A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, Peter
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A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, Peter
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.
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.
Scopes: Refs: Orion ST80, SV 80EDA f7, TS 102ED f11 Newts: AWB 130mm, f5, Z12 f5; Cats: VMC110L, Intes MK66,VMC200L f9.75 EPs: KK Fujiyama Orthoscopics, 2x Vixen NPLs (40-6mm) and BCOs, Baader Mark IV zooms, TV Panoptics, Delos, Plossl 32-8mm. Mixed brand Masuyama/Astroplans Binoculars: Nikon Aculon 10x50, Celestron 15x70, Baader Maxbright. Mounts: Star Seeker IV, Vixen Porta II, Celestron CG5
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Re: A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, P
I have this book, had it for a while now. It’s really quite accessible.
Arry (Bortle 7 area)
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Re: A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, P
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?
Scopes: Refs: Orion ST80, SV 80EDA f7, TS 102ED f11 Newts: AWB 130mm, f5, Z12 f5; Cats: VMC110L, Intes MK66,VMC200L f9.75 EPs: KK Fujiyama Orthoscopics, 2x Vixen NPLs (40-6mm) and BCOs, Baader Mark IV zooms, TV Panoptics, Delos, Plossl 32-8mm. Mixed brand Masuyama/Astroplans Binoculars: Nikon Aculon 10x50, Celestron 15x70, Baader Maxbright. Mounts: Star Seeker IV, Vixen Porta II, Celestron CG5
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Re: A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, P
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.notFritzArgelander wrote: ↑Fri Jul 16, 2021 2:42 amI 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?
Arry (Bortle 7 area)
Telescopes: Sky-Watcher ED72II, Sky-Watcher PDS130, Sky-Explorer SN F4 200mm astrograph and Vixen F11.1 90mm
Cameras: Nikon D5300 modded, Canon Kiss X8i modded, Cooled Canon kiss X4 modded, Atik 16IC and 383 colour, ASI120MC, QHY5LII
Mount: Sky-Explorer HEQ 5 belt driven
Telescopes: Sky-Watcher ED72II, Sky-Watcher PDS130, Sky-Explorer SN F4 200mm astrograph and Vixen F11.1 90mm
Cameras: Nikon D5300 modded, Canon Kiss X8i modded, Cooled Canon kiss X4 modded, Atik 16IC and 383 colour, ASI120MC, QHY5LII
Mount: Sky-Explorer HEQ 5 belt driven
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Re: A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, P
Interesting. I think I'll order that too.
- Juha
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Senior Embedded SW Designer
Telescope: OrionOptics XV12, Mount: CEM120, Tri-pier 360 and alternative dobson mount.
Grab 'n go: Omegon AC 102/660 on AZ-3 mount
Eyepieces: 26 mm Omegon SWAN 70°, 15 mm TV Plössl, 12.5 mm Baader Morpheus, 10 mm TV Delos, 6 mm Baader Classic Ortho, 5 mm TV DeLite, 4 mm and 3 mm TV Radians
Cameras: ZWO ASI 294MM Pro, Omegon veLOX 178C
OAG: TS-Optics TSOAG09, ZWO EFW 7 x 36 mm, ZWO filter sets: LRGB and Ha/OIII/SII
Explore Scientific HR 2" coma corrector, Meade x3 1.25" Barlow, TV PowerMate 4x 2"
Some filters (#80A, ND-96, ND-09, Astronomik UHC)
Laptop: Acer Enduro Urban N3 semi-rugged, Windows 11
LAT 61° 28' 10.9" N, Bortle 5
I don't suffer from insanity. I'm enjoying every minute of it.
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Re: A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, P
I wanted to delete this post, but it seems that I couldn't, so I've edited it thus.
Arry (Bortle 7 area)
Telescopes: Sky-Watcher ED72II, Sky-Watcher PDS130, Sky-Explorer SN F4 200mm astrograph and Vixen F11.1 90mm
Cameras: Nikon D5300 modded, Canon Kiss X8i modded, Cooled Canon kiss X4 modded, Atik 16IC and 383 colour, ASI120MC, QHY5LII
Mount: Sky-Explorer HEQ 5 belt driven
Telescopes: Sky-Watcher ED72II, Sky-Watcher PDS130, Sky-Explorer SN F4 200mm astrograph and Vixen F11.1 90mm
Cameras: Nikon D5300 modded, Canon Kiss X8i modded, Cooled Canon kiss X4 modded, Atik 16IC and 383 colour, ASI120MC, QHY5LII
Mount: Sky-Explorer HEQ 5 belt driven
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Re: A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, P
And so another mystery of the universe is born....
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Re: A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, P
"What's written here is what you just read."
- Juha
Senior Embedded SW Designer
Telescope: OrionOptics XV12, Mount: CEM120, Tri-pier 360 and alternative dobson mount.
