
Author 
Peter Collier 
ISBN10 
9780957389465 
Year 
20170401 
Pages 
274 
Language 
en 
Publisher 
Incomprehensible Books 
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A clear and enjoyable guide to the mathematics of relativity To really understand relativity – one of the cornerstones of modern physics – you have to get to grips with the mathematics. This userfriendly selfstudy guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer GravitationalWave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of nongravitational physical phenomena and has some strangely counterintuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, massenergy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes. Understand even the basics of Einstein's amazing theory and the world will never seem the same again. March 2017. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

Author 
Peter Collier 
ISBN10 
9780957389458 
Year 
20140731 
Pages 
340 
Language 
en 
Publisher 
Peter Collier 
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This book is aimed at the enthusiastic general reader who wants to move beyond the mathslite popularisations in order to tackle the essential mathematics of Einstein's fascinating theories of special and general relativity. One of the cornerstones of modern physics, relativity is based on the concept of fourdimensional spacetime  curved in the vicinity of massenergy, flat in its absence. Special relativity helps explain a huge range of nongravitational physical phenomena and has some strangely counterintuitive (in plain English: very weird) consequences. These include time dilation, length contraction, the relativity of simultaneity, massenergy equivalence and an absolute speed limit. General relativity, a theory of gravity, is at the heart of our understanding of cosmology and black holes. To paraphrase Euclid, there is no royal road to relativity  you have to do the mathematics. This introductory, selfstudy guide is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Schwarzschild solution; simple black holes (and what different observers would see if someone was unfortunate enough to fall into one). Also covered are the mysteries of dark energy and the cosmological constant; plus relativistic cosmology, including the Friedmann equations and FriedmannRobertsonWalker cosmological models. Following the historic 2015 LIGO detection, there is now also an additional chapter on gravitational waves. Understand even the basics of Einstein's amazing theory and the world will never seem the same again.

Author 
George Yuri Rainich 
ISBN10 
9780486798226 
Year 
20140820 
Pages 
192 
Language 
en 
Publisher 
Courier Corporation 
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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.

Author 
Jose Natario 
ISBN10 
3642214525 
Year 
20110801 
Pages 
128 
Language 
en 
Publisher 
Springer Science & Business Media 
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“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski spacetime, nonEuclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quickpaced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.

Author 
James Hammond Smith 
ISBN10 
9780486688954 
Year 
1965 
Pages 
218 
Language 
en 
Publisher 
Courier Corporation 
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Concise, wellwritten treatment of epochal theory of modern physics covers classical relativity and the relativity postulate, time dilation, the twin paradox, momentum and energy, particles of zero mass, electric and magnetic fields and forces and more. Only high school math needed. Replete with examples, ideal for selfstudy. Introduction. 70 illustrations.

Author 
Roger Cooke 
ISBN10 
9781470434830 
Year 
2017 
Pages 
4 
Language 
en 
Publisher 
American Mathematical Soc. 
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This book has three main goals. First, it explores a selection of topics from the early period of the theory of relativity, focusing on particular aspects that are interesting or unusual. These include the twin paradox; relativistic mechanics and its interaction with Maxwell's laws; the earliest triumphs of general relativity relating to the orbit of Mercury and the deflection of light passing near the sun; and the surprising bizarre metric of Kurt Godel, in which time travel is possible. Second, it provides an exposition of the differential geometry needed to understand these topics on a level that is intended to be accessible to those with just two years of universitylevel mathematics as background. Third, it reflects on the historical development of the subject and its significance for our understanding of what reality is and how we can know about the physical universe. The book also takes note of historical prefigurations of relativity, such as Euler's 1744 result that a particle moving on a surface and subject to no tangential acceleration will move along a geodesic, and the work of Lorentz and Poincare on spacetime coordinate transformations between two observers in motion at constant relative velocity. The book is aimed at advanced undergraduate mathematics, science, and engineering majors (and, of course, at any interested person who knows a little universitylevel mathematics). The reader is assumed to know the rudiments of advanced calculus, a few techniques for solving differential equations, some linear algebra, and basics of set theory and groups.

Author 
Tom Lancaster 
ISBN10 
9780199699322 
Year 
201404 
Pages 
485 
Language 
en 
Publisher 
Oxford University Press 
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Quantum field theory provides the theoretical backbone to most modern physics. It explains the standard model of particle physics and the existence of the Higgs boson, the physics of states of matter such as metals, magnets and superconductors, and allows us to understand the behaviour of polymers and biological molecules. However, quantum field theory has a reputation for difficulty, reinforced by a selection of weighty and inaccessible books on the subject aimedfirmly at those who will make future advances in the subject. The authors of this book believe the subject is too important to be restricted to the professionals and have designed this book to bringquantum field theory to a wider audience of physicists. The book is packed with worked examples, witty diagrams, and applications intended to introduce a new audience to this revolutionary theory.

