Science, Seti and Mathematics by Carl L. Devito

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Science, Seti and Mathematics by Carl L. Devito

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Science, Seti and Mathematics Contents

Preface viii
Chapter 1. Where Are We? 1
Remark: Natural Numbers, Sets, and
Subsets 5
Chapter 2. Naïve Questions 7
Remark: Infinite Sets, Correspondences,
Unions, and Intersections 15
Chapter 3. Are We Special? 17
Remark: Systems of Enumeration, Powers
of Ten, Positional Notation, and Casting
Out Nines 23
Chapter 4. Stories—Part One 26
Remark: Human Perception of Motion,
and Mathematical Description of
Physical Fields 32
Chapter 5. Measuring Our Solar Neighborhood 36
Remark: Euclid’s Fifth Postulate,
Non-Euclidean Geometries, and How
Choice of Geometry Affects Physics 43
Chapter 6. The Scotsman 47
Remark: The Fundamental Wave Equation,
Partial Differential Equations, Equations of
Mathematical Physics, and the Function
Concept 51
Chapter 7. The Birth of SETI 54
Remark: Two Functions and Why They
Are Special, the Power of Trigonometry,
and Fourier Series 60
Chapter 8. The Conference at Green Bank 64
Remark: The Drake Equation, Drake’s
Postcard, and Prime Numbers 69
Chapter 9. Stories—Part Two 73
Remark: Development of Calculus, Models
for Time, Differential Calculus and the
Science of Motion, and Derivatives and
Partial Derivatives 84
Chapter 10. Talking to E.T. 89
Remark: Continuity of Space, Area, Integral
Calculus and the Founding of Carthage,
Line Integrals and the CAT Scan 94
Chapter 11. Languages 99
Remark: Real Numbers as the Basis for
Calculus, Complex Numbers and the
Calculus of Complex Functions, Complex
Integration, and Whether Mathematical
Objects Are Real 109
Chapter 12. Paradoxes 113
Remark: Group Theory in Algebra
and Geometry 115
Chapter 13. The Universal Science 119
Remark: Atomic Weights and the
Avogadro Number 127
Chapter 14. The Special Theory of Relativity 129
Remark: Space-Time, Higher Dimensional
Spaces, and Hilbert Space 138
Chapter 15. The General Theory of Relativity 143
Remark: The Geometry of Minkowski’s
4-World, and Why Points Are Zero Dimensional 149
Chapter 16. The University of Colorado Study 152
Remark: Space as Multi-Dimensional, the
Dimension of Sets, and General Topology
and Functional Analysis 160
Chapter 17. Surprise! 163
Remark: Fibonacci Numbers and the
Golden Ratio, Logarithms, Exponentials,
and the Number e, Connections to the
Complex Numbers 165
Chapter 18. Epilogue 169
Remark: Ramanujan 176
Appendix I. Infinite Sets 177
Appendix II. Mars 182
Appendix III. The DeVito-Oehrle Language 185
Bibliography 198
Index 203

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