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11 people found this helpful

ByEricon 14 March 2014

I am slowly catching up on relativity. But my maths was a little bit rusty. I know the basic concepts, but had not used them for a long time. This book is well structured and has enabled me to undertake rapid revision of my basic understanding. Already I am half way through the book (some 170 pages), thoroughly having understood all the concepts and data structures and a total refresher of my relativity knowledge. This is after three days of reading in my spare time.

I can thoroughly recommend this book to anyone interested in understanding general relativity from a physical significance point of view. I can't wait to finish it and then return to my higher level text books with a better understanding of where it is trying to go. He deals with Tensors at a level appropriate to understanding relativity. More advanced topics are left to the reader from other sources.

He cites websites where one can practise the concepts introduced and this certainly helps one to get a feel for the subject.

Great book, I wish I'd found it earlier.

I can thoroughly recommend this book to anyone interested in understanding general relativity from a physical significance point of view. I can't wait to finish it and then return to my higher level text books with a better understanding of where it is trying to go. He deals with Tensors at a level appropriate to understanding relativity. More advanced topics are left to the reader from other sources.

He cites websites where one can practise the concepts introduced and this certainly helps one to get a feel for the subject.

Great book, I wish I'd found it earlier.

12 people found this helpful

ByMr. Steve Lloydon 16 January 2014

I picked up this book because I've always wanted to understand the mathematical ideas and insights - the 'story' if you like - underpinning General Relativity.

I studied Mathematics at Oxford 30 years ago, and took courses in Special and General Relativity. The SR course was very clear and I quickly got the explanation for the formula of the Gamma factor, Minkowski spacetime and 4-momentum and I feel I could probably go through the essentials of the theory all the way to E=MC2 with any reasonably switched on class of Maths GCSE students. However, I just didn't get GR at all, perhaps because there was too much to fit in in a typical course. My recollection was that the course started with some general background on cosmic phenomena that GR informs us about, and then promptly dove into lots of abstruse talk of tensor arithmetic, without any discussion of the physical concepts we were trying to model. I think my initial enthusiasm about determining the secrets of cosmology was eventually washed away by a tsunami of boring talk of summation indices, covariant tensors and other sleep-inducing terms.

I was hoping that this book would succeed where my University course failed. However, it seemed much the same story - a lot of terms and arithmetic conventions without any accompanying physical discussion of the point of the exercise. Add to this the fact that the equations are basically unreadable on Kindle and I found myself skipping past most of the meat of the book.

I'm also a bit disappointed in the treatment of those parts of SR that I am familiar with. The derivation of the Gamma factor seemed a lot more wordy and equation heavy (and therefore less intuitive to the lay reader) than the "Imagine a light clock on a train" story that I'm familiar with, and the equation for the total energy seemed to be plucked out of thin air (was a logical step missed out there?) and again the point was less clearly made than the "conservation of the time-like component of 4-momentum" argument I remember from Uni.

To be fair, the synopsis does say that this is fundamentally a maths book, and you do need to "do the math" to get to the gold. However, it does claim to be a book for the lay reader, and I do wonder what sort of lay reader the author has in mind.

I studied Mathematics at Oxford 30 years ago, and took courses in Special and General Relativity. The SR course was very clear and I quickly got the explanation for the formula of the Gamma factor, Minkowski spacetime and 4-momentum and I feel I could probably go through the essentials of the theory all the way to E=MC2 with any reasonably switched on class of Maths GCSE students. However, I just didn't get GR at all, perhaps because there was too much to fit in in a typical course. My recollection was that the course started with some general background on cosmic phenomena that GR informs us about, and then promptly dove into lots of abstruse talk of tensor arithmetic, without any discussion of the physical concepts we were trying to model. I think my initial enthusiasm about determining the secrets of cosmology was eventually washed away by a tsunami of boring talk of summation indices, covariant tensors and other sleep-inducing terms.

I was hoping that this book would succeed where my University course failed. However, it seemed much the same story - a lot of terms and arithmetic conventions without any accompanying physical discussion of the point of the exercise. Add to this the fact that the equations are basically unreadable on Kindle and I found myself skipping past most of the meat of the book.

I'm also a bit disappointed in the treatment of those parts of SR that I am familiar with. The derivation of the Gamma factor seemed a lot more wordy and equation heavy (and therefore less intuitive to the lay reader) than the "Imagine a light clock on a train" story that I'm familiar with, and the equation for the total energy seemed to be plucked out of thin air (was a logical step missed out there?) and again the point was less clearly made than the "conservation of the time-like component of 4-momentum" argument I remember from Uni.

