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.

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.

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.

This proceedings presents the latest research materials done on group theory from geometrical viewpoint in particular Gromov's theory of hyperbolic groups, Coxeter groups, Tits buildings and actions on real trees. All these are very active subjects.

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

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.

Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.

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.

This book contains articles on maximal regulatory problems, interpolation spaces, multiplicative perturbations of generators, linear and nonlinear evolution equations, integrodifferential equations, dual semigroups, positive semigroups, applications to control theory, and boundary value problems.

The Social Psychology of Everyday Politics examines the ways in which politics permeates everyday life, from the ordinary interactions we have with others to the sense of belonging and identity developed within social groups and communities. Discrimination, prejudice, inclusion and social change, politics is an on-going process that is not solely the domain of the elected and the powerful. Using a social and political psychological lens to examine how politics is enacted in contemporary societies, the book takes an explicitly critical approach that places political activity within collective processes rather than individual behaviors. While the studies covered in the book do not ignore the importance of the individual, they underscore the need to examine the role of culture, history, ideology and social context as integral to psychological processes. Individuals act, but they do not act in isolation from the groups and societies in which they belong. Drawing on extensive international research, with contributions from leaders in the field as well as emerging scholars, the book is divided into three interrelated parts which cover: The politics of intercultural relations Political agency and social change Political discourse and practice Offering insights into how psychology can be applied to some of the most pressing social issues we face, this will be fascinating reading for students of psychology, political science, sociology and cultural studies, as well as anyone working in the area of public policy.

Social interaction in recent years has become the focus of systematic scientific research in a wide variety of academic disciplines. In Communication under the Microscope, Peter Bull shows how communication has become an object of study in its own right, which can be dissected in the finest detail through the use of film and recording technology. In so doing he provides a clear and valuable introduction into the theory and practice of microanalysis. Bull argues that microanalysis is both a distinctive methodology and a distinctive way of thinking about communication. He then focuses on the two principal elements of face-to-face communication: speech and non-verbal behaviour. Communication in particular social contexts is also addressed with related chapters on gender and politics. Finally, the practical aspects of microanalysis are discussed. This unique and thorough review of microanalysis integrates different approaches and draws together research literature which is often diverse and disparate. Presented in a clear and focused style, this book will be of interest to psychologists, social scientists and all students and researchers in the field of communication. Communication is central to many aspects of human life, yet it has only recently become the focus of systematic scientific investigation within a wide variety of academic disciplines. Communication has now become an object of study in its own right, and can be dissected in the finest detail with the use of recording technology (film, audiotape and videotape). This approach has become known as 'microanalysis', and forms the principal theme of Communication under the Microscope.

This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.

Based on presentations given at the NordForsk Network Closing Conference Operator Algebra and Dynamics, held in Gjaargarour, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operatoralgebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science.

It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filteredK-theory over finite topological spaces, "C*"-algebras associated to shift spaces (or subshifts), graph"C*"-algebras, irrational extended rotationalgebras that are shown to be"C*"-alloys, free probability, renewal systems, the Grothendieck Theorem for jointly completelybounded bilinear forms on"C*"-algebras, Cuntz-Li algebrasassociatedwith the"a"-adic numbers, crossed products of injective endomorphisms (the so-called Stacey crossedproducts), the interplay between dynamical systems, operator algebras and wavelets on fractals, "C*"-completions of the Hecke algebra of a Hecke pair, semiprojective"C*-"algebras, and the topologicaldimension of type I"C*"-algebras.

"Operator Algebra and Dynamics"will serve as a useful resource for a broad spectrum of researchers and students in mathematics, physics, and engineering.

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Elliot Aronson is among the 100 most influential psychologists of the 20th Century. He is best known for his theorizing and research on cognitive dissonance theory -- one of the most provocative and enduring theories in contemporary psychology -- and for his design of the "jigsaw classroom," an applied method of reducing conflict and prejudice in multiethnic schools. Throughout his illustrious career, he has championed the application of social-psychological theory and methods for solving such pressing social problems as prejudice, energy efficiency, conflict and miscommunication in relationships, and the reasons why many people justify their mistakes rather than learn from them. Aronson is the only psychologist in the history of the American Psychological Association to have won all three of its top awards: for research, teaching, and writing. In this Festschrift, friends, colleagues, and former students write with warmth, clarity, and humor about Aronson's enduring influence on the field of social psychology and on their own professional lives as researchers, writers, and teachers. Topics covered include contemporary research on cognitive dissonance theory; the changing face of experimentation in social psychology; and applied research on energy policy, education, the legal system, intergroup conflict, and prejudice and discrimination.

Originally published in 1988, the purpose of this book was to explore the interrelations among communication, social cognition and affect. The contributors, selected by the editors, are some of the best known in their fields and they significantly added to the knowledge of this interdisciplinary domain at the time. In late April 1986 the authors met at a conference centre at the University of Kentucky. They presented first drafts of their chapters and exchanged ideas. Out of these interactions came this book, which has a broad interest across several areas of psychology and communication. While answering a number of questions, the authors also posed other questions for future examination.

