Gini Inequality Index
Gini Inequality Index: Methods and Applications features original high-quality peer-reviewed chapters prepared by internationally acclaimed researchers.
Advanced Calculus
Advanced Calculus: Theory and Practice, Second Edition offers a text for a one- or two-semester course on advanced calculus or analysis. The text improves students' problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics. The book explains how various topics in calculus may seem unrelated but have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems.Features of the Second Edition: Improved Organization. Chapters are reorganized to address common preferences.Enhanced Coverage of Axiomatic Systems. A section is added to include Peano's system of axioms for the set of natural numbers and their use in developing the well-known properties of the set N. Expanded and Organized Exercise Collection. There are close to 1,000 new exercises, many of them with solutions or hints. Exercises are classified based on the level of difficulty. Computation-oriented exercises are paired and solutions or hints provided for the odd-numbered questions.Enrichment Material. Historical facts and biographies of over 60 mathematicians.Illustrations. Thirty-five new illustrations are added in order to guide students through examples or proofs.About the Author: John Srdjan Petrovic is a professor at Western Michigan University.
Spatial Econometric Methods in Agricultural Economics Using R
The book describes methods and techniques of spatial data and its use in monitoring agricultural resources, farms management and regional markets. Spatial econometrics models for different data types relevant to statistical units adopted in typical agricultural economics analyses, are introduced.
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.
Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko
Inverse Linear Problems on Hilbert Space and Their Krylov Solvability
This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by finite linear combinations of g, Ag, A2g, A3g, ... The closed subspace generated by the latter vectors is called the Krylov subspace of H generated by g and A. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.After giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods.This subject of this book lies at the boundary of functional analysis/operator theory and numerical analysis/approximation theory and will be of interest to graduate students and researchers in any of these fields.
Variational Views in Mechanics
This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on "Calculus of Variations in Mechanics and Related Fields". The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include: Topology optimizationIdentification of material propertiesOptimal controlPlastic flowsGradient polyconvexityObstacle problemsQuasi-monotonicity Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.
Mathematics of Public Health
Curated by the Fields Institute for Research in Mathematical Sciences from their COVID-19 Math Modelling Seminars, this first in a series of volumes on the mathematics of public health allows readers to access the dominant ideas and techniques being used in this area, while indicating problems for further research. This work brings together experts in mathematical modelling from across Canada and the world, presenting the latest modelling methods as they relate to the COVID-19 pandemic. A primary aim of this book is to make the content accessible so that researchers share the core methods that may be applied elsewhere. The mathematical theories and technologies in this book can be used to support decision makers on critical issues such as projecting outbreak trajectories, evaluating public health interventions for infection prevention and control, developing optimal strategies to return to a new normal, and designing vaccine candidates and informing mass immunization program. Topical coverage includes: basic susceptible-exposed-infectious-recovered (SEIR) modelling framework modified and applied to COVID-19 disease transmission dynamics; nearcasting and forecasting for needs of critical medical resources including personal protective equipment (PPE); predicting COVID-19 mortality; evaluating effectiveness of convalescent plasma treatment and the logistic implementation challenges; estimating impact of delays in contact tracing; quantifying heterogeneity in contact mixing and its evaluation with social distancing; modelling point of care diagnostics of COVID-19; and understanding non-reporting and underestimation. Further, readers will have the opportunity to learn about current modelling methodologies and technologies for emerging infectious disease outbreaks, pandemic mitigation rapid response, and the mathematics behind them. The volume will help the general audience and experts to better understand the important role that mathematics has been playing during this on-going crisis in supporting critical decision-making by governments and public health agencies.
