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A Book of Set Theory
by Charles C PinterSuitable for upper-level undergraduates, this accessible approach to set theory poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity.A historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and sets, functions, relations, partially ordered classes, and the axiom of choice. Other subjects include natural and cardinal numbers, finite and infinite sets, the arithmetic of ordinal numbers, transfinite recursion, and selected topics in the theory of ordinals and cardinals. This updated edition features new material by author Charles C. Pinter.
The Book of Why: The New Science of Cause and Effect
by Judea Pearl Dana MackenzieA Turing Prize-winning computer scientist and statistician shows how understanding causality has revolutionized science and will revolutionize artificial intelligence"Correlation is not causation." This mantra, chanted by scientists for more than a century, has led to a virtual prohibition on causal talk. Today, that taboo is dead. The causal revolution, instigated by Judea Pearl and his colleagues, has cut through a century of confusion and established causality--the study of cause and effect--on a firm scientific basis. His work explains how we can know easy things, like whether it was rain or a sprinkler that made a sidewalk wet; and how to answer hard questions, like whether a drug cured an illness. Pearl's work enables us to know not just whether one thing causes another: it lets us explore the world that is and the worlds that could have been. It shows us the essence of human thought and key to artificial intelligence. Anyone who wants to understand either needs The Book of Why.
The Book on Games of Chance: The 16th-Century Treatise on Probability (Dover Recreational Math)
by Samuel S. Wilks Gerolamo Cardano Sydney Henry GouldMathematics was only one area of interest for Gerolamo Cardano - the sixteenth-century astrologer, philosopher, and physician was also a prolific author and inveterate gambler. Gambling led Cardano to the study of probability, and he was the first writer to recognize that random events are governed by mathematical laws. Published posthumously in 1663, Cardano's Liber de ludo aleae (Book on Games of Chance) is often considered the major starting point of the study of mathematical probability. The Italian scholar formulated some of the field's basic ideas more than a century before the better-known correspondence of Pascal and Fermat. Although his book had no direct influence on other early thinkers about probability, it remains an important antecedent to later expressions of the science's tenets.
The Book on the Book: A Landmark Inquiry into Which Strategies in the Modern Game Actually Work
by Bill FelberDie-hard fanatics will enjoy this comprehensive collection of groundbreaking baseball strategies, analyses, statistics, and studies"Picking up where Michael Lewis left off in Moneyball, he addresses the central questions of risk, reward, and value--on the field and off--and reveals what it takes to win." -John Thorn, editor of Total BaseballThis unique approach to understanding the "tried and true" methodologies of the game of baseball examines conventional elements like the steal, hit and run, and line-up construction. The Book on The Book offers an exciting critique of baseball by placing an actual dollar value on player performance and rating managers based on their on-field moves to determine who are the smartest tacticians.No corner of the ballpark is left unturned as author Bill Felber explores the various methods of team-building, on-field values of players, the role and influence of the general manager in team success, and the importance of park effects. In the vein of the late Leonard Koppett and Bill James, Felber uses mathematical and statistical principles to evaluate the wisdom of standard baseball strategies. Illustrations and a refreshingly engaging style make The Book on The Book the new textbook of baseball analysis.
bookdown: Authoring Books and Technical Documents with R Markdown (Chapman & Hall/CRC The R Series)
by Yihui Xiebookdown: Authoring Books and Technical Documents with R Markdown presents a much easier way to write books and technical publications than traditional tools such as LaTeX and Word. The bookdown package inherits the simplicity of syntax and flexibility for data analysis from R Markdown, and extends R Markdown for technical writing, so that you can make better use of document elements such as figures, tables, equations, theorems, citations, and references. Similar to LaTeX, you can number and cross-reference these elements with bookdown. Your document can even include live examples so readers can interact with them while reading the book. The book can be rendered to multiple output formats, including LaTeX/PDF, HTML, EPUB, and Word, thus making it easy to put your documents online. The style and theme of these output formats can be customized. We used books and R primarily for examples in this book, but bookdown is not only for books or R. Most features introduced in this book also apply to other types of publications: journal papers, reports, dissertations, course handouts, study notes, and even novels. You do not have to use R, either. Other choices of computing languages include Python, C, C++, SQL, Bash, Stan, JavaScript, and so on, although R is best supported. You can also leave out computing, for example, to write a fiction. This book itself is an example of publishing with bookdown and R Markdown, and its source is fully available on GitHub.
