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Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained Hardcover – 30 Aug 2011

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Product details

  • Hardcover: 360 pages
  • Publisher: Springer; 2011 edition (30 Aug. 2011)
  • Language: English
  • ISBN-10: 1461407052
  • ISBN-13: 978-1461407058
  • Product Dimensions: 15.6 x 2.1 x 23.4 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 543,681 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

Review

From the reviews:

“Einstein’s Theory fits in an unusual place for introductory books on the topic. … this work reaches the mathematical, theoretical, and conceptual understanding of a graduate course, assuming just basic algebraic skills. … this is a rare book that can take the motivated reader with an elementary algebra background to a rigorous understanding of general relativity. Summing Up: Recommended. Lower-division undergraduates and general readers.” (E. Kincanon, Choice, Vol. 49 (9), May, 2012)

“This book stands apart from other introductory textbooks on general relativity in that it is aimed at non-science educated readers who nonetheless want to get a thorough understanding of this theory. … The book succeeds quite well in explaining the concepts underlying general relativity in elementary terms without sacrificing mathematical rigor. An additional bonus are the philosophical remarks obviously due to one of the authors being a philosopher himself.” (Helmut Rumpf, Zentralblatt MATH, Vol. 1234, 2012)

From the Back Cover

This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity.

First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory. 

Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained aims to provide the reader with a sound conceptual understanding of both the special and general theories of relativity, and gain an insight into how the mathematics of the theory can be utilized to calculate relativistic effects.

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7 of 7 people found the following review helpful By D. Hawkes on 11 Feb. 2012
Format: Hardcover Verified Purchase
This is an outstanding book on a subject that many authors have failed to portray adequatly.

I have read many books on Einstein's theories and until completing this offering was in a state of confusion having been left with many unanswered questions and a subsequent feeling of inadequacy on my part as a reader. It would seem that Eddington's quoted statement in the preface that mathematical physics cannot be understood by popularisation has proved true - intelligent readers will be left baffled by such attempts. I don't claim to be intelligent but I have certainly been baffled by countless other books on the subject - including Einsteins own attempt to explain things without recourse to maths!

This book introduces all the mathematics necessary to acquire a level of understanding of the treatment of non-euclidean geometries thereby providing the foundations necessary to give the concise formulation of the Einstein field equations. This is achieved by educating the reader in vectors, differential and integral calculus, vector transformations, contravarient and covariant vectors, curvilinear coordinates systems and tensors. In order to achieve an understanding of intrinsic curvature Christoffel symbols and parallel transport are introduced which leads into the Riemann, Ricci and Einstein tensors. Along the way the authors describe philosophical difficulties that along with the deeper understanding of the maths resolve many of the questions that arise from less satisfactory treatments of the subject.

I found the treatment of rotating reference frames and the related subject on gravitational time dilation to be outstanding - possibly as a result of a newly acquired understanding of the maths necessary to describe these complex situations.
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Format: Hardcover Verified Purchase
All new and difficult concepts are crystal-clear explained. I only disagree with the subtitle about ' the mathematically untrained' that will surely be unable to go throughout the entire text. All students studying the subject of Einstein's Theory on relativity should have a wonderful companion in this book.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 7 reviews
39 of 39 people found the following review helpful
Marvellous introduction 21 Jan. 2012
By Joey ooi - Published on Amazon.com
Format: Hardcover
This is simply the clearest and gentlest introduction to the subject of relativity.
This is NOT a popular reading, it does get into the math but the introduction and pace is what sets this text apart.
The authors starts from baby steps and builds up the theory. The pace is easy and explanation are clear and the mathematical details are not left to the reader to figure out like in most text books.The physics is also explained very clearly
From an electronics engineering background and not having dealt with tensors before, this text help me bridge the gap and allows me to fully appreciate the machinery underlying this wonderful theory.I have tried reading Schultz,Lawden etc to understand the subject on my own but this text is a much better intro to the subject.
6 of 6 people found the following review helpful
relativity 31 Dec. 2013
By A Reader - Published on Amazon.com
Format: Hardcover Verified Purchase
This is an excellent book. I am about 1/2 way thru it and the presentation of the necessary math to understand relativity is the best I have ever seen. However, the title "...for the Mathematically Untrained.." is misleading. I think the "mathematically untrained" will find the book rough going; however, for those with a background in college level math, i.e. calculus and vectors in particular will find the book gives a refreshing presentation of these subjects. The careful analysis of a derivative and basis vectors is the best I have ever seen. The geometric approach for derivations such as Christhoffel symbols makes this concept much clearer than an algebraic approach (which by the way, is also shown). I have a BS in physics and a MS in EE and I always felt that school rushed one thru courses with emphasis on problem solving rather than understanding basic principles was probably not a good approach for understanding. I just wish that I had this book early in my academic career.
7 of 8 people found the following review helpful
Glorious, beautiful, top quality 22 Feb. 2014
By Jim Curry - Published on Amazon.com
Format: Hardcover
This is a book of absolutely stunning importance and fantastic quality. Anyone could use it, really, but there is a "best group" of potential users. People who have taken the second course of calculus, the calculus of several variables, will already have made their way through the "heavy lifting" of some preliminary chapters---although that material is also contained here and is correct. So, in theory, a high school student could use this book and learn right up to general relativity in one fell swoop. It could be done, but it would take a lot of effort. I think that almost every young scientist, at more or less the early college stage, would deserve the privilege of reading this most valuable book. It will explain Einstein's theory correctly right up to the true general relativity. It will do it with full mathematical correctness (leaving out some niceties that can be left out), and it will do it in a fully understandable way. So, it is a "best book." For people who would like to understand Special Relativity only, and who would like to muddle through less mathematics, Mermin's book "It's About Time" is really by far the very best, and it uses less mathematics, but only gives you the special theory. For those who are fully confident in mathematics, Woodhouse's two volumes on Special and General Relativity seem to be just the "right" place to start, but it requires that you be in full mathematical fettle to do it. Gron stops and carefully helps you fill that all in, and in a very gentle way. I think everyone will want to read it, even those who don't have to. It's just that wonderful. For those who go beyond this level, Gron has two more books which are worth reading. Woodhouse is a good next step. For Special Relativity, Rindler's book "Introduction to Special Relativity" is really the best and most encyclopaedic reference. For the general theory, if you wish to go beyond Woodhouse, I think it is very nice and suitable to go next to Ohanian's very appealing text "Gravitation and Spacetime." Notice one thing, though. If you were a high school student of some serious persistence, you could use Gron's first volume and leap steadily to the state of the art in and past Ohanian's text in not so long a time. This is a great thing, to gain mastery over a significant area of physics in a relatively short time, and to gain a very full understanding.

