Real Harmonic Analysis
This book presents the material covered in graduate lectures delivered at The Australian National University in 2010. Real Harmonic Analysis originates from the seminal works of Zygmund and Calder籀n, pursued by Stein, Weiss, Fefferman, Coifman, Meyer and many others. Moving from the classical periodic setting to the real line, then to higher dimensional Euclidean spaces and finally to, nowadays, sets with minimal structures, the theory has reached a high level of applicability. This is why it is called real harmonic analysis: the usual exponential functions have disappeared from the picture. Set and function decomposition prevail.
Perturbed Semi-Markov Type Processes I
This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.
An Optimization Primer
This richly illustrated book introduces the subject of optimization to a broad audience with a balanced treatment of theory, models and algorithms. Through numerous examples from statistical learning, operations research, engineering, finance and economics, the text explains how to formulate and justify models while accounting for real-world considerations such as data uncertainty. It goes beyond the classical topics of linear, nonlinear and convex programming and deals with nonconvex and nonsmooth problems as well as games, generalized equations and stochastic optimization.The book teaches theoretical aspects in the context of concrete problems, which makes it an accessible onramp to variational analysis, integral functions and approximation theory. More than 100 exercises and 200 fully developed examples illustrate the application of the concepts. Readers should have some foundation in differential calculus and linear algebra. Exposure to real analysis would be helpful but is not prerequisite.
Learn Math Fast System Volume III
This is the black and white edition of the Learn Math Fast System Volume 3. This book teaches pre-algebra in just a month or two. The older you are the faster you'll learn. Topics include Order of Operations, solving for x, solving for x in terms of y, Ratios, Proportions, Combining Like Terms, Exponents, Square Root, Distributive Property, Slopes, Graphing, Y-Intercept, Linear Equations. The Learn Math Fast System is being used in all 50 States and a dozen other countries with TREMENDOUS success! Read the reviews, it's the one math program that REALLY WORKS! Everything is included; lessons, worksheets, tests, and answers with full solutions.
Poetic Logic and the Origins of the Mathematical Imagination
This book treats eighteenth-century Italian philosopher Giambattista Vico's theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and N繳簽ez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics.The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its "modifications" (his term for "creations"); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts--including mathematics--the mind has allowed humans to establish "the world of civil society," Vico's term for culture and civilization.The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.
Statistics in the Public Interest
This edited volume surveys a variety of topics in statistics and the social sciences in memory of the late Stephen Fienberg. The book collects submissions from a wide range of contemporary authors to explore the fields in which Fienberg made significant contributions, including contingency tables and log-linear models, privacy and confidentiality, forensics and the law, the decennial census and other surveys, the National Academies, Bayesian theory and methods, causal inference and causes of effects, mixed membership models, and computing and machine learning. Each section begins with an overview of Fienberg's contributions and continues with chapters by Fienberg's students, colleagues, and collaborators exploring recent advances and the current state of research on the topic. In addition, this volume includes a biographical introduction as well as a memorial concluding chapter comprised of entries from Stephen and Joyce Fienberg's close friends, former students, colleagues, and other loved ones, as well as a photographic tribute.
Demand Forecasting for Executives and Professionals
This book surveys what executives who make decisions based on forecasts and professionals responsible for forecasts should know about forecasting. It discusses how individuals and firms should think about forecasting and guidelines for good practices. No prior knowledge is assumed in this book.
Data-Driven Seo with Python
Solve SEO problems using data science. This hands-on book is packed with Python code and data science techniques to help you generate data-driven recommendations and automate the SEO workload. This book is a practical, modern introduction to data science in the SEO context using Python. With social media, mobile, changing search engine algorithms, and ever-increasing expectations of users for super web experiences, too much data is generated for an SEO professional to make sense of in spreadsheets. For any modern-day SEO professional to succeed, it is relevant to find an alternate solution, and data science equips SEOs to grasp the issue at hand and solve it. From machine learning to Natural Language Processing (NLP) techniques, Data-Driven SEO with Python provides tried and tested techniques with full explanations for solving both everyday and complex SEO problems.This book is ideal for SEO professionals who want to take their industry skills to the next level and enhance their business value, whether they are a new starter or highly experienced in SEO, Python programming, or both. What You'll LearnSee how data science works in the SEO contextThink about SEO challenges in a data driven wayApply the range of data science techniques to solve SEO issuesUnderstand site migration and relaunches areWho This Book Is ForSEO practitioners, either at the department head level or all the way to the new career starter looking to improve their skills. Readers should have basic knowledge of Python to perform tasks like querying an API with some data exploration and visualization.
