Mathematics of Discrete Structures for Computer Science

Research on connectionist models is one of the most exciting areas in cognitive science, and neural network models of psychopathology have immediate theoretical and empirical appeal. The contributors to this study review theoretical, historical and clinical issues, including the contribution of neural network models to diagnosis, pharmacotherapy and psychotherapy. Models are presented for a range of disorders, including schizophrenia, obsessive-compulsive disorder, dissociative phenomena, autism and Alzheimer's disease. This book will appeal to a broad audience. On the one hand, it will be read with interest by psychiatrists, psychologists and other clinicians and researchers in psychopathology. On the other, it will appeal to those working in cognitive science and artificial intelligence, and particularly those interested in neural network or connectionist models.

Research on connectionist models is one of the most exciting areas in cognitive science, and neural network models of psychopathology have immediate theoretical and empirical appeal. The contributors to this study review theoretical, historical and clinical issues, including the contribution of neural network models to diagnosis, pharmacotherapy and psychotherapy. Models are presented for a range of disorders, including schizophrenia, obsessive-compulsive disorder, dissociative phenomena, autism and Alzheimer's disease. This book will appeal to a broad audience. On the one hand, it will be read with interest by psychiatrists, psychologists and other clinicians and researchers in psychopathology. On the other, it will appeal to those working in cognitive science and artificial intelligence, and particularly those interested in neural network or connectionist models.

The essential guide for anyone wanting a quick introduction to the fundamental ideas underlying photonics. The author uses his forty years of experience in photonics research and teaching to provide intuitive explanations of key concepts, and demonstrates how these relate to the operation of photonic devices and systems. Readers will gain insight into the nature of light and the ways in which it interacts with materials and structures, and learn how these basic ideas are applied in areas such as optical systems, 3D imaging and astronomy. Carefully designed worked examples and end-of-chapter problems enable students to check their understanding, with full solutions available online. Mathematical treatments are kept as simple as possible, allowing readers to grasp even the most complex of concepts. Clear, concise and accessible, this is the perfect guide for undergraduate students taking a first course in photonics, and anyone in academia or industry wanting to review the fundamentals.

The essential guide for anyone wanting a quick introduction to the fundamental ideas underlying photonics. The author uses his forty years of experience in photonics research and teaching to provide intuitive explanations of key concepts, and demonstrates how these relate to the operation of photonic devices and systems. Readers will gain insight into the nature of light and the ways in which it interacts with materials and structures, and learn how these basic ideas are applied in areas such as optical systems, 3D imaging and astronomy. Carefully designed worked examples and end-of-chapter problems enable students to check their understanding, with full solutions available online. Mathematical treatments are kept as simple as possible, allowing readers to grasp even the most complex of concepts. Clear, concise and accessible, this is the perfect guide for undergraduate students taking a first course in photonics, and anyone in academia or industry wanting to review the fundamentals.

This book is concerned with the relationship between semantics and surface structure and in particular with the way in which each is mapped into the other. Jim Miller argues that semantic and syntactic structure require different representations and that semantic structure is far more complex than many analysts realise. He argues further that semantic structure should be based on notions of location and movement. The need for a semantic component of greater complexity is demonstrated by an examination of prepositions, particles, adverbs and verb-prefixes, and is shown to accord with cross-language and historical facts. The volume goes on to consider the sort of rules that are required to map semantic structures onto syntax. Semantics and Syntax tackles fundamental issues and draws together many of the key concepts of traditional grammar and formal linguistics. The general framework for handling syntax, semantics and morphology that it outlines is perhaps a controversial one, but it wil

Scientific thinking has long been linked to music theory and instrument making, yet the profound and often surprising intersections between the sciences and opera during the long nineteenth century are here explored for the first time. These touch on a wide variety of topics, including vocal physiology, theories of listening and sensory communication, technologies of theatrical machinery and discourses of biological degeneration. Taken together, the chapters reveal an intertwined cultural history that extends from backstage hydraulics to drawing-room hypnotism, and from laryngoscopy to theatrical aeronautics. Situated at the intersection of opera studies and the history of science, the book therefore offers a novel and illuminating set of case studies, of a kind that will appeal to historians of both science and opera, and of European culture more generally from the French Revolution to the end of the Victorian period.