At this same level, there is another very good book, which also tries to show all the background mathematics in a very accessible way. That book is Collier's book "A Most Incomprehensible Thing". The book is also very good and very careful and very complete. The good part is that it's much less expensive. The down side is small. In my opinion, many of the details included in Collier's book serve as much to obscure the real point as to help it. So, I find Gron's choice of route to this summit to be better, more direct, safer hiking. Collier's route is also safe enough and very good. I think young people who have great enthusiasm for science will be helped very greatly by this book---very greatly indeed. I think Professor Gron is doing wonderful things indeed to satisfy the passions of young scientists in clear and helpful ways. I don't know him, but his books seem to be the best of the best.
1 of 1 people found the following review helpful
Climbing up a Modern Pyramid To Decipher the Language of GR ... 28 Feb. 2015
By Vazhaspa Spitman - Published on Amazon.com
Format: Hardcover Verified Purchase
"One day," writes Oyvind Gron, "the seventy three year old philosopher Arne Naes appeared at my graduate course on general relativity. He immediately decided that a new type of introduction to the general theory of relativity is needed: an introduction designed to meet the requirements of non-science educated people wanting to get a thorough understanding of this, most remarkable, theory."

Imagine you are deeply curious about concepts of Einstein' theory beyond just misleading popularized qualitative descriptions or strict quantitative textbooks, imagine you are an educated person who has forgotten some basic high school maths but likes to master the field of relativity as excellent as a graduate student, imagine you are a thinker, philosopher or a theoretician who likes to compare her/his concepts of space and time versus that of Einstein in General Relativity ... in all these cases, this book is for you if and only if you are a patient reader.

The book is unique in its genre: not only it starts with low level maths to arrive at the core of one of the most sophisticated theories of the last century, but it is the fruit of corporation between an interested philosopher (Arne Naes) and a professor of physics (Oyvind Gron). It is therefore neither a vulgarized version of the theory, even when it goes into the qualitative discussions, nor a strict textbook jumping between mathematical formulas and mistaking the mathematical formalism with the reality.In other words, although the books deal with mathematics of GR (the general relativity) the authors are aware that beyond the equations are hidden wonders and curious concepts rooted in Einstein's inventive imagination.
The book is in fact written for a reader whose urge for a deeper understanding of Einstein' theory is armed him/her with sufficient patience to climb, step by step, up the mathematical pyramid and decipher the glyphs in which one of the most outstanding theories of the last century has been written.
Does it mean that the book is "perfect"? Not at all! Despite all the efforts by the authors, the reader might sometime feel lost, or discovers that the subject could have been explained more clearly, or the philosophical or mathematical points could be deeper or more radical but the point is that: whereas in such cases the reader may rely on many other references (including her/his own notes and ideas), hardly can s/he find any other book which is on a par with the current book.
As Arne Naes puts it, according to "Sir Arthur Eddington, ... mathematical physics cannot be understood through popularisations" That is the reason beyond the structure of the book and at the end we should confirm the claim made by the authors of the book who "venture to suggest the understanding acquired by the reader [of this book] may be deeper than what is necessary for completing graduate courses ... Only patience is needed."
einstein's theory a rigorous introduction for the mathematically untrained 30 Sept. 2013
By Vivek Joshi - Published on Amazon.com
Format: Hardcover
This is a nice book which introduces the subject at a very basic level, it will be very difficult for someone not being able to understand. GTR cannot be taught at level simpler than this. Anything simpler will not teach the subject in true spirit.The authors have done a great job of bringing this difficult topic ahead in most honest manner for anyone who is actually willing to study.In the end I must add that no book is perfect and some people will certainly find fault in this book.
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