Line up a deck of 52 cards on a table. Randomly choose two cards and switch them. How many switches are needed in order to mix up the deck? Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space this book develops the necessary tools for the asymptotic analysis of these processes. This detailed study culminates with the case-by-case analysis of the cut-off phenomenon discovered by Persi Diaconis. This self-contained text is ideal for graduate students and researchers working in the areas of representation theory, group theory, harmonic analysis and Markov chains. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and the representation theory of the symmetric group.

This practical guide to the psychology of effective communication is suitable for anyone for whom communication in groups is a key part of their job. No previous knowledge of psychology is assumed and the emphasis is on exercises, key point summaries, assessment and improving your skills in everyday situations like committees, project teams, seminars and focus groups.
Suitable as an introduction for psychology students, it will be invaluable for students of business, medicine, allied health, social work and probation, whether studying on a short course or attending an intensive training session as part of their continuing professional development.

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Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. Until now, however, there have been virtually no accessible treatments of group theory that include representations and characters. The classic works in the field require a high level of mathematical sophistication, and other texts omit representations and characters.

Groups and Characters offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, this unique text emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The author presents group theory through the Sylow Theorems and includes the full subgroup structure of A5. Representations and characters are worked out with numerous character tables, along with real and induced characters that lead to the table for S5.

The text includes specific sections that provide the mathematical basis for some of the important applications of group theory in spectroscopy and molecular structure. It also offers numerous exercises-some stressing computation of concrete examples, others stressing development of the mathematical theory.

Groups and Characters provides the ideal grounding for more advanced studies with the classic texts, and for more broad-based work in abstract algebra. Furthermore, physical scientists-whose experience with groups and characters may not be rigorous-will find Groups and Characters the ideal means for gaining a sense of the mathematics lying behind the techniques used in applications.

Group sequential methods answer the needs of clinical trial monitoring committees who must assess the data available at an interim analysis. These interim results may provide grounds for terminating the study-effectively reducing costs-or may benefit the general patient population by allowing early dissemination of its findings. Group sequential methods provide a means to balance the ethical and financial advantages of stopping a study early against the risk of an incorrect conclusion.
Group Sequential Methods with Applications to Clinical Trials describes group sequential stopping rules designed to reduce average study length and control Type I and II error probabilities. The authors present one-sided and two-sided tests, introduce several families of group sequential tests, and explain how to choose the most appropriate test and interim analysis schedule. Their topics include placebo-controlled randomized trials, bio-equivalence testing, crossover and longitudinal studies, and linear and generalized linear models.
Research in group sequential analysis has progressed rapidly over the past 20 years. Group Sequential Methods with Applications to Clinical Trials surveys and extends current methods for planning and conducting interim analyses. It provides straightforward descriptions of group sequential hypothesis tests in a form suited for direct application to a wide variety of clinical trials. Medical statisticians engaged in any investigations planned with interim analyses will find this book a useful and important tool.

Attitudes are evaluations of people, places, things, and ideas. They help us to navigate through a complex world. They provide guidance for decisions about which products to buy, how to travel to work, or where to go on vacation. They color our perceptions of others. Carefully crafted interventions can change attitudes and behavior. Yet, attitudes, beliefs, and behavior are often formed and changed in casual social exchanges. The mere perception that other people favor something, say, rich people, may be sufficient to make another person favor it. People's own actions also influence their attitudes, such that they adjust to be more supportive of the actions. People's belief systems even change to align with and support their preferences, which at its extreme is a form of denial for which people lack awareness. These two volumes provide authoritative, critical surveys of theory and research about attitudes, beliefs, persuasion, and behavior from key authors in these areas. The first volume covers theoretical notions about attitudes, the beliefs and behaviors to which they are linked, and the degree to which they are held outside of awareness. It also discusses motivational and cultural determinants of attitudes, influences of attitudes on behavior, and communication and persuasion. The second volume covers applications to measurement, behavior prediction, and interventions in the areas of cancer, HIV, substance use, diet, and exercise, as well as in politics, intergroup relations, aggression, migrations, advertising, accounting, education, and the environment.

Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*-crossed product algebra. These criteria allow to extend index theorems to such operator classes. This in turn is of great relevance for applications in solid-state physics, in particular, Anderson localized topological insulators as well as topological semimetals. The book also contains a self-contained chapter on duality theory for R-actions. It allows to prove a bulk-boundary correspondence for boundaries with irrational angles which implies the existence of flat bands of edge states in graphene-like systems. This book is intended for advanced students in mathematical physics and researchers alike.

Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

This book, an abridgment of Volumes I and II of the highly respected Group Theory in Physics, presents a carefully constructed introduction to group theory and its applications in physics. The book provides anintroduction to and description of the most important basic ideas and the role that they play in physical problems. The clearly written text contains many pertinent examples that illustrate the topics, even for those with no background in group theory.
This work presents important mathematical developments to theoretical physicists in a form that is easy to comprehend and appreciate. Finite groups, Lie groups, Lie algebras, semi-simple Lie algebras, crystallographic point groups and crystallographic space groups, electronic energy bands in solids, atomic physics, symmetry schemes for fundamental particles, and quantum mechanics are all covered in this compact new edition.
Key Features
* Covers both group theory and the theory of Lie algebras
* Includes studies of solid state physics, atomic physics, and fundamental particle physics
* Contains a comprehensive index
* Provides extensive examples

Imparts a self--contained development of the algebraic theory of Kac--Moody algebras, their representations and close relatives----the Virasoro and Heisenberg algebras. Focuses on developing the theory of triangular decompositions and part of the Kac--Moody theory not specific to the affine case. Also covers lattices, and finite root systems, infinite--dimensional theory, Weyl groups and conjugacy theorems.

We know that positive, fulfilling and satisfying relationships are strong predictors of life satisfaction, psychological health, and physical well-being. This edited volume uses research and theory on the need to belong as a foundation to explore various types of relationships, with an emphasis on the influence of these relationships on employee attitudes, behaviors and well-being. The book considers a wide range of relationships that may affect work attitudes, specifically, supervisory, co-worker, team, customer and non-work relationships. The study of relationships spans many sub-areas within I/O Psychology and Social Psychology, including leadership, supervision, mentoring, work-related social support, work teams, bullying/interpersonal deviance and the work/non work interface.

This work offers concise coverage of the structure theory of semigroups. It examines constructions and descriptions of semigroups and emphasizes finite, commutative, regular and inverse semigroups. Many structure theorems on regular and commutative semigroups are introduced.;College or university bookstores may order five or more copies at a special student price which is available upon request from Marcel Dekker, Inc.

Joint Action: Essays in honour of John Shotter brings together a cross-disciplinary group of fifteen respected international scholars to explain the relevance of John Shotter's work to emerging concerns in twenty-first century social science. Shotter's work extends over forty years and continues to challenge conventional scientific thinking across a range of topics. The disciplines and practices that Shotter's work has informed are well established throughout the English-speaking world. This is the first publication to examine the importance of his influence in contemporary social sciences and it includes authoritative discussions on topics such as social constructionism, democratic practice, organisational change, the affective turn and human relations. The geographical diversity and disciplinary breadth of scholarly contributions imbues the book with international scope and reach. Joint Action presents a contemporary reflection on Shotter's work that demonstrates its influence across a range of substantive topics and practical endeavours and within disciplines including management studies and philosophy as well as psychology. As such, it will appeal to researchers and postgraduate students of social sciences and related disciplines, as well as to those who have heard of Shotter's work and want to know more about its utility and value in relation to their own research or practice.

This volume elucidates some of the very concrete ways in which Americans misperceive the social world and how we are all subject to biases and illusions. As such, it challenges the assumption in much social science theorizing that people are rational actors by exploring how the machinations of cognition, the effect of our past experiences, the news, and social media feeds all factor into our opinion-making process. The chapters highlight common, and often incorrect, perceptions of population diversity, sexual behavior, the economy, health, and relationships. It shows how correcting these misperceptions of the social world can lead to real behavioral and attitudinal change.

The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.

First published in 1985. Routledge is an imprint of Taylor and Francis, an informa company.

Interpersonal coordination is an important feature of all social systems. From everyday activities to playing sport and participating in the performing arts, human behaviour is constrained by the need to continually interact with others. This book examines how interpersonal coordination tendencies in social systems emerge, across a range of contexts and at different scales, with the aim of helping practitioners to understand collective behaviours and create learning environments to improve performance. Showcasing the latest research from scientists and academics, this collection of studies examines how and why interpersonal coordination is crucial for success in sport and the performing arts. It explains the complex science of interpersonal coordination in relation to a variety of activities including competitive team sports, outdoor sports, racket sports, and martial arts, as well as dance. Divided into four sections, this book offers insight into: the nature, history and key concepts of interpersonal coordination factors that influence interpersonal coordination within social systems interpersonal coordination in competitive and cooperative performance contexts methods, tools and devices for improving performance through interpersonal coordination. This book will provide fascinating insights for students, researchers and educators interested in movement science, performance analysis, sport science and psychology, as well as for those working in the performing arts.