Scientific thinking has long been linked to music theory and instrument making, yet the profound and often surprising intersections between the sciences and opera during the long nineteenth century are here explored for the first time. These touch on a wide variety of topics, including vocal physiology, theories of listening and sensory communication, technologies of theatrical machinery and discourses of biological degeneration. Taken together, the chapters reveal an intertwined cultural history that extends from backstage hydraulics to drawing-room hypnotism, and from laryngoscopy to theatrical aeronautics. Situated at the intersection of opera studies and the history of science, the book therefore offers a novel and illuminating set of case studies, of a kind that will appeal to historians of both science and opera, and of European culture more generally from the French Revolution to the end of the Victorian period.

Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention. The authors fix standard notation and terminology, establish the basic common principles, and illustrate the impact of reversibility in such diverse areas as group theory, differential and analytic geometry, number theory, complex analysis and approximation theory. As well as showing connections between different fields, the authors' viewpoint reveals many open questions, making this book ideal for graduate students and researchers. The exposition is accessible to readers at the advanced undergraduate level and above.

This introduction to the theory of Hamiltonian chaos outlines the main results in the field, and goes on to consider implications for quantum mechanics. The study of nonlinear dynamics, and in particular of chaotic systems, is one of the fastest growing and most productive areas in physics and applied mathematics. In its first six chapters, this timely book introduces the theory of classical Hamiltonian systems. The aim is not to be comprehensive but, rather, to provide a mathematical trunk from which the reader will be able to branch out. The main focus is on periodic orbits and their neighbourhood, as this approach is especially suitable as an introduction to the implications of the theory of chaos in quantum mechanics, which are discussed in the last three chapters.

Learning Pharmacology through Clinical Cases by Mario Babbini and Sandeep Bansal uniquely integrates the preclinical disciplines, which is crucial for pharmacological problem solving and learning to think critically. Each case portrays a real-life scenario, promoting a bridge from foundational knowledge to its application. A series of USMLE-style questions with thorough explanations guide the reader through a comprehensive understanding of relevant basic science disciplines such as physiology, pathology, and microbiology, followed by a detailed analysis of the pharmacology.Key FeaturesNearly 50 case studies mirror situations seen in every-day practiceIn-depth coverage of drugs in the context of specific disease states and clinical situationsComprehensive cases encompass medical/family/drug history, physical examination, lab findings, diagnosis, pharmacotherapy, and follow-upOne set of multiple choice questions addresses related basic science content. A second set covers topics related

這套盒書有10本平裝書，每本112頁，藍思分級780L。弗蘭妮·斯坦因不是普通女孩——她是一位瘋狂的科學家。 與雛菊相比，她更喜歡毒藤，當弗蘭妮跳繩時，她會使用她的寵物蛇。 弗蘭妮班上的孩子們認為她很奇怪、古怪，而且簡直令人毛骨悚然。Fans of Goosebumps and Bill Nye the Science Guy will fall head over heels for Franny K. Stein in this collectible paperback boxed set with the first ten laugh-out-loud experimental adventures in the Mad Scientist series.Franny K. Stein is not your average girl—she’s a mad scientist. Her science experiments cause many misadventures from turning herself invisible to causing the ultimate bad hair day and more! Through it all, Franny relies on her wits and stays true to herself to save the day.This delightfully mad paperback collection includes:Lunch Walks Among UsAttack of the 50-Ft. CupidThe Invisible FranThe Fran That Time ForgotFrantastic VoyageThe Fran with Four BrainsThe FrandidateBad Hair DayRecipe for DisasterMood Science

This book highlights accounts of women workers to capture the domains of gendered mobility, which challenges the exalted status conferred on women in the Kerala model of development. It contests and deconstructs the development discourse which considers women's work mobility as an indicator of autonomy and agency using Capability Approach. The concept of 'transformational mobility' and its measurement introduced in the book advances the understanding of mobility, autonomy and agency and the intersectionality in the context of gender and work. Through an in-depth exploration of lived experiences of informal women workers the author illustrates how patriarchal structures are shaped and reinforced by work places, markets and the state. The central question is - can we steer development policies to facilitate collective capabilities for women where informal work arrangements are becoming the norm?

