Analysis (Mathematics)

Segni e algoritmo nell’analisi leibniziana

by Enrico Pasini

Published in M. Panza - C. S. Roero (eds.), Geometria, flussioni e differenziali, Napoli, Istituto italiano per gli studi filosofici – La città del sole, 1995, 385-412

Arcanum Artis Inveniendi: Leibniz and Analysis

by Enrico Pasini

in M. Otte - M. Panza (eds.), Analysis and Synthesis in Math­ematics, «Boston Studies in the Philosophy of Science», Dord­recht, Kluwer, 1997, 35-46

An Introduction to Weak Derivatives

by Jonathan Gleason

The final project for my MATH 275 Basic Theory of Partial Differential Equation course.

We first motivate the definition of a weak derivative in the context of differential equations. After proving a couple... more We first motivate the definition of a weak derivative in the context of differential equations. After proving a couple of preliminary lemmas, we define the notion of a \emph{weak derivative} and prove some basic properties of it. After enough basic theory has been developed, we use it produce ``modulo sets of measure $0$'' versions of classical results from elementary calculus. We then introduce and define Sobolev spaces, equip them with the necessary structure and prove their completeness.

A Homeomorphism of $\mathbb{R}$ that Doesn't Preserve Lebesuge Measurability

by Jonathan Gleason

We construct the Cantor set and subsequently the Cantor function. We then modify the Cantor function to obtain a... more We construct the Cantor set and subsequently the Cantor function. We then modify the Cantor function to obtain a homeomorphism of $\mathbb{R}$ that maps the Cantor set into a set of positive measure (and hence doesn't preserve Lebesgue measurability).

Existence and Uniqueness of Haar Measure

by Jonathan Gleason

The paper I wrote for the 2010 University of Chicago Mathematics REU.

In this paper, we prove existence and uniqueness of left and right Haar measures on a locally compact topological... more In this paper, we prove existence and uniqueness of left and right Haar measures on a locally compact topological group, and show how one can relate left and right Haar measure.

Potocki: Formalización del trayecto vital

by José Angel García Landa

En este artículo examino algunas especulaciones sobre la representación formal de biografías e historias vitales, tal... more En este artículo examino algunas especulaciones sobre la representación formal de biografías e historias vitales, tal como aparecen en el MANUSCRITO ENCONTRADO EN ZARAGOZA, novela-marco de Jan Potocki (1804, 1810). En la persona del geómetra Velázquez, Potocki a la vez satiriza las incipientes especulaciones de la Ilustración sobre una matematización de la psicología y comportamiento humanos, y participa sin embargo de ellas con contribuciones originales y sugerentes, que anticipan algunos elementos de narratologías formalistas posteriores.