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General Field Applicability to Infinite Sets
In this post, we undertake a more focused investigation into the conjecture that every infinite set can be turned into a field, as stated in this post. (We assume the Axiom of Choice throughout.)
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Algebra of Color Mixing
We consider how we can do algebra with colors. In other words, if we take the set of all colors, what algebraic structures can it be endowed with? In this post, we look at the algebra of color mixing: what is the structure of the algebra that is induced by the operation of color mixing? (What properties does color mixing satisfy?)
In this post, we continue the discussion from the previous in the series.
We can think of modular arithmetic as amending operations on Z to “wrap around and stay in Zn.” Can we generalize this idea to arbitrary groups, or even general algebras?
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Sine Angle Product Formula 2
In this post, we continue the discussion from a previous post about the existence of a suitable sine angle product identity.
