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Emmy Noether S Wonderful Theorem

Author: Dwight E. Neuenschwander
Publisher: JHU Press
ISBN: 1421422670
Size: 43.74 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.

Tensor Calculus For Physics

Author: Dwight E. Neuenschwander
Publisher: JHU Press
ISBN: 142141564X
Size: 23.24 MB
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Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism, they encounter the "polarization tensor." However, this piecemeal approach can set students up for misconceptions when they have to learn about tensors in more advanced physics and mathematics studies (e.g., while enrolled in a graduate-level general relativity course or when studying non-Euclidean geometries in a higher mathematics class). Dwight E. Neuenschwander's Tensor Calculus for Physics is a bottom-up approach that emphasizes motivations before providing definitions. Using a clear, step-by-step approach, the book strives to embed the logic of tensors in contexts that demonstrate why that logic is worth pursuing. It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.

Shattered Symmetry

Author: Pieter Thyssen
Publisher: Oxford University Press
ISBN: 019062017X
Size: 39.12 MB
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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.

Women In American History A Social Political And Cultural Encyclopedia And Document Collection 4 Volumes

Author: Peg A. Lamphier
Publisher: ABC-CLIO
ISBN: 1610696034
Size: 31.36 MB
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This four-volume set documents the complexity and richness of women's contributions to American history and culture, empowering all students by demonstrating a more populist approach to the past. • Provides significantly more detail than typical reference works on women's history and culture, enabling readers to better appreciate the contributions of women of all socio-cultural statuses • Covers the astounding range of American women's experience, including women of various economic and racial statuses, religious affiliations, political and ideological identifications, and sexualities • Includes a significant selection of primary documents, thereby combining the educational power of secondary and primary literature to create a richer learning experience for users

Author: Απόστολος Κ Δοξιάδης
ISBN: 9789600329919
Size: 72.27 MB
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An Equation For Every Occasion

Author: John M. Henshaw
Publisher: JHU Press
ISBN: 1421414910
Size: 51.67 MB
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In An Equation for Every Occasion, John M. Henshaw tells fifty-two entertaining true stories, each inspired by a different mathematical equation. His succinct, easy-to-read narratives come from the spheres of sports, business, history, the arts, science, and technology. Anecdotes about famous equations, like E=mc2, appear alongside tales of not-so-famous—but equally fascinating—equations, such as the one that's used to determine the SPF number on a bottle of sunscreen. Drawn from the breadth of human endeavor, Henshaw's stories demonstrate the power and utility of math. He entertains us by exploring the ways that equations can be used to explain, among other things, Ponzi schemes, the placebo effect, "dog years," IQ, the wave mechanics of tsunamis, the troubled modern beekeeping industry, and the Challenger disaster. Smartly conceived and fast paced, his book offers something for anyone curious about math and its impacts. Yet readers will find themselves learning more than just math; they'll learn about the workings of the universe. Once immersed in this book you'll find yourself thirsting for the next equation in this original page-turner.