"The book confronts the points of view of two mathematicians: Pierre Cartier who is one of the pillars of the famous Bourbaki group and Cédric Villani, one of the most brilliant of his generation, who received the Fields Medal in 2010. Mathematician and historian of science Jean Dhombres and philosopher of science Gerhard Heinzmann, both specialists in mathematics, engage in a fruitful dialogue with the two mathematicians, likely to lead ..."
"Gerhard Heinzmann: Indeed, there are initial conditions that have to be satisfied,
but which rarely are. Hence there is initially a sham mathematization which gives
the impression that the entire thing is sound. Cédric Villani: It is true for opinion
polls, but even more true in the fields of finance, or climate. Jean Dhombres:
There are some essential things that should become very early part of the
mathematical background of stud ..."
"Les mathématiques sont bien plus qu’une science, tant elles ont acquis un statut central et tout à fait particulier. Elles sont à la fois un langage permettant d’articuler la réalité et un outil qui façonne le réel, et jouent à ce titre un rôle clé dans le développement des sciences de la nature, des sciences humaines et sociales, et de l’industrie. Leur position centrale dans les mécanismes de sélection et de reproduction qui caractéri ..."
"This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of pr ..."
"This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of pr ..."
Functional Integration(Reprint) Action and Symmetries (Cambridge Monographs on Mathematical Physics) by PierreCartier, Cecile Dewitt-Morette Paperback, 480 Pages, Published 2010 by Cambridge University Press ISBN-13: 978-0-521-14357-8, ISBN: 0-521-14357-8
"Functional integration successfully entered physics as path integrals in the 1942 Ph.D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed, generalised and applied. In the authors' hands, functional integration is shown to be ..."
"In his compelling memoir "Récoltes et Semailles: Réflexions et témoignages sur
un passé de mathématicien" [56], Grothendieck discusses at length his life, his
work, his relations with and his views on the mathematical community. One of
Grothendieck's most striking images there is of mathematics as an edifice under
construction, and of himself as a foremanarchitect. He is deeply critical of what
happened on the worksite after he lef ..."
"This volume is the first in a projected series devoted to the mathematical and philosophical works of the late Claude Chevalley. It covers the main contributions by the author to the theory of spinors. Since its appearance in 1954, "The Algebraic Theory of Spinors" has been a much sought after reference. It presents the whole story of one subject in a concise and especially clear manner. The reprint of the book is supplemented by a seri ..."
"A Collection of Articles Written in Honor of the 60th Birthday of Alexander
Grothendieck Pierre Cartier, Luc Illusie, Nicholas M. Katz, Gérard Laumon, Yuri I.
Manin, Kenneth A. Ribet. H = H(q, a) = {x € L | q(x) = a} the corresponding (affine)
hyperplane; the hyperplane H(q, a) is a vector subspace of L if and only if a = 0.
Theorem 3. Let S C L be a G-orbit which is not contained in H, i.e., S\H : = {x e S c
L | q(x) ;é a} is non- ..."
"Functional integration successfully entered physics as path integrals in the 1942 Ph.D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed, generalised and applied. In the authors' hands, functional integration is shown to be ..."
"... of Alexander Grothendieck Pierre Cartier, Luc Illusie, Nicholas M. Katz, Gérard
Laumon, Yuri I. Manin, Kenneth A. Ribet ... et de l'isomorphisme limHoms_sr(Jn,
G) ~ G(X), n pour tout S'-schéma en groupes commutatif et lisse G. L'énoncé de ..."
"Michael Berry [15] gives an illuminating example from the study of scent weakly
diffusing in random winds. Berry works out the probability that the pheromones
emitted by a female moth reach a male moth, given a realistic diffusion constant
D. Diffusion alone cannot account for males picking up scents from hundreds of
meters away. In fact, females emit pheromones only when there is a wind so that
diffusion is aided by convection. Th ..."
"The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite ..."
"This book contains fifteen articles by eminent specialists in the theory of completely integrable systems, bringing together the diverse approaches to classical and quantum integrable systems and covering the principal current research developments. In the first part of the book, which contains seven papers, the emphasis is on the algebro-geometric methods and the tau-functions. Essential use of Riemann surfaces and their theta function ..."