Overview
- Sets error calculus on rigorous mathematical foundations
- Contains numerous worked out examples and exercices
- Introduces the reader to recent developments and open questions in the field
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About this book
The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician.
Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader’s intuition.By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation.
Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.
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Table of contents (19 chapters)
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Front Matter
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A la Gauss Calculations
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Front Matter
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Probabilistic and Functional Models
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Front Matter
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The Subtleness of the Notion of Bias
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Front Matter
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Error Structures in Applications
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Front Matter
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Authors and Affiliations
About the author
Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.
Bibliographic Information
Book Title: The Mathematics of Errors
Authors: Nicolas Bouleau
DOI: https://doi.org/10.1007/978-3-030-88575-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-88574-8Published: 24 February 2022
Softcover ISBN: 978-3-030-88577-9Published: 25 February 2023
eBook ISBN: 978-3-030-88575-5Published: 23 February 2022
Edition Number: 1
Number of Pages: XII, 448
Number of Illustrations: 63 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Functional Analysis, Mathematical Modeling and Industrial Mathematics, Computational Mathematics and Numerical Analysis