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A Comparative Review Of Recent Researches In Geometry

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A Comparative Review Of Recent Researches In Geometry

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Author : Felix Klein
language : en
Publisher:
Release Date : 1893

A Comparative Review Of Recent Researches In Geometry written by Felix Klein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1893 with Continuous groups categories.

Bulletin Of The New York Mathematical Society

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Author :
language : en
Publisher:
Release Date : 1892

Bulletin Of The New York Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1892 with Mathematics categories.

Geometry From Dynamics Classical And Quantum

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Author : José F. Cariñena
language : en
Publisher: Springer
Release Date : 2014-09-23

Geometry From Dynamics Classical And Quantum written by José F. Cariñena and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-23 with Science categories.

This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.

The Way It Was

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Author : Donald Saari
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

The Way It Was written by Donald Saari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

The formative years of the American Mathematical Society coincided with a time of remarkable development in mathematics. During this period, the Bulletin of the American Mathematical Society and its predecessor, The Bulletin of the New York Mathematical Society, served as a primary vehicle for reporting mathematics to American mathematicians. As a result, some of the most important and fundamental work of early twentieth-century mathematics found its way into the Bulletin. Milestone articles include Hilbert's problems presented at the 1900 Paris International Congress of Mathematicians (ICM), Poincare's 1904 lecture on the future of mathematical physics (with commentary suggesting that he was tantalizingly close to capturing the notion of relativity), and Klein's Erlangen program; all of these articles received added publicity when the first English translation was published in the Bulletin. This book reproduces these and other well-written articles from the early Bulletin, offering readers the best way to experience a slice of that time. Other articles in the book include, in particular, a report to American mathematicians about what happened at that important 1900 ICM meeting and three articles from the scientific portion of the 1904 centennial celebration of the Louisiana Purchase: Darboux describing the development of geometry, Pierpont focusing on nineteenth-century mathematics, and Poincare emphasizing the significance of mathematical physics. Accompanying the transition from the nineteenth to twentieth century was that new important thing called ``mathematical rigor''. Included is an article by Klein reflecting the beliefs of the time with his promotion of rigor. These are just some of the many topics characterizing the early days of the developing American mathematical community. The book offers a captivating review of mathematics through the early years of the Bulletin.

A History Of Mathematics

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Author : Carl B. Boyer
language : en
Publisher: John Wiley & Sons
Release Date : 2011-01-11

A History Of Mathematics written by Carl B. Boyer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-11 with Mathematics categories.

The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

Introduction To Symmetry Analysis

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Author : Brian J. Cantwell
language : en
Publisher: Cambridge University Press
Release Date : 2002-09-26

Introduction To Symmetry Analysis written by Brian J. Cantwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-26 with Mathematics categories.

Henri Poincar

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Author : Jeremy Gray
language : en
Publisher: Princeton University Press
Release Date : 2023-01-03

Henri Poincar written by Jeremy Gray and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-03 with Biography & Autobiography categories.

A comprehensive look at the mathematics, physics, and philosophy of Henri Poincaré Henri Poincaré (1854–1912) was not just one of the most inventive, versatile, and productive mathematicians of all time—he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today. Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world.

Traces the development of mathematics from its beginnings in Babylonia and ancient Egypt to the work of Riemann and Godel in modern times.

A Comparative Review Of Recent Researches In Geometry

A Comparative Review Of Recent Researches In Geometry

Bulletin Of The New York Mathematical Society

Geometry From Dynamics Classical And Quantum

The Way It Was

A History Of Mathematics

Introduction To Symmetry Analysis

Henri Poincar

Revue Semestrielle Des Publications Math Matiques

Revue Semestrielle Des Publications Mathematiques

Mathematical Thought From Ancient To Modern Times

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