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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
Posted in Grad student life, Math, Math History, Math Teaching, Statistics, Teaching
Tagged nature of proof, paradox, probability theory, Zeno of Elea
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What is an Infinitesimal?
A guest post from Reginald Anderson at Kansas State University. Firsttime 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
Posted in Algebraic Geometry, Math Education, Teaching
Tagged Algebraic geometry, Math, Teaching
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A Eulogy Of Lipschitz Maps
A Lipschitz map (/function) is one that does not extend distances by more than a preassigned factor: $f: X \longrightarrow Y$ is Lipschitz if there exists an $L \in \mathbb{R}$ such that $$ \forall x, \ \ \forall y \ … Continue reading
Posted in Analysis, Math
Tagged Change of Variables, Lipschitz Maps, Luzin N Property, Radamacher's Theorem
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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
Intersection of a Chain of Subsets
Assume $\{F_x\}_{x \in \Gamma}$ is a collection of subsets (of a notso 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