The Congruences of a Finite Lattice
The congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems. Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years. It features the author's signature "Proof-by-Picture" method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner. Key features include: an insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensionscomplete proofs, an extensive bibliography and index, and over 180 illustrationsadditional chapters covering new results of the lastseven years, increasing the size of this edition to 430 pages, 360 statements, and 262 referencesThis text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices. Reviews of previous editions: "[This] monograph...is an exceptional work in lattice theory, like all the contributions by this author. The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. -- Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica LII (1), 2007 "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects." -- Mathematical Reviews
Al-Kashi's Miftah Al-Hisab, Volume III: Algebra
Jamshīd al-Kāshī's Miftāḥ al-Ḥisab (Key to Arithmetic) was largely unknown to researchers until the mid-20th century, and has not been translated to English until now. This is the third and final book in a multi-volume set that finally brings al-Kāshī's groundbreaking textbook to English audiences in its entirety. As soon as it was studied by modern researchers, Miftah changed some false assumptions about the history of certain topics in mathematics. Written as a textbook for students of mathematics, astronomy, accounting, engineering, and architecture, Miftah covers a wide range of topics in arithmetic, geometry, and algebra. By sharing al-Kāshī's most comprehensive work with a wider audience, this book will help establish a more complete history of mathematics, and extend al-Kāshī's influence into the 21st century and beyond. The book opens by briefly recounting al-Kāshī's biography, so as to situate readers in the work's rich historical context. His impressive status in the kingdom of Ulugh Beg is detailed, as well as his contributions to both mathematics and astronomy. As a master calculator and astronomer, al-Kāshī's calculations of 2π and sin(1⁰) were by far the most accurate for almost two centuries. His law of cosines is still studied in schools today. This translation contributes to the understanding and appreciation of al-Kāshī's esteemed place in the scientific world. A side-by-side presentation of the source manuscript--one of the oldest known copies--and the English translation is provided on each page. Detailed footnotes are also provided throughout, which will offer readers an even deeper look at the text's mathematical and historical basis. Researchers and students of the history of mathematics will find this volume indispensable in filling in a frequently overlooked time period and region. This volume will also provide anybody interested in the history of Islamic culture with an insightful look at one of the mathematical world's most neglected figures.
Improper Riemann Integrals
The scope of this book is the improper or generalized Riemann integral and infinite sum (series). The reader will study its convergence, principal value, evaluation and application to science and engineering.
Model-Based Clustering, Classification, and Density Estimation Using mclust in R
Model-based clustering and classification methods provide a systematic statistical approach to clustering, classification, and density estimation via mixture modeling. The model-based framework allows the problems of choosing or developing methods to be understood within the context of statistical modeling.
Operator Theory and Analysis of Infinite Networks
This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains.The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators.New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory.
Mathematics for Computation (M4C)
The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.
Complex Feedback Queue Network Models
Queuing theory has become most important discipline of Operation Research. In real world we are facing queues everywhere around us. Sometimes we see very complex type of queue networks. This book includes three complex types of queue network models. These queue network models has been analysed in stochastic environment with the facility of revisit for customer's satisfaction. Practical situations are also given at the end of every chapter. The applicability of these models is not limited to a specific situation; they are applicable to various fields. This book will be helpful for the researchers, who are working on queue network models in stochastic environment.
Climate, Chaos and COVID
Mathematical models are very much in the news now, as they are used to make decisions about our response to such vital areas as COVID-19 and climate change. Frequently, they are blamed for a series of dubious decisions, creating much concern amongst the general public. However, without mathematical models, we would have none of the modern technology that we take for granted, nor would we have modern health care, be able to forecast the climate, cook a potato, have electricity to power our home, or go into space.By explaining technical mathematical concepts in a way that everyone can understand and appreciate, Climate, Chaos and COVID: How Mathematical Models Describe the Universe sets the record straight and lifts the lid off the mystery of mathematical models. It shows why they work, how good they can be, the advantages and disadvantages of using them and how they make the modern world possible. The readers will be able to see the impact that the use of these models has on their lives, and will be able to appreciate both their power and their limitations.The book includes a very large number of both short and long case studies, many of which are taken directly from the author's own experiences of working as a mathematical modeller in academia, in industry, and between the two. These include COVID-19 and climate and how maths saves the whales, powers our home, gives us the material we need to live, and takes us into space.