Boolean Algebra
by R. L. GoodsteinFamous for the number-theoretic first-order statement known as Goodstein's theorem, author R. L. Goodstein was also well known as a distinguished educator. With this text, he offers an elementary treatment that employs Boolean algebra as a simple medium for introducing important concepts of modern algebra.The text begins with an informal introduction to the algebra of classes, exploring union, intersection, and complementation; the commutative, associative, and distributive laws; difference and symmetric difference; and Venn diagrams. Professor Goodstein proceeds to a detailed examination of three different axiomatizations, and an outline of a fourth system of axioms appears in the examples. The final chapter, on lattices, examines Boolean algebra in the setting of the theory of partial order. Numerous examples appear at the end of each chapter, with full solutions at the end.
Boolean Algebra and Its Applications (Dover Books on Computer Science)
by J. Eldon WhitesittThis introduction to Boolean algebra explores the subject on a level accessible even to those with a modest background in mathematics. The first chapter presents the algebra of sets from an intuitive point of view, followed by a formal presentation in chapter two of Boolean algebra as an abstract algebraic system, with no reference to applications. Succeeding chapters offer concise accounts of applications to symbolic logic, focusing on topics of logic common to elementary mathematics and discussing concepts of valid argument and indirect proofs. Additional topics include the algebra of circuits — switching, relay, and computer — as well as the application of the algebra of sets to probability theory. Problems appear throughout the text, with answers to selected problems at the end of the book. Geared toward students of mathematics, computer science, and electrical engineering, this text can be appreciated by anyone who understands college-level mathematics. It will prove particularly valuable to philosophy students and others wishing to study symbolic logic and its applications to computer science.
Boolean Algebra Essentials
by Alan SolomonREA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean algebra in communication systems.
Boolean Functions: Topics in Asynchronicity
by Serban E. VladThe essential guide showing how the unbounded delay model of computation of the Boolean functions may be used in the analysis of the Boolean networks Boolean Functions: Topics in Asynchronicity contains the most current research in several issues of asynchronous Boolean systems. In this framework, asynchronicity means that the functions which model the digital circuits from electronics iterate their coordinates independently on each other and the author—a noted expert in the field—includes a formal mathematical description of these systems. Filled with helpful definitions and illustrative examples, the book covers a range of topics such as morphisms, antimorphisms, invariant sets, path connected sets, attractors. Further, it studies race freedom, called here the technical condition of proper operation, together with some of its generalized and strengthened versions, and also time reversal, borrowed from physics and also from dynamical systems, together with the symmetry that it generates. This book: Presents up-to-date research in the field of Boolean networks, Includes the information needed to understand the construction of an asynchronous Boolean systems theory and contains proofs, Employs use of the language of algebraic topology and homological algebra. Written formathematicians and computer scientists interested in the theory and applications of Boolean functions, dynamical systems, and circuits, Boolean Functions: Topics in Asynchronicity is an authoritative guide indicating a way of using the unbounded delay model of computation of the Boolean functions in the analysis of the Boolean networks.
Boolean Functions and Their Applications in Cryptography (Advances in Computer Science and Technology #0)
by Chuan-Kun Wu Dengguo FengThis book focuses on the different representations and cryptographic properties of Booleans functions, presents constructions of Boolean functions with some good cryptographic properties. More specifically, Walsh spectrum description of the traditional cryptographic properties of Boolean functions, including linear structure, propagation criterion, nonlinearity, and correlation immunity are presented. Constructions of symmetric Boolean functions and of Boolean permutations with good cryptographic properties are specifically studied. This book is not meant to be comprehensive, but with its own focus on some original research of the authors in the past. To be self content, some basic concepts and properties are introduced. This book can serve as a reference for cryptographic algorithm designers, particularly the designers of stream ciphers and of block ciphers, and for academics with interest in the cryptographic properties of Boolean functions.
Boolean Networks as Predictive Models of Emergent Biological Behaviors (Elements in the Structure and Dynamics of Complex Networks)
by Jordan C. Rozum Colin Campbell Eli Newby Fatemeh Sadat Nasrollahi Réka AlbertInteracting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions – from molecules in gene regulatory networks to species in ecological networks – and the often-incomplete state of system knowledge, such as the unknown values of kinetic parameters for biochemical reactions. Boolean networks have emerged as a powerful tool for modeling these systems. This Element provides a methodological overview of Boolean network models of biological systems. After a brief introduction, the authors describe the process of building, analyzing, and validating a Boolean model. They then present the use of the model to make predictions about the system's response to perturbations and about how to control its behavior. The Element emphasizes the interplay between structural and dynamical properties of Boolean networks and illustrates them in three case studies from disparate levels of biological organization.
