Category Archives: Math

Solvitur Ambulando

An algebraist, a finitist, and a determinist walk into a statistics classroom. They are all the same person and worse: the teacher, so the joke is on the students. For reasons still partly obscure to me, my department has given … Continue reading

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What is an Infinitesimal?

A guest post from Reginald Anderson at Kansas State University. First-time learners of calculus often struggle with the notion of an infinitesimal, and considering $\frac{dy}{dx}$ literally as a fraction can lead students astray in Calculus III and differential equations, when … Continue reading

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A Eulogy Of Lipschitz Maps

A Lipschitz map (/function) is one that does not extend distances by more than a pre-assigned factor: $f: X \longrightarrow Y$ is Lipschitz if there exists an $L \in \mathbb{R}$ such that $$ \forall x, \ \¬† \forall y \ … Continue reading

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Introduction to Ideal Class Groups

Algebraic number theory is a really interesting subject, but unlike some other subjects, it’s not 100% clear what objects people study. This post provides an introduction to the¬†class group of a finite dimensional field extension of $\mathbb{Q}$, an object often … Continue reading

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Intersection of a Chain of Subsets

Assume $\{F_x\}_{x \in \Gamma}$ is a collection of subsets (of a not-so important set!) such that every two are comparable, i.e for any $x$ and $y$, either $F_x \subset F_y \ \ $ or $\ \ F_x \supset F_y \ … Continue reading

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