A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, Peter

[notFritzArgelander]

There seems to be more than one member interested in this book. I've acquired it and it looks to be readily accessible as the TOC shows. I've copied more detail from the mathematical portions to give a flavor of what's required. The mathematics in the text is augmented by links to online help notes so as to make it more efficient to get to the physics.

1 FOUNDATION MATHEMATICS 1.1 Introduction 1.2 Definitions and symbols 1.3 Units and constants 1.4 Expressions, equations and functions 1.5 Getting a feel for functions 1.5.1 Graphs of simple functions 1.6 Simplifying and rearranging equations and expressions 1.7 Trigonometric functions 1.7.1 Basic trigonometric functions 1.7.2 Radians 1.7.3 Trigonometric identities 1.8 Powers and logarithms 1.8.1 Powers 1.8.2 Logarithms 1.8.3 The constant e and natural logarithms 1.8.4 The exponential function 1.9 Coordinate systems 1.9.1 Cartesian coordinates 1.9.2 Plane polar coordinates 1.9.3 Spherical coordinates 1.10 Calculus 1.10.1 Differential calculus 1.10.2 Integral calculus 1.10.3 Taylor series 1.11 Parametric equations 1.12 Matrices 1.12.1 Matrix multiplication 1.12.2 Identity matrix 1.12.3 Inverse matrix 1.12.4 Symmetric matrices 1.12.5 Diagonal matrices 1.13 Introducing vectors 1.13.1 Vector fields 1.13.2 Gradient of a scalar field 1.13.3 Divergence of a vector field 1.14 Euclidean geometry 1.14.1 The Euclidean metric 1.15 Index notation

2 NEWTONIAN MECHANICS
3 SPECIAL RELATIVITY

4 INTRODUCING THE MANIFOLD 4.1 Introduction 4.2 Riemannian manifolds and the metric 4.3 Surface of a sphere

5 SCALARS, VECTORS, ONE-FORMS AND TENSORS 5.1 Introduction 5.2 Scalars 5.3 Contravariant vectors and one-forms 5.3.1 An abstraction 5.3.2 An infinitesimal displacement 5.3.3 Contravariant vector coordinate transformations 5.3.4 One-form coordinate transformations 5.3.5 More detail - contravariant vectors 5.3.6 More detail - one-forms 5.3.7 More abstraction 5.4 Tensors 5.4.1 Tensor transformation 5.4.2 The rules of tensor algebra

6 MORE ON CURVATURE 6.1 Introduction 6.2 Connection coefficients 6.3 Covariant differentiation 6.4 Parallel transport of vectors 6.5 Geodesics 6.6 The Riemann curvature tensor 6.7 The Ricci tensor and Ricci scalar 6.7.1 The Ricci tensor 6.7.2 The Ricci scalar

7 GENERAL RELATIVITY
8 THE NEWTONIAN LIMIT
9 THE SCHWARZSCHILD METRIC
10 SCHWARZSCHILD BLACK HOLES
11 COSMOLOGY
12 GRAVITATIONAL WAVES

APPENDIX: The Riemann curvature tensor

Collier, Peter. A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity (p. 7-11). Incomprehensible Books. Kindle Edition.

Anyway the reason for starting this thread is so that if anyone who wants to read the book can post comments and questions here.

[Gmetric]

I have this book, had it for a while now. It’s really quite accessible.

[notFritzArgelander]

I have this book, had it for a while now. It’s really quite accessible.

I just picked it up yesterday. I don't discount the possibility that some folks might need pointers. I'm willing to help in that event. Perhaps you would too?

[Gmetric]

I have this book, had it for a while now. It’s really quite accessible.

I just picked it up yesterday. I don't discount the possibility that some folks might need pointers. I'm willing to help in that event. Perhaps you would too?

I’m not sure that I could be of much help besides, I might have a few questions and need a few pointer myself. … But, if by asking for guidance it helps others, then I’d be glad to be of some service.

[turboscrew]

Interesting. I think I'll order that too.

[Gmetric]

I wanted to delete this post, but it seems that I couldn't, so I've edited it thus.

[notFritzArgelander]

I wanted to delete this post, but it seems that I couldn't, so I've edited it thus.

And so another mystery of the universe is born....

[turboscrew]

I wanted to delete this post, but it seems that I couldn't, so I've edited it thus.

"What's written here is what you just read."

[chasmanian]

thank you nFA.

[turboscrew]

Ordered the book, an another, which, I think, has a nick name "black hole".
https://www.adlibris.com/fi/kirja/gravi ... 0691177793

[notFritzArgelander]

Ordered the book, an another, which, I think, has a nick name "black hole".
https://www.adlibris.com/fi/kirja/gravi ... 0691177793

I think that the explanatory "boxes" embedded in the text do a wonderful job of smoothing the path.