The Lore of Large Numbers
| Author | : Philip J. Davis |
| Publisher | : |
| Total Pages | : 184 |
| Release | : 1961 |
| Genre | : Number theory |
| ISBN | : |
The Theory Of Large Numbers
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The Laws of Large Numbers
| Author | : Pál Révész |
| Publisher | : Academic Press |
| Total Pages | : 177 |
| Release | : 2014-06-20 |
| Genre | : Mathematics |
| ISBN | : 1483269027 |
The Law of Large Numbers deals with three types of law of large numbers according to the following convergences: stochastic, mean, and convergence with probability 1. The book also investigates the rate of convergence and the laws of the iterated logarithm. It reviews measure theory, probability theory, stochastic processes, ergodic theory, orthogonal series, Huber spaces, Banach spaces, as well as the special concepts and general theorems of the laws of large numbers. The text discusses the laws of large numbers of different classes of stochastic processes, such as independent random variables, orthogonal random variables, stationary sequences, symmetrically dependent random variables and their generalizations, and also Markov chains. It presents other laws of large numbers for subsequences of sequences of random variables, including some general laws of large numbers which are not related to any concrete class of stochastic processes. The text cites applications of the theorems, as in numbers theory, statistics, and information theory. The text is suitable for mathematicians, economists, scientists, statisticians, or researchers involved with the probability and relative frequency of large numbers.
The Politics of Large Numbers
| Author | : Alain Desrosières |
| Publisher | : Harvard University Press |
| Total Pages | : 386 |
| Release | : 1998 |
| Genre | : History |
| ISBN | : 9780674009691 |
Begins with study of history of statistics, and shows how the evolution of modern statistics has been inextricably bound up with the knowledge and power of governments.
Really Big Numbers
| Author | : Richard Evan Schwartz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 194 |
| Release | : 2014-06-30 |
| Genre | : Juvenile Nonfiction |
| ISBN | : 1470414252 |
In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the vast universe of numbers.
Large Deviations in Physics
| Author | : Angelo Vulpiani |
| Publisher | : Springer |
| Total Pages | : 323 |
| Release | : 2014-05-16 |
| Genre | : Science |
| ISBN | : 3642542514 |
This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.
A Course in Large Sample Theory
| Author | : Thomas S. Ferguson |
| Publisher | : Routledge |
| Total Pages | : 140 |
| Release | : 2017-09-06 |
| Genre | : Mathematics |
| ISBN | : 1351470051 |
A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.
Theory of U-Statistics
| Author | : Vladimir S. Korolyuk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 558 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 9401735158 |
The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc.
An Introduction to Markov Processes
| Author | : Daniel W. Stroock |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 196 |
| Release | : 2005-03-30 |
| Genre | : Mathematics |
| ISBN | : 9783540234517 |
Provides a more accessible introduction than other books on Markov processes by emphasizing the structure of the subject and avoiding sophisticated measure theory Leads the reader to a rigorous understanding of basic theory
The Mathematical Theory of Communication
| Author | : Claude E Shannon |
| Publisher | : University of Illinois Press |
| Total Pages | : 141 |
| Release | : 1998-09-01 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 025209803X |
Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
An Illustrated Theory of Numbers
| Author | : Martin H. Weissman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 341 |
| Release | : 2020-09-15 |
| Genre | : Education |
| ISBN | : 1470463717 |
News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.