The E. M. Stein Lectures on Hardy Spaces
​The book The E. M. Stein Lectures on Hardy Spaces is based on a graduate course on real variable Hardy spaces which was given by E.M. Stein at Princeton University in the academic year 1973-1974. Stein, along with C. Fefferman and G. Weiss, pioneered this subject area, removing the theory of Hardy spaces from its traditional dependence on complex variables, and to reveal its real-variable underpinnings.This book is based on Steven G. Krantz's notes from the course given by Stein. The text builds on Fefferman's theorem that BMO is the dual of the Hardy space. Using maximal functions, singular integrals, and related ideas, Stein offers many new characterizations of the Hardy spaces. The result is a rich tapestry of ideas that develops the theory of singular integrals to a new level. The final chapter describes the major developments since 1974.This monograph is of broad interest to graduate students and researchers in mathematical analysis. Prerequisites for the book include a solid understanding of real variable theory and complex variable theory. A basic knowledge of functional analysis would also be useful.
Stochastic Komatu-Loewner Evolutions
The present monograph on stochastic Komatu-Loewner evolutions (SKLEs) provides the first systematic extension of the Schramm-Loewner evolution (SLE) theory from a simply connected planar domain to multiply connected domains by using the Brownian motion with darning (BMD) that has arisen in a recent study of the boundary theory of symmetric Markov processes.This volume is presented in an accessible manner for the interested researchers and graduate students. It also brings new insights into SLEs as special cases of SKLEs. Mathematically, it can be viewed as a powerful application of stochastic analysis via BMDs to complex analysis.
The Stieltjes Integral
This book provides a detailed, rigorous treatment of the Stieltjes integral. It offers an accessible treatment of the subject to students who have had a one semester course in analysis. This book is suitable for a second semester course in analysis, and also for independent study or as the foundation for a senior thesis or Masters project.
Modeling and Simulation for Collective Dynamics
The thematic program Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications was held at the Institute for Mathematical Sciences at the National University of Singapore, from September 2019 to March 2020. Leading experts presented tutorials and special lectures geared towards the participating graduate students and junior researchers.Readers will find in this significant volume four expanded lecture notes with self-contained tutorials on modeling and simulation for collective dynamics including individual and population approaches for population dynamics in mathematical biology, collective behaviors for Lohe type aggregation models, mean-field particle swarm optimization, and consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints.This volume serves to inspire graduate students and researchers who will embark into original research work in kinetic models for collective dynamics and their applications.
Multiaxial Notch Fracture and Fatigue
This book presents unified fatigue life prediction equations for a low/medium/high cycle fatigue of metallic materials, relevant to plain materials and notched components.
Introductory Statistics for Data Analysis
This book describes the probability theory associated with frequently used statistical procedures and the relation between probability theory and statistical inference. The first third of the book is dedicated to probability theory including topics relating to events, random variables, and the Central Limit Theorem. Statistical topics then include parameter estimation with confidence intervals, hypothesis testing, chi-square tests, t tests, and several non-parametric tests. Flow charts are frequently used to facilitate an understanding of the material considered. The examples and problems in the book all concern simple data sets which can be analyzed with a simple calculator; however, the R code required to complete many examples and problems is provided as well for those that are interested.
Analytical Methods of HPLC, LCMS/MS
HPLC, LCMS/MS has become the preferred analytical methods for the Estimation of Pharmaceutical Drugs and related compounds due to its versatility, specificity and selectivity. And as Such the objectives of the present work are detailed as under.* To develop and validate Stability indicating analytical methods for separation, identification and Simultaneous estimation of some Pharmaceutical drugs using RP-HPLC, LCMS/MS, analytical methods.* To develop new analytical methods for some of the important drugs in pure and Pharmaceuticals dosage forms.* To conduct pharmacokinetic studies.The results collected from the above studies are useful for the proper review and assessment of the effectiveness and safety data obtained for the estimation of Pharmaceutical drugs.
Lectures on Variational Analysis
This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.
Principles and Applications of Dimensional Analysis and Similarity
The book provides a summary of the historical evolution of dimensional analysis, and frames the problem of dimensions, systems of units and similarity in a vision dominated by the conventions that formalise even the exact sciences.The first four chapters address the definitions, with few dimensional analysis theorems and similarity criteria. There is also the analysis of self-similarity, both of first and second kind, with a couple of completely solved problems, framed within the group theory. From chapter 5 onward, the focus is on applications in some of the engineering sectors. The number of topics is necessarily limited, but, almost always, there are details, calculations and treatment of assumptions. The book contains descriptions of some of the experimental apparatuses currently used for the realisation of physical models, such as the wind tunnel, the shaking table, the centrifuge, and with the exclusion of many others, which can be found in specialist monographies. Measurement techniques and instrumentation and statistical data processing is also available in other books. Some more specific notions, required by the context, are reported in the appendix, where appears also the description of numerous dimensionless groups, all of engineering interest, but with the exclusion of many others related to physical processes of electrical nature or physics of particles. A glossary lists the meaning of some specific terms typical of dimensional analysis and used in the book.