To be fair, the synopsis does say that this is fundamentally a maths book, and you do need to "do the math" to get to the gold. However, it does claim to be a book for the lay reader, and I do wonder what sort of lay reader the author has in mind.

ByEricon 14 March 2014

I am slowly catching up on relativity. But my maths was a little bit rusty. I know the basic concepts, but had not used them for a long time. This book is well structured and has enabled me to undertake rapid revision of my basic understanding. Already I am half way through the book (some 170 pages), thoroughly having understood all the concepts and data structures and a total refresher of my relativity knowledge. This is after three days of reading in my spare time.

I can thoroughly recommend this book to anyone interested in understanding general relativity from a physical significance point of view. I can't wait to finish it and then return to my higher level text books with a better understanding of where it is trying to go. He deals with Tensors at a level appropriate to understanding relativity. More advanced topics are left to the reader from other sources.

He cites websites where one can practise the concepts introduced and this certainly helps one to get a feel for the subject.

Great book, I wish I'd found it earlier.

I can thoroughly recommend this book to anyone interested in understanding general relativity from a physical significance point of view. I can't wait to finish it and then return to my higher level text books with a better understanding of where it is trying to go. He deals with Tensors at a level appropriate to understanding relativity. More advanced topics are left to the reader from other sources.

He cites websites where one can practise the concepts introduced and this certainly helps one to get a feel for the subject.

Great book, I wish I'd found it earlier.

ByAmazon Customeron 22 December 2013

This book, despite it's off-putting title, is quite simply one of the best self-study textbooks that I have ever read.

It assumes zero mathematical background, and guides you with relative ease (pun partially intended) to the manipulation of Ricci tensors, Lorentz transformations and Minkowski spacetime etc.

As one reviewer put it, this is a "new gold standard". If you want to see how a clear exposition, without any patronising oversimplification, of a complex topic is done, read this book.

By the end you will have an enriched and enhanced world to inhabit, one in which you have acquainted yourself with one of the handful of remarkable ideas that can truly be classified as great.

It assumes zero mathematical background, and guides you with relative ease (pun partially intended) to the manipulation of Ricci tensors, Lorentz transformations and Minkowski spacetime etc.

As one reviewer put it, this is a "new gold standard". If you want to see how a clear exposition, without any patronising oversimplification, of a complex topic is done, read this book.

By the end you will have an enriched and enhanced world to inhabit, one in which you have acquainted yourself with one of the handful of remarkable ideas that can truly be classified as great.

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ByDavid Hampshireon 12 November 2013

The author is to be thanked for his efforts. I graduated in physics many years ago and always wanted to get a reasonable understanding of general relativity which was not studied in my degree course. For my purposes this book was just what I needed and better places me to understand more advanced books.

The book has its weaknesses. For example Section 8.3 seems rather long winded and there appears to be a more straight forward approach in Hobson et al (see below). Section 9.4.8 on the gravitational deflection of light could be better written with less hand waving. I also spotted some typos and incorrect cross references but these are relatively few for a book of this type.

I have an alternative book entitled "General Relativity: An Introduction for Physicists" by Hobson, Efstathiou and Lasenby (Cambridge University Press). The two books complement each other well in that Collier is very good in the basics with Hobson et al excelling in the applications of general relativity and addresses most of the weaknesses in Chapters 8 and 9 of Collier. For those who have gone through this book and wish to read further about the applications and more complete derivations then I would recommend Hobson et al.

The book has its weaknesses. For example Section 8.3 seems rather long winded and there appears to be a more straight forward approach in Hobson et al (see below). Section 9.4.8 on the gravitational deflection of light could be better written with less hand waving. I also spotted some typos and incorrect cross references but these are relatively few for a book of this type.

I have an alternative book entitled "General Relativity: An Introduction for Physicists" by Hobson, Efstathiou and Lasenby (Cambridge University Press). The two books complement each other well in that Collier is very good in the basics with Hobson et al excelling in the applications of general relativity and addresses most of the weaknesses in Chapters 8 and 9 of Collier. For those who have gone through this book and wish to read further about the applications and more complete derivations then I would recommend Hobson et al.

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ByMrs. Lon 7 June 2014

For any physics student/enthusiast this book represents excellent value. My father, who is a retired physics lecturer bought a copy and then ordered a second for my son, who is studying physics at university

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ByMr. Steve Lloydon 16 January 2014

I picked up this book because I've always wanted to understand the mathematical ideas and insights - the 'story' if you like - underpinning General Relativity.

