Notes

Short expository articles on the mathematics behind my research, as well as on other subjects I enjoy studying.

Geometria básica: uma visão abrangente

Quarenta iniciativas para problemas de geometria plana e espacial, das retas paralelas e dos ângulos notáveis à relação de Euler, a partir do manual manuscrito de Marcelo…

Oct 15, 2026

The history of generalized ODEs and non-absolute integration in Brazil

History

Generalized ODEs

Integration theory

How Kurzweil’s generalized ODEs and non-absolute integration took root in Brazil, from Štefan Schwabik’s visit to São Paulo in 1989 to the São Carlos school, with an…

Oct 13, 2026

Introduction to differential geometry: plane curves and initial concepts

Differential geometry

Parametrized curves, regularity, arc length and reparametrization, with the cycloid, trochoids, epicycloids, hypocycloids and Bernoulli’s lemniscate as first examples.

Oct 13, 2026

When Riemann and Lebesgue aren’t enough

Integration theory

Generalized ODEs

Why a variable mesh is all you need: Cousin’s lemma, the Kurzweil integral and its Fundamental Theorem of Calculus, generalized ODEs, and why measure differential equations…

Oct 11, 2026

Categories

Geometria básica: uma visão abrangente

The history of generalized ODEs and non-absolute integration in Brazil

Introduction to differential geometry: plane curves and initial concepts

When Riemann and Lebesgue aren’t enough