Optimal Quantification and Symmetry
This book offers a unique new look at the familiar quantification theory from the point of view of mathematical symmetry and spatial symmetry. Symmetry exists in many aspects of our life--for instance, in the arts and biology as an ingredient of beauty and equilibrium, and more importantly, for data analysis as an indispensable representation of functional optimality. This unique focus on symmetry clarifies the objectives of quantification theory and the demarcation of quantification space, something that has never caught the attention of researchers.Mathematical symmetry is well known, as can be inferred from Hirschfeld's simultaneous linear regressions, but spatial symmetry has not been discussed before, except for what one may infer from Nishisato's dual scaling. The focus on symmetry here clarifies the demarcation of quantification analysis and makes it easier to understand such a perennial problem as that of joint graphical display in quantification theory. The new framework will help advance the frontier of further developments of quantification theory. Many numerical examples are included to clarify the details of quantification theory, with a focus on symmetry as its operational principle. In this way, the book is useful not only for graduate students but also for researchers in diverse areas of data analysis.
Ligeti's Macroharmonies
In the third and final book of his iconic piano etudes Gy繹rgy Ligeti charts a new path relative to the rest of his musical output, representing a significant arrival in a composer's oeuvre known for its stylistic transformations. This monograph is the first dedicated study of these capstone works, investigating them through a novel lens of statistical-graphical analysis that illuminates their compositional uniqueness as well as broader questions regarding the perception of stability in musical texture.With nearly 200 graphical illustrations and a detailed commentary, this examination reveals the unique manner in which Ligeti treads between tonality and atonality--a key idea in his late style--and the centrality of processes related to broader scale areas (or "macroharmony") in articulating structures and narratives. The analytical techniques developed here are a powerful tool for investigating macroharmonic stability that can be applied to a wide range of repertoire beyond these works.This book is intended for graduate-level and professional music theorists, musicologists, performers and mathematicians.
Quantitative Epidemiology
This book is designed to train graduate students across disciplines within the fields of public health and medicine, with the goal of guiding them in the transition to independent researchers. It focuses on theories, principles, techniques, and methods essential for data processing and quantitative analysis to address medical, health, and behavioral challenges. Students will learn to access to existing data and process their own data, quantify the distribution of a medical or health problem to inform decision making; to identify influential factors of a disease/behavioral problem; and to support health promotion and disease prevention. Concepts, principles, methods and skills are demonstrated with SAS programs, figures and tables generated from real, publicly available data. In addition to various methods for introductory analysis, the following are featured, including 4-dimensional measurement of distribution and geographic mapping, multiple linear and logistic regression, Poissonregression, Cox regression, missing data imputing, and statistical power analysis.
Introductory Applied Statistics
This book offers an introduction to applied statistics through data analysis, integrating statistical computing methods. It covers robust and non-robust descriptive statistics used in each of four bivariate statistical models that are commonly used in research: ANOVA, proportions, regression, and logistic. The text teaches statistical inference principles using resampling methods (such as randomization and bootstrapping), covering methods for hypothesis testing and parameter estimation. These methods are applied to each statistical model introduced in preceding chapters.Data analytic examples are used to teach statistical concepts throughout, and students are introduced to the R packages and functions required for basic data analysis in each of the four models. The text also includes introductory guidance to the fundamentals of data wrangling, as well as examples of write-ups so that students can learn how to communicate findings. Each chapter includes problems for practice or assessment. Supplemental instructional videos are also available as an additional aid to instructors, or as a general resource to students. This book is intended for an introductory or basic statistics course with an applied focus, or an introductory analytics course, at the undergraduate level in a two-year or four-year institution. This can be used for students with a variety of disciplinary backgrounds, from business, to the social sciences, to medicine. No sophisticated mathematical background is required.
