Time-Delay Systems and Their Applications
Time-delay systems occupy a place of central importance in all areas of science. Time-delays are often related to Physico-chemical processes, electric networks, hydraulic networks, heredity in population growth, the economy, and other related industries. Such time-delay systems can be represented by delay differential equations, delay discrete equations, or delay fractional differential equations. Some real-world problems can be modeled in a more accurate way by including time-delays. Such systems are often used to model phenomena in scientific and technological problems. These models are used in computer engineering, viscoelastic systems, diffusion processes, signal analysis, biology, forced oscillations, control theory, disease modeling, finance, and population dynamics. Recently, several attempts have been made to find an analytical solution for time-delay systems under different conditions, which leads to results on stability analysis, control problems, observability, and iterative learning control for linear or nonlinear continuous delay systems, discrete delay systems, impulsive delay systems or fractional order delay systems. The first objective of this work is to obtain the exact solutions of linear or nonlinear continuous delay systems, discrete delay systems, and fractional order delay systems. After that, as an application, the representation of solutions of these systems is used to derive the finite time stability, Hyers-Ulam stability, and controllability results. To prove the effectiveness of the proposed approach, the obtained results will be illustrated by applications, and compared with the outcomes in the existing literature.
Research Directions in Symplectic and Contact Geometry and Topology
This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past few decades, and this volume provides an accessible introduction into many active research problems in this area. The papers were written with a broad audience in mind so as to reach a wide range of mathematicians at various levels. Aside from teaching readers about developing research areas, this book will inspire researchers to ask further questions to continue to advance the field.The volume contains both original results and survey articles, presenting the results of collaborative research on a wide range of topics. These projects began at the Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology (WiSCon) in July 2019 at ICERM, Brown University. Each group of authors includedfemale and nonbinary mathematicians at different career levels in mathematics and with varying areas of expertise. This paved the way for new connections between mathematicians at all career levels, spanning multiple continents, and resulted in the new collaborations and directions that are featured in this work.
Graph Data Science with Neo4j
Supercharge your data with the limitless potential of Neo4j 5, the premier graph database for cutting-edge machine learningPurchase of the print or Kindle book includes a free PDF eBookKey Features: Extract meaningful information from graph data with Neo4j's latest version 5Use Graph Algorithms into a regular Machine Learning pipeline in PythonLearn the core principles of the Graph Data Science Library to make predictions and create data science pipelines.Book Description: Neo4j, along with its Graph Data Science (GDS) library, is a complete solution to store, query, and analyze graph data. As graph databases are getting more popular among developers, data scientists are likely to face such databases in their career, making it an indispensable skill to work with graph algorithms for extracting context information and improving the overall model prediction performance.Data scientists working with Python will be able to put their knowledge to work with this practical guide to Neo4j and the GDS library that offers step-by-step explanations of essential concepts and practical instructions for implementing data science techniques on graph data using the latest Neo4j version 5 and its associated libraries. You'll start by querying Neo4j with Cypher and learn how to characterize graph datasets. As you get the hang of running graph algorithms on graph data stored into Neo4j, you'll understand the new and advanced capabilities of the GDS library that enable you to make predictions and write data science pipelines. Using the newly released GDSL Python driver, you'll be able to integrate graph algorithms into your ML pipeline.By the end of this book, you'll be able to take advantage of the relationships in your dataset to improve your current model and make other types of elaborate predictions.What You Will Learn: Use the Cypher query language to query graph databases such as Neo4jBuild graph datasets from your own data and public knowledge graphsMake graph-specific predictions such as link predictionExplore the latest version of Neo4j to build a graph data science pipelineRun a scikit-learn prediction algorithm with graph dataTrain a predictive embedding algorithm in GDS and manage the model storeWho this book is for: If you're a data scientist or data professional with a foundation in the basics of Neo4j and are now ready to understand how to build advanced analytics solutions, you'll find this graph data science book useful. Familiarity with the major components of a data science project in Python and Neo4j is necessary to follow the concepts covered in this 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.
Spatial Networks
This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks.The book puts a special emphasis on analyzing complex systems which are organized under the form of networks where nodes and edges are embedded in space. In these networks, space is relevant, and topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields, ranging from urbanism to epidemiology.This subject is therefore at the crossroad of many fields and is of potential interest to a broad audience comprising physicists, mathematicians, engineers, geographers or urbanists. In this book, the author has expanded his previous book ("Morphogenesis of Spatial Networks") to serve as a textbook and reference on this topic for a wide range of students and professional researchers.
