In this book, 23 contributors offer new insights on key issues in mathematics education in early childhood. The chapters cover all mathematics curriculum-related issues in early childhood (number, geometry, patterns and structures and mathematics in daily life). Special attention is given to teachers knowledge and innovative research issues such as quantifiers among young children. Contributors are: Abraham Arcavi, Ruthi Barkai, Douglas H. Clements, Bat-Sheva Eylon, Dina Hassidov, Rina Hershkowitz, Leah Ilani, Bat-Sheva Ilany, Candace Joswick, Esther Levenson, Zvia Markovits, Zemira Mevarech, Joanne Mulligan, Sherman Rosenfeld, Flavia Santamaria, Julie Sarama, Juhaina Awawdeh Shahbari, Amal Sharif-Rasslan, Tal Sharir, Nora Scheuer, Pessia Tsamir, Dina Tirosh and Ana Clara Ventura.
This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind's concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course.
This concise text provides a clear and digestible introduction to completing quantitative research. Taking you step-by-step through the process of completing your quantitative research project, it offers guidance on: · Formulating your research question · Completing literature reviews and meta-analysis · Formulating a research design and specifying your target population and data source · Choosing an appropriate method and analysing your findings Part of The SAGE Quantitative Research Kit, this book will give you the know-how and confidence needed to succeed on your quantitative research journey.
We commonly think of society as made of and by humans, but with the proliferation of machine learning and AI technologies, this is clearly no longer the case. Billions of automated systems tacitly contribute to the social construction of reality by drawing algorithmic distinctions between the visible and the invisible, the relevant and the irrelevant, the likely and the unlikely - on and beyond platforms. Drawing on the work of Pierre Bourdieu, this book develops an original sociology of algorithms as social agents, actively participating in social life. Through a wide range of examples, Massimo Airoldi shows how society shapes algorithmic code, and how this culture in the code guides the practical behaviour of the code in the culture, shaping society in turn. The 'machine habitus' is the generative mechanism at work throughout myriads of feedback loops linking humans with artificial social agents, in the context of digital infrastructures and pre-digital social structures. Machine Habitus will be of great interest to students and scholars in sociology, media and cultural studies, science and technology studies and information technology, and to anyone interested in the growing role of algorithms and AI in our social and cultural life.
The development of inexpensive and fast computers, coupled with the discovery of efficient algorithms for dealing with polynomial equations, has enabled exciting new applications of algebraic geometry and commutative algebra. Algebraic Geometry for Robotics and Control Theory shows how tools borrowed from these two fields can be efficiently employed to solve relevant problem arising in robotics and control theory.After a brief introduction to various algebraic objects and techniques, the book first covers a wide variety of topics concerning control theory, robotics, and their applications. Specifically this book shows how these computational and theoretical methods can be coupled with classical control techniques to: solve the inverse kinematics of robotic arms; design observers for nonlinear systems; solve systems of polynomial equalities and inequalities; plan the motion of mobile robots; analyze Boolean networks; solve (possibly, multi-objective) optimization problems; characterize the robustness of linear; time-invariant plants; and certify positivity of polynomials.
From cells in our bodies to measuring the universe, big numbers are everywhere We all know that numbers go on forever, that you could spend your life counting and never reach the end of the line, so there can't be such a thing as a 'biggest number'. Or can there? To find out, David Darling and Agnijo Banerjee embark on an epic quest, revealing the answers to questions like: are there more grains of sand on Earth or stars in the universe? Is there enough paper on Earth to write out the digits of a googolplex? And what is a googolplex? Then things get serious. Enter the strange realm between the finite and the infinite, and float through a universe where the rules we cling to no longer apply. Encounter the highest number computable and infinite kinds of infinity. At every turn, a cast of wild and wonderful characters threatens the status quo with their ideas, and each time the numbers get larger.
Once the rarified stuff of scientists and statisticians, data are now at the heart of our global digital economy, transforming everything from how we perceive the value of a professional athlete to the intelligence gathering activities of governments. We are told that the right data can turn an election, help predict crime, improve our businesses, our health and our capacity to make decisions. Beginning with a simple question - how do most people encounter and experience data? - Nathaniel Tkacz sets out on a path at odds with much of the contemporary discussion about data. When we encounter data, he contends, it is often in highly routinised ways, through formatted displays and for specific cognitive tasks. What data are and can do is largely a matter of how they are formatted. To understand our 'datafied' societies, we need to turn our attention to data's formats and the powers of formatting. This book offers an account of one such format: the dashboard. From their first appearance with the horse and carriage, Tkacz guides readers on the historical development of this format. Through analyses of car dashboards, early managerial dashboards, and the gradual emergence of dashboards as a computer display technology, Tkacz shows how today's digital dashboards came to be, and how their cultural history conditions the present. Highly original and wide-ranging, this book will change how you think about data.
