Time Series
Focusing on Bayesian approaches and computations using analytic and simulation-based methods for inference, Time Series: Modeling, Computation, and Inference, Second Edition integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling, analysis and forecasting, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and contacts research frontiers in multivariate time series modeling and forecasting. It presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. It explores the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian formulations and computation, including use of computations based on Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. It illustrates the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, environmental science, and finance. Along with core models and methods, the book represents state-of-the art approaches to analysis and forecasting in challenging time series problems. It also demonstrates the growth of time series analysis into new application areas in recent years, and contacts recent and relevant modeling developments and research challenges. New in the second edition: Expanded on aspects of core model theory and methodology. Multiple new examples and exercises. Detailed development of dynamic factor models. Updated discussion and connections with recent and current research frontiers.
Spatio-Temporal Models for Ecologists
This book introduces a minimal set of principles and numerical techniques for spatio-temporal statistics that can be used to implement a wide range of real-world ecological analyses regarding animal movement, population dynamics, community composition, causal attribution, and spatial dynamics.
Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems
This monograph is devoted to the analysis and solution of singular differential games and singular $H_{\inf}$ control problems in both finite- and infinite-horizon settings. Expanding on the authors' previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach. After a brief introduction, solvability conditions are presented for the regular differential games and $H_{\inf}$ control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic $H_{\inf}$ control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text, and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections.Singular Linear-Quadratic Zero-Sum Differential Games and $H_{\inf}$ Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these area
Probability, Information, and Physics
This book deals with two main topics. The first is a theory that aims to unify the many interpretations of probability presented in the literature. The second uses this comprehensive theory of probability to answer the questions of quantum mechanics that have long been debated. The entire book proposes original solutions that several experimental cases substantiate.
Shop Mathematics, Part 1
This book is a comprehensive guide to shop mathematics, covering everything from simple arithmetic to more advanced topics like algebra and geometry. It is an essential resource for anyone working in the manufacturing, engineering, or construction industries. The clear explanations and practical examples make it easy to understand even the most complex concepts.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A First Study of the Relation Between Percentage of Illiteracy and Death Rate in American Cities
This book presents a pioneering study of the relation between percentage of illiteracy and death rate in American cities. The study is based on statistical analysis of data from various sources and provides insights into the social and economic factors that affect literacy and health. The book is an important historical document and an inspiration for further research in social epidemiology.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Choice And Chance
This is a textbook on arithmetic and algebra, aimed at students studying mathematics during the late 19th century. The book covers topics such as probability theory, permutations, and combinations, and includes numerous examples and exercises to help students develop their skills.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Theory of Probability
This seminal work on probability theory establishes the foundations of the field, including calculus-based approaches to probability, the law of large numbers, and the central limit theorem. The authors draw on examples from physics, biology, and economics to illustrate the concepts and demonstrate their practical applications. First published in 1902, this book remains an important reference for mathematicians and scientists today.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Biometrika; Volume 2
This journal publishes cutting-edge research in biostatistics and mathematical biology. Its articles cover a broad range of subjects, including epidemiology, genetics, and ecology.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Methods of Earthwork Computations
This practical guide to earthwork computations provides a comprehensive overview of the mathematical principles and methods used in determining volume, area, and elevation of land surfaces. With step-by-step instructions, examples, and sample problems, the book is an essential tool for civil engineers, surveyors, and construction professionals.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Philosophies, Puzzles and Paradoxes
Aimed at undergraduate students of statistics and researchers interested in the philosophical foundations of statistics. Of interest to philosophers of science, as well as a general audience interested in puzzles and paradoxes.
Journal of the Royal Statistical Society; Volume 1
The Journal of the Royal Statistical Society is a leading publication in the field of statistics. With articles on a wide range of topics, from probability theory to data analysis, it provides a comprehensive overview of the latest developments in the field. A must-read for statisticians and data scientists.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elementary Functions and Applications
This math book covers the study of elementary functions and their applications for the field of engineering. It provides a comprehensive overview of the different functions that are commonly used in engineering calculations and explains how they work. The book is aimed at students and professionals working in different fields of engineering who want to deepen their understanding of these mathematical concepts.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Theory of Probability
This seminal work on probability theory establishes the foundations of the field, including calculus-based approaches to probability, the law of large numbers, and the central limit theorem. The authors draw on examples from physics, biology, and economics to illustrate the concepts and demonstrate their practical applications. First published in 1902, this book remains an important reference for mathematicians and scientists today.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Studies on Divergent Series and Summability; Volume 2
This book presents a detailed study of divergent series and their summability. The author explores various methods for summability of divergent series, including Ces?ro summation, Abel summation, and Borel summation. The book is suitable for advanced students and researchers in mathematics and related fields.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A First Study of the Relation Between Percentage of Illiteracy and Death Rate in American Cities
This book presents a pioneering study of the relation between percentage of illiteracy and death rate in American cities. The study is based on statistical analysis of data from various sources and provides insights into the social and economic factors that affect literacy and health. The book is an important historical document and an inspiration for further research in social epidemiology.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Predictive Analytics in System Reliability
This book provides engineers and researchers knowledge to help them in system reliability analysis using machine learning, artificial intelligence, big data, genetic algorithm, information theory, multi-criteria decision making, and other techniques. It will also be useful to students learning reliability engineering.The book brings readers up to date with how system reliability relates to the latest techniques of AI, big data, genetic algorithm, information theory, and multi-criteria decision making and points toward future developments in the subject.
