Intuition In Mathematics And Physics

Author : Ronny Desmet
Publisher : Unknown
Page : 246 pages
File Size : 42,7 Mb
Release : 2016-06-16
Category : Electronic
ISBN : 1940447135

Get Book

Intuition in Mathematics and Physics by Ronny Desmet Pdf

Despite the many revolutions in science and philosophy since Newton and Hume, the outdated idea of an inevitable war between the abstractions of science and the deep intuitions of humankind is reconfirmed, again and again. The history of science is interpreted and presented as a succession of victories over the army of our misleading intuitions, and each success of science is marketed as a defeat of intuition. Instead of endorsing the modern dogma that a truth cannot be scientific unless it hurts the deep intuitions of mankind, and that we cannot be scientific unless we tame the authority of our intuition, the authors of this collection highlight developments in 20th and early 21st century science and philosophy that have the potential to support, or even further, Whitehead's philosophical integration of the abstractions of mathematics and physics with the deep intuitions of humankind. Instead of accepting the authority of science-inspired philosophers to reduce and disenchant nature and humankind in the name of our most successful scientific theories, the authors stress the contemporary relevance of Whitehead's philosophical research program of thinking things together - science and intuition; facts and values - to promote the fundamental coherence that is required to start building an ecological civilization.

Author : Michael Spivak
Publisher : Unknown
Page : 733 pages
File Size : 55,5 Mb
Release : 2010
Category : Mechanics
ISBN : 0914098322

Get Book

Physics for Mathematicians by Michael Spivak Pdf

Author : H. Fischbein
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 52,7 Mb
Release : 2005-12-19
Category : Education
ISBN : 9780306472374

Get Book

Intuition in Science and Mathematics by H. Fischbein Pdf

In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. - To reveal the educational implications of the idea, developed for science and mathematics education. Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates - definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge (1 962) and of Noddings and Shore (1 984).) A notable exception is the book by Westcott (1968), which combines theoretical analyses with the author’s own experimental studies. But, so far, no attempt has been made to identify systematically those findings, spread throughout the research literature, which could contribute to the deciphering of the mechanisms of intuition. Very often the relevant studies do not refer explicitly to intuition. Even when this term is used it occurs, usually, as a self-evident, common sense term.

Author : Frederick W. Byron,Robert W. Fuller
Publisher : Courier Corporation
Page : 674 pages
File Size : 55,6 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486135069

Get Book

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 : Roger Penrose
Publisher : Vintage
Page : 1136 pages
File Size : 44,9 Mb
Release : 2021-06-09
Category : Science
ISBN : 9780593315309

Get Book

The Road to Reality by Roger Penrose Pdf

**WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin

Author : Thomas A. Garrity
Publisher : 清华大学出版社有限公司
Page : 380 pages
File Size : 48,9 Mb
Release : 2004
Category : Mathematics
ISBN : 7302090858

Get Book

All the Mathematics You Missed by Thomas A. Garrity Pdf

Author : Sanjoy Mahajan
Publisher : MIT Press
Page : 152 pages
File Size : 42,7 Mb
Release : 2010-03-05
Category : Education
ISBN : 9780262265591

Get Book

Street-Fighting Mathematics by Sanjoy Mahajan Pdf

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Author : Emily Carson,Renate Huber
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 53,8 Mb
Release : 2006-01-24
Category : Mathematics
ISBN : 1402040393

Get Book

Intuition and the Axiomatic Method by Emily Carson,Renate Huber Pdf

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.

Author : Richard P. Feynman
Publisher : Basic Books
Page : 0 pages
File Size : 51,6 Mb
Release : 2001-09-19
Category : Science
ISBN : 0738206504

Get Book

Six Easy Pieces & Six Not-so-easy Pieces by Richard P. Feynman Pdf

This volume comprises of two collections of instructive essays on physics. Written for a general audience and keeping both technical language and mathematics to a minimum, Feynman introduces the basics of physics, atoms, energy, gravitation, quantum force, and the relationship of physics to other subjects.

Author : Richard Courant,David Hilbert
Publisher : John Wiley & Sons
Page : 852 pages
File Size : 49,6 Mb
Release : 2008-09-26
Category : Science
ISBN : 9783527617241

Get Book

Methods of Mathematical Physics by Richard Courant,David Hilbert Pdf

Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.

Author : Giovanni Boniolo,Paolo Budinich,Majda Trobok
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 50,5 Mb
Release : 2005-12-05
Category : Science
ISBN : 9781402031076

Get Book

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 : Richard P. Feynman
Publisher : Addison-Wesley Longman
Page : 328 pages
File Size : 52,6 Mb
Release : 1996-09-08
Category : Computers
ISBN : UOM:39015038101401

Get Book

Lectures On Computation by Richard P. Feynman Pdf

Covering the theory of computation, information and communications, the physical aspects of computation, and the physical limits of computers, this text is based on the notes taken by one of its editors, Tony Hey, on a lecture course on computation given b

Author : Matt A. Bernstein,William A. Friedman
Publisher : John Wiley & Sons
Page : 189 pages
File Size : 48,5 Mb
Release : 2011-09-20
Category : Mathematics
ISBN : 9781118210642

Get Book

Thinking About Equations by Matt A. Bernstein,William A. Friedman Pdf

An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension. Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.

Author : Philip W. Anderson
Publisher : World Scientific
Page : 710 pages
File Size : 40,8 Mb
Release : 1994
Category : Science
ISBN : 9810217188

Get Book

A Career in Theoretical Physics by Philip W. Anderson Pdf

Theory of ferroelectric behaviour of barium titanate. Use of stochastic methods in line broadening problems. Theory of dirty superconductors.

Author : Don Koks
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 41,8 Mb
Release : 2006-09-15
Category : Science
ISBN : 9780387309439

Get Book

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.