Irrational Philosophy? Kronecker's Constructive Philosophy and Finding the Real Roots of a Polynomial
The prominent mathematician Leopold Kronecker (1823 – 1891) is often relegated to footnotes and mainly remembered for his strict philosophical position on the foundation of mathematics. He held that… Expand
An Introduction to Proofs with Set Theory
- Computer Science, Mathematics
- Synthesis Lectures on Mathematics & Statistics
This text is distilled from the lecture notes for a course focused on set theory subject matter as a means of teachin... Expand
Hilbert's Synthesis on Foundation of Geometry
The relations between intuition, axiomatic method and formalism in Hilbert's foundational studies has been discussed several times, but geometrical ones still have unclear sides and there is not a… Expand
Theological Underpinnings of the Modern Philosophy of Mathematics.
Abstract The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern is nineteenth-century mathematics. Theology was present… Expand
Proofs and Retributions, Or: Why Sarah Can’t Take Limits
The small, the tiny, and the infinitesimal (to quote Paramedic) have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that… Expand
Extratores de características acústicas inspirados no sistema periférico auditivo
Extrair informacoes de sinais acusticos e uma tarefa bastante comum dentro das areas de processamento de sinais e reconhecimento de padroes. De uma maneira geral, os sistemas de processamento tem… Expand
‘+1’: Scholem and the Paradoxes of the Infinite
This article draws on several crucial and unpublished manuscripts from the Scholem Archive in exploration of Gershom Scholem's youthful statements on mathematics and its relation to… Expand
An Integer Construction of Infinitesimals: Toward a Theory of Eudoxus Hyperreals
- Mathematics, Computer Science
- Notre Dame J. Formal Log.
A construction of the real number system based on almost homomorphisms of the integers Z was proposed by Schanuel, Arthan, and others. We combine such a construction with the ultrapower or limit… Expand
Squeezing, striking, and vocalizing: Is number representation fundamentally spatial?
- Medicine, Psychology
The results suggest that number representation is not fundamentally spatial, but builds on a deeper magnitude sense that manifests spatially and nonspatial mediated by magnitude, stimulus modality, and reporting condition. Expand
Histoire du théorème de Jordan de la décomposition matricielle (1870-1930). Formes de représentation et méthodes de décomposition.
L'histoire du theoreme de Jordan est abordee sous l'angle d'une question d'identite posee sur la periode qui separe la date de 1870 et l'enonce par Camille Jordan d'une forme canonique des… Expand