Exploratory Galois Theory
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Exploratory Galois Theory
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Author : John Swallow
language : en
Publisher: Cambridge University Press
Release Date : 2004-10-11
Exploratory Galois Theory written by John Swallow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-11 with Computers categories.
Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. The text is appropriate for traditional lecture courses, for seminars, or for self-paced independent study by undergraduates and graduate students.
A Classical Introduction To Galois Theory
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Author : Stephen C. Newman
language : en
Publisher: John Wiley & Sons
Release Date : 2012-05-29
A Classical Introduction To Galois Theory written by Stephen C. Newman and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-29 with Mathematics categories.
Explore the foundations and modern applications of Galois theory Galois theory is widely regarded as one of the most elegant areas of mathematics. A Classical Introduction to Galois Theory develops the topic from a historical perspective, with an emphasis on the solvability of polynomials by radicals. The book provides a gradual transition from the computational methods typical of early literature on the subject to the more abstract approach that characterizes most contemporary expositions. The author provides an easily-accessible presentation of fundamental notions such as roots of unity, minimal polynomials, primitive elements, radical extensions, fixed fields, groups of automorphisms, and solvable series. As a result, their role in modern treatments of Galois theory is clearly illuminated for readers. Classical theorems by Abel, Galois, Gauss, Kronecker, Lagrange, and Ruffini are presented, and the power of Galois theory as both a theoretical and computational tool is illustrated through: A study of the solvability of polynomials of prime degree Development of the theory of periods of roots of unity Derivation of the classical formulas for solving general quadratic, cubic, and quartic polynomials by radicals Throughout the book, key theorems are proved in two ways, once using a classical approach and then again utilizing modern methods. Numerous worked examples showcase the discussed techniques, and background material on groups and fields is provided, supplying readers with a self-contained discussion of the topic. A Classical Introduction to Galois Theory is an excellent resource for courses on abstract algebra at the upper-undergraduate level. The book is also appealing to anyone interested in understanding the origins of Galois theory, why it was created, and how it has evolved into the discipline it is today.
Actions Of Groups
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Author : John McCleary
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-05
Actions Of Groups written by John McCleary and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-05 with Mathematics categories.
An undergraduate text with an active learning approach introducing representation theory and Galois theory topics using group actions.
Pt I And Ii
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Author : Oak Ridge National Laboratory
language : en
Publisher:
Release Date : 1974
Pt I And Ii written by Oak Ridge National Laboratory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Electric power distribution categories.
A Transition To Advanced Mathematics
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Author : William Johnston
language : en
Publisher: OUP USA
Release Date : 2009-07-27
A Transition To Advanced Mathematics written by William Johnston and has been published by OUP USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-27 with Mathematics categories.
Preface 1. Mathematical Logic 2. Abstract Algebra 3. Number Theory 4. Real Analysis 5. Probability and Statistics 6. Graph Theory 7. Complex Analysis Answers to Questions Answers to Odd Numbered Questions Index of Online Resources Bibliography Index.
Quantum Field Theory In A Semiotic Perspective
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Author : Hans Günter Dosch
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Quantum Field Theory In A Semiotic Perspective written by Hans Günter Dosch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Science categories.
Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincaré, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism.
The Foundations Of Ethology
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Author : K. Lorenz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Foundations Of Ethology written by K. Lorenz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Psychology categories.
This book is a contribution to the history of ethology-not a definitive history, but the personal view of a major figure in that story. It is all the more welcome because such a grand theme as ethology calls for a range of perspectives. One reason is the overarching scope of the subject. Two great questions about life that constitute much of biology are "How does it work (structure and function)?" and "How did it get that way (evolu tion and ontogeny)?" Ethology addresses the antecedent of "it. " Of what are we trying to explain the mechanism and development? Surely behav ior, in all its wealth of detail, variation, causation, and control, is the main achievement of animal evolution, the essential consequence of animal structure and function, the raison d' etre of all the rest. Ethology thus spans between and overlaps with the ever-widening circles of ecol ogy over the eons and the ever-narrowing focus of physiology of the neurons. Another reason why the history of ethology needs perspectives is the recency of its acceptance. For such an obviously major aspect of animal biology, it is curious how short a time-less than three decades-has seen the excitement of an active field and a substantial fraternity of work ers, the addition of professors and courses to departments and curricula in biology (still far from universal}, and the normal complement of spe cial journals, symposia, and sessions at congresses.
Digestible Quantum Field Theory
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Author : Andrei Smilga
language : en
Publisher: Springer
Release Date : 2017-12-30
Digestible Quantum Field Theory written by Andrei Smilga and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-30 with Science categories.
This book gives an intermediate level treatment of quantum field theory, appropriate to a reader with a first degree in physics and a working knowledge of special relativity and quantum mechanics. It aims to give the reader some understanding of what QFT is all about, without delving deep into actual calculations of Feynman diagrams or similar. The author serves up a seven‐course menu, which begins with a brief introductory Aperitif. This is followed by the Hors d'oeuvres, which set the scene with a broad survey of the Universe, its theoretical description, and how the ideas of QFT developed during the last century. In the next course, the Art of Cooking, the author recaps on some basic facts of analytical mechanics, relativity, quantum mechanics and also presents some nutritious “extras” in mathematics (group theory at the elementary level) and in physics (theory of scattering). After these preparations, the reader should have a good appetite for the Entrées ‐ the central par t of the book where the Standard Model is described and explained. After Trou Normand, the restive pause including human stories about physicists and no formulas, the author serves the Dessert, devoted to supersymmetry (a very beautiful theory that is still awaiting a direct experimental confirmation), to general relativity and to the mystery of quantum gravity.
Children S Exploration And Cultural Formation
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Author : Mariane Hedegaard
language : en
Publisher: Springer Nature
Release Date : 2020-02-28
Children S Exploration And Cultural Formation written by Mariane Hedegaard and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-28 with Education categories.
This open access book examines the educational conditions that support cultures of exploration in kindergartens. It conceptualises cultures of exploration, whether those cultures are created through children’s own engagement or are demanded of them through undertaking specific tasks within different institutional settings. It shows how the conditions for children’s exploration form a web of activities in different settings with social relationships, local landscapes and artefacts. The book builds on the understanding of cultural traditions as deeply implicated in the developmental processes, meaning that local considerations must be reflected in education for sustainable futures. Therefore the book examines and conceptualises exploration and cultural formation through locally situated cases and navigates toward global educational concepts. The book provides different windows into how children may explore in everyday practice settings in kindergarten, and contributes to a loci-based, ecological, integral knowledge relevant for early childhood education.
Inventory Of Current Energy Research And Development
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Author : Oak Ridge National Laboratory
language : en
Publisher:
Release Date : 1972
Inventory Of Current Energy Research And Development written by Oak Ridge National Laboratory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Electric power distribution categories.