The Decline Effect
A crisis is coming for everyone who uses math and science. For decades now, the classical model of probability (the indifference principle and the Gaussian distribution) has been breaking down and revealing its limitations in fields from economics to epidemiology. Now a new approach has revealed the underlying non-classical principle behind all these 'anomalous' laws: - Pareto's law of elite incomes - Zipf's law of word frequencies - Lotka's law of scientific publications - Kleiber's law of metabolic rates - the Clausewitz-Dupuy law of combat friction - Moore's law of computing costs - the Wright-Henderson cost law - Weibull's law of electronics failures - the Flynn Effect in IQ scores - Benford's law of digit frequencies - Farr's law of epidemics - Hubbell's neutral theory of biodiversity - Rogers' law of innovation classes - Wilson's law of island biogeography - Smeed's law of traffic fatalitiesThe general law behind all these particular laws (and countless others) is the "decline effect". As a system ages or grows in size, the rules of probability subtly change. Entropy increases, rare items become rarer, and average performance measures decline. The human meaning of a decline may be positive (decreasing costs, falling epidemic mortality) or negative (lower customer loyalty, decreasing efficiency), but the mathematical pattern is always the same. The implications are enormous, as these examples show: All epidemic diseases decline in infectiousness and in lethality. HIV-AIDS went from a highly infectious, 95-percent fatal disease, to a survivable condition with a latency of decades. COVID-19 went from a death rate of 7 percent in early 2020, to under 2 percent in 2022.Hereditary dynasties around the world declined smoothly in lifespan, from hundreds of years to tens of years. When democracies replaced monarchies, the decline (in spans of party control) continued.
Functional Analysis
This textbook provides an introduction to functional analysis suitable for lecture courses to final year undergraduates or beginning graduates.Starting from the very basics of metric spaces, the book adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, including the spectral theorem, the Gelfand transform, and Banach algebras. Various applications, such as least squares approximation, inverse problems, and Tikhonov regularization, illustrate the theory. Over 1000 worked examples and exercises of varying difficulty present the reader with ample material for reflection.This new edition of Functional Analysis has been completely revised and corrected, with many passages rewritten for clarity, numerous arguments simplified, and a good amount of new material added, including new examples and exercises. The prerequisites, however, remain the same with only knowledge of linear algebra and real analysis of a singlevariable assumed of the reader.
The Decline Effect
A crisis is coming for everyone who uses math and science. For decades now, the classical model of probability (the indifference principle and the Gaussian distribution) has been breaking down and revealing its limitations in fields from economics to epidemiology. Now a new approach has revealed the underlying non-classical principle behind all these 'anomalous' laws: - Pareto's law of elite incomes - Zipf's law of word frequencies - Lotka's law of scientific publications - Kleiber's law of metabolic rates - the Clausewitz-Dupuy law of combat friction - Moore's law of computing costs - the Wright-Henderson cost law - Weibull's law of electronics failures - the Flynn Effect in IQ scores - Benford's law of digit frequencies - Farr's law of epidemics - Hubbell's neutral theory of biodiversity - Rogers' law of innovation classes - Wilson's law of island biogeography - Smeed's law of traffic fatalitiesThe general law behind all these particular laws (and countless others) is the "decline effect". As a system ages or grows in size, the rules of probability subtly change. Entropy increases, rare items become rarer, and average performance measures decline. The human meaning of a decline may be positive (decreasing costs, falling epidemic mortality) or negative (lower customer loyalty, decreasing efficiency), but the mathematical pattern is always the same. The implications are enormous, as these examples show: All epidemic diseases decline in infectiousness and in lethality. HIV-AIDS went from a highly infectious, 95-percent fatal disease, to a survivable condition with a latency of decades. COVID-19 went from a death rate of 7 percent in early 2020, to under 2 percent in 2022.Hereditary dynasties around the world declined smoothly in lifespan, from hundreds of years to tens of years. When democracies replaced monarchies, the decline (in spans of party control) continued.
