-Explores the development of elementary students’ understanding of the mathematics of measure, demonstrating how measurement can serve as an anchor for supporting a deeper understanding of future mathematics learning, as well as learning in other STEM disciplines. -Describes a learning progression built on benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage—an approach relevant for scholars, teacher educators, and specialists in math education. -Written by two leading researchers in math and science education, who draw from decades of experience in K-5 classroom research. -Accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.

This book engages with contemporary, and often polarizing, debates surrounding the risks of adolescent use of digital media and internet technologies. By drawing on multiple research studies, the text synthesizes current understandings of the impacts of social network use, online gaming, pornography, and phenomena, including cyberbullying, cyberstalking, and internet addiction, to develop recommendations for the effective identification of at-risk youth, as well as strategies for informed communication about online risks and opportunities. It shows how media discussion of risks to children and teenagers from new technology is highly emotive and often exaggerated, rooted in the “moral panic” surrounding new cultural practices that young people engage in, but which adults do not understand. Online risks are thus conceptualized as centering on three areas, specific to adolescence, which have undergone radical changes due to new internet technology. These include young people’s identity, the types of content that are accessed, and social relationships. The author shows how these matters stem from the potential of new technology to establish new interpersonal connections, emphasizing how it brings opportunities, as much as risks. As such, he provides a uniquely balanced discussion of potential dangers, while also emphasizing the opportunities for social, academic, and personal growth which new technologies afford young people. It will be indispensable for researchers and clinicians interested in assessing levels of online risk, as well as scholars and educators with interests in cyberpsychology, social psychology, cyber culture, social aspects of computing and media, and adolescent development.

The theory developed for 2 4-additive codes is the starting point for much generalization about codes over mixed alphabets. They have opened a new, emergent area of research. The techniques used for 2 4-linear codes are being generalized and applied to more general codes. By example, these codes have contributed to the classification of many nonlinear codes. Moreover, they can be considered as the starting point of many different generalizations given over mixed alphabets, thereby representing a useful area of research. Since 2010, more than 30 papers have been published about the codes considered in the book, which includes important classes of binary codes (1-perfect, Hadamard, etc.) that are not linear in general. For example, much recent research has shown the application of the techniques described for the family of cyclic 2 4-linear codes. Topics and Features: Examines everything from the basic definitions to very advanced results Provides numerous examples, succinctly and comprehensively gathering and using the relevant information Includes examples using commands from a new Magma package, developed mostly by the same authors Proposes algorithms, for instance to describe coding and decoding strategies This unique volume will be eminently suitable for researchers working on coding theory over rings, especially over mixed alphabets. Experts will find commands and algorithms that will be useful in the generalization to codes over mixed alphabets. Additionally, by outlining the basic theory of codes over mixed alphabets and providing numerous examples, the book will be useful to researchers wanting to be introduced to the topic. The authors are all affiliated with the Dept. of Information and Communications Engineering at the Universitat Autonoma de Barcelona, Spain. Joaquim Borges and Cristina Fernandez-Cordoba are Associate Professors, Jaume Pujol is a now retired Associate Professor, Josep Rifa is Professor Emeritus, and Merce Villanueva is Associate Professor.

This book lays the foundation for a theory of uniformization of p-adic hyperbolic curves and their moduli. On one hand, this theory generalizes the Fuchsian and Bers uniformizations of complex hyperbolic curves and their moduli to nonarchimedian places. That is why in this book, the theory is referred to as p-adic Teichmuller theory, for short. On the other hand, the theory may be regarded as a fairly precise hyperbolic analog of the Serre-Tate theory of ordinary abelian varieties and their moduli. The theory of uniformization of p-adic hyperbolic curves and their moduli was initiated in a previous work by Mochizuki. And in some sense, this book is a continuation and generalization of that work. This book aims to bridge the gap between the approach presented and the classical uniformization of a hyperbolic Riemann surface that is studied in undergraduate complex analysis. Features: Presents a systematic treatment of the moduli space of curves from the point of view of p-adic Galois representations. Treats the analog of Serre-Tate theory for hyperbolic curves. Develops a p-adic analog of Fuchsian and Bers uniformization theories. Gives a systematic treatment of a ""nonabelian example"" of p-adic Hodge theory. Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