Theory of Agglomerative Hierarchical Clustering
This book discusses recent theoretical developments in agglomerative hierarchical clustering. The general understanding of agglomerative hierarchical clustering is that its theory was completed long ago and there is no room for further methodological studies, at least in its fundamental structure. This book has been planned counter to that view: it will show that there are possibilities for further theoretical studies and they will be not only for methodological interests but also for usefulness in real applications. When compared with traditional textbooks, the present book has several notable features. First, standard linkage methods and agglomerative procedure are described by a general algorithm in which dendrogram output is expressed by a recursive subprogram. That subprogram describes an abstract tree structure, which is used for a two-stage linkage method for a greater number of objects. A fundamental theorem for single linkage using a fuzzy graph is proved, which uncovers several theoretical features of single linkage. Other theoretical properties such as dendrogram reversals are discussed. New methods using positive-definite kernels are considered, and some properties of the Ward method using kernels are studied. Overall, theoretical features are discussed, but the results are useful as well for application-oriented users of agglomerative clustering.
Causal Inference
A nontechnical guide to the basic ideas of modern causal inference, with illustrations from health, the economy, and public policy. Which of two antiviral drugs does the most to save people infected with Ebola virus? Does a daily glass of wine prolong or shorten life? Does winning the lottery make you more or less likely to go bankrupt? How do you identify genes that cause disease? Do unions raise wages? Do some antibiotics have lethal side effects? Does the Earned Income Tax Credit help people enter the workforce? Causal Inference provides a brief and nontechnical introduction to randomized experiments, propensity scores, natural experiments, instrumental variables, sensitivity analysis, and quasi-experimental devices. Ideas are illustrated with examples from medicine, epidemiology, economics and business, the social sciences, and public policy.
Dissipative Lattice Dynamical Systems
There is an extensive literature in the form of papers (but no books) on lattice dynamical systems. The book focuses on dissipative lattice dynamical systems and their attractors of various forms such as autonomous, nonautonomous and random. The existence of such attractors is established by showing that the corresponding dynamical system has an appropriate kind of absorbing set and is asymptotically compact in some way.There is now a very large literature on lattice dynamical systems, especially on attractors of all kinds in such systems. We cannot hope to do justice to all of them here. Instead, we have focused on key areas of representative types of lattice systems and various types of attractors. Our selection is biased by our own interests, in particular to those dealing with biological applications. One of the important results is the approximation of Heaviside switching functions in LDS by sigmoidal functions.Nevertheless, we believe that this book will provide the reader with a solid introduction to the field, its main results and the methods that are used to obtain them.
Turnpike Phenomenon and Symmetric Optimization Problems
Written by a leading expert in turnpike phenomenon, this book is devoted to the study of symmetric optimization, variational and optimal control problems in infinite dimensional spaces and turnpike properties of their approximate solutions. The book presents a systematic and comprehensive study of general classes of problems in optimization, calculus of variations, and optimal control with symmetric structures from the viewpoint of the turnpike phenomenon. The author establishes generic existence and well-posedness results for optimization problems and individual (not generic) turnpike results for variational and optimal control problems. Rich in impressive theoretical results, the author presents applications to crystallography and discrete dispersive dynamical systems which have prototypes in economic growth theory.This book will be useful for researchers interested in optimal control, calculus of variations turnpike theory and their applications, suchas mathematicians, mathematical economists, and researchers in crystallography, to name just a few.
Empowering Novel Geometric Algebra for Graphics and Engineering
This book constitutes the proceedings of the Workshop Empowering Novel Geometric Algebra for Graphics and Engineering, ENGAGE 2022, held in conjunction with Computer Graphics International conference, CGI 2022, which took place virtually, in September 2022. The 10 full papers included in this volume were carefully reviewed and selected from 12 submissions. The workshop focused specifically on important aspects of geometric algebra including algebraic foundations, digitized transformations, orientation, conic fitting, protein modelling, digital twinning, and multidimensional signal processing.
Calculus
Calculus is important for first-year undergraduate students pursuing mathematics, physics, economics, engineering, and other disciplines where mathematics plays a significant role. The book provides a thorough reintroduction to calculus with an emphasis on logical development arising out of geometric intuition. The author has restructured the subject matter in the book by using Tarski's version of the completeness axiom, introducing integration before differentiation and limits, and emphasizing benefits of monotonicity before continuity. The standard transcendental functions are developed early in a rigorous manner and the monotonicity theorem is proved before the mean value theorem. Each concept is supported by diverse exercises which will help the reader to understand applications and take them nearer to real and complex analysis.
