Elie Cartan 1869 1951
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| Author | : M. A. Akivis |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 334 |
| Release | : 2011-07-14 |
| Genre | : Mathematics |
| ISBN | : 0821853554 |
This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.
| Author | : Élie Cartan |
| Publisher | : Courier Corporation |
| Total Pages | : 193 |
| Release | : 2012-04-30 |
| Genre | : Mathematics |
| ISBN | : 0486137325 |
Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.
| Author | : Ioan James |
| Publisher | : Mathematical Association of America |
| Total Pages | : 286 |
| Release | : 2003-02-06 |
| Genre | : Mathematics |
| ISBN | : 9780521817776 |
Ioan James introduces and profiles sixty mathematicians from the era when mathematics was freed from its classical origins to develop into its modern form. The subjects, all born between 1700 and 1910, come from a wide range of countries, and all made important contributions to mathematics, through their ideas, their teaching, and their influence. James emphasizes their varied life stories, not the details of their mathematical achievements. The book is organized chronologically into ten chapters, each of which contains biographical sketches of six mathematicians. The men and women James has chosen to portray are representative of the history of mathematics, such that their stories, when read in sequence, convey in human terms something of the way in which mathematics developed. Ioan James is a professor at the Mathematical Institute, University of Oxford. He is the author of Topological Topics (Cambridge, 1983), Fibrewise Topology (Cambridge, 1989), Introduction to Uniform Spaces (Cambridge, 1990), Topological and Uniform Spaces (Springer-Verlag New York, 1999), and co-author with Michael C. Crabb of Fibrewise Homotopy Theory (Springer-Verlag New York, 1998). James is the former editor of the London Mathematical Society Lecture Note Series and volume editor of numerous books. He is the organizer of the Oxford Series of Topology symposia and other conferences, and co-chairman of the Task Force for Mathematical Sciences of Campaign for Oxford.
| Author | : Patrick Popescu-Pampu |
| Publisher | : Springer |
| Total Pages | : 181 |
| Release | : 2016-08-26 |
| Genre | : Mathematics |
| ISBN | : 3319423126 |
Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena.
| Author | : David Broward |
| Publisher | : David Broward |
| Total Pages | : 351 |
| Release | : 2017-12-05 |
| Genre | : Education |
| ISBN | : 171701674X |
In all the ancient spiritual texts water is depicted as the Source of all Creation from which everything else came into existence. All over the world, in our forefathers' traditions and rituals water is associated with the Primordial substance that has the power to heal, give us strength, and take away the sins. At the same time, modern scientific discoveries proved that our ancestors' beliefs, traditions, and rituals are a legacy and not some simple bet-time stories. Learn how your Emotions, Thoughts, and Intentions are influencing your Life, carried by the life-giving substance we call Water. “This book covers a world of topics about water, from different religious texts, the chemistry and physics of H2O, studies over the past century on observations of fresh water, homeopathy, crystal structure, and different vibrations and forms of water, and back to religion. I learned so much.” (Amazon customer review) “A thorough, well-researched discussion of the significance of water--not only as a fundamental element of our biology and the structure of our planet and the universe--but also its metaphysical, philosophical, and theological importance historically and cross-culturally.” (Amazon customer review)
| Author | : Yong Gan |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 170 |
| Release | : 2012-03-28 |
| Genre | : Technology & Engineering |
| ISBN | : 9535104470 |
Continuum Mechanics is the foundation for Applied Mechanics. There are numerous books on Continuum Mechanics with the main focus on the macroscale mechanical behavior of materials. Unlike classical Continuum Mechanics books, this book summarizes the advances of Continuum Mechanics in several defined areas. Emphasis is placed on the application aspect. The applications described in the book cover energy materials and systems (fuel cell materials and electrodes), materials removal, and mechanical response/deformation of structural components including plates, pipelines etc. Researchers from different fields should be benefited from reading the mechanics approached to real engineering problems.
| Author | : John Petrovic |
| Publisher | : CRC Press |
| Total Pages | : 623 |
| Release | : 2020-08-05 |
| Genre | : Mathematics |
| ISBN | : 1351339494 |
Advanced Calculus: Theory and Practice, Second Edition offers a text for a one- or two-semester course on advanced calculus or analysis. The text improves students’ problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics. The book explains how various topics in calculus may seem unrelated but have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems. Features of the Second Edition: Improved Organization. Chapters are reorganized to address common preferences. Enhanced Coverage of Axiomatic Systems. A section is added to include Peano’s system of axioms for the set of natural numbers and their use in developing the well-known properties of the set N. Expanded and Organized Exercise Collection. There are close to 1,000 new exercises, many of them with solutions or hints. Exercises are classified based on the level of difficulty. Computation-oriented exercises are paired and solutions or hints provided for the odd-numbered questions. Enrichment Material. Historical facts and biographies of over 60 mathematicians. Illustrations. Thirty-five new illustrations are added in order to guide students through examples or proofs. About the Author: John Srdjan Petrovic is a professor at Western Michigan University.
| Author | : Pierre-André Chiappori |
| Publisher | : Now Publishers Inc |
| Total Pages | : 165 |
| Release | : 2009 |
| Genre | : Efficient market theory |
| ISBN | : 1601982887 |
The Economics and Mathematics of Aggregation provides a general characterization of group behavior in a market environment. A crucial feature of the authors' approach is that they do not restrict the form of individual preferences or the nature of individual consumptions. The authors allow for public as well as private consumption, for intragroup production, and for any type of consumption externalities across group members. The main questions addressed are: what restrictions (if any) on the aggregate demand function characterize the efficient behavior of the group and when is it possible to recover the underlying structure - namely, individual preferences, the decision process and the resulting intragroup transfers - from the group's aggregate behavior? The Economics and Mathematics of Aggregation takes an alternative, axiomatic perspective -- the 'collective' approach -- and assumes that the group always reaches Pareto efficient decisions. The authors view efficiency as a natural assumption in many contexts and as a natural benchmark in all cases. Finally, even in the presence of asymmetric information, first best efficiency is a natural benchmark. However, it is important to note that no restriction is placed on the form of the decision process beyond efficiency.
| Author | : Christophe Letellier |
| Publisher | : World Scientific |
| Total Pages | : 393 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 9814374423 |
Chaos theory deals with the description of motion (in a general sense) which cannot be predicted in the long term although produced by deterministic system, as well exemplified by meteorological phenomena. It directly comes from the Lunar theory — a three-body problem — and the difficulty encountered by astronomers to accurately predict the long-term evolution of the Moon using “Newtonian” mechanics. Henri Poincaré's deep intuitions were at the origin of chaos theory. They also led the meteorologist Edward Lorenz to draw the first chaotic attractor ever published. But the main idea consists of plotting a curve representative of the system evolution rather than finding an analytical solution as commonly done in classical mechanics. Such a novel approach allows the description of population interactions and the solar activity as well. Using the original sources, the book draws on the history of the concepts underlying chaos theory from the 17th century to the last decade, and by various examples, show how general is this theory in a wide range of applications: meteorology, chemistry, populations, astrophysics, biomedicine, etc.
| Author | : Julien Bernard |
| Publisher | : Springer Nature |
| Total Pages | : 433 |
| Release | : 2019-10-09 |
| Genre | : Science |
| ISBN | : 3030115275 |
This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrödinger, Eddington). This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.
