The Mathematical Universe
Springer International Publishing (Verlag)
978-3-030-50648-3 (ISBN)
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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.
lt;br />Dedication
Acknowledgements
About the Author
Prologue
Preface
1. The Mystery of Mathematics
Let us be reasonable
All set
Where is Mathematics?
Fine tuning
A blast from the past: Euclid's geometry
Taking the Fifth further
Pi in the sky
Off to Monte Carlo
Smashed pi
The divine Isoperimetric Inequality
2. From Here to Infinity
Zeno's Paradox
Summing Up
In what Universe is this true?
The power of e
Fast money
What is normal?
Multiplying ad infinitum
3. Imaginary Worlds
The Strange Case of
The ''s have it
The God-like Euler identity
Even more imaginaries - quaternions
But wait, there is more - octonians
The world's hardest problem - the Riemann Hypothesis
4. Random Universe
Going steady
Brownian Motion
Life is a gamble
The dating game
The world of entropy - order to chaos
Information entropy
5. Order from Chaos
Cellular Automata
Life as a game
Infectious disease model - SIR
Mimicking Darwin
One-dimensional CA
The whole is greater than the sum of its parts
Bees and termites
... And ants
Bacteria count
A hive of Mathematics: Fibonacci
Dynamical systems
Messrs. Fatou, Julia and Mandelbrot
The fractal Universe
6. Mathematics in Space
Faster than a speeding bullet
Down to Earth
Heavens above
Light-years
The great recession
The Universe is flat
Measuring the invisible: Black holes
A galaxy far, far away
7. The Unreality of Reality
Miniature Universe
Quantum world
Infinite space
Qubits
It is all relative, Albert
That equation
What time is it anyway?
Matters of gravity
Time in motion
Radiation
Symmetry and groups
8. The Unknowable Universe
Gödel incompleteness
Halting problem
EMX
Where is it, Dr. Heisenberg?
Summing up
Appendix I: Being Reasonable
Appendix II: Hyperbolic Geometry and Minkowski Spacetime
Appendix III: The Uncountable Real Numbers
Appendix IV: c 2 = c: Square and Line have Same Cardinality
Appendix V: Geometric Series
Appendix VI: Cesàro Sums
Appendix VII: Rotating a Vector via a Quaternion
Appendix VIII: Quaternions q 2 = -1
Appendix IX: Riemann Zeta Function
Appendix X: Random Walk Code
Appendix XI: Age of the Solar System
Appendix XII: Chelyabinsk Meteoroid
Appendix XIII: Logic Gates
Appendix XIV: Galaxy Distance via Cepheids
Appendix XV: Time Dilation
Appendix XVI: Expansion of the Universe
Bibliography
Index
| Erscheint lt. Verlag | 10.9.2020 |
|---|---|
| Reihe/Serie | Popular Science | Springer Praxis Books |
| Zusatzinfo | X, 280 p. 123 illus., 61 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 168 x 240 mm |
| Themenwelt | Sachbuch/Ratgeber ► Natur / Technik ► Naturwissenschaft |
| Mathematik / Informatik ► Mathematik | |
| Naturwissenschaften ► Physik / Astronomie ► Relativitätstheorie | |
| Schlagworte | basic math for physics • beginner quantum mechanics • beginner theory of relativity • ceullular automata • Euclid's Gemoetry • explain dynamical systems • Fibonacci • golden ratio • notion of infinity |
| ISBN-10 | 3-030-50648-7 / 3030506487 |
| ISBN-13 | 978-3-030-50648-3 / 9783030506483 |
| Zustand | Neuware |
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