This 2002 book is a comprehensive analysis of the forces of the Spanish left - interpreted broadly - during the civil war of 1936–9, and the first of its kind for more than thirty years. It argues two crucial propositions. First, that the wartime responses (and limitations) of the Spanish left - republicans, socialists, communists and anarcho-syndicalists - can be understood only in relation to their pre-war experiences, world views, organisational structures and the wider Spanish context of acute uneven development which had moulded their organisations over previous decades. Second, that the overarching influence that shaped the evolution of the Republic between 1936 and 1939 was the war itself: the book explores the complex, cumulative effects of a civil war fought under the brutally destabilising conditions of an international arms embargo.

The best-selling, Pulitzer Prize–winning author of The Road returns with the second of a two-volume masterpiece: Stella Maris is an intimate portrait of grief and longing, as a young woman in a psychiatric facility seeks to understand her own existence.1972, BLACK RIVER FALLS, WISCONSIN: Alicia Western, twenty years old, with forty thousand dollars in a plastic bag, admits herself to the hospital. A doctoral candidate in mathematics at the University of Chicago, Alicia has been diagnosed with paranoid schizophrenia, and she does not want to talk about her brother, Bobby. Instead, she contemplates the nature of madness, the human insistence on one common experience of the world; she recalls a childhood where, by the age of seven, her own grandmother feared for her; she surveys the intersection of physics and philosophy; and she introduces her cohorts, her chimeras, the hallucinations that only she can see. All the while, she grieves for Bobby, not quite dead, not quite hers. Told entire

The best-selling, Pulitzer Prize–winning author of The Road returns with the second of a two-volume masterpiece: Stella Maris is an intimate portrait of grief and longing, as a young woman in a psychiatric facility seeks to understand her own existence.1972, BLACK RIVER FALLS, WISCONSIN: Alicia Western, twenty years old, with forty thousand dollars in a plastic bag, admits herself to the hospital. A doctoral candidate in mathematics at the University of Chicago, Alicia has been diagnosed with paranoid schizophrenia, and she does not want to talk about her brother, Bobby. Instead, she contemplates the nature of madness, the human insistence on one common experience of the world; she recalls a childhood where, by the age of seven, her own grandmother feared for her; she surveys the intersection of physics and philosophy; and she introduces her cohorts, her chimeras, the hallucinations that only she can see. All the while, she grieves for Bobby, not quite dead, not quite hers. Told entire

Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Part I introduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various A- and B-models in mirror symmetry and their connections through toric and tropical geometry. Part III deals with mirror symmetry for Riemann surfaces. The main mathematical ideas are illustrated by means of simple examples coming mainly from the theory of surfaces, helping the reader connect theory with intuition.

Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Part I introduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various A- and B-models in mirror symmetry and their connections through toric and tropical geometry. Part III deals with mirror symmetry for Riemann surfaces. The main mathematical ideas are illustrated by means of simple examples coming mainly from the theory of surfaces, helping the reader connect theory with intuition.

An analysis of the first and most comprehensive study of the influence of movies on American youth, the Payne Fund Studies. First published in 1933, these studies are intrinsically important for their insights and conclusions regarding the effects of movies on behaviour. They are, moreover, also an important landmark of modern social science research, demonstrating the rapid evolution of this discipline in American academic institutions over the first three decades of the century. Based on more recently discovered primary sources, whose contents are published here for the first time, this volume also reproduces the long-missing first Payne Fund study in its entirety.

This is the first of two volumes announcing the emergence of the new legal realism as a field of study. At a time when the legal academy is turning to social science for new approaches, these volumes chart a new course for interdisciplinary research by synthesizing law on the ground, empirical research, and theory. Volume 1 lays the groundwork for this novel and comprehensive approach with an innovative mix of theoretical, historical, pedagogical, and empirical perspectives. Their empirical work covers such wide-ranging topics as the financial crisis, intellectual property battles, the legal disenfranchisement of African-American landowners, and gender and racial prejudice on law school faculties. The methodological blueprint offered here will be essential for anyone interested in the future of law-and-society.