Information Retrieval and Natural Language Processing
This book gives a comprehensive view of graph theory in informational retrieval (IR) and natural language processing(NLP). This book provides number of graph techniques for IR and NLP applications with examples. It also provides understanding of graph theory basics, graph algorithms and networks using graph. The book is divided into three parts and contains nine chapters. The first part gives graph theory basics and graph networks, and the second part provides basics of IR with graph-based information retrieval. The third part covers IR and NLP recent and emerging applications with case studies using graph theory. This book is unique in its way as it provides a strong foundation to a beginner in applying mathematical structure graph for IR and NLP applications. All technical details that include tools and technologies used for graph algorithms and implementation in Information Retrieval and Natural Language Processing with its future scope are explained in a clear and organized format.
A History of Mathematical Impossibility
Many of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and compass, the solution of the quintic equation by radicals, Fermat's last theorem, and the impossibility of proving the parallel postulate from the other axioms of Euclidean geometry. This book tells the history of these and many other impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square. L羹tzen argues that the role of impossibility results have changed over time. At first, they were considered rather unimportant meta-statements concerning mathematics but gradually they obtained the role of important proper mathematical results that can and should be proved. While mathematical impossibility proofs are more rigorous than impossibility arguments in other areas of life, mathematicians have employed great ingenuity to circumvent impossibilities by changing the rules of the game. For example, complex numbers were invented in order to make impossible equations solvable. In this way, impossibilities have been a strong creative force in the development of mathematics, mathematical physics, and social science.
Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory
This book presents a novel unified treatment of inverse problems in optimal control and noncooperative dynamic game theory. It provides readers with fundamental tools for the development of practical algorithms to solve inverse problems in control, robotics, biology, and economics. The treatment involves the application of Pontryagin's minimum principle to a variety of inverse problems and proposes algorithms founded on the elegance of dynamic optimization theory. There is a balanced emphasis between fundamental theoretical questions and practical matters. The text begins by providing an introduction and background to its topics. It then discusses discrete-time and continuous-time inverse optimal control. The focus moves on to differential and dynamic games and the book is completed by consideration of relevant applications. The algorithms and theoretical results developed in Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory provide new insights into information requirements for solving inverse problems, including the structure, quantity, and types of state and control data. These insights have significant practical consequences in the design of technologies seeking to exploit inverse techniques such as collaborative robots, driver-assistance technologies, and autonomous systems. The book will therefore be of interest to researchers, engineers, and postgraduate students in several disciplines within the area of control and robotics.
Formal Methods Teaching
This book constitutes the proceedings of the 5th International Workshop on Formal Methods Teaching, FMTea 2023, which was held in L羹beck, Germany, in March 2023.The 7 full papers presented in this volume were carefully reviewed and selected from 10 submissions. FMTea 2023 aim is to support a worldwide improvement in learning Formal Methods, mainly by teaching but also via self-learning.
Why Accounting Is Not Boring
I wrote the first edition long before I went on the Path of the Peacemaker- The Iroquois Legend. When first published in 1975 I had founded Second City in Toronto but that is another story. Just ask Andrew Alexander. For the past 47 Years I have been on an adventure that will be covered in the Sequel to this Book. This book is a book of humor even though the Tax department insisted that it was a notebook. I won my case and was exempt from excise tax in Canada. The sequel will introduce you to information you do not know you do not know, this book is the introduction.
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.
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.
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.
Fluids Under Control
This volume presents state-of-the-art developments in theoretical and applied fluid mechanics. Chapters are based on lectures given at a workshop in the summer school Fluids under Control, held in Prague on August 25, 2021. Readers will find a thorough analysis of current research topics, presented by leading experts in their respective fields. Specific topics covered include: Magnetohydrodynamic systemsThe steady Navier-Stokes-Fourier systemBoussinesq equationsFluid-structure-acoustic interactions Fluids under Control will be a valuable resource for students interested in mathematical fluid mechanics.
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.
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.
