What Did Mathematics Do To Physics

Author : Giovanni Boniolo,Paolo Budinich,Majda Trobok
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 43,8 Mb
Release : 2005-03-10
Category : Mathematics
ISBN : 1402031068

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The Role of Mathematics in Physical Sciences by Giovanni Boniolo,Paolo Budinich,Majda Trobok Pdf

Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics? These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics. The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics.

Author : Michael Spivak
Publisher : Unknown
Page : 733 pages
File Size : 47,5 Mb
Release : 2010
Category : Mechanics
ISBN : 0914098322

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Physics for Mathematicians by Michael Spivak Pdf

Author : Frederick W. Byron,Robert W. Fuller
Publisher : Courier Corporation
Page : 674 pages
File Size : 47,9 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486135069

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Mathematics of Classical and Quantum Physics by Frederick W. Byron,Robert W. Fuller Pdf

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Author : Yves Gingras,Université du Québec à Montréal. Groupe de recherche en épistémologie comparée
Publisher : [Montréal] : Groupe de recherche en épistémologie comparée, Université du Québec à Montréal
Page : 41 pages
File Size : 43,5 Mb
Release : 2001
Category : Electronic
ISBN : 2894490747

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What Did Mathematics Do to Physics? by Yves Gingras,Université du Québec à Montréal. Groupe de recherche en épistémologie comparée Pdf

Author : Vincent F. Hendricks,Klaus F. Jørgensen,Jesper Lützen,Stig A. Pedersen
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 45,8 Mb
Release : 2007-01-17
Category : Philosophy
ISBN : 9781402051951

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Interactions by Vincent F. Hendricks,Klaus F. Jørgensen,Jesper Lützen,Stig A. Pedersen Pdf

The main theme of this anthology is the unique interaction between mathematics, physics and philosophy during the beginning of the 20th century. In this book, ten renowned philosopher-historians probe insightfully into key conceptual questions of pre-quantum mathematical physics. The result is a diverse yet thematically focused compilation of first class papers on mathematics, physics and philosophy, and a source-book on the interaction between them.

Author : Jane McDonnell
Publisher : Springer
Page : 394 pages
File Size : 46,7 Mb
Release : 2016-11-17
Category : Mathematics
ISBN : 9783319409764

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The Pythagorean World by Jane McDonnell Pdf

This book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.

Author : Gesche Pospiech,Marisa Michelini,Bat-Sheva Eylon
Publisher : Springer
Page : 385 pages
File Size : 45,8 Mb
Release : 2019-07-02
Category : Science
ISBN : 9783030046279

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Mathematics in Physics Education by Gesche Pospiech,Marisa Michelini,Bat-Sheva Eylon Pdf

This book is about mathematics in physics education, the difficulties students have in learning physics, and the way in which mathematization can help to improve physics teaching and learning. The book brings together different teaching and learning perspectives, and addresses both fundamental considerations and practical aspects. Divided into four parts, the book starts out with theoretical viewpoints that enlighten the interplay of physics and mathematics also including historical developments. The second part delves into the learners’ perspective. It addresses aspects of the learning by secondary school students as well as by students just entering university, or teacher students. Topics discussed range from problem solving over the role of graphs to integrated mathematics and physics learning. The third part includes a broad range of subjects from teachers’ views and knowledge, the analysis of classroom discourse and an evaluated teaching proposal. The last part describes approaches that take up mathematization in a broader interpretation, and includes the presentation of a model for physics teachers’ pedagogical content knowledge (PCK) specific to the role of mathematics in physics.

Author : Mark Levi
Publisher : Princeton University Press
Page : 201 pages
File Size : 47,9 Mb
Release : 2023-01-24
Category : Mathematics
ISBN : 9780691244174

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The Mathematical Mechanic by Mark Levi Pdf

Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.

Author : Michael Stone,Paul Goldbart
Publisher : Cambridge University Press
Page : 821 pages
File Size : 41,5 Mb
Release : 2009-07-09
Category : Science
ISBN : 9781139480611

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Mathematics for Physics by Michael Stone,Paul Goldbart Pdf

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Author : Melvin Goldstein
Publisher : Trafford Publishing
Page : 874 pages
File Size : 50,6 Mb
Release : 2003-03-06
Category : Science
ISBN : 9781412253550

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Physics Foibles by Melvin Goldstein Pdf