Searching for N
"Searching for N" is a captivating collection of articles that takes readers on a journey through the fascinating world of number theory and beyond. Written by a mathematics enthusiast, this book presents classic topics like prime numbers and divisibility, but also includes surprises like short stories, anecdotes, and informational articles on a variety of different subjects. Readers will find a diverse range of chapters that explore intriguing topics such as Concrete Calculator-Word Primes, Summation of Infinite Series, Zen Master Bodhidharma, Iteration Problems, Barbelo and Gnosticism, Artificial Intelligence, and more. Each chapter attempts to offer a unique perspective on number theory, and other subjects. By delving into apparently unrelated subjects, the author attempts to uncover the interconnectedness of mathematics with our surroundings. Whether you are a seasoned mathematician or simply curious about numbers, this book is sure to engage your mind and spark your imagination. But "Searching for N" is more than just a book on number theory. It is also a story of perseverance and passion for mathematics. The author, Fitzroy, struggled with the complexity of number theory and found himself unable to solve the most challenging problems. However, he refused to give up on his dream of contributing something to the world of mathematics. Determined to find his own path, Fitzroy turned to writing as a way to express his ideas and insights. He began crafting short stories that explored the mysteries of the human psyche, often incorporating abstract concepts and philosophical ideas into his writing. Despite his struggles with mathematical problem-solving, a few of his stories resonated with readers and were admired for their emotional power and insight. Join Fitzroy on his journey through "Searching for N" and discover the beauty and power of number theory, and the importance of perseverance and passion in pursuing one's dreams.
Generalized Radon Transforms and Imaging by Scattered Particles
A generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models of various imaging modalities. The GRTs integrating along smooth curves and surfaces (lines, planes, circles, spheres, amongst others) have been studied at great lengths for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. Recently, an interesting new class of GRTs emerged at the forefront of research in integral geometry. The two common features of these transforms are the presence of a 'vertex' in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).This book covers the relevant imaging modalities, their mathematical models, and the related GRTs. The discussion of the latter comprises a thorough exploration of their known mathematical properties, including injectivity, inversion, range description and microlocal analysis. The mathematical background required for reading most of the book is at the level of an advanced undergraduate student, which should make its content attractive for a large audience of specialists interested in imaging. Mathematicians may appreciate certain parts of the theory that are particularly elegant with connections to functional analysis, PDEs and algebraic geometry.
Geometry, Geodesics, and the Universe
The story of the development of geometry is told as it emerged from the concepts of the ancient Greeks, familiar from high school, to the four-dimensional space-time that is central to our modern vision of the universe. The reader is first reacquainted with the geometric system compiled by Euclid with its postulates thought to be self-evident truths. A particular focus is on Euclid's fifth postulate, the Parallel Postulate and the many efforts to improve Euclid's system over hundreds of years by proving it from the first four postulates. Two thousand years after Euclid, in the process that would reveal the Parallel Postulate as an independent postulate, a new geometry was discovered that changed the understanding of geometry and mathematics, while paving the way for Einstein's General Relativity. The mathematics to describe the non-Euclidean geometries and the geometric universe of General Relativity is initiated in the language of mathematics available to a general audience. The story is told as a mathematical narrative, bringing the reader along step by step with all the background needed in analytic geometry, the calculus, vectors, and Newton's laws to allow the reader to move forward to the revolutionary extension of geometry by Riemann that would supply Einstein with the language needed to overthrow Newton's universe. Using the mathematics acquired for Riemannian geometry, the principles behind Einstein's General Relativity are described and their realization in the Field Equations is presented. From the Field Equations, it is shown how they govern the curved paths of light and that of planets along the geodesics formed from the geometry of space-time, and how they provide a picture of the universe's birth, expansion, and future. Thus, Euclid's geometry while no longer thought to spring from perceived absolute truths as the ancients believed, ultimately provided the seed for a new understanding of geometry that in its infinite variety became central to the description of the universe, marking mathematics as a one of the great modes of human expression.