This book adopts an interdisciplinary approach to investigate the development of mathematical reasoning in both children and adults and to show how understanding the learner's cognitive processes can help teachers develop better strategies to teach mathematics. This contributed volume departs from the interdisciplinary field of psychology of mathematics education and brings together contributions by researchers from different fields and disciplines, such as cognitive psychology, neuroscience and mathematics education. The chapters are presented in the light of the three instances that permeate the entire book: the learner, the teacher, and the teaching and learning process. Some of the chapters analyse the didactic challenges that teachers face in the classroom, such as how to interpret students' reasoning, the use of digital technologies, and their knowledge about mathematics. Other chapters examine students' opinions about mathematics, and others analyse the ways in which students solve situations that involve basic and complex mathematical concepts. The approaches adopted in the description and interpretation of the data obtained in the studies documented in this book point out the limits, the development, and the possibilities of students' thinking, and present didactic and cognitive perspectives to the learning scenarios in different school settings. Mathematical Reasoning of Children and Adults: Teaching and Learning from an Interdisciplinary Perspective will be a valuable resource for both mathematics teachers and researchers studying the development of mathematical reasoning in different fields, such as mathematics education, educational psychology, cognitive psychology, and developmental psychology.

Updated classic statistics text, with new problems and examples Probability and Statistical Inference, Third Edition helps students grasp essential concepts of statistics and its probabilistic foundations. This book focuses on the development of intuition and understanding in the subject through a wealth of examples illustrating concepts, theorems, and methods. The reader will recognize and fully understand the why and not just the how behind the introduced material. In this Third Edition, the reader will find a new chapter on Bayesian statistics, 70 new problems and an appendix with the supporting R code. This book is suitable for upper-level undergraduates or first-year graduate students studying statistics or related disciplines, such as mathematics or engineering. This Third Edition Introduces an all-new chapter on Bayesian statistics and offers thorough explanations of advanced statistics and probability topics Includes 650 problems and over 400 examples - an excellent resource for the mathematical statistics class sequence in the increasingly popular "flipped classroom" format Offers students in statistics, mathematics, engineering and related fields a user-friendly resource Provides practicing professionals valuable insight into statistical tools Probability and Statistical Inference offers a unique approach to problems that allows the reader to fully integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.

Featuring research from the 2017 research symposium of the Association for Women in Mathematics, this volume presents recent findings in pure mathematics and a range of advances and novel applications in fields such as engineering, biology, and medicine. Featured topics include geometric group theory, generalized iterated wreath products of cyclic groups and symmetric groups, Conway-Coxeter friezes and mutation, and classroom experiments in teaching collegiate mathematics. A review of DNA topology and a computational study of learning-induced sequence reactivation during sharp-wave ripples are also included in this volume. Numerous illustrations and tables convey key results throughout the book. This volume highlights research from women working in academia, industry, and government. It is a helpful resource for researchers and graduate students interested in an overview of the latest research in mathematics.

This book discusses and chronicles various types of manufacturing processes, including casting and molding, machining, joining, shearing, and forming. It refers to repetitive, discrete, job shop, process manufacturing (continuous), and process manufacturing (batch). It also offers detailed examples from the nuclear, electronic, plastics, adhesives, inks, packaging, chemical, and pharmaceutical industries. Advanced Manufacturing Operations Technologies: Principles, Applications, and Design Correlations in Chemical Engineering Fields of Practice fills the gap in the connection between production and regulated applications in several industries. It highlights established concepts and provides a new fresh outlook by concentrating on and creating linkages in the implementation of practices in manufacturing and safe clean energy systems. Case studies for the overall design, installations, and construction of manufacturing operations in various industries as well as the standard operating procedures are offered. The book also discusses the correlation between design strategies including step-by-step processes to ensure the reliability, safety, and efficacy of products. The fundamentals of controlled techniques, quality by design, risk assessment, and management are covered in support of operations applications and continuous improvement. This comprehensive book is helpful to all professionals, students, and academicians in many scientific disciplines that utilize fundamental principles of chemical engineering. It is engineering-driven and will be of use to those in industrial and manufacturing, chemical, biochemical, mechanical engineering, and automated control systems fields.