The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.

The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.

A comprehensive textbook in which the author describes the science of waves in liquids and gases. Drawing on a subject of enormous extent and variety, he provides his readers with a thorough analysis of the most important and representative types of waves including sound waves, shock waves, waterwaves of all kinds, and the so-called internal waves (inside atmospheres and oceans) due to intensity stratification. Emphasis throughout is on the most generally useful fundamental ideas of wave science, including the principles of how waves interact with flows. This standard work on one of the great subdivisions of the dynamics of fluids is lucidly written and will be invaluable to engineers, physicists, geophysicists, applied mathematicians or any research worker concerned with wave motions or fluid fllows. It is especially suitable as a textbook for courses at the final year undergraduate or graduate level.

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. Accompanying the mathematical derivations are full implementations of dozens of numerical methods in Python, as well as more than 250 end-of-chapter problems. Numerical methods and physics examples are clearly separated, allowing this introductory book to be later used as a reference; the penultimate section in each chapter is an in depth project, tackling physics problems which cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. Accompanying the mathematical derivations are full implementations of dozens of numerical methods in Python, as well as more than 250 end-of-chapter problems. Numerical methods and physics examples are clearly separated, allowing this introductory book to be later used as a reference; the penultimate section in each chapter is an in depth project, tackling physics problems which cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the

With this comprehensive and accessible introduction to the field, you will gain all the skills and knowledge needed to work with current and future audio, speech, and hearing processing technologies. Topics covered include mobile telephony, human-computer interfacing through speech, medical applications of speech and hearing technology, electronic music, audio compression and reproduction, big data audio systems and the analysis of sounds in the environment. All of this is supported by numerous practical illustrations, exercises, and hands-on MATLAB® examples on topics as diverse as psychoacoustics (including some auditory illusions), voice changers, speech compression, signal analysis and visualisation, stereo processing, low-frequency ultrasonic scanning, and machine learning techniques for big data. With its pragmatic and application driven focus, and concise explanations, this is an essential resource for anyone who wants to rapidly gain a practical understanding of speech and audi

'Mass terms' like water, rice and traffic, have proved very difficult to accommodate in any theory of meaning since, unlike count nouns such as house or dog, they cannot be treated as denoting sets of individuals. In this study, motivated by the need to design a computer program for understanding natural language utterances containing mass terms, Harry Bunt provides a thorough analysis of the problem and offers an original and detailed solution. An extension of classical set theory, Ensemble Theory, is defined. This provides the formal basis of a framework for the analysis of natural language meaning which Dr Bunt calls two-level model-theoretic semantics. The validity of the framework is convincingly demonstrated by the detailed analysis of a fragment of English including sentences with quantified and modified mass terms. This significant advance in our understanding of the formal syntactic and semantic properties of mass terms will be of interest not only to linguists and logicians,

The first edition of this popular book on particle physics received universal acclaim for its clear and readable style. In this second edition the authors have brought the subject right up to date, including the discovery of the 'top quark' and the search for the Higgs particle. The book is the result of a collaboration between a world-famous elementary particle physicist and a physicist specialising in popular science writing. Together they have produced a fascinating account of the search for the fundamental building blocks of matter. This lucid and entertaining accountwill fascinate anyone wishing to keep pace with this part of the progress of human knowledge, from scientifically educated general readers through to professional physicists.

In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is often to study a corresponding inequality; for example, using sub and superharmonic functions to study harmonic functions. Another unusual feature of the present book is that it is based on integral representation formulae and nonlinear potentials, which have not been widely investigated so far. This approach can also be used to tackle higher order differential equations. The book will appeal to graduate students interested in analysis, researchers in pure and applied mathematics, and engineers who work with partial differential equations. Readers will require only a basic knowledge of functional analysis, measure theory and Sobolev spaces.