The science of Physics is based on observations that lead to the formulation of mathematical relationships between measured quantities. Some would consider Physics an exact science. Its discoveries and laws are basic to understanding in all areas of science and technology. Four Physics foibles 1) Kurt Godel proved that there are unknowables in our mathematics. 2) Werner Heisenberg showed that there are uncertainties in our measurements. 3) Entropy says that we can only predict the probabilities of events. 4)Chaos Theory deals with things that are effectively impossible to predict like turbulence and long term weather forecasting. The word foible as defined by Webster: An odd feature or mild failing in a person's character a weakness. In fencing, the weaker part of a sword blade. It is the acceptance of these foibles in Physics that has led to broader understanding. In the process of examining these 'weaknesses' in science, many creative and practical solutions have been discovered. There are a number of original computer programs throughout the book. No other person, living or dead - other than the author - has edited or examined the programs. No effort has been made to optimize any of these programs. The author has relied on the computer's results to serve as his default editor. Computer programs are included that take you through puzzles and paradoxes, distribute molecules, follow ameba populations, prove and disprove Murphy's Law, flip coins, and play lottery and casino games. Many have asked about the book. Some with a technical background - and some not - have questioned: What do dice, poker, lotto, and heads-or-tails have to do with Physics? The mathematical study of games of chance is as old as mathematics itself. The connection between games of chance and Nature's laws can be rigorously refined in the field of Statistical Mathematics. If you can analyze multiple coin flips, you can view molecular distribution. If you can understand the results of a game of Roulette, you can understand Radioactive decay. Also included are polls, number systems, wave packets, the search for Pi and the elusive Random, Internet quotes, and more. And in the the process of reading, stop and listen to the words of the science gurus displayed in cartoons throughout.

Author : Michael M. Woolfson,Malcolm S. Woolfson
Publisher : Oxford University Press
Page : 805 pages
File Size : 54,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780199289295

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Mathematics for Physics by Michael M. Woolfson,Malcolm S. Woolfson Pdf

Mathematics for Physics features both print and online support, with many in-text exercises and end-of-chapter problems, and web-based computer programs, to both stimulate learning and build understanding.

Author : Robert D. Richtmyer
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642463785

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Principles of Advanced Mathematical Physics by Robert D. Richtmyer Pdf

A first consequence of this difference in texture concerns the attitude we must take toward some (or perhaps most) investigations in "applied mathe matics," at least when the mathematics is applied to physics. Namely, those investigations have to be regarded as pure mathematics and evaluated as such. For example, some of my mathematical colleagues have worked in recent years on the Hartree-Fock approximate method for determining the structures of many-electron atoms and ions. When the method was intro duced, nearly fifty years ago, physicists did the best they could to justify it, using variational principles, intuition, and other techniques within the texture of physical reasoning. By now the method has long since become part of the established structure of physics. The mathematical theorems that can be proved now (mostly for two- and three-electron systems, hence of limited interest for physics), have to be regarded as mathematics. If they are good mathematics (and I believe they are), that is justification enough. If they are not, there is no basis for saying that the work is being done to help the physicists. In that sense, applied mathematics plays no role in today's physics. In today's division of labor, the task of the mathematician is to create mathematics, in whatever area, without being much concerned about how the mathematics is used; that should be decided in the future and by physics.

Author : Ian Hacking
Publisher : Cambridge University Press
Page : 307 pages
File Size : 48,8 Mb
Release : 2014-01-30
Category : Mathematics
ISBN : 9781107050174

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Why Is There Philosophy of Mathematics At All? by Ian Hacking Pdf

Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.

Author : A. McAulay
Publisher : Forgotten Books
Page : 122 pages
File Size : 46,7 Mb
Release : 2017-11-25
Category : Science
ISBN : 0331922657

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Utility of Quaternions in Physics (Classic Reprint) by A. McAulay Pdf

Excerpt from Utility of Quaternions in Physics IT is a curious phenomenon in the History of Mathematics that the greatest work of the greatest Mathematician of the century which prides itself upon being the most enlightened the world has yet seen, has suffered the most chilling neglect. The cause of this is not at first sight obvious. We have here little to do with the benefit provided by Quaternions to Pure Mathematics. The reason for the neglect here may be that Hamilton himself has developed the Science to such an extent as to make successors an impossibility. One cannot however resist a strong suspicion that were the subject even studied we should hear more from Pure Mathematicians, of Hamilton's valuable results. This reason at any rate cannot be assigned for the neglect'of the Physical side of Quaternions. Hamilton has done but little in this field, and yet when we ask what Mathematical Physicists have been tempted by the bait to win easy laurels (to put the incentive on no higher grounds), the answer must be scarcely one. Prof. Tait is the grand exception to this. But well known Physicist though he be, his fellow-workers for the most part render themselves incapable of appreciating his valuable services by studying the subject if at all only as dilettanti. The number who read a small amount in Quaternions is by no means small, but those who get further than what is recommended by Maxwell as imperatively necessary are but a small percentage of the whole. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Don Koks
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 53,9 Mb
Release : 2006-09-15
Category : Science
ISBN : 9780387309439

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Explorations in Mathematical Physics by Don Koks Pdf

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.