Contemporary Mathematical Thinking
This book deals with the evolution of mathematical thought during the 20th century. Representing a unique point of view combining mathematics, philosophy and history on this issue, it presents an original analysis of key authors, for example Bourbaki, Grothendieck and Husserl. As a product of 19th and early 20th century science, a canon of knowledge or a scientific ideology, mathematical structuralism had to give way. The succession is difficult, still in progress, and uncertain. To understand contemporary mathematics, its progressive liberation from the slogans of "modern mathematics" and the paths that remain open today, it is first necessary to deconstruct the history of this long dominant current. Another conception of mathematical thought emerged in the work of mathematicians such as Hilbert or Weyl, which went beyond the narrow epistemological paths of science in the making. In this tradition, mathematical thought was accompanied by a philosophical requirement. Modernity teaches us to revive it. The book is intended for a varied public: mathematicians concerned with understanding their discipline, philosophers of science, and the erudite public curious about the progress of mathematics.
Why Accounting Is Not Boring
I wrote the first edition long before I went on the Path of the Peacemaker- The Iroquois Legend. When first published in 1975 I had founded Second City in Toronto but that is another story. Just ask Andrew Alexander. For the past 47 Years I have been on an adventure that will be covered in the Sequel to this Book. This book is a book of humor even though the Tax department insisted that it was a notebook. I won my case and was exempt from excise tax in Canada. The sequel will introduce you to information you do not know you do not know, this book is the introduction.
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.
Classification Theory. Second Edition with a new introduction
This book is for readers who have learned about first order logic; G繹del's completeness theorem; the L繹wenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories T; mainly countable. That is, properties dividing them in some sense between understandable and complicated ones.The main test problem is the number of models of T of the infinite cardinal l as a function of l. This culminates in the so-called main gap theorem saying the number is either maximal or quite small in suitable sense. Toward this, other properties are introduced and investigated, such as being stable or being super stable, where can we define dimension and weight, particularly for super stable theories.
Journal of Applied Logics. The IfCoLog Journal of Logics and their Applications. Volume 10, number 1, January 2023
The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
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.
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.
Marks’ first lessons in geometry; In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc.
Marks' first lessons in geometry; In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc., has been regarded as significant work throughout human history, and in order to ensure that this work is never lost, we have taken steps to ensure its preservation by republishing this book in a contemporary format for both current and future generations. This entire book has been retyped, redesigned, and reformatted. Since these books are not made from scanned copies, the text is readable and clear.
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.
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 .
Visual Complex Analysis
Complex Analysis is the powerful fusion of the complex numbers (involving the 'imaginary' square root of -1) with ordinary calculus, resulting in a tool that has been of central importance to science for more than 200 years. This book brings this majestic and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. The 501 diagrams of the original edition embodied geometrical arguments that (for the first time) replaced the long and often opaque computations of the standard approach, in force for the previous 200 years, providing direct, intuitive, visual access to the underlying mathematical reality. This new 25th Anniversary Edition introduces brand-new captions that fully explain the geometrical reasoning, making it possible to read the work in an entirely new way--as a highbrow comic book!
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.
A Lambda Calculus Satellite
In 1936 the notion of intuitive computability was operationalized in two different ways: via Turing machines and via lambda-calculus. The difference consisted in manipulating beads (bits) for the former approach versus manipulating trees (rewriting lambda-terms) for the latter. Both proposals turned out to formalize the same notion of computability, and led to the Church-Turing Thesis, claiming that intuitive computability is captured in the correct way.This resulted in the foundation of imperative and functional programming. Variants of lambda-calculus are being used in another powerful field of applications, namely proof-checking, the basis for certifying mathematical theorems and thereby high tech industrial products. These two areas of research are still being actively investigated and make lambda-calculus a major tool in the present stages of science and of the industrial revolution.In this book lambda-calculus is considered from another angle: as a study of these tree-like structures, investigating the relation between their shape and their action. This is like studying numbers qualitatively, rather than for their applications dealing quantitatively with objects and phenomena in the world.Barendregt's book 'The Lambda Calculus, its Syntax and Semantics' (1981/84), does treat the subject from the same methodological viewpoint, and includes several open conjectures. In the more than four decades that have passed, most - but not all - of these conjectures have been solved, sometimes in ingenious PhD theses. This 'Satellite' to the aforementioned book presents these solutions in a uniform style and adds other topics of interest.
