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E-raamat: Mathematical Universe: From Pythagoras to Planck

  • Formaat: EPUB+DRM
  • Sari: Springer Praxis Books
  • Ilmumisaeg: 18-Nov-2020
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030506490
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Mathematical Universe: From Pythagoras to PlanckSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Springer Praxis Books
  • Ilmumisaeg: 18-Nov-2020
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030506490
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I first had a quick look, then I started reading it. I couldn't stop. 
-Gerard 't Hooft (Nobel Prize, in Physics 1999)

This is a book about the mathematical nature of our Universe.
 
Armed with no more than basic high school mathematics, Dr. Joel L. Schiff takes you on a foray through some of the most intriguing aspects of the world around us. Along the way, you will visit the bizarre world of subatomic particles, honey bees and ants, galaxies, black holes, infinity, and more. Included are such goodies as measuring the speed of light with your microwave oven, determining the size of the Earth with a stick in the ground and the age of the Solar System from meteorites, understanding how the Theory of Relativity makes your everyday GPS system possible, and so much more.
 
These topics are easily accessible to anyone who has ever brushed up against the Pythagorean Theorem and the symbol p, with the lightest dusting of algebra. Through this book, science-curious readers will come to appreciate the patterns, seeming contradictions, and extraordinary mathematical beauty of our Universe.

      
Dedication viii
Acknowledgements x
About the Author xi
Foreword xii
Prologue xiv
Preface xvii
1 The Mystery of Mathematics
1(38)
Let us be reasonable
3(4)
All set
7(2)
Where is Mathematics?
9(3)
Fine tuning
12(5)
A blast from the past: Euclid's geometry
17(3)
Taking the Fifth further
20(8)
Pi in the sky
28(2)
Off to Monte Carlo
30(2)
Smashed pi
32(3)
The divine Isoperimetric Inequality
35(4)
2 From Here to Infinity
39(37)
Zeno's Paradox
41(11)
Summing up
52(8)
In what Universe is this true?
60(7)
The power of e
67(4)
Fast money
71(1)
What is normal?
72(2)
Multiplying ad infinitum
74(2)
3 Imaginary Worlds
76(23)
The Strange Case of x2 + 1 = 0
77(3)
The 'i's have it
80(2)
The God-like Euler identity
82(4)
Even more imaginaries -- quaternions
86(3)
But wait, there is more -- octonians
89(2)
The world's hardest problem -- the Riemann Hypothesis
91(8)
4 Random Universe
99(21)
Going steady
99(4)
Brownian Motion
103(1)
Life is a gamble
103(2)
Exponential decay
105(1)
The dating game
106(3)
Empowering laws
109(4)
The world of entropy -- order to chaos
113(3)
Information entropy
116(4)
5 Order from Chaos
120(48)
Cellular Automata
120(7)
Life as a game
127(4)
Infectious disease model -- SIR
131(1)
Mimicking Darwin
132(5)
One-dimensional CA
137(5)
The whole is greater than sum of its parts
142(1)
Bees and termites
143(1)
... And ants
144(3)
Bacteria count
147(2)
A hive of Mathematics: Fibonacci
149(3)
Dynamical systems
152(5)
Messrs, Fatou, Julia, and Mandelbrot
157(5)
The fractal Universe
162(6)
6 Mathematics in Space
168(26)
Faster than a speeding bullet
168(5)
Down to Earth
173(2)
Heavens above
175(3)
Light-years
178(2)
The great recession
180(5)
The Universe is flat
185(3)
Measuring the invisible: Black holes
188(4)
A galaxy far, far, away
192(2)
7 The Unreality of Reality
194(51)
Miniature Universe
195(4)
Quantum world
199(7)
Infinite space
206(3)
Qubits
209(4)
It is all relative, Albert
213(4)
That equation
217(1)
What time is it anyway?
218(1)
Matters of gravity
219(9)
Time in motion
228(6)
Radiation
234(2)
Symmetry and groups
236(9)
8 The Unknowable Universe
245(8)
Godel incompleteness
245(1)
Halting problem
246(1)
EMX
247(1)
Where is it, Dr. Heisenberg?
248(2)
Summing up
250(3)
Appendix I Being Reasonable 253(3)
Appendix II Hyperbolic Geometry and Minkowski Spacetime 256(3)
Appendix III The Uncountable Real Numbers 259(2)
Appendix IV c2 = c: Square and Line have Same Cardinality 261(2)
Appendix V Geometric Series 263(2)
Appendix VI Cesaro Sums 265(1)
Appendix VII Rotating a Vector via a Quaternion 266(3)
Appendix VIII Quaternions q2 = --1 269(1)
Appendix IX Riemann Zeta Function 270(4)
Appendix X Random Walk Code 274(2)
Appendix XI Age of the Solar System 276(3)
Appendix XII Chelyabinsk Meteoroid 279(1)
Appendix XIII Logic Gates 280(3)
Appendix XIV Galaxy Distance via Cepheids 283(3)
Appendix XV Time Dilation 286(3)
Appendix XVI Expansion of the Universe 289(2)
Bibliography 291(3)
Index 294
Joel Schiff  has a PhD in Mathematics from the University of California Los Angeles and spent his academic career at the University of Auckland, New Zealand. He is the author of seven other books, four of which are mathematical in nature. He and his wife discovered the asteroid 12926 Brianmason from their own observatory. Schiff was also the publisher of the international quarterly, Meteorite, for many years.  
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