REPRESENTATIONS AS MEANS AND ENDS: REPRESENTABILITY AND HABITUATION IN MATHEMATICAL ANALYSIS DURING THE FIRST PART OF THE NINETEENTH CENTURY

2008 ◽  
Author(s):  
HENRIK KRAGH SØRENSEN
Keyword(s):  
Nineteenth Century ◽  
Mathematical Analysis ◽  
Means And Ends

Questions of generality as probes into nineteenth-century mathematical analysis

2017 ◽  
Author(s):  
Renaud Chorlay
Keyword(s):  
Nineteenth Century ◽  
Set Theory ◽  
Mathematical Analysis ◽  
Analytic Functions ◽  
Function Theory ◽  
The Third ◽  
Point Set

This article examines ways of expressing generality and epistemic configurations in which generality issues became intertwined with epistemological topics, such as rigor, or mathematical topics, such as point-set theory. In this regard, three very specific configurations are discussed: the first evolving from Niels Henrik Abel to Karl Weierstrass, the second in Joseph-Louis Lagrange’s treatises on analytic functions, and the third in Emile Borel. Using questions of generality, the article first compares two major treatises on function theory, one by Lagrange and one by Augustin Louis Cauchy. It then explores how some mathematicians adopted the sophisticated point-set theoretic tools provided for by the advocates of rigor to show that, in some way, Lagrange and Cauchy had been right all along. It also introduces the concept of embedded generality for capturing an approach to generality issues that is specific to mathematics.

Poisson's Memoirs on Electricity: Academic Politics and a New Style in Physics

1983 ◽  
Vol 16 (3) ◽  
pp. 239-259 ◽  
Author(s):  
R. W. Home
Keyword(s):  
Nineteenth Century ◽  
Mathematical Analysis ◽  
Mathematical Physics ◽  
Mathematical Creativity ◽  
Academic Politics ◽  
Major Figure

Siméon Denis Poisson (1781–1840) was a major figure in French science throughout the first forty years of the nineteenth century. Though his papers lack the brilliant mathematical creativity of some of those published by even more gifted contemporaries such as Joseph Fourier (1768–1830) and Augustin-Louis Cauchy (1789–1857), they nevertheless display a formidable talent for mathematical analysis, applied with great industry and success in a large number of investigations ranging over the whole domain of mathematical physics. Several were of such importance that even on their own they would have sufficed to win him lasting fame.

scholarly journals Mathematical Understanding and the role of Counterexamples and Pathologies: a case study in Mathematical Analysis.

2018 ◽  
Vol 18 (36) ◽  
pp. 7-17
Author(s):  
Carmen Martínez-Adame
Keyword(s):  
Nineteenth Century ◽  
Partial Response ◽  
Mathematical Analysis ◽  
Mathematical Object ◽  
Mathematical Understanding ◽  
The Subject ◽  
Nineteenth And Twentieth Centuries ◽  
Definition Of

Pathological objects and counterexamples play an important role in mathematical understanding even though there is no precise definition of them.What is a pathological object? What makes a mathematical object pathological?The aim of this paper is to try to give a partial response to these questions from the standpoint of mathematical analysis in the nineteenth and twentieth centuries. We will describe briefly how the notion of function changed dramatically in the nineteenth century and we will study how this change brought on important philosophical consequences for the subject implying that the notion of pathology relies upon certain properties occurring only in a few instances.

John Edensor Littlewood, 9 June 1885 - 6 September 1977

1978 ◽  
Vol 24 ◽  
pp. 323-367 ◽  
Keyword(s):  
Nineteenth Century ◽  
Complex Variable ◽  
Mathematical Analysis ◽  
Natural Philosophy ◽  
Young Men ◽  
English School ◽  
Pure Mathematics ◽  
The World ◽  
The Subject ◽  
The Prestige

In 1900 pure mathematics in this country was at a low ebb. Since the days of Newton mathematics had come to be regarded as ancillary to natural philosophy. In the nineteenth century this attitude had been confirmed by the prestige of Stokes, Clerk Maxwell, Kelvin and others. On the continent the nineteenth century was as fruitful in pure mathematics as England was barren. The central property of functions of a complex variable was found by Cauchy, and further light was shed on the theory by Riemann and Weierstrass. France, Germany and Italy had many pure mathematicians of the first rank. The leading British scholars, notably Cayley, had been solitary figures and had not led young men into research. After 1900, the principal architect of an English school of mathematical analysis was G. H. Hardy (1877-1947). In strengthening the foundations and building on them he found a partner in the subject of this memoir, J. E. Littlewood (1885-1977). The inspiration of their personalities, their research and their teaching established by 1930 a school of analysis second to none in the world.

Density waves in disk galaxies

1967 ◽  
Vol 31 ◽  
pp. 313-317 ◽  
Author(s):  
C. C. Lin ◽  
F. H. Shu
Keyword(s):  
Mathematical Analysis ◽  
Spiral Structure ◽  
Stellar System ◽  
Collective Modes ◽  
Disk Galaxies ◽  
Spiral Pattern ◽  
Density Waves ◽  
The Galaxy ◽  
Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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