Boolean Reasoning: The Logic of Boolean Equations
by Frank Markham BrownA systematic treatment of Boolean reasoning, this concise, newly revised edition combines the works of early logicians with recent investigations, including previously unpublished research results.For the benefit of readers without formal training in mathematics, the text starts with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras, based on Huntington's postulate. It defines operators for elimination, division, and expansion, providing a coherent and systematic basis for subsequent discussions of syllogistic reasoning, the solution of Boolean equations, and functional deduction.Examples and end-of-chapter problems appear throughout the book, many taken from the design for switching systems. Two concluding chapters deal with applications; one applies Boolean reasoning to diagnostic problems, and the other discusses the design of multiple-output logic-circuits.
Boolean Representations of Simplicial Complexes and Matroids (Springer Monographs in Mathematics)
by John Rhodes Pedro V. SilvaThis self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context. Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes.
Boom-Bust Cycle, Asymmetrical Fiscal Response and the Dutch Disease
by Rabah Arezki Kareem IsmailA report from the International Monetary Fund.
Boomerang Kids: The Demography of Previously Launched Adults (SpringerBriefs in Population Studies)
by D. Nicole FarrisCombining statistical analyses and personal interviews, this book examines the phenomenon of adult children in the United States who have returned to living with their parents in the family home. It uses both data and narrative to fully detail how such co-residency has shaped this ever-increasing demographic group, who are often referred to as "previously launched adults" or " boomerang children. " The author first presents quantitative research using data obtained from the National Survey of Families and Households. Readers will discover the various demographic, household, and economic variables that might lead an individual to move back in with his or her family. This statistical analysis is complemented by 50 qualitative interviews that offer a more in-depth look at the trend from the point of view of those who have experienced it. These interviews of both adult children and their parents cover such areas as personal background, the effects of returning to the parental home, and self-esteem issues. In addition, the book offers cross-country comparisons by looking at the prevalence of this phenomenon in China and Greece. It discusses the different cultural contexts in which adult child and parent co-residence is not seen as particularly deviant, as it is in America, as well as identifies some of the demographic and economic factors that would cause those in different countries to continue to live with their parents. This book furthers research into the sociological study of the family. The quantitative analyses describe the large scale trends and their implications, the interviews provide an important personal context, while the cross-country comparisons offer additional perspectives. Overall, readers will gain a complete picture of this unprecedented demographic shift in the United States, including important policy implications and the plight of young adults coming of age in the 21st century.
Boosting Software Development Using Machine Learning (Artificial Intelligence-Enhanced Software and Systems Engineering #7)
by Satchidananda Dehuri Margarita N. Favorskaya Rajib Mall Tirimula Rao BenalaThis book explores the transformative effects of AI and ML on software engineering. It emphasizes the potential of cutting-edge software development technologies such as Generative AI and ML applications. This book incorporates data-driven strategies across the entire software development life cycle, from requirements elicitation and design to coding, testing, and deployment. It illustrates the evolution from traditional frameworks to agile and DevOps methodologies. The potential of Generative AI for automating repetitive tasks and enhancing code quality is highlighted, along with ML applications in optimizing testing, effort estimation, design pattern recognition, fault prediction, debugging, and security through anomaly detection. These techniques have significantly improved software development efficiency, predictability, and project management effectiveness. While remarkable progress has been made, much remains to be done in this evolving area. This edited book is a timely effort toward advancing the field and promoting interdisciplinary collaboration in addressing ethical, security, and technical challenges.
Bootstrap Methods
by Michael R. ChernickA practical and accessible introduction to the bootstrap method----newly revised and updatedOver the past decade, the application of bootstrap methods to new areas of study has expanded, resulting in theoretical and applied advances across various fields. Bootstrap Methods, Second Edition is a highly approachable guide to the multidisciplinary, real-world uses of bootstrapping and is ideal for readers who have a professional interest in its methods, but are without an advanced background in mathematics.Updated to reflect current techniques and the most up-to-date work on the topic, the Second Edition features:The addition of a second, extended bibliography devoted solely to publications from 1999-2007, which is a valuable collection of references on the latest research in the fieldA discussion of the new areas of applicability for bootstrap methods, including use in the pharmaceutical industry for estimating individual and population bioequivalence in clinical trialsA revised chapter on when and why bootstrap fails and remedies for overcoming these drawbacksAdded coverage on regression, censored data applications, P-value adjustment, ratio estimators, and missing dataNew examples and illustrations as well as extensive historical notes at the end of each chapterWith a strong focus on application, detailed explanations of methodology, and complete coverage of modern developments in the field, Bootstrap Methods, Second Edition is an indispensable reference for applied statisticians, engineers, scientists, clinicians, and other practitioners who regularly use statistical methods in research. It is also suitable as a supplementary text for courses in statistics and resampling methods at the upper-undergraduate and graduate levels.
