Tabla de Contenidos: “…The roots of science -- An ancient theorem and a modern question -- Kinds of number in the physical world -- Magical complex numbers -- Geometry of logarithms, powers, and roots -- Real-number calculus -- Complex-number calculus -- Riemann surfaces and complex mappings -- Fourier decomposition and hyperfunctions -- Surfaces -- Hypercomplex numbers -- Manifolds of n dimensions -- Symmetry groups -- Calculus on manifolds -- Fibre bundles and gauge connections -- The ladder of infinity -- Spacetime -- Minkowskian geometry -- The classical fields of Maxwell and Einstein -- Lagrangians and Hamiltonians -- The quantum particle -- Quantum algebra, geometry, and spin -- The entangled quantum world -- Dirac's electron and antiparticles -- The standard model of particle physics -- Quantum field theory -- The Big Bang and its thermodynamic legacy -- Speculative theories of the early universe -- The measurement paradox -- Gravity's role in quantum state reduction -- Supersymmetry, supra-dimensionality, and strings -- Einstein's narrower path: loop variables -- More radical perspectives: twistor theory -- Where lies the road to reality?…”

Tabla de Contenidos: “…Ch. 1: Mathematical Modeling in Biology -- Ch. 2: How to Construct a Model -- Ch. 3: Deriving Classic Models in Ecology and Evolutionary Biology -- Primer 1: Functions and Approximations -- Ch. 4: Numerical and Graphical Techniques-Developing a Feeling for Your Model -- Ch. 5: Equilibria and Stability Analyses-One-Variable Models -- Ch. 6: General Solutions and Transformations-One-Variable Models -- Primer 2: Linear Algebra -- Ch. 7: Equilibria and Stability Analyses-Linear Models with Multiple Variables -- Ch. 8: Equilibria and Stability Analyses-Nonlinear Models with Multiple Variables -- Ch. 9: General Solutions and Transformations-Models with Multiple Variables -- Ch. 10: Dynamics of Class-Structured Populations -- Ch. 11: Techniques for Analyzing Models with Periodic Behavior -- Ch. 12: Evolutionary Invasion Analysis -- Primer 3: Probability Theory -- Ch. 13: Probabilistic Models -- Ch. 14: Analyzing Discrete Stochastic Models -- Ch. 15: Analyzing Continuous Stochastic Models-Diffusion in Time and Space -- Appendix 1: Commonly Used Mathematical Rules -- Appendix 2: Some Important Rules from Calculus -- Appendix 3: The Perron-Frobenius Theorem -- Appendix 4: Finding Maxima and Minima of Functions -- Appendix 5: Moment-Generating Functions -- Index of Definitions, Recipes, and Rules -- General Index.…”
Contributor biographical information
Publisher description
Table of contents only