Doing Mathematics Convention Subject Calculation Analogy 2nd Edition

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Doing Mathematics Convention Subject Calculation Analogy 2nd Edition

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Author : Martin H Krieger
language : en
Publisher: World Scientific
Release Date : 2015-01-15

Doing Mathematics Convention Subject Calculation Analogy 2nd Edition written by Martin H Krieger and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-15 with Mathematics categories.

Doing Mathematics discusses some ways mathematicians and mathematical physicists do their work and the subject matters they uncover and fashion. The conventions they adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies they discover and employ, all depend on the mathematics — what will work out and what won't. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connections between algebra and topology, and the series of rigorous proofs of the stability of matter. The many and varied solutions to the two-dimensional Ising model of ferromagnetism make sense as a whole when they are seen in an analogy developed by Richard Dedekind in the 1880s to algebraicize Riemann's function theory; by Robert Langlands' program in number theory and representation theory; and, by the analogy between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics. In effect, we begin to see 'an identity in a manifold presentation of profiles,' as the phenomenologists would say.This second edition deepens the particular examples; it describe the practical role of mathematical rigor; it suggests what might be a mathematician's philosophy of mathematics; and, it shows how an 'ugly' first proof or derivation embodies essential features, only to be appreciated after many subsequent proofs. Natural scientists and mathematicians trade physical models and abstract objects, remaking them to suit their needs, discovering new roles for them as in the recent case of the Painlevé transcendents, the Tracy-Widom distribution, and Toeplitz determinants. And mathematics has provided the models and analogies, the ordinary language, for describing the everyday world, the structure of cities, or God's infinitude.

Doing Mathematics

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Author : Martin H. Krieger
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2015-01-21

Doing Mathematics written by Martin H. Krieger and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-21 with Mathematics categories.

Doing Mathematics discusses some ways mathematicians do their work and the subject matter that is being worked upon and created. It argues that the conventions we adopt, the subject areas we delimit, what we can prove and calculate about the physical world, and the analogies that work for mathematicians, all depend on mathematics what will work out and what won't. And how mathematics, as it is done, is shaped and supported, or not, by convention, subject matter, calculation, and analogy. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connection between algebra and topology, rigorous proofs of the stability of matter, solutions to the two-dimensional Ising model of ferromagnetism, and their connection to the Langlands program in number theory and representation theory and a relationship of number theory, function theory, and analysis begun by Dedekind. This second edition deepens each chapter: mathematical rigor and the philosophy of mathematics; finance and big data in statistics; the need for perseverance and the inevitable inelegance in a first proof; the recurrent appearance of the Bethe Ansatz and Hopf algebras in these lattice models; solutions of the Kondo model as epitomizing these themes; analogies between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics; Edward Frenkel's use of the Weil threefold-analogy in the geometric Langlands program; the warehouse of mathematical objects and how it is enlarged; and how recent developments in set theory are analogous with developments in systematic theology as attempts to be articulate about what others take as vague or beyond analysis.

Primes And Particles

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Author : Martin H. Krieger
language : en
Publisher: Springer Nature
Release Date : 2024-02-22

Primes And Particles written by Martin H. Krieger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-22 with Mathematics categories.

Many philosophers, physicists, and mathematicians have wondered about the remarkable relationship between mathematics with its abstract, pure, independent structures on one side, and the wilderness of natural phenomena on the other. Famously, Wigner found the "effectiveness" of mathematics in defining and supporting physical theories to be unreasonable, for how incredibly well it worked. Why, in fact, should these mathematical structures be so well-fitting, and even heuristic in the scientific exploration and discovery of nature? This book argues that the effectiveness of mathematics in physics is reasonable. The author builds on useful analogies of prime numbers and elementary particles, elementary structure kinship and the structure of systems of particles, spectra and symmetries, and for example, mathematical limits and physical situations. The two-dimensional Ising model of a permanent magnet and the proofs of the stability of everyday matter exemplify such effectiveness, and the power of rigorous mathematical physics. Newton is our original model, with Galileo earlier suggesting that mathematics is the language of Nature.

Doing Physics Second Edition

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Author : Martin H. Krieger
language : en
Publisher: Indiana University Press
Release Date : 2012-11-19

Doing Physics Second Edition written by Martin H. Krieger and has been published by Indiana University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-19 with Biography & Autobiography categories.

Doing Physics makes concepts of physics easier to grasp by relating them to everyday knowledge. Addressing some of the models and metaphors that physicists use to explain the physical world, Martin H. Krieger describes the conceptual world of physics by means of analogies to economics, anthropology, theater, carpentry, mechanisms such as clockworks, and machine tool design. The interaction of elementary particles or chemical species, for example, can be related to the theory of kinship—who can marry whom is like what can interact with what. Likewise, the description of physical situations in terms of interdependent particles and fields is analogous to the design of a factory with its division of labor among specialists. For the new edition, Krieger has revised the text and added a chapter on the role of mathematics and formal models in physics. Doing Physics will be of special interest to economists, political theorists, anthropologists, and sociologists as well as philosophers of science.

