Download or read book Hermann Weyl 1885 1985 written by C.N. Yang and published by Springer Science & Business Media. This book was released on 1986-11 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published for the Eidgenössische Technische Hochschule Zürich

Download or read book Essays in the History of Lie Groups and Algebraic Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2001 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passagefrom local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former,Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groupsand algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields.The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.

Download or read book Mathematical Implications of Einstein Weyl Causality written by Hans Jürgen Borchers and published by Springer. This book was released on 2007-02-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a systematic approach to such fundamental questions as: What mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The author proposes an axiomatization of the physics inspired notion of Einstein-Weyl causality and investigating the consequences in terms of possible topological spaces. One significant result is that the notion of causality can effectively be extended to discontinuum.

Download or read book Collected Papers written by Armand Borel and published by Springer Science & Business Media. This book was released on 1983 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the papers published by A. Borel from 1983 to 1999. About half of them are research papers, written on his own or in collaboration, on various topics pertaining mainly to algebraic or Lie groups, homogeneous spaces, arithmetic groups (L2-spectrum, automorphic forms, cohomology and covolumes), L2-cohomology of symmetric or locally symmetric spaces, and to the Oppenheim conjecture. Other publications include surveys and personal recollections (of D. Montgomery, Harish-Chandra, and A. Weil), considerations on mathematics in general and several articles of a historical nature: on the School of Mathematics at the Institute for Advanced Study, on N. Bourbaki and on selected aspects of the works of H. Weyl, C. Chevalley, E. Kolchin, J. Leray, and A. Weil. The book concludes with an essay on H. Poincaré and special relativity. Some comments on, and corrections to, a number of papers have also been added.

Download or read book Compact Lie Groups written by Mark R. Sepanski and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Coverage includes the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The book develops the necessary Lie algebra theory with a streamlined approach focusing on linear Lie groups.

Download or read book The Symbolic Universe written by Jeremy Gray and published by Oxford University Press, USA. This book was released on 1999 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics was transformed between 1890 and 1930, and this volume provides a detailed history of the era and emphasizes the key role of geometrical ideas. Topics include the application of n-dimensional differential geometry to mechanics and theoretical physics, the philosophical questions on the reality of geometry, and the nature of geometry and its connections with psychology, special relativity, Hilbert's efforts to axiomatize relativity, and Emmy Noether's work in physics.

Download or read book 100 Years Of Gravity And Accelerated Frames The Deepest Insights Of Einstein And Yang mills written by Jong-ping Hsu and published by World Scientific. This book was released on 2005-08-26 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers presents ideas and problems arising over the past 100 years regarding classical and quantum gravity, gauge theories of gravity, and spacetime transformations of accelerated frames. Both Einstein's theory of gravity and the Yang-Mills theory are gauge invariant. The invariance principles in physics have transcended both kinetic and dynamic properties and are at the very heart of our understanding of the physical world. In this spirit, this book attempts to survey the development of various formulations for gravitational and Yang-Mills fields and spacetime transformations of accelerated frames, and to reveal their associated problems and limitations.The aim is to present some of the leading ideas and problems discussed by physicists and mathematicians. We highlight three aspects: formulations of gravity as a Yang-Mills field, first discussed by Utiyama; problems of gravitational theory, discussed by Feynman, Dyson and others; spacetime properties and the physics of fields and particles in accelerated frames of reference.These unfulfilled aspects of Einstein and Yang-Mills' profound thoughts present a great challenge to physicists and mathematicians in the 21st century.

Download or read book Weyl and the Problem of Space written by Julien Bernard and published by Springer Nature. This book was released on 2019-10-09 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Adventure of Reason written by Paolo Mancosu and published by OUP Oxford. This book was released on 2014-01-09 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.

Download or read book The Reign of Relativity written by Thomas Ryckman and published by Oxford University Press. This book was released on 2005 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein's theory of 'general relativity' (1915) was a defining event for 20th century philosophy of science. During the decisive first ten years of the theory's existence, two main ideas dominated its philosophical reception. Ryckman's book is an extended argument concerning these ideas.

Download or read book Emergence of the Theory of Lie Groups written by Thomas Hawkins and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.

Download or read book History of Topology written by I.M. James and published by Elsevier. This book was released on 1999-08-24 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

Download or read book Origins of Logical Empiricism written by Ronald N. Giere and published by U of Minnesota Press. This book was released on 1996 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logical empiricism remains a strong influence in the philosophy of science, despite the discipline's shift toward more historical and naturalistic approaches. This latest volume in the eminent Minnesota Studies in the Philosophy of Science series examines the main features of the intellectual milieu from which logical empiricism sprang, providing the first critical exploration of this context by authors within the Anglo-American analytic tradition of philosophy. These articles challenge the idea that logical empiricism has its origins in traditional British empiricism, pointing instead to a movement of scientific philosophy that flourished in the German-speaking areas of Europe in the first four decades of the twentieth century. The intellectual refugees from the Third Reich who brought logical empiricism to North America did so in an environment influenced by Einstein's new physics, the ascension of modern logic, the birth of the social sciences as rivals to traditional humanistic philosophy, and other large-scale social, political, and cultural themes.

Download or read book And Yet It Is Heard written by Tito M. Tonietti and published by Springer. This book was released on 2014-05-16 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: We bring into full light some excerpts on musical subjects which were until now scattered throughout the most famous scientific texts. The main scientific and musical cultures outside of Europe are also taken into consideration. The first and most important property to underline in the scientific texts examined here is the language they are written in. This means that our multicultural history of the sciences necessarily also becomes a review of the various dominant languages used in the different historical contexts. In this volume, the history of the development of the sciences is told as it happened in real contexts, not in an alienated ideal world.

Download or read book The Princeton Companion to Mathematics written by Timothy Gowers and published by Princeton University Press. This book was released on 2010-07-18 with total page 1057 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ultimate mathematics reference book This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries—written especially for this book by some of the world's leading mathematicians—that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music—and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors include: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, and Doron Zeilberger

Download or read book Topological Foundations Of Electromagnetism Second Edition written by Terence William Barrett and published by World Scientific. This book was released on 2022-05-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aims of the book are: (1) to extend Maxwell theory to non-Abelian group forms; (2) to demonstrate that the foundations of electromagnetism are topological; (3) to show the multi-disciplinary nature of communications; (4) to demonstrate the effectiveness of modulated signals in penetrating media; (5) to demonstrate that geometric (Clifford) algebra is the appropriate algebra describing modulated signals.The book is important in indicating that the classical theory of electromagnetism, or Maxwell theory, can be developed to address situations and signals of differing symmetry form, and that different topological spaces require that development.

Download or read book The Best Writing on Mathematics 2010 written by Mircea Pitici and published by Princeton University Press. This book was released on 2021-09-14 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year’s most memorable writing on mathematics This anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City's traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more. In addition to presenting the year's most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it's headed.