“…The paradoxical nature of space and the problem of infinitesimals are aspects of a discussion which debates the premises of the work of Newton, Einstein and other scientific giants, presenting these ideas in a philosophical context. …”

Tabla de Contenidos: “…3.2.5 Finite-sample breakdown point 61 -- 3.3 Maximum asymptotic bias 62 -- 3.4 Balancing robustness and efficiency 64 -- 3.5 *“Optimal” robustness 66 -- 3.5.1 Bias- and variance-optimality of location estimators 66 -- 3.5.2 Bias optimality of scale and dispersion estimators 66 -- 3.5.3 The infinitesimal approach 67 -- 3.5.4 The Hampel approach 68 -- 3.5.5 Balancing bias and variance: the general problem 70 -- 3.6 Multidimensional parameters 70 -- 3.7 *Estimators as functionals 72 -- 3.8 Appendix: Proofs of results 76 -- 3.8.1 IF of general M-estimators 76 -- 3.8.2 Maximum BP of location estimators 76 -- 3.8.3 BP of location M-estimators 77 -- 3.8.4 Maximum bias of location M-estimators 79 -- 3.8.5 The minimax bias property of the median 80 -- 3.8.6 Minimizing the GES 80 -- 3.8.7 Hampel optimality 82 -- 3.9 Problems 85 -- 4 Linear Regression 1 87 -- 4.1 Introduction 87 -- 4.2 Review of the least squares method 91 -- 4.3 Classical methods for outlier detection 94 -- 4.4 Regression M-estimators 97 -- 4.4.1 M-estimators with known scale 99 -- 4.4.2 M-estimators with preliminary scale 100 -- 4.4.3 Simultaneous estimation of regression and scale 102 -- 4.5 Numerical computing of monotone M-estimators 103 -- 4.5.1 The L1 estimator 103 -- 4.5.2 M-estimators with smooth 𝜓-function 104 -- 4.6 BP of monotone regression estimators 104 -- 4.7 Robust tests for linear hypothesis 106 -- 4.7.1 Review of the classical theory 106 -- 4.7.2 Robust tests using M-estimators 108 -- 4.8 *Regression quantiles 109 -- 4.9 Appendix: Proofs and complements 110 -- 4.9.1 Why equivariance? …”

“…Nonstandard analysis was originally developed by Robinson to rigorously justify infinitesimals like df and dx in expressions like df/dx in Leibniz' calculus or even to justify concepts like \delta-`functions'. …”

“…But Berkeley was a polymath who contributed to a variety of different disciplines, not well distinguished from philosophy in the eighteenth century, including the theory and psychology of vision, the nature and functioning of language, the debate over infinitesimals in mathematics, political philosophy, economics, chemistry (including his favoured panacea, tar-water), and theology. …”

“…With more than 600 images and figures illustrating the various ways readers can document the world of the infinitesimal, this book is not only a technical guide, but also a source of inspiration giving readers ideas to run with and make their own. …”

“….- Verwenden Sie Python-Code und Bibliotheken wie SymPy, NumPy und scikit-learn, um grundlegende mathematische Konzepte wie Infinitesimalrechnung, lineare Algebra, Statistik und maschinelles Lernen zu erkunden- Verstehen Sie Techniken wie lineare und logistische Regression und neuronale Netze durch gut nachvollziehbare Erklärungen und ein Minimum an mathematischer Terminologie- Wenden Sie deskriptive Statistik und Hypothesentests auf einen Datensatz an, um p-Werte und statistische Signifikanz zu interpretieren- Manipulieren Sie Vektoren und Matrizen und führen Sie Matrixzerlegung durch- Vertiefen Sie Ihre Kenntnisse in Infinitesimal- und Wahrscheinlichkeitsrechnung, Statistik und linearer Algebra und wenden Sie sie auf Regressionsmodelle einschließlich neuronaler Netze an- Erfahren Sie, wie Sie Ihre Kenntnisse und Fähigkeiten in der Datenanalyse optimieren und gängige Fehler vermeiden, um auf dem Data-Science-Arbeitsmarkt zu überzeugen…”