Proceedings Of The Second International Scientific Conference Intelligent Information Technologies For Industry Iiti 17

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Author : Ajith Abraham
language : en
Publisher: Springer
Release Date : 2017-09-30

Proceedings Of The Second International Scientific Conference Intelligent Information Technologies For Industry Iiti 17 written by Ajith Abraham and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-30 with Technology & Engineering categories.

This volume of Advances in Intelligent Systems and Computing highlights key scientific achievements and innovations in all areas of automation, informatization, computer science, and artificial intelligence. It gathers papers presented at the IITI 2017, the Second International Conference on Intelligent Information Technologies for Industry, which was held in Varna, Bulgaria on September 14–16, 2017. The conference was jointly co-organized by Technical University of Varna (Bulgaria), Technical University of Sofia (Bulgaria), VSB Technical University of Ostrava (Czech Republic) and Rostov State Transport University (Russia). The IITI 2017 brought together international researchers and industrial practitioners interested in the development and implementation of modern technologies for automation, informatization, computer science, artificial intelligence, transport and power electrical engineering. In addition to advancing both fundamental research and innovative applications, the conference is intended to establish a new dissemination platform and an international network of researchers in these fields.

Shelter Island Ii

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Author : Roman Jackiw
language : en
Publisher: Courier Dover Publications
Release Date : 2016-02-17

Shelter Island Ii written by Roman Jackiw and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-17 with Science categories.

In 1947 J. Robert Oppenheimer organized a historic conference of physicists at Shelter Island, located off the eastern tip of Long Island, to discuss recent advances in theoretical physics and the direction of future research. Over three decades later, the physics community held another meeting, the 1983 Shelter Island Conference on Quantum Field Theory and the Fundamental Problems of Physics. This volume is the record of the 1983 conference; it also includes much valuable information on the 1947 conference, for which no formal proceedings were ever published. The latter-day conference included many of the participants from the prior event as well as younger physicists who have since become prominent figures in this field. Consequently, this volume is a vital document in the history of physics, of value to students and researchers in many branches of the subject. Topics include the new inflationary universe scenario; supersymmetry; Stephen Hawking's presentation, "The Cosmological Constant Is Probably Zero"; superunification and the seven-sphere; time as a dynamical variab≤ induced gravity; and an extensive and previously unpublished paper by Edward Witten on Kaluza-Klein theories. Contributors include Stephen L. Adler, Hans Bethe, M. J. Duff, Murray Gell-Mann, Alan H. Guth, Stephen W. Hawking, Roman Jackiw, Toichiro Kinoshita, W. E. Lamb, Jr., T. D. Lee, A. D. Linde, R. E. Marshak, Y. Nambu, K. Nishijima, John H. Schwarz, Silvan S. Schweber, Steven Weinberg, Victor Weisskopf, P. C. West, Edward Witten, and Bruno Zumino.

Handbook Of The History And Philosophy Of Mathematical Practice

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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26

Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.

The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques

A Creative Philosophy Of Anticipation

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Author : Jamie Brassett
language : en
Publisher: Routledge
Release Date : 2021-04-25

A Creative Philosophy Of Anticipation written by Jamie Brassett and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-25 with Social Science categories.

This edited collection highlights the valuable ontological and creative insights gathered from anticipation studies, which orients itself to the future in order to recreate the present. The gathered essays engage with many writers from speculative metaphysics to poetic philosophy, ancient writing systems to the fringes of pataphysics. The book situates itself as a creative intervention in and with various thinkers, designers, artists, scientists and poets to offer insight into ways of anticipating. It brings together philosophical practices for which creativity is both a fundamental area of consideration and a mode of working, a characterization of recent Continental Philosophy which takes a departure from traditional futures studies thinking. This book will be of interest to scholars and research in futures studies, anticipation, philosophy, creative practice and theories about creative practice, as well as the intersections between philosophy, creativity and business.

The Year Of Our Lord 1943

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Author : Alan Jacobs
language : en
Publisher: Oxford University Press
Release Date : 2018

The Year Of Our Lord 1943 written by Alan Jacobs and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with History categories.

The Year of Our Lord 1943 tells the story of how five Christian intellectuals - Jacques Maritain, T. S. Eliot, C. S. Lewis, W. H. Auden, and Simone Weil - sought to provide a plan for the moral and spiritual renewal of the Western democracies in the post-World War II world.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2008

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.