This book focuses on safer sex discussion and practice in close, personal relationships, emphasizing research on individuals in personal relationship types that are experiencing a rise in HIV infection and AIDS. Moving beyond studies of gay adult males and IV drug-users, this work paints a clear picture of the very real risk that exists for these less-studied, more general populations, so individuals may better personalize the risk and engage in more preventative measures. Authors Tara M. Emmers-Sommer and Mike Allen examine issues surrounding safer sex, utilizing research that focuses on how individuals struggle with personalizing the HIV and AIDS risk and how they cope with safer sex issues. Safer Sex in Personal Relationships takes readers on a journey through a variety of close relationship types. It begins by highlighting awareness to the global enormity of HIV and AIDS and providing a link between the global and personal, and the need to make HIV and AIDS awareness part of everyday talk and personal relationship structure. It then focuses on: *safer sex in close relationships, both heterosexual and homosexual; *marital relationships and the importance of safe sex discussion and awareness in marriages; *HIV and AIDS from a multicultural perspective; *HIV and AIDS in aged populations; and *increasing awareness, understanding, and compassion of those living with HIV and AIDS. This book will appeal to scholars and students concerned with HIV and AIDS in personal relationships. It will be an invaluable text for courses on interpersonal communication and relationships; family, marital, human sexuality, sex and gender, gay and lesbian relationships, and sexual education; and relational conflict across communication, psychology, and sociology disciplines.

The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations.

These books grew out of the perception that a number of important conceptual and theoretical advances in research on small group behavior had developed in recent years, but were scattered in rather fragmentary fashion across a diverse literature. Thus, it seemed useful to encourage the formulation of summary accounts. A conference was held in Hamburg with the aim of not only encouraging such developments, but also encouraging the integration of theoretical approaches where possible. These two volumes are the result. Current research on small groups falls roughly into two moderately broad categories, and this classification is reflected in the two books. Volume I addresses theoretical problems associated with the consensual action of task-oriented small groups, whereas Volume II focuses on interpersonal relations and social processes within such groups. The two volumes differ somewhat in that the conceptual work of Volume I tends to address rather strictly defined problems of consensual action, some approaches tending to the axiomatic, whereas the conceptual work described in Volume II is generally less formal and rather general in focus. However, both volumes represent current conceptual work in small group research and can claim to have achieved the original purpose of up-to-date conceptual summaries of progress on new theoretical work.

The disintegration of the Soviet Union in 1991 left 25 million Russians living outside the Russian Federation. This important new book explores their social identity, examining the mutually held perceptions, fears and resulting nationalism of both the ethnic Russians living outside the Russian Federation and the indigenous, or 'titular', populations they live amongst. Based on a unique study involving national surveys conducted in Belarus, Ukraine, Moldova, Georgia and Kazakhstan, the book maps the main individual, intergroup and cross-national factors that shape the fears of 'titulars' and Russians as well as the possible consequences and the risk of ethnic conflict in the five republics. There is detailed statistical analysis of how background factors (personal and national) affect intergroup perceptions; along with discussion of mutual stereotypes, social distance, language and the perception of citizenship and analysis of the dynamics of assimilation and separation of Russians in former soviet states. The attitudes of both groups to other smaller minority groups are also examined. This book provides significant new conclusions on the complexity of intergroup relations and seeks to relate these findings to a general theory of intergroup relations. It will be essential reading for those working in this area within the disciplines of Psychology, Sociology and Politics.

Originally published in 1963, this book was one of the first to explore group process and working with groups. The introductory chapter tells us that working with groups requires three skills: and understanding of theory, a knowledge of its application, and trained experience in its use. It goes on to discuss these points, helping the reader towards an understanding of group processes and making decisions in groups. This title is an early example of author's explorations of groups and group work, which were to be a major factor in the establishment of group-work practice in Britain over the following years.

The Science of Attitudes is the first book to integrate classic and modern research in the field of attitudes at a scholarly level. Designed primarily for advanced undergraduates and graduate students, the presentation of research will also be useful for current scholars in all disciplines who are interested in how attitudes are formed and changed. The treatment of attitudes is both thorough and unique, taking a historical approach while simultaneously highlighting contemporary views and controversies. The book traces attitudes research from the inception of scientific study following World War II to the issues and methods of research that are prominent features of today's research. Researchers in the field of attitudes will be particularly interested in classic and modern research on the organization, structure, strength and function of attitudes. Researchers in the field of persuasion will be particularly interested in work on attitude change focusing on propositional and associative learning, metacognition and dynamic theories of dissonance, balance and reactance. The book is designed to present the integration of the properties of the attitude with the dynamic considerations of attitude change. The Science of Attitudes is also the first book on attitudes to devote entire chapters to work on implicit measurements, resistance to persuasion, and social neuroscience.

The Handbook of Cubic Math unveils the theory involved in Rubik's Cube's solution, the potential applications of that theory to other similar puzzles, and how the cube provides a physical example for many concepts in mathematics where such examples are difficult to find. Nonetheless, the authors have been able to cover and explain these topics in a way which is easily understandable to the layman, suitable for a junior-high-school or high-school course in math, and appropriate for a college course in modern algebra. This manual will satisfy the experts' curiosity about the moves that lead to the solution of the cube and will offer a useful supplementary teaching aid to the beginners.

In this single volume, William N. Elwood has gathered potent evidence of the impact that the HIV/AIDS epidemic has had on the world, its communities, and its inhabitants, and he addresses the role of communication in affecting the way in which people respond to AIDS. With a multidisciplinary group of contributors and topics ranging from political rhetoric to interpersonal discourse, Power in the Blood offers a multitude of ways in which to think about power, politics, HIV prevention, and people living with HIV. Readers will be able to use this information in class discussions, program designs, grant applications, and research, as well as in their own lives. With this volume, Elwood makes a thoroughly convincing argument that communication is the key to understanding, treating, and preventing AIDS, and he inspires further action toward the goal of ending the AIDS crisis.