The Mathematics of Errors

The Mathematics of Errors is a book that provides a rigorous and systematic approach to the calculus of errors, suitable for both engineers and mathematicians. It covers sensitivity analysis, stochastic analysis, and Dirichlet forms, with detailed applications in various fields. The author, Nicolas Bouleau, is a renowned mathematician known for his work in error propagation and has directed the mathematics center of Ecole des Ponts ParisTech.

Format: Paperback / softback
Length: 448 pages
Publication date: 25 February 2023
Publisher: Springer Nature Switzerland AG

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 readers' 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.

Weight: 700g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030885779
Edition number: 1st ed. 2021