First published in 1987. Routledge is an imprint of Taylor and Francis, an informa company.

This book is a useful and accessible introduction to symmetry principles in particle physics. New ideas are explained in a way that throws considerable light on difficult concepts, such as Lie groups and their representations. This book begins with introdutions both to the types of symmetries known in physics and to group theory and representation theory. Successive chapters deal with the symmetric groups and their Young diagrams, braid groups, Lie groups and algebras, Cartan's classification of semi-simple groups, and the Lie groups most used in physics are treated in detail. Gauge groups are discussed, and applications to elementary particle physics and multiquark systems introduced throughout the book where appropriate. Many worked examples are also included. There is a growing interestinthe quatk structure of hadrons and in theories of particle interactions based on the principle of gauge symmetries. In this book the concepts of group theory are clearly explained and their applications to subnuclear physics brought up-to-date.

Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.

David Riesman's The Lonely Crowd: A Study in the Changing American Character is one of the best-known books in the history of sociology - holding a mirror up to contemporary America and showing the nation its own character as it had never seen it before. Its success is a testament to Riesman's mastery of one key critical thinking skill: interpretation. In critical thinking, interpretation focuses on understanding the meaning of evidence, and is frequently characterized by laying down clear definitions, and clarifying ideas and categories for the reader. All these processes are on full display in The Lonely Crowd - which, rather than seeking to challenge accepted wisdom or generate new ideas, provides incisive interpretations and definitions of ideas and data from a variety of sources. Above all, Riesman's book is a work of categorization - a form of interpretation that can be vital to building and communicating systematic arguments. With the aid of his two co-authors (Nathan Glazer and Reuel Denney), he defined three cultural types that formed a perfect pattern for understanding mid-century American society and the changes it was undergoing. The clarity of the book's definitions tapped directly into the zeitgeist of the 1950s, powering it to best-seller status and an audience that extended far beyond academia.

Signs of Identity presents an interdisciplinary introduction to collective identity, using insights from social psychology, anthropology, sociology and the humanities. It takes the basic concept of semiotics - the sign - as its central notion, and specifies in detail in what ways identity can be seen as a sign, how it functions as a sign, and how signs of identity are related to those who have that identity. Recognizing that the sense of belonging is both the source of solidarity and discrimination, the book argues for the importance of emotional attachment to collective identity. The argument is supported by a large number of real-life examples of how collective emotions affect group formation, collective action and inter-group relations. By addressing the current issues of authenticity and the Self, multiculturalism, intersectionality and social justice, the book helps to stimulate discussion of the contested topics of identity in contemporary society.

Although love and relationships have been focal points for poets and philosophers for thousands of years, these topics had not traditionally been the focus of empirical research. As a result, very little was known about how couples maintained happiness and satisfaction in their relationships, or how relationships deteriorated, ultimately ending in separation or divorce. However, since the early 1980s, relationships research has blossomed as a field - and is now one of the most vibrant topics in social psychology and beyond. This volume brings together the latest research on couple functioning from the perspectives of social and personality psychology, neurobiology, health, and clinical psychology. Additionally, the research presented highlights the use of survey, experimental, implicit, and longitudinal methods, as well as specialized techniques employed in neuroscience, psychophysiology, and psychoneuroimmunology in the study of couple level processes. The underlying aim of this volume is to examine how these theories and methods converge to provide a deeper, holistic model of couples' processes and functioning. With its state-of-the-art, integrative overview of this exciting discipline, The Science of the Couple is essential reading for social psychologists, clinicians, and anyone with an interest in the dynamics of interpersonal relationships.

This book joins together disclosure, privacy, and secrecy to pursue a greater understanding of how people are both public and private in their interactions. To be social yet autonomous, known yet unknown, independent yet dependent on others is essential to the communicative world. How do people manage these seemingly incongruous goals? This book argues that they actively work at balancing simultaneous needs of being both public and private. It highlights many different ways that people balance their public needs with their privacy needs underscoring the multidimensional nature of balance. The chapters also show that the opposing needs occur within a variety of contexts, from health issues, such as HIV/AIDS, to television talk shows. Readers will discover that avoiding disclosure is a dominant theme. In this way, the authors demonstrate how people balance privacy and secrecy by deemphasizing openness. Taken as a whole, this volume offers a refreshing new look at age-old concerns.

Gathers and unifies the results of the theory of noncommutative semigroup rings, primarily drawing on the literature of the last 10 years, and including several new results. Okninski (Warsaw U., Poland) restricts coverage to the ring theoretical properties for which a systematic treatment is current