The Mathematics Of Relativity For The Rest Of Us

The Mathematics of Relativity for the Rest of Us is intended to give the generally educated reader a thorough and factual understanding of Einstein's theory of relativity - including the difficult mathematical concepts, even if the reader is not trained in higher mathematics.

The author's strategy is to rely on fundamental geometry, algebra and logic as a basis for an understanding of special and general relativity, as well as their relationship to quantum mechanics, suitable for the amateur scientist or mathematician. The text has been updated to include recent developments. The book may also be of value to undergraduate students.

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Based on the ideas of Einstein and Minkowski, this concise treatment is derived from the author's many years of teaching the mathematics of relativity at the University of Michigan. Geared toward advanced undergraduates and graduate students of physics, the text covers old physics, new geometry, special relativity, curved space, and general relativity. Beginning with a discussion of the inverse square law in terms of simple calculus, the treatment gradually introduces increasingly complicated situations and more sophisticated mathematical tools. Changes in fundamental concepts, which characterize relativity theory, and the refinements of mathematical technique are incorporated as necessary. The presentation thus offers an easier approach without sacrifice of rigor. Dover (2014) republication of the edition published by John Wiley & Sons, New York, 1950. See every Dover book in print at www.doverpublications.com

The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: tensor analysis the special theory of relativity the general theory of relativity and Einstein’s field equations spherically symmetric solutions and experimental confirmations static and stationary space-time domains black holes cosmological models algebraic classifications and the Newman-Penrose equations the coupled Einstein-Maxwell-Klein-Gordon equations appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland, Jadavpur University, India, Carnegie-Mellon University, USA, and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.

Louis S. Jagerman MD, an experienced clinical ophthalmologist and science author, demystifies and explains the mathematical background for modern refractive surgery. No ophthalmologist needs to be perplexed by Zernike polynomials or Fourier transforms. No need for you to be intimidated by technical and mathematical intricacies of waterfronts, lenslets, and aberrometers. No need to dread questions from curious colleagues, educated patients, and persuasive salespersons. This short book, with its clear diagrams, well-explained equations, and extensive index, will provide a form grasp of the mathematical basis for your refractive practice. At the same time, you will witness how brilliant mathematics, drawn from diverse sources, can be applied to modern medical science and patient care.

This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics. It emerged from lecture notes originally conceived for a one-semester course in Mathematical Relativity which has been taught at the Instituto Superior Técnico (University of Lisbon, Portugal) since 2010 to Masters and Doctorate students in Mathematics and Physics. Mostly self-contained, and mathematically rigorous, this book can be appealing to graduate students in Mathematics or Physics seeking specialization in general relativity, geometry or partial differential equations. Prerequisites include proficiency in differential geometry and the basic principles of relativity. Readers who are familiar with special relativity and have taken a course either in Riemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.

Excerpt from The Mathematical Theory of Relativity This book includes ten lectures on the Mathematical Theory of Relativity, as I have developed it during the last twelve years. These lectures were delivered at the Massachusetts Institute of Technology during the Spring Term of the academic year 1925 - 1926. I desire to express to this Institute my deepest gratitude for the invitation which has been extended to me to give these lectures. It was very pleasant to think that I would be able to collaborate in the scientific research of this important and celebrated institution, and to renew the ties of friendship with the intellectual elite of the American people. I have not been disappointed in my hopes. The cordial reception extended to me by my colleagues in the Departments of Physics and Mathe maties, the interesting conversations and exchanges of ideas I have had with them, have played no small part in creating this feeling. In the domain of thought we are all citizens of the same country. Barriers appear only where science ceases to cast its light; and these frontiers recede ever toward more remote regions. Thanks to science, the world becomes vaster and richer. The only revolutionists are scholars and artists, for they create new conditions and they change the aspect of the universe. To be sure, this evolution sometimes carries along with it sudden and terrible changes. Think of the Great War! The present adaptation towards the universality due to science is still painqy felt in many countries. In my fatherland, scientific reconstruction was greatly helped by the C. R. B. This Committee for Relief in Belgium was organized, during the war, for avoiding famine and, in collaboration with other American organizations, has helped Belgium very much in its new organization of teaching and scientific research. Indeed, Belgium will always remember with thankfulness and admiration that noble initiative of the United States of America. 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.