Author 
Andrew Liddle 
ISBN10 
9781118690253 
Year 
20150427 
Pages 
200 
Language 
en 
Publisher 
John Wiley & Sons 
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An Introduction to Modern Cosmology Third Edition is an accessible account of modern cosmological ideas. The Big Bang Cosmology is explored, looking at its observational successes in explaining the expansion of the Universe, the existence and properties of the cosmic microwave background, and the origin of light elements in the universe. Properties of the very early Universe are also covered, including the motivation for a rapid period of expansion known as cosmological inflation. The third edition brings this established undergraduate textbook uptodate with the rapidly evolving observational situation. This fully revised edition of a bestseller takes an approach which is grounded in physics with a logical flow of chapters leading the reader from basic ideas of the expansion described by the Friedman equations to some of the more advanced ideas about the early universe. It also incorporates uptodate results from the Planck mission, which imaged the anisotropies of the Cosmic Microwave Background radiation over the whole sky. The Advanced Topic sections present subjects with more detailed mathematical approaches to give greater depth to discussions. Student problems with hints for solving them and numerical answers are embedded in the chapters to facilitate the reader’s understanding and learning. Cosmology is now part of the core in many degree programs. This current, clear and concise introductory text is relevant to a wide range of astronomy programs worldwide and is essential reading for undergraduates and Masters students, as well as anyone starting research in cosmology. Supplementary material, including fullcolour images, updates and links for students and instructors, is available on the author’s website: http://www.roe.ac.uk/~arl/.

Author 
Pedro G. Ferreira 
ISBN10 
9780547554907 
Year 
20140204 
Pages 
288 
Language 
en 
Publisher 
Houghton Mifflin Harcourt 
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“Ferreira masterfully portrays the science and scientists behind general relativity’s starcrossed history and argues that even now we are only just beginning to realize its vitality as a tool for understanding the cosmos.” —Scientific American Einstein’s theory of general relativity is possibly the most perfect intellectual achievement of modern physics. For almost a century now, physicists have been delving into Einstein’s theory, seeking an understanding of the history of the universe, the origin of time, and the evolution of solar systems, stars, and galaxies. The expanding universe, the lightspeed barrier, black holes, wormholes, time travel—general relativity has allowed scientists’ imaginations to take flight with new possibilities, revealing a universe that is much stranger than anyone ever expected. Just in time for the theory’s hundredyear anniversary, physicist Pedro Ferreira’s The Perfect Theory explains just how staggering an achievement general relativity was while bringing to life the infighting that it sparked in the field of physics over the past century. “A rollicking good read . . . With crisp explanations and narrative flair, Ferreira offers us a fun, fresh take on a magnificent part of modern science.” —Steven Strogatz, author of The Joy of x “One of the best popular accounts of how Einstein and his followers have been trying to explain the universe for decades.” —Kirkus Reviews, starred review

Author 
George Hrabovsky 
ISBN10 
9780141976235 
Year 
20130129 
Pages 
256 
Language 
en 
Publisher 
Penguin UK 
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In this unconventional and stimulating primer, worldclass physicist Leonard Susskind and citizenscientist George Hrabovsky combine forces to provide a brilliant first course in modern physics. Unlike most popular physics books  which give readers a taste of what physicists know but not what they actually do  Susskind and Hrabovsky teach the skills you need to do physics yourself. Combining crystalclear explanations of the laws of the universe with basic exercises, the authors cover the minimum  the theoretical minimum of the title  that readers need to master in order to study more advanced topics. In a lucid, engaging style, they introduce all the key concepts, from classical mechanics to general relativity to quantum theory. Instead of shying away from the equations and maths that are essential to any understanding of physics, The Theoretical Minimum provides a toolkit that you won't find in any other popular science book.

Author 
Yvonne ChoquetBruhat 
ISBN10 
9780199666454 
Year 
20150120 
Pages 
279 
Language 
en 
Publisher 
Oxford University Press 
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General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics. Based on Yvonne ChoquetBruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity. The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the ReissnerNordstrom and interior Schwarzchild solutions. The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory.

Author 
Bernard Schutz 
ISBN10 
9780521887052 
Year 
20090514 
Pages 
393 
Language 
en 
Publisher 
Cambridge University Press 
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Second edition of a widelyused textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.

Author 
Giancarlo Bernacchi 
ISBN10 
9781326230975 
Year 
201105 
Pages 
130 
Language 
en 
Publisher 
Lulu.com 
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An informal, semplified introduction to the Maths of General Relativity. (revised edition) No particular mathematical background is required beyond calculus with a little bit of partial derivatives.

Author 
T. Padmanabhan 
ISBN10 
9781139485395 
Year 
20100128 
Pages 

Language 
en 
Publisher 
Cambridge University Press 
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Covering all aspects of gravitation in a contemporary style, this advanced textbook is ideal for graduate students and researchers in all areas of theoretical physics. The 'Foundation' section develops the formalism in six chapters, and uses it in the next four chapters to discuss four key applications  spherical spacetimes, black holes, gravitational waves and cosmology. The six chapters in the 'Frontier' section describe cosmological perturbation theory, quantum fields in curved spacetime, and the Hamiltonian structure of general relativity, among several other advanced topics, some of which are covered indepth for the first time in a textbook. The modular structure of the book allows different sections to be combined to suit a variety of courses. Over 200 exercises are included to test and develop the reader's understanding. There are also over 30 projects, which help readers make the transition from the book to their own original research.

Author 
Tevian Dray 
ISBN10 
9781466510005 
Year 
20141020 
Pages 
321 
Language 
en 
Publisher 
CRC Press 
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Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.