Ten years from now, what do you want or expect your students to remember from your course? We realized that in ten years what matters will be how students approach a problem using the tools they carry with them- common sense and common knowledge- not the particular mathematics we chose for the curriculum. Using our text, students work regularly with real data in moderately complex everyday contexts, using mathematics as a tool and common sense as a guide. The focus is on problems suggested by the news of the day and topics that matter to students, like inflation, credit card debt, and loans. We use search engines, calculators, and spreadsheet programs as tools to reduce drudgery, explore patterns, and get information. Technology is an integral part of today's world- this text helps students use it thoughtfully and wisely. This second edition contains revised chapters and additional sections, updated examples and exercises, and complete rewrites of critical material based on feedback from students and teachers who have used this text. Our focus remains the same: to help students to think carefully- and critically- about numerical information in everyday contexts.

The first edition of this book, published in German, came into being as the result of lectures which the authors held over a period of several years since 1953 at the Universities of Helsinki and Zurich. The Introduction, which follows, provides information on what moti vated our presentation of an absolute, coordinate- and dimension-free infinitesimal calculus. Little previous knowledge is presumed of the reader. It can be recom mended to students familiar with the usual structure, based on co ordinates, of the elements of analytic geometry, differential and integral calculus and of the theory of differential equations. We are indebted to H. Keller, T. Klemola, T. Nieminen, Ph. Tondeur and K. 1. Virtanen, who read our presentation in our first manuscript, for important critical remarks. The present new English edition deviates at several points from the first edition (d. Introduction). Professor I. S. Louhivaara has from the beginning to the end taken part in the production of the new edition and has advanced our work by suggestions on both content and form. For his important support we wish to express our hearty thanks. We are indebted also to W. Greub and to H. Haahti for various valuable remarks. Our manuscript for this new edition has been translated into English by Doctor P. Emig. We express to him our gratitude for his careful interest and skillful attention during this work."

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well.

The book begins with a brief review of supersymmetry and the construction of the minimal supersymmetric standard model and approaches to supersymmetry breaking. General non-perturbative methods are also reviewing leading to the development of holomorphy and the Affleck-Dine-Seiberg superpotential as powerful tools for analyzing supersymmetric theories. Seiberg duality is discussed in detail, with many example applications provided, with special attention paid to its use in understanding dynamical supersymmetry breaking. The Seiberg-Witten theory of monopoles is introduced through the analysis of simpler N=1 analogues. Superconformal field theories are described along with the most recent development known as "a-maximization." Supergravity theories are examined in 4, 10, and 11 dimensions, allowing for a discussion of anomaly and gaugino mediation, and setting the stage for the anti-de-Sitter/conformal field theory correspondence. This book is unique in containing an overview of the important developments in supersymmetry since the publication of "Supersymmetry and Supergravity" by Wess and Bagger. It also strives to cover topics that are of interest to both formal and phenomenological theorists.

This book presents a simple and original theory of distributions, both real and vector, adapted to the study of partial differential equations. It deals with value distributions in a Neumann space, that is, in which any Cauchy suite converges, which encompasses the Banach and Frechet spaces and the same "weak" spaces. Alongside the usual operations - derivation, product, variable change, variable separation, restriction, extension and regularization - Distributions presents a new operation: weighting. This operation produces properties similar to those of convolution for distributions defined in any open space. Emphasis is placed on the extraction of convergent sub-sequences, the existence and study of primitives and the representation by gradient or by derivatives of continuous functions. Constructive methods are used to make these tools accessible to students and engineers.

It will enable parents to guide their children comfortably into the world of mathematics, using everyday examples that present themselves amidst the hustle and bustle of daily life. And it requires no special knowledge or training; just a positive attitude and a sharpening of your interactions with your children to familiarise them with maths concepts through play.

This interdisciplinary graduate text gives a full, explicit, coherent and up-to-date account of the modern theory of neural information processing systems and is aimed at student with an undergraduate degree in any quantitative discipline (e.g. computer science, physics, engineering, biology, or mathematics). The book covers all the major theoretical developments from the 1940s tot he present day, using a uniform and rigorous style of presentation and of mathematical notation. The text starts with simple model neurons and moves gradually to the latest advances in neural processing. An ideal textbook for postgraduate courses in artificial neural networks, the material has been class-tested. It is fully self contained and includes introductions to the various discipline-specific mathematical tools as well as multiple exercises on each topic.

