Emmy Noether's Wonderful Theorem

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Author: Dwight E. Neuenschwander

Publisher: JHU Press

ISBN: 1421422689

Category: Science

Page: 344

View: 3126

"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. -- Cliff Chancey, University of Northern Iowa

Shattered Symmetry

Group Theory From the Eightfold Way to the Periodic Table

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Author: Pieter Thyssen,Arnout Ceulemans

Publisher: Oxford University Press

ISBN: 019062017X

Category: Science

Page: 400

View: 8349

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.

Applied Mathematics

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Author: J. David Logan

Publisher: John Wiley & Sons

ISBN: 1118501705

Category: Mathematics

Page: 680

View: 1446

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.

Emmy Noether

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Author: Hermann Weyl

Publisher: N.A

ISBN: N.A

Category: Algebra, Abstract

Page: 20

View: 8417

The heritage of Emmy Noether

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Author: Mina Teicher

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 101

View: 715

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.

Algebra

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Author: B.L. van der Waerden,Emil Artin,Emmy Noether

Publisher: Springer

ISBN: N.A

Category: Mathematics

Page: 265

View: 4987

This beautiful and eloquent text transformed the graduate teaching of algebra in Europe and the United States. It clearly and succinctly formulated the conceptual and structural insights which Noether had expressed so forcefully and combined it with the elegance and understanding with which Artin had lectured. This text is a reprinted version of the original English translation of the first volume of B.L. van der Waerden’s Algebra.

Newsletter

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Women mathematicians

Page: N.A

View: 9426

Ideals, Varieties, and Algorithms

An Introduction to Computational Algebraic Geometry and Commutative Algebra

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Author: David A. Cox,John B. Little,Donal O'Shea

Publisher: N.A

ISBN: N.A

Category: Algèbre commutative - Informatique

Page: 513

View: 8431

Symmetry and the Beautiful Universe

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Author: Leon M. Lederman,Christopher T. Hill

Publisher: Pyr Books

ISBN: N.A

Category: Science

Page: 363

View: 8962

Explains the concept of symmetry and its ramifications for art, music, and life on Earth, describing how symmetry is found everywhere in the universe.