Foundations of Quantitative Finance: Book V General Measure and Integration Theory
Every finance professional wants and needs a competitive edge. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not-and that is the competitive edge these books offer the astute reader.
Integral Equations and Integral Transforms
This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of mathematics and physics. The book covers a range of topics including Volterra and Fredholm integral equations, the second kind of integral equations with symmetric kernels, eigenvalues and eigen functions, the Hilbert-Schmidt theorem, and the solution of Abel integral equations by using an elementary method. In addition, the book covers various integral transforms including Fourier, Laplace, Mellin, Hankel, and Z-transforms. One of the unique features of the book is a general method for the construction of various integral transforms and their inverses, which is based on the properties of delta function representation in terms of Green's function of a Sturm-Liouville type ordinary differential equation and its applications to physical problems. The book is divided into two parts: integral equations and integral transforms.Each chapter is supplemented with numerous illustrative examples to aid in understanding. The clear and concise presentation of the topics covered makes this book an ideal resource for students, researchers, and professionals interested in the theory and application of linear integral equations and integral transforms.
The Mathematical Theory of Probabilities and Its Application to Frequency Curves and Statistical Methods
This groundbreaking text provides a detailed overview of the mathematical foundations of probability theory and their applications in statistics and data analysis. With clear explanations of complex concepts and theories, this book is an essential resource for anyone working in the fields of math, science, or engineering.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Structural Equation Modeling Using R/SAS
There has been considerable attention to making the methodologies of structural equation modeling available to researchers, practitioners, and students along with commonly used software. Structural Equation Modelling Using R/SAS aims to bring it all together to provide a concise point-of-reference.
Eco-Stats: Data Analysis in Ecology
This book introduces ecologists to the wonderful world of modern tools for data analysis, especially multivariate analysis. For biologists with relatively little prior knowledge of statistics, it introduces a modern, advanced approach to data analysis in an intuitive and accessible way. The book begins by reviewing some core principles in statistics, and relates common methods to the linear model, a general framework for modeling data where the response is continuous. This is then extended to discrete data using generalized linear models, to designs with multiple sampling levels via mixed models, and to situations where there are multiple response variables via model-based approaches to multivariate analysis. Along the way there is an introduction to: important principles in model selection; adaptations of the model to handle non-linearity and cyclical variables; dependence due to structured correlation in time, space or phylogeny; and design-based techniques for inference that can relax some of the modelling assumptions. It concludes with a range of advanced topics in model-based multivariate analysis relevant to the modern ecologist, including fourth corner, latent variable and copula models. Examples span a variety of applications including environmental monitoring, species distribution modeling, global-scale surveys of plant traits, and small field experiments on biological controls. Math Boxes throughout the book explain some of the core ideas mathematically for readers who want to delve deeper, and R code is used throughout. Accompanying code, data, and solutions to exercises can be found in the ecostats R package on CRAN.
Bayesian Nonparametrics for Causal Inference and Missing Data
Bayesian nonparametric (BNP) methods can be used to flexibly model joint or conditional distributions, as well as functional relationships. These methods, along with causal and/or missingness assumptions, can be used with the g-formula to infer causal effects.
An Elementary Treatise on Frontier's Series & Spherical, Cylindrical & Ellipsoidal Harmonics
An exploration of the mathematical principles underlying the study of harmonic functions on the sphere, cylinder, and ellipsoid, this comprehensive textbook is an essential resource for anyone interested in the frontiers of applied mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Grundz羹ge Der Wahrscheinlichkeits-Rechnung
Originally published in the mid-19th century, this classic work on probability theory has stood the test of time. Hagen's clear and insightful exposition of the subject has made this book a favorite among mathematicians and students alike. Whether you are a beginner or an expert in probability theory, you will find this book to be an indispensable resource.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control
Basic Gambling Mathematics
This book explains the mathematics involved in analyzing games of chance, including casino games, horse racing and other sports, and lotteries. It is also suitable as a textbook for an introductory course on probability. Numerous examples and end-of-chapter exercises illustrate the mathematical ideas in a range of casino games.
