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Algorithms and complexity in mathematics, epistemology, and science : proceedings of 2015 and 2016 ACMES Conferences

Author: Nicolas Fillion; Robert M Corless; Ilias Kotsireas
Publisher: New York, NY : Springer, [2019]
Series: Fields Institute communications, v. 82.
Edition/Format:   eBook : Document : Conference publication : EnglishView all editions and formats
Summary:
ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from  Read more...
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Genre/Form: Electronic books
Conference papers and proceedings
Congresses
Additional Physical Format: Printed edition:
Printed edition:
Material Type: Conference publication, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Nicolas Fillion; Robert M Corless; Ilias Kotsireas
ISBN: 9781493990511 1493990519 1493990500 9781493990504 9781493990528 1493990527
OCLC Number: 1084756988
Description: 1 online resource : illustrations
Contents: 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 View2.1 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 Pendulum5.4 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 4.5 The Grounding of Physics in Observation and Experiment4.6 Is the Complexity of Grounding Different in Physics than Math?; 4.7 Claims to Universality; 4.8 Argumentation in Physics; 4.8.1 Deduction from the Absolute Foundations; 4.8.2 Argumentation in Elementary Physics; 4.9 Reasoning About Things That Are Partially Understood; 5 An Example Word Problem; 6 Historical Context and Related Work; 6.1 Before Hilbert; 6.2 Hilbert's Sixth Problem and the Axiomatization of Physics; 6.3 Philosophy; 6.3.1 Is Pavel a Bad Reinvention of Logical Positivism?; 6.4 Artificial Intelligence 6.4.1 Knowledge-Based Physical Reasoning6.4.2 AI Programs That Induce Scientific Theories; 6.4.3 Bayesian Inference of Structure; 6.4.4 Domingos and the Master Algorithm; 7 Potential Philosophical Impact; 8 Conclusions: Whither Pavel?; References; An Applied/Computational Mathematician's View of Uncertainty Quantification for Complex Systems; 1 Introduction; 2 Uncertainty Quantification (UQ); 3 Types of Input Noises; 4 Discretization of Stochastic Processes; 5 Approximation of Solutions of PDEs with Random Inputs; 6 Quo Vadis Uncertainty Quantification?; References
Series Title: Fields Institute communications, v. 82.
Responsibility: editors, Ncolas Fillion, Robert M. Corless and Ilias S. Kotsireas.

Abstract:

ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in  Read more...

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