The strategically sound combination of edge computing and artificial intelligence (AI) results in a series of distinct innovations and disruptions enabling worldwide enterprises to visualize and realize next-generation software products, solutions and services. Businesses, individuals, and innovators are all set to embrace and experience the sophisticated capabilities of Edge AI. With the faster maturity and stability of Edge AI technologies and tools, the world is destined to have a dazzling array of edge-native, people-centric, event-driven, real-time, service-oriented, process-aware, and insights-filled services. Further on, business workloads and IT services will become competent and cognitive with state-of-the-art Edge AI infrastructure modules, AI algorithms and models, enabling frameworks, integrated platforms, accelerators, high-performance processors, etc. The Edge AI paradigm will help enterprises evolve into real-time and intelligent digital organizations. Applied Edge AI: Concepts, Platforms, and Industry Use Cases focuses on the technologies, processes, systems, and applications that are driving this evolution. It examines the implementation technologies; the products, processes, platforms, patterns, and practices; and use cases. AI-enabled chips are exclusively used in edge devices to accelerate intelligent processing at the edge. This book examines AI toolkits and platforms for facilitating edge intelligence. It also covers chips, algorithms, and tools to implement Edge AI, as well as use cases. FEATURES The opportunities and benefits of intelligent edge computing Edge architecture and infrastructure AI-enhanced analytics in an edge environment Encryption for securing information An Edge AI system programmed with Tiny Machine learning algorithms for decision making An improved edge paradigm for addressing the big data movement in IoT implementations by integrating AI and caching to the edge Ambient intelligence in healthcare services and in development of consumer electronic systems Smart manufacturing of unmanned aerial vehicles (UAVs) AI, edge computing, and blockchain in systems for environmental protection Case studies presenting the potential of leveraging AI in 5G wireless communication
Third-variable effect refers to the effect transmitted by third-variables that intervene in the relationship between an exposure and a response variable. Differentiating between the indirect effect of individual factors from multiple third-variables is a constant problem for modern researchers. Statistical Methods for Mediation, Confounding and Moderation Analysis Using R and SAS introduces general definitions of third-variable effects that are adaptable to all different types of response (categorical or continuous), exposure, or third-variables. Using this method, multiple third- variables of different types can be considered simultaneously, and the indirect effect carried by individual third-variables can be separated from the total effect. Readers of all disciplines familiar with introductory statistics will find this a valuable resource for analysis. Key Features: Parametric and nonparametric method in third variable analysis Multivariate and Multiple third-variable effect analysis Multilevel mediation/confounding analysis Third-variable effect analysis with high-dimensional data Moderation/Interaction effect analysis within the third-variable analysis R packages and SAS macros to implement methods proposed in the book
Bayesian Modeling and Computation in Python aims to help beginner Bayesian practitioners to become intermediate modelers. It uses a hands on approach with PyMC3, Tensorflow Probability, ArviZ and other libraries focusing on the practice of applied statistics with references to the underlying mathematical theory. The book starts with a refresher of the Bayesian Inference concepts. The second chapter introduces modern methods for Exploratory Analysis of Bayesian Models. With an understanding of these two fundamentals the subsequent chapters talk through various models including linear regressions, splines, time series, Bayesian additive regression trees. The final chapters include Approximate Bayesian Computation, end to end case studies showing how to apply Bayesian modelling in different settings, and a chapter about the internals of probabilistic programming languages. Finally the last chapter serves as a reference for the rest of the book by getting closer into mathematical aspects or by extending the discussion of certain topics. This book is written by contributors of PyMC3, ArviZ, Bambi, and Tensorflow Probability among other libraries.
This is a concise, easy to use, step-by-step guide for applied researchers conducting exploratory factor analysis (EFA) using Stata. In this book, Dr. Watkins systematically reviews each decision step in EFA with screen shots of Stata code and recommends evidence-based best practice procedures. This is an eminently applied, practical approach with few or no formulas and is aimed at readers with little to no mathematical background. Dr. Watkins maintains an accessible tone throughout and uses minimal jargon and formula to help facilitate grasp of the key issues users will face when applying EFA, along with how to implement, interpret, and report results. Copious scholarly references and quotations are included to support the reader in responding to editorial reviews. This is a valuable resource for upper level undergraduate and postgraduate students, as well as for more experienced researchers undertaking multivariate or structure equation modeling courses across the behavioral, medical, and social sciences.
This book investigates statistical observables for anomalous and nonergodic dynamics, focusing on the dynamical behaviors of particles modelled by non-Brownian stochastic processes in the complex real-world environment. Statistical observables are widely used for anomalous and nonergodic stochastic systems, thus serving as a key to uncover their dynamics. This study explores the cutting edge of anomalous and nonergodic diffusion from the perspectives of mathematics, computer science, statistical and biological physics, and chemistry. With this interdisciplinary approach, multiple physical applications and mathematical issues are discussed, including stochastic and deterministic modelling, analyses of (stochastic) partial differential equations (PDEs), scientific computations and stochastic analyses, etc. Through regularity analysis, numerical scheme design and numerical experiments, the book also derives the governing equations for the probability density function of statistical observables, linking stochastic processes with PDEs. The book will appeal to both researchers of electrical engineering expert in the niche area of statistical observables and stochastic systems and scientists in a broad range of fields interested in anomalous diffusion, especially applied mathematicians and statistical physicists.