An integrated collection of essays examining the politics, social networks, law, historiography, and literature of the later Roman world. The volume treats three central themes: the first section looks at political and social developments across the period and argues that, in spite of the stress placed upon traditional social structures, many elements of Roman life remained only slightly changed. The second section focuses upon biographical texts and shows how late-antique authors adapted traditional modes of discourse to new conditions. The final section explores the first years of the reign of Theodosius I and shows how he built upon historical foundations while unfurling new methods for utilising, presenting, and commemorating imperial power. These papers analyse specific events and local developments to highlight examples of both change and continuity in the Roman world from 284–450.

This book examines the role and character of Homer's people, laoi, in Homeric story-telling, arguing that Homeric poetry is crucially concerned with the people as a basis for communal life. Both The Iliad and The Odyssey are read as sustained meditations on the processes involved in protecting and destroying the people. The investigation draws on a wide range of approaches from formulaic analysis to the study of early performance contexts. From a close reading of the Homeric epics, Homer's people emerge as a community without effective social structures. When this is viewed from the perspective of Homeric performances in the polis, a contrast between Homer's laoi and the founding people of ritual emerges. While the former typically perish, the survival of the latter is secured by the establishment of successful institutions.

This book examines the role and character of Homer's people, laoi, in Homeric story-telling, arguing that Homeric poetry is crucially concerned with the people as a basis for communal life. Both The Iliad and The Odyssey are read as sustained meditations on the processes involved in protecting and destroying the people. The investigation draws on a wide range of approaches from formulaic analysis to the study of early performance contexts. From a close reading of the Homeric epics, Homer's people emerge as a community without effective social structures. When this is viewed from the perspective of Homeric performances in the polis, a contrast between Homer's laoi and the founding people of ritual emerges. While the former typically perish, the survival of the latter is secured by the establishment of successful institutions.

This book is about animals and humans - their common features and their gradual and principle differences. It tells of democracy in baboons, prostitution in hummingbirds, bigamy in wrens, baby sitting in jackals, of chimpanzees at the computer console and of the super-ego of dogs - but it is also about the labour productivity of hunter and gatherer peoples, incest avoidance in animals and humans and of the myths about matriarchy. In a language accessible to any interested layman, Georg Breuer, gives a balanced account of the main ideas and achievements of sociobiology and the main criticisms levelled against it. According to him sociobiology has given many a valuable impetus but sometimes presents a distorted or one-sided view. In particular it has not answered or addressed the question of why man, and man only, is able to identify and feel sympathy with any other human being. The evolution of this most human of all traits confers on us the capability for charity and solidarity and for

Join the Cat in the Hat as he explains how to measure circles and calculate pi in this perfect choice for Pi Day celebrations and nurturing a love of math and numbers!The Cat in the Hat makes calculating pi—one of the most fascinating numbers in mathematics—as easy as pie! Using a piece of string and two sticks, the Cat first shows beginning readers how to draw a perfect circle. Then, using a can and a piece of ribbon, he shows how to measure a circle's circumference and diameter, and to use those measurements to calculate pi. Also included is information about the history of measurement and famous Pi Pioneers!Written in simple rhyme, Happy Pi Day is a natural choice for celebrating Pi Day (held annually on March 14), and for nurturing a child's interest in math. Fans of the hit PBS show The Cat in the Hat Knows a Lot About That! will be delighted at this new addition to the Learning Library series.

Synaesthesia is a fascinating cognitive phenomenon where one type of stimulation evokes the sensation of another. For example, synaesthetes might perceive colours when listening to music, or tastes in the mouth when reading words. This book provides an insight into the idiosyncratic nature of synaesthesia by exploring its relationships with other dimensions of individual differences. Many characteristics of linguistic-colour synaesthetes are covered including personality, temperament, intelligence, creativity, emotionality, attention, memory, imagination, colour perception, body lateralization and gender. Aleksandra Maria Rogowska proposes that linguistic-colour synaesthesia can be considered as an abstract form of a continuous variable in the broader context of cross- and intra-modal associations. There has been a resurgence of interest in synaesthesia and this book will appeal to students and scientists of psychology, cognitive science and social science, and to those who are fascina