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.
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
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.
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
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
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.
Theories of Paradox in the Middle Ages
Paradoxes seized the attention of logicians in the middle ages, and were used both as tests for the viability of theories of logic, language, epistemology, and possibly every philosophical issue, and also in the specific genre of insolubles as needing a theoretical solution, usually involving issues about signification, truth, knowledge and modality. Numerous theories were developed, not only in the Latin West, but also in the Islamic world and in the Byzantine tradition. Some of these theories are well known, others barely investigated, if at all. The papers in this volume discuss and contrast a range of these theories and consider their advantages and drawbacks, and their relation to more recent theories of paradox and antinomy. Several of the papers were presented at a workshop organised at the University of St Andrews, Scotland, as part of the Leverhulme-funded project 'Theories of Paradox in Fourteenth-Century Logic: Edition and Translation of Key Texts'.
Investigations into the Predicate Calculus
Oiva Ketonen (1913--2000) was the closest to a student the creator of modern proof theory Gerhard Gentzen ever had. Their encounter took place in 1938--39 in G繹ttingen, with Ketonen hoping to receive a suitable topic for a doctoral dissertation and Gentzen instead deeply immersed in attempts at proving the consistency of analysis. Ketonen's thesis of 1944, his only work in logic, introduced what is today called the G3-sequent calculus. It is his best-known discovery, a sequent calculus for classical propositional logic the logical rules of which are all invertible. Few read his thesis, the results of which were instead made available through a long review by Paul Bernays. Ketonen's calculus is the basis of Evert Beth's tableau method and of the sequent calculi in Stephen Kleene's influential {\it Introduction to Metamathematics}. A second result was a sharpening of the midsequent theorem, by which the number of quantifier inferences with eigenvariables could be minimized. The existence of a weakest possible midsequent followed, in the sense that if any midsequent is derivable, a weakest one is. Turning this into a contrapositive, Ketonen found a purely syntactic method for proofs of underivability that he applied to affine plane geometry. His result, in modern terms, was a positive solution to the word problem for the universal fragment of plane affine geometry, with a syntactic proof of underivability of the parallel postulate from the rest of the affine axioms as a corollary.
Linear and Complex Analysis for Applications
This book develops an understanding of sophisticated tools by using them. Complex variable theory is developed. The first three chapters and selected topics make a nice course. This course should appeal to faculty who want an integrated treatment of linear algebra and complex analysis, including applications and also reviewing vector analysis. S
Finite Geometries
Finite Geometries stands out from recent textbooks on the subject of finite geometries by having a broader scope. This textbook explains the recent proof techniques using polynomials in case of Desarguesian planes.
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
A First Course In Chaotic Dynamical Systems
A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second EditionThe long-anticipated revision of this well-liked textbook offers many new additions. In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Mandelbrot and Julia sets were barely ten years old when the first edition appeared, and most of the research involving these objects then centered around iterations of quadratic functions. This research has expanded to include all sorts of different types of functions, including higher-degree polynomials, rational maps, exponential and trigonometric functions, and many others. Several new sections in this edition are devoted to these topics.The area of dynamical systems covered in A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition is quite accessible to students and also offers a wide variety of interesting open questions for students at the undergraduate level to pursue. The only prerequisite for students is a one-year calculus course (no differential equations required); students will easily be exposed to many interesting areas of current research. This course can also serve as a bridge between the low-level, often non-rigorous calculus courses, and the more demanding higher-level mathematics courses.Features More extensive coverage of fractals, including objects like the Sierpinski carpet and othersthat appear as Julia sets in the later sections on complex dynamics, as well as an actualchaos "game." More detailed coverage of complex dynamical systems like the quadratic familyand the exponential maps. New sections on other complex dynamical systems like rational maps. A number of new and expanded computer experiments for students to perform. About the AuthorRobert L. Devaney is currently professor of mathematics at Boston University. He received his PhD from the University of California at Berkeley under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets.
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.
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.
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.
Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck
This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian.Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource formany researchers in geometry, analysis, and mathematical physics.
Math Mammoth Grade 5 Answer Keys
Math Mammoth Grade 5 Answer Keys contains the answer keys to Math Mammoth Grade 5-A and 5-B student worktexts, to all the chapter tests, the end-of-year test, and the cumulative review lessons.