Bootstrap Methods: With Applications in R
by Gerhard Dikta Marsel ScheerThis book provides a compact introduction to the bootstrap method. In addition to classical results on point estimation and test theory, multivariate linear regression models and generalized linear models are covered in detail. Special attention is given to the use of bootstrap procedures to perform goodness-of-fit tests to validate model or distributional assumptions. In some cases, new methods are presented here for the first time. The text is motivated by practical examples and the implementations of the corresponding algorithms are always given directly in R in a comprehensible form. Overall, R is given great importance throughout. Each chapter includes a section of exercises and, for the more mathematically inclined readers, concludes with rigorous proofs. The intended audience is graduate students who already have a prior knowledge of probability theory and mathematical statistics.
Bootstrap Methods and their Application
by A. C. Davison D. V. HinkleyBootstrap methods are computer-intensive methods of statistical analysis, which use simulation to calculate standard errors, confidence intervals, and significance tests. The methods apply for any level of modelling, and so can be used for fully parametric, semiparametric, and completely nonparametric analysis. This 1997 book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. S-Plus programs for implementing the methods described in the text are available from the supporting website.
Borders in Mathematics Pre-Service Teacher Education
by Nenad Radakovic Limin JaoThis book examines the current state of the field of mathematics pre-service teacher education through the theme of borders. Borders are ubiquitous; they can be used to define, classify, organize, make sense of, and/or group. There are many ways that the concept of a border illuminates the field of mathematics pre-service teacher education. Consequently, there are a multitude of responses to these borders: researchers and practitioners question, challenge, cross, blur, and erase them. Chapters include the following topics: explorations of mathematics across topics (e.g., geometry, algebra, probability) and with other disciplines (e.g., science, the arts, social sciences); challenging gender, cultural, and racial borders; exploring the structure and curriculum of teacher education programs; spaces inhabited by teacher education programs (e.g., university, community); and international collaborations and programs to promote cross-cultural sharing and learning. The book targets a readership of researchers and graduate students in integrated education studies, teacher education, practitioners of mathematics education, curriculum developers, and educational administrators and policy makers.
The Borel-Cantelli Lemma
by Tapas Kumar ChandraThis monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it embodies the classical versions of these lemma, together with the well known as well as the most recent extensions of them due to Barndorff-Nielsen, Balakrishnan and Stepanov, Erdos and Renyi, Kochen and Stone, Petrov and the present author. The versions of the second Borel-Cantelli Lemma for pair wise negative quadrant dependent sequences, weakly *-mixing sequences, mixing sequences (due to Renyi) and for many other dependent sequences are all included. The special feature of the book is a detailed discussion of a strengthened form of the second Borel-Cantelli Lemma and the conditional form of the Borel-Cantelli Lemmas due to Levy, Chen and Serfling. All these results are well illustrated by means of many interesting examples. All the proofs are rigorous, complete and lucid. An extensive list of research papers, some of which are forthcoming, is provided. The book can be used for a self study and as an invaluable research reference on the present topic.
Born at the Right Time
by Doug OwramIt is rare in history for people to link their identity with their generation, and even rarer when children and adolescents actually shape society and influence politics. Both phenomena aptly describe the generation born in the decade following the Second World War. These were the baby boomers, viewed by some as the spoiled, selfish generation that had it all, and by others as a shock wave that made love and peace into tangible ideals. In this book, Doug Owram brings us the untold story of this famous generation as it played out its first twenty-five years in Canadian society.Beginning with Dr Spock's dictate that this particular crop of babies must be treated gently, Owram explores the myth and history surrounding this group, from its beginning at war's end to the close of the 1960s. The baby boomers wielded extraordinary power right from birth, Owram points out, and laid their claim on history while still in diapers. He sees the generation's power and sense of self stemming from three factors: its size, its affluent circumstance, and its connection with the 1960s - the fabulous decade of free love, flower power, women's liberation, drugs, protest marches, and rock 'n' roll. From Davy Crockett hats and Barbie dolls to the civil-rights movement and the sexual revolution, the concerns of this single generation became predominant themes for all of society. Thus, Owram's history of the baby-boomers is in many ways a history of the era.Doug Owram has written extensively on cultural icons, Utopian hopes, and the gap between realities and images - all powerful themes in the story of this idealistic generation. A well-researched, lucid, and humorous book, Born at the Right Time is the first Canadian history of the baby-boomers and the society they helped to shape.
