Search Results for "emmy-noether-s-wonderful-theorem"

Emmy Noether's Wonderful Theorem

Emmy Noether's Wonderful Theorem

  • Author: Dwight E. Neuenschwander
  • Publisher: JHU Press
  • ISBN: 1421422670
  • Category: Mathematics
  • Page: 344
  • View: 8345
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"In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."—Albert Einstein The year was 1915, and the young mathematician Emmy Noether had just settled into Göttingen University when Albert Einstein visited to lecture on his nearly finished general theory of relativity. Two leading mathematicians of the day, David Hilbert and Felix Klein, dug into the new theory with gusto, but had difficulty reconciling it with what was known about the conservation of energy. Knowing of her expertise in invariance theory, they requested Noether’s help. To solve the problem, she developed a novel theorem, applicable across all of physics, which relates conservation laws to continuous symmetries—one of the most important pieces of mathematical reasoning ever developed. Noether’s "first" and "second" theorem was published in 1918. The first theorem relates symmetries under global spacetime transformations to the conservation of energy and momentum, and symmetry under global gauge transformations to charge conservation. In continuum mechanics and field theories, these conservation laws are expressed as equations of continuity. The second theorem, an extension of the first, allows transformations with local gauge invariance, and the equations of continuity acquire the covariant derivative characteristic of coupled matter-field systems. General relativity, it turns out, exhibits local gauge invariance. Noether’s theorem also laid the foundation for later generations to apply local gauge invariance to theories of elementary particle interactions. In Dwight E. Neuenschwander’s new edition of Emmy Noether’s Wonderful Theorem, readers will encounter an updated explanation of Noether’s "first" theorem. The discussion of local gauge invariance has been expanded into a detailed presentation of the motivation, proof, and applications of the "second" theorem, including Noether’s resolution of concerns about general relativity. Other refinements in the new edition include an enlarged biography of Emmy Noether’s life and work, parallels drawn between the present approach and Noether’s original 1918 paper, and a summary of the logic behind Noether’s theorem.

Shattered Symmetry

Shattered Symmetry

Group Theory From the Eightfold Way to the Periodic Table

  • Author: Pieter Thyssen,Arnout Ceulemans
  • Publisher: Oxford University Press
  • ISBN: 019062017X
  • Category: Science
  • Page: 400
  • View: 1597
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The standard model of subatomic particles and the periodic table of the atoms have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. The purpose of the book is to share the admiration for the power and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic symmetries that govern the motions of the particles. The trail follows the lines of parentage linking groups upstream to the unitary symmetry of the eightfold way of quarks, and to the four-dimensional symmetry of the hydrogen atom. Along the way the theory of symmetry groups is gradually introduced with special emphasis on graphical representations. The final challenge is to open up the structure of Mendeleev's table which goes beyond the symmetry of the hydrogen atom. Breaking this symmetry to accommodate the multi-electron atoms requires to leave the common ground of linear algebras and explore the potential of non-linearity.

The Princeton Companion to Applied Mathematics

The Princeton Companion to Applied Mathematics

  • Author: Nicholas J. Higham
  • Publisher: Princeton University Press
  • ISBN: 1400874475
  • Category: Mathematics
  • Page: 1016
  • View: 1605
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This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Lectures of Sidney Coleman on Quantum Field Theory

Lectures of Sidney Coleman on Quantum Field Theory

Foreword by David Kaiser

  • Author: Bryan Gin-ge Chen,David Derbes,David Griffiths,Brian Hill,Richard Sohn,Yuan-Sen Ting
  • Publisher: World Scientific Publishing
  • ISBN: 9814635529
  • Category: Science
  • Page: 1196
  • View: 3482
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'Sidney Coleman was the master teacher of quantum field theory. All of us who knew him became his students and disciples. Sidney’s legendary course remains fresh and bracing, because he chose his topics with a sure feel for the essential, and treated them with elegant economy.' Frank WilczekNobel Laureate in Physics 2004 Sidney Coleman was a physicist's physicist. He is largely unknown outside of the theoretical physics community, and known only by reputation to the younger generation. He was an unusually effective teacher, famed for his wit, his insight and his encyclopedic knowledge of the field to which he made many important contributions. There are many first-rate quantum field theory books (the venerable Bjorken and Drell, the more modern Itzykson and Zuber, the now-standard Peskin and Schroeder, and the recent Zee), but the immediacy of Prof. Coleman's approach and his ability to present an argument simply without sacrificing rigor makes his book easy to read and ideal for the student. Part of the motivation in producing this book is to pass on the work of this outstanding physicist to later generations, a record of his teaching that he was too busy to leave himself.

Applied Mathematics

Applied Mathematics

  • Author: J. David Logan
  • Publisher: John Wiley & Sons
  • ISBN: 1118501705
  • Category: Mathematics
  • Page: 680
  • View: 4485
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Praise for the Third Edition “Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference.” —MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and natural sciences. The Fourth Edition covers both standard and modern topics, including scaling and dimensional analysis; regular and singular perturbation; calculus of variations; Green’s functions and integral equations; nonlinear wave propagation; and stability and bifurcation. The book provides extended coverage of mathematical biology, including biochemical kinetics, epidemiology, viral dynamics, and parasitic disease. In addition, the new edition features: Expanded coverage on orthogonality, boundary value problems, and distributions, all of which are motivated by solvability and eigenvalue problems in elementary linear algebra Additional MATLAB® applications for computer algebra system calculations Over 300 exercises and 100 illustrations that demonstrate important concepts New examples of dimensional analysis and scaling along with new tables of dimensions and units for easy reference Review material, theory, and examples of ordinary differential equations New material on applications to quantum mechanics, chemical kinetics, and modeling diseases and viruses Written at an accessible level for readers in a wide range of scientific fields, Applied Mathematics, Fourth Edition is an ideal text for introducing modern and advanced techniques of applied mathematics to upper-undergraduate and graduate-level students in mathematics, science, and engineering. The book is also a valuable reference for engineers and scientists in government and industry.

The heritage of Emmy Noether

The heritage of Emmy Noether

  • Author: Mina Teicher
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: 101
  • View: 6404
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Named for the noted mathematician, the Emmy Noether Research Institute for Mathematicsheld a two-day conference dedicated to her heritage and her influence on mathematics and physics in the 20th and 21st centuries. This volume presents the proceedings of that conference. It includes a comprehensive description of her contributions to commutative and noncommutative algebra, algebraic geometry, topology, and physics given by world experts in these fields. Also included is a profile of her life. The volume is a comprehensive collection of Noether's valuable contributions tomathematics and physics.

Emmy Noether

Emmy Noether

  • Author: Hermann Weyl
  • Publisher: N.A
  • ISBN: N.A
  • Category: Algebra, Abstract
  • Page: 20
  • View: 3374
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Math Makers

Math Makers

The Lives and Works of 50 Famous Mathematicians

  • Author: Alfred S. Posamentier,Christian Spreitzer
  • Publisher: Prometheus Books
  • ISBN: 9781633885202
  • Category: Biography & Autobiography
  • Page: 440
  • View: 874
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"Two veteran math educators concisely profile leading mathematicians throughout history highlighting their often unusual personalities and lives while giving average readers insights into the importance of their mathematical discoveries."--

Symmetry and the Beautiful Universe

Symmetry and the Beautiful Universe

  • Author: Leon M. Lederman,Christopher T. Hill
  • Publisher: Pyr Books
  • ISBN: N.A
  • Category: Science
  • Page: 363
  • View: 413
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Explains the concept of symmetry and its ramifications for art, music, and life on Earth, describing how symmetry is found everywhere in the universe.