I studied Mathematics at Oxford 30 years ago, and took courses in Special and General Relativity. The SR course was very clear and I quickly got the explanation for the formula of the Gamma factor, Minkowski spacetime and 4-momentum and I feel I could probably go through the essentials of the theory all the way to E=MC2 with any reasonably switched on class of Maths GCSE students. However, I just didn't get GR at all, perhaps because there was too much to fit in in a typical course. My recollection was that the course started with some general background on cosmic phenomena that GR informs us about, and then promptly dove into lots of abstruse talk of tensor arithmetic, without any discussion of the physical concepts we were trying to model. I think my initial enthusiasm about determining the secrets of cosmology was eventually washed away by a tsunami of boring talk of summation indices, covariant tensors and other sleep-inducing terms.

I was hoping that this book would succeed where my University course failed. However, it seemed much the same story - a lot of terms and arithmetic conventions without any accompanying physical discussion of the point of the exercise. Add to this the fact that the equations are basically unreadable on Kindle and I found myself skipping past most of the meat of the book.

I'm also a bit disappointed in the treatment of those parts of SR that I am familiar with. The derivation of the Gamma factor seemed a lot more wordy and equation heavy (and therefore less intuitive to the lay reader) than the "Imagine a light clock on a train" story that I'm familiar with, and the equation for the total energy seemed to be plucked out of thin air (was a logical step missed out there?) and again the point was less clearly made than the "conservation of the time-like component of 4-momentum" argument I remember from Uni.

To be fair, the synopsis does say that this is fundamentally a maths book, and you do need to "do the math" to get to the gold. However, it does claim to be a book for the lay reader, and I do wonder what sort of lay reader the author has in mind.

I studied Mathematics at Oxford 30 years ago, and took courses in Special and General Relativity. The SR course was very clear and I quickly got the explanation for the formula of the Gamma factor, Minkowski spacetime and 4-momentum and I feel I could probably go through the essentials of the theory all the way to E=MC2 with any reasonably switched on class of Maths GCSE students. However, I just didn't get GR at all, perhaps because there was too much to fit in in a typical course. My recollection was that the course started with some general background on cosmic phenomena that GR informs us about, and then promptly dove into lots of abstruse talk of tensor arithmetic, without any discussion of the physical concepts we were trying to model. I think my initial enthusiasm about determining the secrets of cosmology was eventually washed away by a tsunami of boring talk of summation indices, covariant tensors and other sleep-inducing terms.

I was hoping that this book would succeed where my University course failed. However, it seemed much the same story - a lot of terms and arithmetic conventions without any accompanying physical discussion of the point of the exercise. Add to this the fact that the equations are basically unreadable on Kindle and I found myself skipping past most of the meat of the book.

I'm also a bit disappointed in the treatment of those parts of SR that I am familiar with. The derivation of the Gamma factor seemed a lot more wordy and equation heavy (and therefore less intuitive to the lay reader) than the "Imagine a light clock on a train" story that I'm familiar with, and the equation for the total energy seemed to be plucked out of thin air (was a logical step missed out there?) and again the point was less clearly made than the "conservation of the time-like component of 4-momentum" argument I remember from Uni.

To be fair, the synopsis does say that this is fundamentally a maths book, and you do need to "do the math" to get to the gold. However, it does claim to be a book for the lay reader, and I do wonder what sort of lay reader the author has in mind.

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12 people found this helpful.
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Byakyon 2 January 2014

I would highly recommend this to anyone who's interested in delving below the level of "popular science" level.

The mathematics is very clearly laid out. The language used throughout is almost 'conversational', which I felt made the text much easier to read.

You still need a reasonable background in maths and physics to fully understand the material covered. That said, the author makes the material very accessible and I think this should be required reading for anyone who sets themselves the challenge of understanding Einstein's general theory of relativity.

The mathematics is very clearly laid out. The language used throughout is almost 'conversational', which I felt made the text much easier to read.

You still need a reasonable background in maths and physics to fully understand the material covered. That said, the author makes the material very accessible and I think this should be required reading for anyone who sets themselves the challenge of understanding Einstein's general theory of relativity.

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ByWalter Vanhimbeeckon 19 May 2014

Peter Collier introduces the reader into the theories of special and general relativity in a way that makes me wonder why no one else tried to do it before him. This brilliant book full of wit and with an intresting portion of history is the best way to grasp the mathematics of the theory on a level that you never expected.

