عنوان

Algorithms and complexity in mathematics, epistemology, and science :

1493990500

1493990519

1493990527

9781493990504

9781493990511

9781493990528

9781493990504

Algorithms and complexity in mathematics, epistemology, and science :

[Book]

proceedings of 2015 and 2016 ACMES Conferences /

editors, Ncolas Fillion, Robert M. Corless and Ilias S. Kotsireas.

New York, NY :

Springer,

[2019]

1 online resource :

illustrations

Fields Institute communications ;

volume 82

Includes bibliographical references.

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

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

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

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

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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 theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.

Springer Nature

com.springer.onix.9781493990511

9781493990504

9781493990528

Algorithms, Congresses.

Complexity (Philosophy), Congresses.

Mathematics, Congresses.

Science-- Mathematics, Congresses.

Technological complexity, Congresses.

Algorithms.

Complexity (Philosophy)

MATHEMATICS-- Numerical Analysis.

Mathematics.

Science-- Mathematics.

Technological complexity.

MAT-- 041000

PBKS

PBKS

Corless, Robert M.

Fillion, Nicolas,1981-

Kotsireas, Ilias

ACMES Conference(2015 :, Western University)

ACMES Conference(2016 :, Western University)

20200823035123.0

pn

[Book]

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