Regression
Now in its second edition, this textbook provides an applied and unified introduction to parametric, nonparametric and semiparametric regression that closes the gap between theory and application. The most important models and methods in regression are presented on a solid formal basis, and their appropriate application is shown through numerous examples and case studies. The most important definitions and statements are concisely summarized in boxes, and the underlying data sets and code are available online on the book's dedicated website. Availability of (user-friendly) software has been a major criterion for the methods selected and presented.The chapters address the classical linear model and its extensions, generalized linear models, categorical regression models, mixed models, nonparametric regression, structured additive regression, quantile regression and distributional regression models. Two appendices describe the required matrix algebra, as well as elements of probability calculus and statistical inference.In this substantially revised and updated new edition the overview on regression models has been extended, and now includes the relation between regression models and machine learning, additional details on statistical inference in structured additive regression models have been added and a completely reworked chapter augments the presentation of quantile regression with a comprehensive introduction to distributional regression models. Regularization approaches are now more extensively discussed in most chapters of the book.The book primarily targets an audience that includes students, teachers and practitioners in social, economic, and life sciences, as well as students and teachers in statistics programs, and mathematicians and computer scientists with interests in statistical modeling and data analysis. It is written at an intermediate mathematical level and assumes only knowledge of basic probability, calculus, matrix algebra and statistics.
Fiber Bundles
​This book presents a critical overview of statistical fiber bundle models, including existing models and potential new ones. The authors focus on both the physical and statistical aspects of a specific load-sharing example: the breakdown for circuits of capacitors and related dielectrics. In addition, they investigate some areas of open research.This book is designed for graduate students and researchers in statistics, materials science, engineering, physics, and related fields, as well as practitioners and technicians in materials science and mechanical engineering.
Basic Topology 3
This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.
Mathematical Logic
This book gathers together a colorful set of problems on classical Mathematical Logic, selected from over 30 years of teaching. The initial chapters start with problems from supporting fields, like set theory (ultrafilter constructions), full-information game theory (strategies), automata, and recursion theory (decidability, Kleene's theorems). The work then advances toward propositional logic (compactness and completeness, resolution method), followed by first-order logic, including quantifier elimination and the Ehrenfeucht- Fra簿ss矇 game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson's theory, Peano's axiom system, and G繹del's incompleteness theorems. Finally, the book touches universal graphs, tournaments, and the zero-one law in Mathematical Logic. Instructors teaching Mathematical Logic, as well as students who want to understand its concepts and methods, can greatly benefit from this work. The style and topics have been specially chosen so that readers interested in the mathematical content and methodology could follow the problems and prove the main theorems themselves, including G繹del's famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.
Quantifying Counterfactual Military History
Forces shaping human history are complex, but the course of history is undeniably changed on many occasions by conscious acts. These may be premeditated or responsive, calmly calculated or performed under great pressure. They may also be successful or catastrophic, but how are historians to make such judgements and appeal to evidence in support of their conclusions? Further, and crucially, how exactly are we to distinguish probable unrealized alternatives from improbable ones? This book describes some of the modern statistical techniques that can begin to answer this question, as well as some of the difficulties in doing so. Using simple, well-quantified cases drawn from military history, we claim that statistics can now help us to navigate the near-truths, the envelope around the events with which any meaningful historical analysis must deal, and to quantify the basis of such analysis. Quantifying Counterfactual Military History is intended for a general audience who are interested in learning more about statistical methods both in military history and for wider applications.Key Features: This book demonstrates how modern statistical techniques can measure the impact of counterfactual decisions. It examines the importance of counterfactual reasoning for both modern scholars and historical actors. It combines historical narrative, mathematical precision and data to create a straightforward presentation of both factual and counterfactual military history. It provides an original contribution to the debate over the validity and rigour of works of counterfactual history. It is written in a manner accessible to readers who have no formal training in History or Statistics.
Quantifying Counterfactual Military History
Forces shaping human history are complex, but the course of history is undeniably changed on many occasions by conscious acts. These may be premeditated or responsive, calmly calculated or performed under great pressure. They may also be successful or catastrophic, but how are historians to make such judgements and appeal to evidence in support of their conclusions? Further, and crucially, how exactly are we to distinguish probable unrealized alternatives from improbable ones? This book describes some of the modern statistical techniques that can begin to answer this question, as well as some of the difficulties in doing so. Using simple, well-quantified cases drawn from military history, we claim that statistics can now help us to navigate the near-truths, the envelope around the events with which any meaningful historical analysis must deal, and to quantify the basis of such analysis. Quantifying Counterfactual Military History is intended for a general audience who are interested in learning more about statistical methods both in military history and for wider applications. Key Features: This book demonstrates how modern statistical techniques can measure the impact of counterfactual decisions. It examines the importance of counterfactual reasoning for both modern scholars and historical actors. It combines historical narrative, mathematical precision and data to create a straightforward presentation of both factual and counterfactual military history. It provides an original contribution to the debate over the validity and rigour of works of counterfactual history. It is written in a manner accessible to readers who have no formal training in History or Statistics.
