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.

• I. Error computations à la Gauss.- 1. The different approaches.- 2. Finite dimensional examples.- 3. An intuitive introduction to error structures.- 4. Weakly and strongly random errors.- II. Probabilistic and Functional Models.- 5. Strongly continuous semi-groups and Dirichlet forms.- 6. Error structures.- 7. Images and products of error structures.- 8. The gradient and the sharp and other calculation tools.- 9. Error structures on fundamental spaces.- III. The subtleness of the notion of bias.- 10. Approximation and bias operators.- 11. Computations and simulation methods.- IV. Error structures and its applications.- 12. Statistical identification of error structures.- 13. The instantaneous structure of a stochastic process.- 14. Models inspired by finance.- 15. Examples in Physics.- 16. The principle of arbitrary functions and error structures.- V. Historical elements and research themes.- 17. Error calculations from Gauss and Laplace.- 18. Extensions and open questions.- Hints forexercises.- Pedagogical References.- Chronological Bibliography.

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.

• I. Error computations à la Gauss.- 1. The different approaches.- 2. Finite dimensional examples.- 3. An intuitive introduction to error structures.- 4. Weakly and strongly random errors.- II. Probabilistic and Functional Models.- 5. Strongly continuous semi-groups and Dirichlet forms.- 6. Error structures.- 7. Images and products of error structures.- 8. The gradient and the sharp and other calculation tools.- 9. Error structures on fundamental spaces.- III. The subtleness of the notion of bias.- 10. Approximation and bias operators.- 11. Computations and simulation methods.- IV. Error structures and its applications.- 12. Statistical identification of error structures.- 13. The instantaneous structure of a stochastic process.- 14. Models inspired by finance.- 15. Examples in Physics.- 16. The principle of arbitrary functions and error structures.- V. Historical elements and research themes.- 17. Error calculations from Gauss and Laplace.- 18. Extensions and open questions.- Hints forexercises.- Pedagogical References.- Chronological Bibliography.

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.

• I. Error computations à la Gauss.- 1. The different approaches.- 2. Finite dimensional examples.- 3. An intuitive introduction to error structures.- 4. Weakly and strongly random errors.- II. Probabilistic and Functional Models.- 5. Strongly continuous semi-groups and Dirichlet forms.- 6. Error structures.- 7. Images and products of error structures.- 8. The gradient and the sharp and other calculation tools.- 9. Error structures on fundamental spaces.- III. The subtleness of the notion of bias.- 10. Approximation and bias operators.- 11. Computations and simulation methods.- IV. Error structures and its applications.- 12. Statistical identification of error structures.- 13. The instantaneous structure of a stochastic process.- 14. Models inspired by finance.- 15. Examples in Physics.- 16. The principle of arbitrary functions and error structures.- V. Historical elements and research themes.- 17. Error calculations from Gauss and Laplace.- 18. Extensions and open questions.- Hints forexercises.- Pedagogical References.- Chronological Bibliography.