An Introduction to Geometrical Probability PDF Download
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Author: A.M. Mathai
Publisher: CRC Press
ISBN: 9789056996819
Category : Mathematics
Languages : en
Pages : 580
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Book Description
A useful guide for researchers and professionals, graduate and senior undergraduate students, this book provides an in-depth look at applied and geometrical probability with an emphasis on statistical distributions. A meticulous treatment of geometrical probability, kept at a level to appeal to a wider audience including applied researchers who will find the book to be both functional and practical with the large number of problems chosen from different disciplines A few topics such as packing and covering problems that have a vast literature are introduced here at a peripheral level for the purpose of familiarizing readers who are new to the area of research.
Author: A.M. Mathai
Publisher: CRC Press
ISBN: 9789056996819
Category : Mathematics
Languages : en
Pages : 580
Get Book Here
Book Description
A useful guide for researchers and professionals, graduate and senior undergraduate students, this book provides an in-depth look at applied and geometrical probability with an emphasis on statistical distributions. A meticulous treatment of geometrical probability, kept at a level to appeal to a wider audience including applied researchers who will find the book to be both functional and practical with the large number of problems chosen from different disciplines A few topics such as packing and covering problems that have a vast literature are introduced here at a peripheral level for the purpose of familiarizing readers who are new to the area of research.
Author: Daniel A. Klain
Publisher: Cambridge University Press
ISBN: 9780521596541
Category : Mathematics
Languages : en
Pages : 196
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Book Description
The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.
Author: Ovidiu Calin
Publisher: Springer
ISBN: 3319077791
Category : Mathematics
Languages : en
Pages : 389
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Book Description
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.
Author: David F. Anderson
Publisher: Cambridge University Press
ISBN: 110824498X
Category : Mathematics
Languages : en
Pages : 447
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Book Description
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Dimitri Bertsekas
Publisher: Athena Scientific
ISBN: 188652923X
Category : Mathematics
Languages : en
Pages : 544
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Book Description
An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.
Author: Shun-ichi Amari
Publisher: Springer
ISBN: 4431559787
Category : Mathematics
Languages : en
Pages : 378
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Book Description
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
Author: David Patrick
Publisher:
ISBN: 9781934124109
Category : Counting
Languages : en
Pages : 0
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Book Description
Author: Aldrovandi Ruben
Publisher: World Scientific
ISBN: 9813146834
Category : Science
Languages : en
Pages : 844
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Book Description
This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear. The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students. In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.
Author: Edward P C Kao
Publisher: World Scientific
ISBN: 9811245452
Category : Mathematics
Languages : en
Pages : 391
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Book Description
The main objective of this text is to facilitate a student's smooth learning transition from a course on probability to its applications in various areas. To achieve this goal, students are encouraged to experiment numerically with problems requiring computer solutions.