Data Science in Practice
Data Science in Practice is the ideal introduction to data science. With or without math skills, here, you get the all-round view that you need for your projects. This book describes how to properly question data, in order to unearth the treasure that data can be. You will get to know the relevant analysis methods, and will be introduced to the programming language R, which is ideally suited for data analysis. Associated tools like notebooks that make data science programming easily accessible are included in this introduction. Because technology alone is not enough, this book also deals with problems in project implementation, illuminates various fields of application, and does not forget to address ethical aspects. Data Science in Practice includes many examples, notes on errors, decision-making aids, and other practical tips. This book is ideal as a complementary text for university students, and is a useful learning tool for those moving into more data-related roles.Key Features: Success factors and tools for all project phases Includes application examples for various subject areas Introduces many aspects of Data Science, from requirements analysis to data acquisition and visualization
An Introduction to the Math of Voting Methods
Some modern political discussions are focused on electoral reform and the mechanics of democracy. For instance, Maine and Alaska recently adopted new procedures for statewide elections that involve Ranked Choice Voting, while a similar ballot measure in Massachusetts was only narrowly defeated. Meanwhile, countries all over the world use other voting methods with runoffs or scores. It's important for people to be aware of how different voting methods work in practice so that we can have productive debates about which to use in various situations.​Accordingly, this book will teach you about a variety of voting methods through concrete examples and clear explanations. Each chapter illustrates a different type of voting method using basic definitions, real-world examples, a list of pros and cons, and detailed practice problems with solutions. No prior mathematical or political knowledge is assumed. In fact, the prose is designed for a wide audience, making this book ideal for a general education mathematics course or anyone else who is curious to learn about different methods of voting.
Numerical Techniques in MATLAB
In this book, various numerical methods are discussed in a comprehensive way. It delivers a mixture of theory, examples and MATLAB practicing exercises to help the students in improving their skills. The MATLAB codes are mentioned in the end of each topic. Throughout the text, a balance between theory, examples and programming is maintained.
The Football Maths Book - The Birthday Party
"The Football Maths book - The Birthday Party"is a maths teaching aid for 7-8 year old football fans. It is a fun way for children to improve boththeir maths skills and their soccer knowledge.Children will learn about match times, how to reada league table, calculating goals for and against, player heights, football pitch layouts and many more football terms. At the same time they will learn about polygons, patterns, logic puzzles, angles, times tables and much more.
A Book for Thinkers!
The idea for this book came to the author when he was talking with some men and women who had been looking at and thinking about how to better understand some of today's problems. They said they would appreciate and enjoy activities to help them understand new issues and arrive at better and valid conclusions, but they added to please keep it simple.
A Book for Thinkers!
The idea for this book came to the author when he was talking with some men and women who had been looking at and thinking about how to better understand some of today's problems. They said they would appreciate and enjoy activities to help them understand new issues and arrive at better and valid conclusions, but they added to please keep it simple.
A Data Analyst Walks Into a Bar(graph)
This book is about silly research studies and how they can both be illustrative of the research process and funny (with the focus on funny). This book has a two-fold purpose. The first is to show that research studies, even with the best of intention, can be flawed to the point of being ridiculous. The second is to show the reader how they can develop their own study, using available software and techniques to develop a new hobby. Have you ever imagined what it was like to perform a research study? Well, here is your chance. Read the book and maybe you can laugh and learn at the same time.
Integral Inequalities and Generalized Convexity
The book covers several new research findings in the area of generalized convexity and integral inequalities. Integral inequalities using various type of generalized convex functions are applicable in many branches of mathematics such as mathematical analysis, fractional calculus, and discrete fractional calculus.
Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification
This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference "Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification", held on the occasion of Chari's 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari's significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorificationQuantum affine algebras and cluster algebrasSteinberg groups for Jordan pairsDynamical quantum determinants and PfaffiansInteractions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.
