emmy noether s wonderful theorem

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Emmy Noether S Wonderful Theorem

Author : Dwight E. Neuenschwander
ISBN : 9781421422688
Genre : Science
File Size : 84. 77 MB
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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. -- Cliff Chancey, University of Northern Iowa

Emmy Noether

Author : M. B. W. Tent
ISBN : 9781439865347
Genre : Mathematics
File Size : 65. 93 MB
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This book, written primarily for the young adult reader, tells the life story of Emmy Noether, the most important female mathematician of our time. Because no one expected her to grow into an important scientist, the records of her early life are sketchy. After all, it was assumed that she would grow up to be a wife and mother. Instead, she was a genius who chose a distinctive path. The author has woven this charming story of Emmy Noether’s life around the events that appear in the oral and written records, fleshing out the story with details about life in Germany at the time and what we know about how bright children explore mathematics.

Emmy Noether 1882 1935

Author : DICK
ISBN : 9781468405354
Genre : Mathematics
File Size : 79. 61 MB
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N 1964 at the World's Fair in New York I City one room was dedicated solely to mathematics. The display included a very at tractive and informative mural, about 13 feet long, sponsored by one of the largest com puter manufacturing companies and present ing a brief survey of the history of mathemat ics. Entitled, "Men of Modern Mathematics," it gives an outline of the development of that science from approximately 1000 B. C. to the year of the exhibition. The first centuries of this time span are illustrated by pictures from the history of art and, in particular, architec ture; the period since 1500 is illuminated by portraits of mathematicians, including brief descriptions of their lives and professional achievements. Close to eighty portraits are crowded into a space of about fourteen square feet; among them, only one is of a woman. Her face-mature, intelligent, neither pretty nor handsome-may suggest her love of sci- 1 Emmy Noether ence and creative gift, but certainly reveals a likeable personality and a genuine kindness of heart. It is the portrait of Emmy Noether ( 1882 - 1935), surrounded by the likenesses of such famous men as Joseph Liouville (1809-1882), Georg Cantor (1845-1918), and David Hilbert (1862 -1943). It is accom panied by the following text: Emmy Noether, daughter of the mathemati cian Max, was often called "Der Noether," as if she were a man.

A Beautiful Question

Author : Frank Wilczek
ISBN : 9780143109365
Genre : Mathematics
File Size : 46. 14 MB
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A respected physicist presents a survey of related discoveries, from Plato and Pythagoras up to the present, that explore how intertwined ideas about beauty and art are with scientific understandings of the cosmos.

Symmetry And The Beautiful Universe

Author : Leon M. Lederman
ISBN : 9781615920419
Genre : Science
File Size : 24. 19 MB
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When scientists peer through a telescope at the distant stars in outer space or use a particle-accelerator to analyze the smallest components of matter, they discover that the same laws of physics govern the whole universe at all times and all places. Physicists call the eternal, ubiquitous constancy of the laws of physics symmetry. Symmetry is the basic underlying principle that defines the laws of nature and hence controls the universe. This all-important insight is one of the great conceptual breakthroughs in modern physics and is the basis of contemporary efforts to discover a grand unified theory to explain all the laws of physics. Nobel Laureate Leon M. Lederman and physicist Christopher T. Hill explain the supremely elegant concept of symmetry and all its profound ramifications to life on Earth and the universe at large in this eloquent, accessible popular science book. They not only clearly describe concepts normally reserved only for physicists and mathematicians, but they also instill an appreciation for the profound beauty of the universe’s inherent design. Central to the story of symmetry is an obscure, unpretentious, but extremely gifted German mathematician named Emmy Noether. Though still little known to the world, she impressed no less a scientist than Albert Einstein, who praised her "penetrating mathematical thinking." In some of her earliest work she proved that the law of the conservation of energy was connected to the idea of symmetry and thus laid the mathematical groundwork for what may be the most important concept of modern physics. Lederman and Hill reveal concepts about the universe, based on Noether’s work, that are largely unknown to the public and have wide-reaching implications in connection with the Big Bang, Einstein’s theory of relativity, quantum mechanics, and many other areas of physics. Through ingenious analogies and illustrations, they bring these astounding notions to life. This book will open your eyes to a universe you never knew existed. From the Trade Paperback edition.

Euler S Gem

Author : David S. Richeson
ISBN : 1400838568
Genre : Mathematics
File Size : 28. 72 MB
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Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

A History Of Algebra

Author : Bartel L. van der Waerden
ISBN : 9783642515996
Genre : Mathematics
File Size : 63. 53 MB
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Lagrangian Interaction

Author : Noel Doughty
ISBN : 9780429973161
Genre : Science
File Size : 64. 30 MB
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This book is an introduction to Lagrangian mechanics, starting with Newtonian physics and proceeding to topics such as relativistic Lagrangian fields and Lagrangians in General Relativity, electrodynamics, Gauge theory, and relativistic gravitation. The mathematical notation used is introduced and explained as the book progresses, so it can be understood by students at the undergraduate level in physics or applied mathmatics, yet it is rigorous enough to serve as an introduction to the mathematics and concepts required for courses in relativistic quantum field theory and general relativity.

Emmy Noether

Author : Emmy Noether
ISBN : 0824715500
Genre : Biography & Autobiography
File Size : 23. 53 MB
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Quantum Mechanics

Author : Nouredine Zettili
ISBN : 9780470746561
Genre : Science
File Size : 80. 35 MB
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Quantum Mechanics: Concepts and Applications provides a clear, balanced and modern introduction to the subject. Written with the student’s background and ability in mind the book takes an innovative approach to quantum mechanics by combining the essential elements of the theory with the practical applications: it is therefore both a textbook and a problem solving book in one self-contained volume. Carefully structured, the book starts with the experimental basis of quantum mechanics and then discusses its mathematical tools. Subsequent chapters cover the formal foundations of the subject, the exact solutions of the Schrödinger equation for one and three dimensional potentials, time-independent and time-dependent approximation methods, and finally, the theory of scattering. The text is richly illustrated throughout with many worked examples and numerous problems with step-by-step solutions designed to help the reader master the machinery of quantum mechanics. The new edition has been completely updated and a solutions manual is available on request. Suitable for senior undergradutate courses and graduate courses.

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