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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
Comments Off on Solvitur Ambulando
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
Comments Off on What is an Infinitesimal?
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
1 Comment
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