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions - like zigzag persistence and multiparameter persistence - and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
The book introduces classical inequalities in vector and functional spaces with applications to probability. It develops new analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales, to transformed Brownian motions and diffusions, to Markov and point processes, renewal, branching and shock processes.In this third edition, the inequalities for martingales are presented in two chapters for discrete and time-continuous local martingales with new results for the bound of the norms of a martingale by the norms of the predictable processes of its quadratic variations, for the norms of their supremum and their p-variations. More inequalities are also covered for the tail probabilities of Gaussian processes and for spatial processes.This book is well-suited for undergraduate and graduate students as well as researchers in theoretical and applied mathematics.
A powerful and urgent call to action: to improve our lives and our societies, we must demand open access to data for all. Information is power, and the time is now for digital liberation. Access Rules mounts a strong and hopeful argument for how informational tools at present in the hands of a few could instead become empowering machines for everyone. By forcing data-hoarding companies to open access to their data, we can reinvigorate both our economy and our society. Authors Viktor Mayer-Schönberger and Thomas Ramge contend that if we disrupt monopoly power and create a level playing field, digital innovations can emerge to benefit us all. Over the past twenty years, Big Tech has managed to centralize the most relevant data on their servers, as data has become the most important raw material for innovation. However, dominant oligopolists like Facebook, Amazon, and Google, in contrast with their reputation as digital pioneers, are actually slowing down innovation and progress by withholding data for the benefit of their shareholders--at the expense of customers, the economy, and society. As Access Rules compellingly argues, ultimately it is up to us to force information giants, wherever they are located, to open their treasure troves of data to others. In order for us to limit global warming, contain a virus like COVID-19, or successfully fight poverty, everyone--including citizens and scientists, start-ups and established companies, as well as the public sector and NGOs--must have access to data. When everyone has access to the informational riches of the data age, the nature of digital power will change. Information technology will find its way back to its original purpose: empowering all of us to use information so we can thrive as individuals and as societies.
In recent years, the fast-paced development of social information and networks has led to the explosive growth of data. A variety of big data have emerged, encouraging researchers to make business decisions by analysing this data. However, many challenges remain, especially concerning data security and privacy. Big data security and privacy threats permeate every link of the big data industry chain, such as data production, collection, processing, and sharing, and the causes of risk are complex and interwoven. Blockchain technology has been highly praised and recognised for its decentralised infrastructure, anonymity, security, and other characteristics, and it will change the way we access and share information. In this book, the author demonstrates how blockchain technology can overcome some limitations in big data technology and can promote the development of big data while also helping to overcome security and privacy challenges. The author investigates research into and the application of blockchain technology in the field of big data and assesses the attendant advantages and challenges while discussing the possible future directions of the convergence of blockchain and big data. After mastering concepts and technologies introduced in this work, readers will be able to understand the technical evolution, similarities, and differences between blockchain and big data technology, allowing them to further apply it in their development and research. Author: Shaoliang Peng is the Executive Director and Professor of the College of Computer Science and Electronic Engineering, National Supercomputing Centre of Hunan University, Changsha, China. His research interests are high-performance computing, bioinformatics, big data, AI, and blockchain.
Mobile Edge Artificial Intelligence: Opportunities and Challenges presents recent advances in wireless technologies and nonconvex optimization techniques for designing efficient edge AI systems. The book includes comprehensive coverage on modeling, algorithm design and theoretical analysis. Through typical examples, the powerfulness of this set of systems and algorithms is demonstrated, along with their abilities to make low-latency, reliable and private intelligent decisions at network edge. With the availability of massive datasets, high performance computing platforms, sophisticated algorithms and software toolkits, AI has achieved remarkable success in many application domains. As such, intelligent wireless networks will be designed to leverage advanced wireless communications and mobile computing technologies to support AI-enabled applications at various edge mobile devices with limited communication, computation, hardware and energy resources.
Introduction to Number Theory covers the essential content of an introductory number theory course including divisibility and prime factorization, congruences, and quadratic reciprocity. The instructor may also choose from a collection of additional topics. Aligning with the trend toward smaller, essential texts in mathematics, the author strives for clarity of exposition. Proof techniques and proofs are presented slowly and clearly. The book employs a versatile approach to the use of algebraic ideas. Instructors who wish to put this material into a broader context may do so, though the author introduces these concepts in a non-essential way. A final chapter discusses algebraic systems (like the Gaussian integers) presuming no previous exposure to abstract algebra. Studying general systems helps students to realize unique factorization into primes is a more subtle idea than may at first appear; students will find this chapter interesting, fun and quite accessible. Applications of number theory include several sections on cryptography and other applications to further interest instructors and students alike.
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