Non-Gaussian Autoregressive-Type Time Series
1. Basics of Time Series.- 2. Statistical Inference for Stationary Time Series.- 3. AR Models with Stationary Non-Gaussian Positive Marginals.- 4. AR Models with Stationary Non-Gaussian Real-Valued Marginals.- 5. Some Nonlinear AR-type Models for Non-Gaussian Time series.- 6. Linear Time Series Models with Non-Gaussian Innovations.- 7. Autoregressive-type Time Series of Counts.
Topology and Approximate Fixed Points
This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory.This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces-and fundamental properties of their topologies-are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Fr矇chet-Urysohn property.The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies.By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.
Functional Analysis
This textbook presents the principles of functional analysis in a clear and concise way. The first three chapters describe the general notions of distance, integral, and norm, as well as their relations. Fundamental examples are provided in the three chapters that follow: Lebesgue spaces, dual spaces, and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the P籀lya-Szegő and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis in relation to integration and differentiation. Starting from elementary analysis and introducing relevant research, this work is an excellent resource for students in mathematics and applied mathematics. The second edition of Functional Analysis includes several improvements as well as the addition of supplementary material. Specifically, the coverage of advanced calculus and distribution theory has been completely rewritten and expanded. New proofs, theorems, and applications have been added as well for readers to explore.
Getting Started in Mathematical Life Sciences
This book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author's lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter "Notch Signaling in Embryology and Cancer", published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.
Singularly Perturbed Problems
This book collects papers from the Special Issue "Singularly Perturbed Problems: Asymptotic Analysis and Approximate Solution", published in Axioms. These papers cover different aspects of singular perturbation theory and its applications: axiomatic approach in the analytic theory of singular perturbations; asymptotic solution of various types of singularly perturbed integral-differential and integral equations with weakly and rapidly varying kernels of the integral operators; propagation of two-dimensional periodic perturbations in a viscous continuously stratified fluid; asymptotic analysis of the stochastic linear-quadratic optimal control problem with two fast timescales in the dynamics; asymptotic solution of singularly perturbed Cauchy problem for different types of differential equations with "simple" turning points; asymptotic analysis of the complete Euclidean space controllability for different types of singularly perturbed differential systems with time delays; asymptotic solution of singularly perturbed systems in the critical case by the orthogonal projector method; application of the direct scheme method to asymptotic solution of one class of optimal control problems with three-tempo state variables; asymptotic analysis and solution of a cheap control linear quadratic zero-sum differential game; analysis of asymptotic behavior of the solutions for one class of singularly perturbed Neumann boundary value problems .
Combinatorics
Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, the book presents an introduction to enumerative and algebraic combinatorics emphasizing bijective methods.
Principles of Fourier Analysis
Strikingly different from typical presentations, Principles of Fourier Analysis provides an introduction to and comprehensive overview of the mathematical theory of Fourier analysis as it is used in applications in engineering, science, and mathematics.
Statistical Evidence
This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm.
Statistical Methods for Spatial Data Analysis
Statistical Methods for Spatial Data Analysis is a comprehensive treatment of statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain. The authors deliver an outstanding treatment of semivariogram estimation and modeling, spatial analysis in the s
Introduction to Probability with R
This text presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers. Ancillary material is accessible online.
Understanding Real Analysis
This book is a one-semester text for an introduction to real analysis. The author's primary aims are to develop ideas already familiar from elementary calculus in a rigorous manner and to help students deeply understand some basic but crucial mathematical ideas.