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ByZbygnyu Thiewon 1 August 2014

Einstein's achievements are foundation stones of modern physical theory, but like so many are quite impenetrable to laymen. Numerous books have explained their conceptual basis in terms that are too simplistic to be satisfying, since they either omit the mathematics altogether, or, like Max Born's superlative book on relativity, use very simplified alternatives. "You can't understand it without the maths" is the dismissive response by the High Priests of Science to any persistent enquiry. Yet there would be many, like the present writer, who suspect that they are intellectually equal to understanding at least some of the maths, but lack time and motivation for so tedious an undertaking.

If you're one of them, here's your chance to put your suspicion to the test.

Most people think that mathematics is about calculation. Whilst true of Elementary Maths, Higher Maths is a very different animal. Key to understanding it is to realize that it is a formal symbology for representing and manipulating abstract concepts. In Pure Maths, these have no physical interpretation; but in Theoretical Physics, some or all of the initial symbols are given correlates in physical theory. This is not unique; alchemists have a large symbology with well-defined real-world interpretations, as do many occult schools and secret societies. The difference with Applied Advanced Mathematics is the carefully-constructed set of rules for manipulating the symbols - Higher Algebras, if you like. The initial symbols are expanded into parameters within these algebras, which may or may not have physical correlates, and manipulated according to the rules to produce results, sometimes amenable to numeric solutions, that are claimed to describe or predict physical equivalents.

This is a fascinating intellectual exercise that can be followed if the underlying concepts are clearly grasped. Few have the patience or interest needed to master the mechanics of calculation, nor is there any need for this if one seeks only understanding rather than calculational expertise. Peter Collier has done all such aspirants the inestimable favour of plodding through the luminous fields of theory and barren wastes of exercises to emerge, not only with a clear conceptual perspective, but the ability to condense and present it in very readable form.

This book is a valuable contribution to a wider understanding of the inner workings of modern theories that have subtle but profound consequences in today's knowledge-based societies. The High Priests will doubtless wish him exiled to the Siberian tundras along with the likes of Edward Snowden. The rest of us can sing his praises.

If you're one of them, here's your chance to put your suspicion to the test.

Most people think that mathematics is about calculation. Whilst true of Elementary Maths, Higher Maths is a very different animal. Key to understanding it is to realize that it is a formal symbology for representing and manipulating abstract concepts. In Pure Maths, these have no physical interpretation; but in Theoretical Physics, some or all of the initial symbols are given correlates in physical theory. This is not unique; alchemists have a large symbology with well-defined real-world interpretations, as do many occult schools and secret societies. The difference with Applied Advanced Mathematics is the carefully-constructed set of rules for manipulating the symbols - Higher Algebras, if you like. The initial symbols are expanded into parameters within these algebras, which may or may not have physical correlates, and manipulated according to the rules to produce results, sometimes amenable to numeric solutions, that are claimed to describe or predict physical equivalents.

This is a fascinating intellectual exercise that can be followed if the underlying concepts are clearly grasped. Few have the patience or interest needed to master the mechanics of calculation, nor is there any need for this if one seeks only understanding rather than calculational expertise. Peter Collier has done all such aspirants the inestimable favour of plodding through the luminous fields of theory and barren wastes of exercises to emerge, not only with a clear conceptual perspective, but the ability to condense and present it in very readable form.

This book is a valuable contribution to a wider understanding of the inner workings of modern theories that have subtle but profound consequences in today's knowledge-based societies. The High Priests will doubtless wish him exiled to the Siberian tundras along with the likes of Edward Snowden. The rest of us can sing his praises.

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ByRoberton 27 July 2014

Really amazing approaching to introducing a complicated subject with equations and not just the general idea. Sections on non-Euclidean geometry a reasonable explanation of the concepts. Better to include references to some of the proofs like the Bianchi identity. Good explanation of the energy momentum tensor and the sections on cosmology quite easy to follow.

Overall a great first step on the basic equations and differential geometry to stimulate further reading. Should include some cross references to some of the more difficult proofs.

Great to read alongside Daniel Flesich's book on vectors and tensors, especially on the connection coefficients and the curvature tensor.

Overall a great first step on the basic equations and differential geometry to stimulate further reading. Should include some cross references to some of the more difficult proofs.

Great to read alongside Daniel Flesich's book on vectors and tensors, especially on the connection coefficients and the curvature tensor.

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Byboaswhipon 17 February 2014

The booked delivers what it promised and something that I've always wanted to learn about, relativity theory was broken down and digested in very easily understood parts ... if you have some prior grounding the concepts of calculates and vectors. If you don't have this grounding you can still get through the material but probably have a bit more work to do.

Great book that doesn't waffle just helps one understand.

Great book that doesn't waffle just helps one understand.

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