Grab 'n go: Omegon AC 102/660 on AZ-3 mount
Eyepieces: 26 mm Omegon SWAN 70°, 15 mm TV Plössl, 12.5 mm Baader Morpheus, 10 mm TV Delos, 6 mm Baader Classic Ortho, 5 mm TV DeLite, 4 mm and 3 mm TV Radians
Cameras: ZWO ASI 294MM Pro, Omegon veLOX 178C
OAG: TS-Optics TSOAG09, ZWO EFW 7 x 36 mm, ZWO filter sets: LRGB and Ha/OIII/SII
Explore Scientific HR 2" coma corrector, Meade x3 1.25" Barlow, TV PowerMate 4x 2"
Some filters (#80A, ND-96, ND-09, Astronomik UHC)
Laptop: Acer Enduro Urban N3 semi-rugged, Windows 11
LAT 61° 28' 10.9" N, Bortle 5
I don't suffer from insanity. I'm enjoying every minute of it.
Senior Embedded SW Designer
Telescope: OrionOptics XV12, Mount: CEM120, Tri-pier 360 and alternative dobson mount.
Grab 'n go: Omegon AC 102/660 on AZ-3 mount
Eyepieces: 26 mm Omegon SWAN 70°, 15 mm TV Plössl, 12.5 mm Baader Morpheus, 10 mm TV Delos, 6 mm Baader Classic Ortho, 5 mm TV DeLite, 4 mm and 3 mm TV Radians
Cameras: ZWO ASI 294MM Pro, Omegon veLOX 178C
OAG: TS-Optics TSOAG09, ZWO EFW 7 x 36 mm, ZWO filter sets: LRGB and Ha/OIII/SII
Explore Scientific HR 2" coma corrector, Meade x3 1.25" Barlow, TV PowerMate 4x 2"
Some filters (#80A, ND-96, ND-09, Astronomik UHC)
Laptop: Acer Enduro Urban N3 semi-rugged, Windows 11
LAT 61° 28' 10.9" N, Bortle 5
I don't suffer from insanity. I'm enjoying every minute of it.
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Re: A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, P
Ordered the book, an another, which, I think, has a nick name "black hole".
https://www.adlibris.com/fi/kirja/gravi ... 0691177793
https://www.adlibris.com/fi/kirja/gravi ... 0691177793
- Juha
Senior Embedded SW Designer
Telescope: OrionOptics XV12, Mount: CEM120, Tri-pier 360 and alternative dobson mount.
Grab 'n go: Omegon AC 102/660 on AZ-3 mount
Eyepieces: 26 mm Omegon SWAN 70°, 15 mm TV Plössl, 12.5 mm Baader Morpheus, 10 mm TV Delos, 6 mm Baader Classic Ortho, 5 mm TV DeLite, 4 mm and 3 mm TV Radians
Cameras: ZWO ASI 294MM Pro, Omegon veLOX 178C
OAG: TS-Optics TSOAG09, ZWO EFW 7 x 36 mm, ZWO filter sets: LRGB and Ha/OIII/SII
Explore Scientific HR 2" coma corrector, Meade x3 1.25" Barlow, TV PowerMate 4x 2"
Some filters (#80A, ND-96, ND-09, Astronomik UHC)
Laptop: Acer Enduro Urban N3 semi-rugged, Windows 11
LAT 61° 28' 10.9" N, Bortle 5
I don't suffer from insanity. I'm enjoying every minute of it.
Senior Embedded SW Designer
Telescope: OrionOptics XV12, Mount: CEM120, Tri-pier 360 and alternative dobson mount.
Grab 'n go: Omegon AC 102/660 on AZ-3 mount
Eyepieces: 26 mm Omegon SWAN 70°, 15 mm TV Plössl, 12.5 mm Baader Morpheus, 10 mm TV Delos, 6 mm Baader Classic Ortho, 5 mm TV DeLite, 4 mm and 3 mm TV Radians
Cameras: ZWO ASI 294MM Pro, Omegon veLOX 178C
OAG: TS-Optics TSOAG09, ZWO EFW 7 x 36 mm, ZWO filter sets: LRGB and Ha/OIII/SII
Explore Scientific HR 2" coma corrector, Meade x3 1.25" Barlow, TV PowerMate 4x 2"
Some filters (#80A, ND-96, ND-09, Astronomik UHC)
Laptop: Acer Enduro Urban N3 semi-rugged, Windows 11
LAT 61° 28' 10.9" N, Bortle 5
I don't suffer from insanity. I'm enjoying every minute of it.
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Re: A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity Collier, P
I think that the explanatory "boxes" embedded in the text do a wonderful job of smoothing the path.turboscrew wrote: ↑Wed Jul 21, 2021 8:53 pm Ordered the book, an another, which, I think, has a nick name "black hole".
https://www.adlibris.com/fi/kirja/gravi ... 0691177793
Scopes: Refs: Orion ST80, SV 80EDA f7, TS 102ED f11 Newts: AWB 130mm, f5, Z12 f5; Cats: VMC110L, Intes MK66,VMC200L f9.75 EPs: KK Fujiyama Orthoscopics, 2x Vixen NPLs (40-6mm) and BCOs, Baader Mark IV zooms, TV Panoptics, Delos, Plossl 32-8mm. Mixed brand Masuyama/Astroplans Binoculars: Nikon Aculon 10x50, Celestron 15x70, Baader Maxbright. Mounts: Star Seeker IV, Vixen Porta II, Celestron CG5
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