R for Quantitative Chemistry
R for Quantitative Chemistry is an exploration of how the R language can be applied to a wide variety of problems in what is typically termed "Quantitative Chemistry" or sometimes "Analytical Chemistry". Topics include: basic statistics, spectroscopic data, acid base equilibria and titrations, binding curves (of great current interest for biomedical applications), Fourier Transforms, and chemical kinetics and enzyme kinetics. An innovative feature is the discussion (as an alternative to the less stable nls packages) of the simplex adaptation subplex (R package) coupled with Monte Carlo analysis to determine confidence intervals for estimated parameters resulting from least squares optimization. Chemists who are interested in learning R as a research tool as well as Chemists who are teaching Quantitative Chemistry, as well as their students will be interested. This book is useful as most R books approach data analysis from an economic, social, medical, or biological context. Analysis of chemical data draws upon specific numerical models and a different set R programming and packages than is typically discussed in other disciplines. This book will be based upon, in large part, actual experimental data and will include end of chapter questions and projects. Readers are encouraged to email the author at gosserch@gmail.com and to follow the accompanying blog on Medium "R Programming for Quantitative Chemistry".　　 Key Features: Elements of R programming for Chemists Literature Based Examples Includes Binding Assay Analysis Integrates theory, experiment, and R programming
Big Data Analytics
Successfully navigating the data-driven economy presupposes a certain understanding of the technologies and methods to gain insights from Big Data. This book aims to help data science practitioners to successfully manage the transition to Big Data. 　Building on familiar content from applied econometrics and business analytics, this book introduces the reader to the basic concepts of Big Data Analytics. The focus of the book is on how to productively apply econometric and machine learning techniques with large, complex data sets, as well as on all the steps involved before analysing the data (data storage, data import, data preparation). The book combines conceptual and theoretical material with the practical application of the concepts using R and SQL. The reader will thus acquire the skills to analyse large data sets, both locally and in the cloud. Various code examples and tutorials, focused on empirical economic and business research, illustrate practical techniques to handle and analyse Big Data.　　 Key Features: 　　- Includes many code examples in R and SQL, with R/SQL scripts freely provided online. 　- Extensive use of real datasets from empirical economic research and business analytics, with data files freely provided online. 　- Leads students and practitioners to think critically about where the bottlenecks are in practical data analysis tasks with large data sets, and how to address them. 　　 The book is a valuable resource for data science practitioners, graduate students and researchers who aim to gain insights from big data in the context of research questions in business, economics, and the social sciences.　
Exploring Data Science with R and the Tidyverse
This book introduces the reader to data science using R and the tidyverse. No prerequisite knowledge is needed in college-level programming or mathematics (e.g., calculus or statistics). The book is self-contained so readers can immediately begin building data science workflows without needing to reference extensive amounts of external resources for onboarding. The contents are targeted for undergraduate students but are equally applicable to students at the graduate level and beyond. The book develops concepts using many real-world examples to motivate the reader. Upon completion of the text, the reader will be able to: Gain proficiency in R programming Load and manipulate data frames, and "tidy" them using tidyverse tools Conduct statistical analyses and draw meaningful inferences from them Perform modeling from numerical and textual data Generate data visualizations (numerical and spatial) using ggplot2 and understand what is being represented An accompanying R package "edsdata" contains synthetic and real datasets used by the textbook and is meant to be used for further practice. An exercise set is made available and designed for compatibility with automated grading tools for instructor use.
Lateral Solutions to Mathematical Problems
This book offers a fresh approach to mathematical problem solving via lateral thinking. This book is appropriate for interested high school students, undergraduates and postgraduates, looking for relief from technical material and also looking for insight into the methodology of mathematics.
Recreations
Bell's book is a delightful introduction to the wonders of recreational mathematics, offering a wide range of puzzles, games, and brainteasers designed to stimulate the mind and challenge the imagination. The author's playful style and deep appreciation for the beauty and elegance of mathematics make this book a joy to read for mathematicians and non-mathematicians alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Groups of Order P3Q2
As a well-known mathematician and group theorist, the author of this book provides a deep dive into the properties and characteristics of groups of order p3q2. Covering topics such as group actions, subgroups, and isomorphisms, this book is an essential resource for anyone interested in this specialized area of mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Statistical Study Of Infant Mortality
Phelps presents a thorough analysis of the factors contributing to infant mortality rates in this seminal work of public health research.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Mensuration
Hall's book is a comprehensive guide to the principles and applications of mensuration, the branch of mathematics concerned with measuring length, area, and volume. From calculating the area of irregular polygons to finding the volume of geometric solids, this book covers a wide range of topics in clear, easy-to-understand language. This is an essential read for any student or professional working in a field that requires skills in mathematical measurement.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Big Data Analytics and Knowledge Discovery
This book constitutes the proceedings of the 25th International Conference on Big Data Analytics and Knowledge Discovery, DaWaK 2023, which took place in Penang, Malaysia, during August 29-30, 2023. The 18 full papers presented together with 19 short papers were carefully reviewed and selected from a total of 83 submissions. They were organized in topical sections as follows: Data quality; advanced analytics and pattern discovery; machine learning; deep learning; and data management.