Dependence Modeling with Copulas
This book covers recent advances in the field, including vine copula modeling of high-dimensional data. The author develops vine copula models and generalizations, discusses other multivariate constructions and parametric copula families, and presents dependence and tail properties to assist readers in copula model selection. He also covers infe
Bayesian Analysis for Population Ecology
Emphasizing model choice and model averaging, this book presents Bayesian methods for analyzing complex ecological data. Providing a basic introduction to Bayesian methods, the book includes detailed descriptions of methods that deal with covariate data and covers techniques at the forefront of research, such as model discrimination and model av
The Mathematics of Politics
It is because mathematics is often misunderstood, it is commonlybelieved it has nothing to say about politics. The high schoolexperience with mathematics, for so many the lasting impressionof the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Thosebelieving this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoningabout politics. In the search for ideal ways to make certain kindsof decisions, a lot of wasted effort can be averted if mathematics can determine thatfinding such an ideal is actually impossible in the first place.In the first three parts of this book, we address the following threepolitical questions: (1) Is there a good way to choose winners of elections?(2) Is there a good way to apportion congressional seats?(3) Is there a good way to make decisions in situations of conflict anduncertainty?In the fourth and final part of this book, we examine the ElectoralCollege system that is used in the United States to select a president.There we bring together ideas that are introduced in each of the threeearlier parts of the book.
Complex Variables
Complex Variables: A Physical Approach with Applications, Second Edition offers a notable revision. The emphasis remains on theory and practice. The first part of the text focuses on the fundamental concepts. The author then moves on to a detailed look at how complex variables are used in the real world.
Calculus of One Variable
This book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course.
Sports Math
Can you really keep your eye on the ball? How is massive data collection changing sports?Sports science courses are growing in popularity. The author's course at Roanoke College is a mix of physics, physiology, mathematics, and statistics. Many students of both genders find it exciting to think about sports. Sports problems are easy to create and state, even for students who do not live sports 24/7. Sports are part of their culture and knowledge base, and the opportunity to be an expert on some area of sports is invigorating. This should be the primary reason for the growth of mathematics of sports courses: the topic provides intrinsic motivation for students to do their best work.From the Author: "The topics covered in Sports Science and Sports Analytics courses vary widely. To use a golfing analogy, writing a book like this is like hitting a drive at a driving range; there are many directions you can go without going out of bounds. At the driving range, I pick out a small target to focus on, and that is what I have done here. I have chosen a sample of topics I find very interesting. Ideally, users of this book will have enough to choose from to suit whichever version of a sports course is being run.""The book is very appealing to teach from as well as to learn from. Students seem to have a growing interest in ways to apply traditionally different areas to solve problems. This, coupled with an enthusiasm for sports, makes Dr. Minton's book appealing to me."--Kevin Hutson, Furman University
Non-Smooth and Complementarity-Based Distributed Parameter Systems
Rectifiability
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside. This title is also available as open access on Cambridge Core.
Homological Methods in Banach Space Theory
Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century. This book, written by two world experts on homological methods in Banach space theory, gives functional analysts a new perspective on their field and new tools to tackle its problems. All techniques and constructions from homological algebra and category theory are introduced from scratch and illustrated with concrete examples at varying levels of sophistication. These techniques are then used to present both important classical results and powerful advances from recent years. Finally, the authors apply them to solve many old and new problems in the theory of (quasi-) Banach spaces and outline new lines of research. Containing a lot of material unavailable elsewhere in the literature, this book is the definitive resource for functional analysts who want to know what homological algebra can do for them.
The ASQ Certified Six Sigma Black Belt Handbook, Fourth Edition
Fully updated to reflect the 2022 ASQ Certified Six Sigma Black Belt (CSSBB) Body of Knowledge (BoK), The ASQ Certified Six Sigma Black Belt Handbook, Fourth Edition is ideal for candidates studying for the CSSBB examination. This comprehensive reference focuses on the core areas of organization-wide planning and deployment, team management, and each of the DMAIC project phases. The fourth edition of this handbook offers thorough explanations of statistical concepts in a straightforward way. It also reflects the latest technology and applications of Six Sigma and lean tools. Updates you will find in the fourth edition include: New topics and tools, such as return on investment calculations, the roles of coaching and finance in projects, process-decision program charts, interrelationship digraphs, A3 analysis, maturity models, key behavior indicators, and audit MSA A new chapter on risk analysis and managementRevamped statistics sectionsNew tables, figures, and examples to help illustrate key points
Models and Methods for Quantum Condensation and Fluids
The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose-Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.