Bornologies and Lipschitz Analysis
by Gerald BeerThis monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of its members. The largest bornology is the power set of the space and the smallest is the bornology of its finite subsets. Between these lie (among others) the metrically bounded subsets, the relatively compact subsets, the totally bounded subsets, and the Bourbaki bounded subsets. Classes of functions are intimately connected to various bornologies; e.g., (1) a function is locally Lipschitz if and only if its restriction to each relatively compact subset is Lipschitz; (2) a subset is Bourbaki bounded if and only if each uniformly continuous function on the space is bounded when restricted to the subset. A great deal of attention is given to the variational notions of strong uniform continuity and strong uniform convergence with respect to the members of a bornology, leading to the bornology of UC-subsets and UC-spaces. Spaces on which its uniformly continuous real-valued functions are stable under pointwise product are characterized in terms of the coincidence of the Bourbaki bounded subsets with a usually larger bornology. Special attention is given to Lipschitz and locally Lipschitz functions. For example, uniformly dense subclasses of locally Lipschitz functions within the real-valued continuous functions, Cauchy continuous functions, and uniformly continuous functions are presented. It is shown very generally that a function between metric spaces has a particular metric property if and only if whenever it is followed in a composition by a real-valued Lipschitz function, the composition has the property. Bornological convergence of nets of closed subsets, having Attouch-Wets convergence as a prototype, is considered in detail. Topologies of uniform convergence for continuous linear operators between normed spaces is explained in terms of the bornological convergence of their graphs. Finally, the idea of a bornological extension of a topological space is presented, and all regular extensions can be so realized.
Bose-Einstein-Kondensate in höheren Bändern des hexagonalen Gitters: Von rf-Techniken einer Gitterstabilisierung hin zum dynamischen Quantenphasenübergang
by Julius SeegerDieses Buch beschreibt die erstmalige, erfolgreiche Realisierung unkonventioneller Superfluide in höheren Bändern des hexagonalen optischen Gitters. Der Populationstransfer und der anschließende dynamische Quantenphasenübergang werden ausführlich diskutiert. Schließlich werden die Metastabilität und Zerfallskanäle des ultrakalten Systems experimentell nachgewiesen. Durch die Reduktion von Phasenrauschen des optischen Gitters konnte die Lebensdauer des ultrakalten Ensembles um etwa eine Größenordnung erhöht werden. Weiterhin werden die optische Phasenregelschleife und Intensitätsstabilisierung des Gitters vorgestellt. Mit den in diesem Buch beschriebenen Ergebnissen und technologischen Entwicklungen werden die derzeit bestehenden Grenzen der Quantensimulation mittels ultrakalter Gase in optischen Gittern aufgehoben und der Weg für zahlreiche nachfolgende Untersuchungen bereitet.
The Boston Globe Story of the Red Sox: More Than a Century of Championships, Challenges, and Characters
by The Boston Globe Chad FinnExperience the illustrious and passionate history of the Boston Red Sox, one of the most storied franchises in baseball, as it happened through the articles, features, and lens of their hometown and national news outlet, The Boston Globe. The Boston Red Sox are the most winning baseball team in the 21st century with four World Series titles, and they're not slowing down any time soon. Two of the most prominent organizations in Boston, The Boston Globe and the Boston Red Sox, combine to share a tour de force history of the heralded baseball franchise from the very beginning in 1901, when they were known as the Boston Americans. The Boston Globe Story of the Red Sox includes more than 300 articles chronicling the team's rich history as told through the best sports writing and coverage from the beloved Globe reporters, led by veteran sports columnist and an EPPY Award finalist Chad Finn. Relive some of the biggest moments in franchise history, such as their first baseball title ever in 1901, Carlton Fisk's wave home run in 1975, David Ortiz's postseason heroics, and the most dominant Red Sox team ever in 2018. With a foreword from beloved former Sox pitcher and broadcaster, Dennis Eckersley, and Illustrated throughout with hundreds of photographs through every era, and updated through 2022, this beautiful archive celebrates two beloved organizations, and shares the hometown story of one of the world's most popular baseball teams.