Oshkosh Public Library

The mathematical universe, from Pythagoras to Planck, Joel L. Schiff

eng

Includes bibliographical references and index

illustrations

index present

non fiction

The mathematical universe

bibliography

1244452267

Joel L. Schiff

Springer-Praxis books in popular science

from Pythagoras to Planck

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 x2 + 1 = 0 -- The 'i'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 -- Exponential decay -- The dating game -- Empowering laws -- 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 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 -- : 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: q2 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