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Emmy Noether´s Wonderful Theorem
Dwight E. Neuenschwander
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Description for Emmy Noether´s Wonderful Theorem
Paperback. 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. Num Pages: 344 pages, 20, 5 black & white illustrations, 15 black & white line drawings. BIC Classification: PBKQ; PBX; PH. Category: (U) Tertiary Education (US: College). Dimension: 229 x 152 x 21. .
In the judgment of the most competent living mathematicians, Fraulein 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 Goettingen 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.
Product Details
Publisher
Johns Hopkins University Press
Format
Paperback
Publication date
2017
Condition
New
Number of Pages
344
Place of Publication
Baltimore, MD, United States
ISBN
9781421422671
SKU
V9781421422671
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-50
About Dwight E. Neuenschwander
Dwight E. Neuenschwander is a professor of physics at Southern Nazarene University. He is a columnist for the Observer, the magazine of the Society for Physics Students, and the author of Tensor Calculus for Physics: A Concise Guide.
Reviews for Emmy Noether´s Wonderful Theorem
As this book is well written and contains a very good set of exercises, it can serve as the primary text for a special topics course.
Choice
Nadis gives no technical details, but Neuenschwander does, in a book for physics majors with a strong background in mathematics; the book does not shy away from Lie groups and the study of invariants. This new edition delves into distinctions between two Noether theorems and adds more exercises, references, and details.
Mathematics Magazine
Neuenschwander sets out from the beginning to help the reader who must be familiar with calculus and a few other standard topics, but who is not yet fluent in these areas... His role is to be the teacher on the side, prompting the reader with interesting observations and questions... He anticipates problems, guides you yet also makes you think things through... Not only a very worthwhile read for its content but also for its style.
Ken Zetie, St. Paul's School
Mathematical Gazette
Well-written... Throughout there is reference to the life of Emmy Noether, including the many difficulties related to being a woman in a man's world... I am glad her story is given an airing here as she fails to be as famous as she undoubtedly should be.
Phil Dyke, FIMA
Mathematics Today
Technical and yet ultimately poetic book on Emmy Neother's wonderful theorems... Neuenschwander's work is recommended for anyone who wants to gain a deeper understanding and appreciation of the physics and mathematics behind Emmy Noether's work, as well as the particular challenges she faced in her life.
Miriam R. Aczel, Centre for Environmental Policy, Imperial College London
Contemporary Physics
Choice
Nadis gives no technical details, but Neuenschwander does, in a book for physics majors with a strong background in mathematics; the book does not shy away from Lie groups and the study of invariants. This new edition delves into distinctions between two Noether theorems and adds more exercises, references, and details.
Mathematics Magazine
Neuenschwander sets out from the beginning to help the reader who must be familiar with calculus and a few other standard topics, but who is not yet fluent in these areas... His role is to be the teacher on the side, prompting the reader with interesting observations and questions... He anticipates problems, guides you yet also makes you think things through... Not only a very worthwhile read for its content but also for its style.
Ken Zetie, St. Paul's School
Mathematical Gazette
Well-written... Throughout there is reference to the life of Emmy Noether, including the many difficulties related to being a woman in a man's world... I am glad her story is given an airing here as she fails to be as famous as she undoubtedly should be.
Phil Dyke, FIMA
Mathematics Today
Technical and yet ultimately poetic book on Emmy Neother's wonderful theorems... Neuenschwander's work is recommended for anyone who wants to gain a deeper understanding and appreciation of the physics and mathematics behind Emmy Noether's work, as well as the particular challenges she faced in her life.
Miriam R. Aczel, Centre for Environmental Policy, Imperial College London
Contemporary Physics