Download or read book The Shift from Classical to Modern Probability written by Vinicius Gontijo Lauar and published by . This book was released on 2018 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we describe the historical shift from the classical to the modern definition of probability. We present the key ideas and insights in that process, from the first definition of Bernoulli, to Kolmogorov's modern foundations discussing some of the limitations of the old approach and the efforts of many mathematicians to achieve a satisfactory definition of probability. For our study, we've looked, as much as possible, at original sources and provided detailed proofs of some important results that the authors have written in an abbreviated style. We then use this historical results to investigate the conceptualization of probability proposed and fostered by undergraduate and graduate probability textbooks through their theoretical discourse and proposed exercises. Our findings show that, despite textbooks give an axiomatic definition of probability, the main aspects of the modern approach are overshadowed by other content. Undergraduate books may be stimulating the development of classical probability with many exercises using proportional reasoning while graduate books concentrate the exercises on other mathematical contents such as measure and set theory without necessarily proposing a reflection on the modern conceptualization of probability.
Download or read book A History of the Central Limit Theorem written by Hans Fischer and published by Springer Science & Business Media. This book was released on 2010-10-08 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Download or read book Creating Modern Probability written by Jan von Plato and published by Cambridge University Press. This book was released on 1998-01-12 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author charts the history and development of modern probability theory.
Download or read book Foundations of Modern Probability written by Olav Kallenberg and published by Springer Science & Business Media. This book was released on 2002-01-08 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Download or read book From Classical to Modern Probability written by Pierre Picco and published by Birkhäuser. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.
Download or read book From Classical to Modern Probability written by Pierre Picco and published by Springer Science & Business Media. This book was released on 2003-10-24 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the lecture notes of six courses delivered at a CIMPA Summer School in Temuco, Chile, in January 2001. The courses are: asymptotic of the heat kernel in unbounded domains; spin systems with long range interactions; non-linear Dirichlet problem and non-linear integration; first-passage percolation; central limit theorem for Markov processes; stochastic orders and stopping times in Brownian motion. The level of each course is that of a graduate course, but the material will also be of interest for the specialist.
Download or read book Creating Modern Probability written by Jan von Plato and published by Cambridge University Press. This book was released on 1994-01-28 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book to chart the history and development of modern probability theory. It shows how in the first thirty years of this century probability theory became a mathematical science. The author also traces the development of probabilistic concepts and theories in statistical and quantum physics. There are chapters dealing with chance phenomena, as well as the main mathematical theories of today, together with their foundational and philosophical problems. Among the theorists whose work is treated at some length are Kolmogorov, von Mises and de Finetti. The principal audience for the book comprises philosophers and historians of science, mathematicians concerned with probability and statistics, and physicists. The book will also interest anyone fascinated by twentieth-century scientific developments because the birth of modern probability is closely tied to the change from a determinist to an indeterminist world-view.
Download or read book Foundations of Modern Probability written by Olav Kallenberg and published by Springer Nature. This book was released on 2021-02-07 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Download or read book A Modern Approach to Probability Theory written by Bert E. Fristedt and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.
Download or read book Probability The Classical Limit Theorems written by Henry McKean and published by Cambridge University Press. This book was released on 2014-11-27 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: A leading authority sheds light on a variety of interesting topics in which probability theory plays a key role.
Download or read book Modern Classical Homotopy Theory written by Jeffrey Strom and published by American Mathematical Society. This book was released on 2023-01-19 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.
Download or read book Measure Integral and Probability written by Marek Capinski and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.
Download or read book Classical Probability in the Enlightenment New Edition written by Lorraine Daston and published by Princeton University Press. This book was released on 2023-08-08 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: An award-winning history of the Enlightenment quest to devise a mathematical model of rationality What did it mean to be reasonable in the Age of Reason? Enlightenment mathematicians such as Blaise Pascal, Jakob Bernoulli, and Pierre Simon Laplace sought to answer this question, laboring over a theory of rational decision, action, and belief under conditions of uncertainty. Lorraine Daston brings to life their debates and philosophical arguments, charting the development and application of probability theory by some of the greatest thinkers of the age. Now with an incisive new preface, Classical Probability in the Enlightenment traces the emergence of new kind of mathematics designed to turn good sense into a reasonable calculus.
Download or read book A Modern Approach to Probability Theory written by Bert E. Fristedt and published by Springer Science & Business Media. This book was released on 1996-12-23 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.
Download or read book Probability and Stochastics written by Erhan Çınlar and published by Springer Science & Business Media. This book was released on 2011-02-21 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The book is based on the author’s lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics. Erhan Cinlar has received many awards for excellence in teaching, including the President’s Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.
Download or read book Fisher Neyman and the Creation of Classical Statistics written by Erich L. Lehmann and published by Springer Science & Business Media. This book was released on 2011-07-25 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical statistical theory—hypothesis testing, estimation, and the design of experiments and sample surveys—is mainly the creation of two men: Ronald A. Fisher (1890-1962) and Jerzy Neyman (1894-1981). Their contributions sometimes complemented each other, sometimes occurred in parallel, and, particularly at later stages, often were in strong opposition. The two men would not be pleased to see their names linked in this way, since throughout most of their working lives they detested each other. Nevertheless, they worked on the same problems, and through their combined efforts created a new discipline. This new book by E.L. Lehmann, himself a student of Neyman’s, explores the relationship between Neyman and Fisher, as well as their interactions with other influential statisticians, and the statistical history they helped create together. Lehmann uses direct correspondence and original papers to recreate an historical account of the creation of the Neyman-Pearson Theory as well as Fisher’s dissent, and other important statistical theories.
Download or read book Semiotic Approach to the Theology of Inculturation written by Cyril Orji and published by James Clarke & Company. This book was released on 2017-08-31 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Semiotic Approach to the Theology of Inculturation argues that though it is a difficult and delicate task, inculturation is still a requisite demand of a World Church and that without it the Church is unrecognisable and unsustainable. The book also suggests that the past failures of inculturation experiments in Africa can be overcome only by critically applying the science of semiotics, which can serve as an antidote to the nature of human knowing and reductionism that characterised earlier attempts to make Christianity African to the African. Drawing from the semiotic works of C.S. Peirce, Clifford Geertz, and Bernard Lonergan, Cyril Orji shows why semiotics is best suited to an African theology of inculturation and offers ten pinpointed precepts, identified as 'Habits', which underline the attentiveness, reasonableness, and responsibility required in a semiotic approach to a theology of inculturation. The 'Habits' are also akin to the imperatives inherent in the notion of catholicity - that catholicity is not identified with uniformity but with reconciled diversity, and also that catholicity demands different forms in different places, times, and cultural settings.
