Algorithms and Complexity in Mathematics, Epistemology, and Science - Info and Reading Options

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Intro -- Preface -- Contents -- Contributors -- Ethics and the Continuum Hypothesis -- 1 The Continuum Hypothesis -- 2 Pure Versus Applied Mathematics -- 3 Ethics for Mathematicians -- 4 Mathematical Methods -- 5 The Moral -- 6 Facing Problems -- 7 How Does the Refutation of CH Work? -- References -- Further Reading -- How to Generate All Possible Rational Wilf-Zeilberger Pairs? -- 1 Introduction -- 2 Residue Criteria -- 3 Structure Theorems -- 3.1 The Differential Case -- 3.2 The (q)-Shift Case -- 3.3 The Mixed Case -- 4 Conclusion -- References -- Backward Error Analysis for Perturbation Methods -- 1 Introduction -- 2 The Basic Method from the BEA Point of View -- 2.1 Regular Perturbation BEA-Style -- 2.2 Conditioning and Sensitivity -- 3 Algebraic Equations -- 3.1 Regular Perturbation -- 3.1.1 Scalar Equations -- 3.1.2 Simple Computer Algebra Solution -- 3.1.3 Systems of Algebraic Equations -- 3.1.4 Solving Algebraic Systems by the Davidenko Equation -- 3.2 Puiseux Series -- 3.3 Singular Perturbation -- 3.4 Optimal Backward Error -- 3.5 A Hyperasymptotic Example -- 4 Divergent Asymptotic Series -- 5 Initial-Value Problems -- 5.1 Duffing's Equation -- 5.1.1 Regular Expansion -- 5.1.2 Lindstedt's Method -- 5.2 Morrison's Counterexample -- 5.3 The Lengthening Pendulum -- 5.4 Optimal Backward Error Again -- 5.5 Vanishing Lag Delay DE -- 6 Concluding Remarks -- References -- Proof Verification Technology and Elementary Physics -- 1 Memories of Jonathan Borwein -- 2 Mathematical Proof Verification Software -- 3 Formal Proof and Proof Technology in Mathematics -- 3.1 What Hasn't Been Done for Math -- 3.2 Word Problems -- 4 Physics -- 4.1 The Potential Value of This Undertaking -- 4.2 The Bayesian Formulation -- 4.3 Straw Man: The Tee-Shirt Model of Pavel -- 4.4 The Equations Are More Complicated than Their Tee-Shirt Version

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