This interdisciplinary graduate text gives a full, explicit, coherent and up-to-date account of the modern theory of neural information processing systems and is aimed at student with an undergraduate degree in any quantitative discipline (e.g. computer science, physics, engineering, biology, or mathematics). The book covers all the major theoretical developments from the 1940s tot he present day, using a uniform and rigorous style of presentation and of mathematical notation. The text starts with simple model neurons and moves gradually to the latest advances in neural processing. An ideal textbook for postgraduate courses in artificial neural networks, the material has been class-tested. It is fully self contained and includes introductions to the various discipline-specific mathematical tools as well as multiple exercises on each topic.

The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This first volume includes ten chapters written by experts well-known in their areas. The book studies the analysis of queues with interdependent arrival and service times, characteristics of fluid queues, modifications of retrial queueing systems and finite-source retrial queues with random breakdowns, repairs and customers' collisions. Some recent tendencies in the asymptotic analysis include the average and diffusion approximation of Markov queueing systems and networks, the diffusion and Gaussian limits of multi-channel queueing networks with rather general input flow, and the analysis of two-time-scale nonhomogenous Markov chains using the large deviations principle. The book also analyzes transient behavior of infinite-server queueing models with a mixed arrival process, the strong stability of queueing systems and networks, and applications of fast simulation methods for solving high-dimension combinatorial problems.

This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories have been used extensively in the theory of semigroups. Conversely, some developments in that area may inspire further developments in Universal Algebra. On the other hand, techniques of semi group theory have naturally been employed in the study of semilattices. Several papers in this volume elaborate on these interactions.

Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form more complex ones. Coming historically from algebraic topology, operads intervene now as important objects in computer science and in combinatorics. A lot of operads involving combinatorial objects highlight some of their properties and allow to discover new ones. This book portrays the main elements of this theory under a combinatorial point of view and exposes the links it maintains with computer science and combinatorics. Examples of operads appearing in combinatorics are studied. The modern treatment of operads consisting in considering the space of formal power series associated with an operad is developed. Enrichments of nonsymmetric operads as colored, cyclic, and symmetric operads are reviewed.

Award-winning Steven Strogatz, one of the foremost popularisers of maths, has written a witty and fascinating account of maths' most compelling ideas and how, so often, they are an integral part of everyday life. Maths is everywhere, often where we don't even realise. Award-winning professor Steven Strogatz acts as our guide as he takes us on a tour of numbers that - unbeknownst to the unitiated - connect pop culture, literature, art, philosophy, current affairs, business and even every day life. In The Joy of X, Strogatz explains the great ideas of maths - from negative numbers to calculus, fat tails to infinity - with clarity, wit and insight. He is the maths teacher you never had and this book is perfect for the smart and curious, the expert and the beginner.

Many people think mathematics is useless. They're wrong. In the UK, the 2.8 million people employed in mathematical science occupations contributed GBP208 billion to the economy in a single year -- that's 10 per cent of the workforce contributing 16 per cent of the economy. What's the Use? asks why there is such a vast gulf between public perceptions of mathematics and reality. It shows how mathematics is vital, often in surprising ways, behind the scenes of daily life. How politicians pick their voters. How an absurd little puzzle solved 300 years ago leads to efficient methods for kidney transplants. How an Irish mathematician's obsession with a new number system improves special effects in movies and computer games. How SatNav relies on at least six mathematical techniques. And how a bizarre, infinitely wiggly curve, helps to optimise deliveries to your door.

• Utilizes case studies from different disciplines and sectors within engineering and other related technical areas to demonstrate how to go from data, to insight, and to decision making • Introduces various approaches to build models that exploits different algorithms • Discusses predictive models that can be built through machine learning and used to mine patterns from large datasets • Explores the augmentation of technical and mathematical materials with explanatory worked examples • Includes a glossary, lecture notes, self-assessments, and worked-out practice exercises