Quantum information and computation is a rapidly expanding and cross-disciplinary subject. This book, first published in 2006, gives a self-contained introduction to the field for physicists, mathematicians and computer scientists who want to know more about this exciting subject. After a step-by-step introduction to the quantum bit (qubit) and its main properties, the author presents the necessary background in quantum mechanics. The core of the subject, quantum computation, is illustrated by a detailed treatment of three quantum algorithms: Deutsch, Grover and Shor. The final chapters are devoted to the physical implementation of quantum computers, including the most recent aspects, such as superconducting qubits and quantum dots, and to a short account of quantum information. Written at a level suitable for undergraduates in physical sciences, no previous knowledge of quantum mechanics is assumed, and only elementary notions of physics are required. The book includes many short exer

Mathematical modeling and computer simulation are useful tools for improving materials processing. While courses in materials processing have covered modeling, they have traditionally been devoted to one particular class of materials, that is, polymers, metals, or ceramics. This text offers a different approach, presenting an integrated treatment of metallic and non-metallic materials. The authors show that a common base of knowledge - specifically, the fundamentals of heat transfer and fluid mechanics - provides a unifying theme for these seemingly disparate areas. Emphasis is placed on understanding basic physical phenomena and knowing how to include them in a model. The book also treats selected numerical methods, showing the relationship between the physical system, analytical solution, and the numerical scheme. A wealth of practical, realistic examples are provided, as well as homework exercises. Students, and practising engineers who must deal with a wide variety of materials a

This book, first published in 2000, is about children's learning and problem-solving behaviour. It reflects the increasingly close integration seen in recent years between social and cognitive approaches to researching the learning process. In particular, Paul Light and Karen Littleton examine the ways in which interactions between children influence learning outcomes. They begin by placing this topic in a broad theoretical and empirical context and go on to present a substantial series of their own experimental studies, which focus on children of late primary and early secondary school age. These investigations address peer facilitation of problem solving, social comparison effects on learning and social context effects upon the interpretation of tasks. Many of the studies involve computer-based learning but the findings have implications both for classroom practice and the understanding of the learning process. This book will be a valuable tool for researchers, teachers and practitio

This book, first published in 2000, is about children's learning and problem-solving behaviour. It reflects the increasingly close integration seen in recent years between social and cognitive approaches to researching the learning process. In particular, Paul Light and Karen Littleton examine the ways in which interactions between children influence learning outcomes. They begin by placing this topic in a broad theoretical and empirical context and go on to present a substantial series of their own experimental studies, which focus on children of late primary and early secondary school age. These investigations address peer facilitation of problem solving, social comparison effects on learning and social context effects upon the interpretation of tasks. Many of the studies involve computer-based learning but the findings have implications both for classroom practice and the understanding of the learning process. This book will be a valuable tool for researchers, teachers and practitio

Twenty-nine playful poems from the maven of math poetry + ingenious high-concept art = countless hours of mind-blowing, mathematical fun.Award-winning author Betsy Franco is back with another pitch-perfect performance that explores a range of math topics―from fractions and time measurements to geometry and graphs―in a way that relates math to the daily lives of children. Even the most mathematically disinclined will warm to these innovative poems, illustrated with game-changing wit and whimsy by Priscilla Tey, whose clever mechanical “Numbots” guide readers through a surreal playground of calculated delights. From multiplying mice to missing socks, from stinky scales to bug races, this collection of imaginative verse subtracts the mystery, fear, and loathing from mathematics, making it engrossing and fun for all.

This 1994 book introduces the tools of modern differential geometry, exterior calculus, manifolds, vector bundles and connections, to advanced undergraduate and beginning graduate students in mathematics, physics and engineering. The book covers both classical surface theory and the modern theory of connections and curvature, and includes a chapter on applications to theoretical physics. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. The powerful and concise calculus of differential forms is used throughout. Through the use of numerous concrete examples, the author develops computational skills in the familiar Euclidean context before exposing the reader to the more abstract setting of manifolds. There are nearly 200 exercises, making the book ideal for both classroom use and self-study.