Quaternionic Integral Transforms
This book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which have been organized and introduced by the book's editor. Each chapter presents summaries of predefined themes and provides the reader with a basis for further exploration of the topic. As one of the experimental projects initiated by Springer Nature for AI book content generation, this book shows the latest developments in the field. It will be a useful reference for students and researchers who are interested in exploring the latest developments in quaternion integral transforms.
Accelerated Linux API for Software Diagnostics
The book contains the full transcript of Software Diagnostics Services training with 16 hands-on exercises on various topics related to Linux API. Knowledge of Linux API is necessary for: DevelopmentMalware analysisVulnerability analysis and exploitationReversingDiagnosticsDebuggingMemory forensicsCrash and hang analysisSecure codingStatic code analysisTrace and log analysisThe training uses a unique and innovative pattern-oriented analysis approach and provides: OverviewClassificationPatternsInternalsDevelopment examplesAnalysis examplesComparison with Windows API
Hornbooks and Inkwells
This book presents a detailed study of divergent series and their summability. The author explores various methods for summability of divergent series, including Ces?ro summation, Abel summation, and Borel summation. The book is suitable for advanced students and researchers in mathematics and related fields.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Secretariat and Man o’ War
I began this book with the express purpose of making it the definitive comparison of Secretariat and Man o' War. I feel that I've succeeded. By engaging the discipline of applied statistics to compare the legendary achievements of these two horses, I am being completely honest about my two primary audiences-the serious Thoroughbred racing fan and those desiring a clearer comparison of runner quality that only the lens of basic statistics can provide. The statistics in this book are basic and are completely explained as the text progresses. They are not difficult-provided one is motivated to compare Thoroughbreds on an objective rather than subjective level and to spend a modicum of extra time learning the minimal eight-grade-level computations the statistics require. I personally wish all readers well on their journey into what is possibly a groundbreaking area, thereby showing their willingness to accept a very modest challenge.
Science, Music, and Mathematics
Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. In this book he offers an extraordinary synthesis, revealing the many deep connections between science, music, and mathematics. He avoids equations and technical jargon. The connections are deep in the sense of being embedded in our very nature, rooted in biological evolution over hundreds of millions of years.Michael guides us through biological evolution, perception psychology, and even unconscious science and mathematics, all the way to the scientific uncertainties about the climate crisis.He also has a message of hope for the future. Contrary to popular belief, he holds that biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is far more than a simple competition between selfish genes. Instead, he argues, in some ways it is more like the turbulent, eddying flow in a river or in an atmospheric jet stream, a complex process spanning a vast range of timescales.Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has long been interested in how different branches of science can better communicate with each other, and with the public. His work harnesses aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication, principles related to the way music works -- music of any genre.This Second Edition sharpens the previous discussion of communication skills and their importance for today's great problems, ranging from the widely discussed climate crisis to the need to understand the strengths and weaknesses of artificial intelligence.
Stochastic Elasticity
Stochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains.Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.
Science, Music, and Mathematics
Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. In this book he offers an extraordinary synthesis, revealing the many deep connections between science, music, and mathematics. He avoids equations and technical jargon. The connections are deep in the sense of being embedded in our very nature, rooted in biological evolution over hundreds of millions of years.Michael guides us through biological evolution, perception psychology, and even unconscious science and mathematics, all the way to the scientific uncertainties about the climate crisis.He also has a message of hope for the future. Contrary to popular belief, he holds that biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is far more than a simple competition between selfish genes. Instead, he argues, in some ways it is more like the turbulent, eddying flow in a river or in an atmospheric jet stream, a complex process spanning a vast range of timescales.Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has long been interested in how different branches of science can better communicate with each other, and with the public. His work harnesses aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication, principles related to the way music works -- music of any genre.This Second Edition sharpens the previous discussion of communication skills and their importance for today's great problems, ranging from the widely discussed climate crisis to the need to understand the strengths and weaknesses of artificial intelligence.
