The book is very well bound for a paperback and has good paper within its covers. The font is well - sized for those of us that need spectacles to read.
* The construction pre-degree, undergraduate, post graduate?
As before, no book can cover every bit of the topic its written to explain, but this book uses a familiar mathematical background of a 'level and undergraduate degree math and builds securely upon this. It will help you greatly if you can handle matrices and differential equations with both partial and standard a' level or engineering / Math degree level differential equations and Vector Calculus. The Math degree student may have an easier time with parts of this book. This topic method i am trying to comprehend in 'layers' and not the whole concepts all at the same time. So i will return to this book after other in depth studies.
* Its construction
The book is divided into two main parts, the preliminary explanation of the math's required to help later on, and the theory underpinning what it is describing mathematically. The author has spread of both new and familiar together designed to strengthen your overall knowledge. These preliminary bits stretch from Chapter one to chapter 5. Personally, I found the tensors introductory (chapter 5) and spread through the book just is a bit too brief to be used as it is on its own, and may need more work elsewhere or its my weakness at this time? See the latter part of this review for books that helped my comprehension of Tensors, for example. I have now a working knowledge though just not absolutely rock - hard!
* Example of the level of mathematical working
The motion of fluids and particles is clearly explained and the preliminary stuff is up to chapter 5 this is linked to further examinations. For example, it applies 4 x 4 matrices in symbolic format. In particular, i am fascinated with the 4 x 4 symbolic matrix showing an strong, symmetrical construction for the properties of Electromagnetism on page 23.
* What the mathematics is applied to explain
For example subjects with a strong mathematical content than are flown through - in a positive manner - as follows; Curvature, Space time of the forth dimension, Riemann Tensors, Hyperbolic Minkowski space, Einstein's Equation, The 'Schwarzschild Radius' and its connection to black holes and more, Rotation of the perihelion of the planet Mercury an other stuff that's interesting to read and comprehend at this level. The later topics are a lot briefer and its curtailed in both descriptively and mathematically. The form of these equations take is an art in its self, and you need an understanding of the equation's and what its related too and what its driving to explain.
The book has a lovely mix of simplified math techniques strongly built upon previous levels of understanding. Its fun, but tough in places to read! This book has been a pleasure to tackle and I have learned a good amount of new understanding and linking to math skills. The SUMS series of books have proved again a great way to tackle topics in a well chosen way, carefully explained and designed. I humbly recommend that your read it start through to the end as its broadly resistant to jumping over topics.
* Update: If you in the market for a glorious in - a - minds - eye book of both General and Special relativity, i humbly recommend the following
Einstein's Universe: The Layperson's Guide Paperback - 24 Feb 2005 by Nigel Calder
* You may find these volumes of help too
A Student's Guide to Vectors and Tensors Paperback - 22 Sep 2011 by Daniel Fleisch
A Student's Guide to Lagrangian and Hamiltonian Paperback - 21 Nov 2013 by Patrick Hamill
If, however you study, you feel this area needs more help than this book is giving you, I have found it helpful to access a well - known video sharing website, and enter into its search engine, say 'Tensors', or 'General Relativity'. This combined help may be just enough to explain it to you in terms you can comprehend. Its a great lift to have a streamed videos AND you need to read the linked books too at the same time. This is based on in - depth studies from Dec '14 to May '15, covering Tensor Analysis, and General Relativity too. I feel an understanding for these topics and its been six months of almost daily studying to reach this state. I admit that its been hard at times but definitely fun to try.
Its a real pleasure to see a clearly laid out undergraduate-oientated introduction to GR hich is predominantly aimed at those with a mathematical background. Consequently it is uncluttered and easy to follow.Most importantly the guidance notes on the solutions are a dream especially for students self-studying who do not have access to a tutor.
I can see myself using this and referring to it frequently.Definitely an instant favourite. A great start point for further and higher studies in GR and theoretical/mathematical physics.