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Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
This book explores what social psychology can contribute to our understanding of real-life problems and how it can inform rational interventions in any area of social life. By reviewing some of the most recent achievements in applying social psychology to pressing contemporary problems, Forgas, Crano, and Fiedler convey a fundamentally optimistic message about social psychology's achievements and prospects. The book is organized into four sections. Part I focuses on the basic issues and methods of applying social psychology to real-life problems, discussing evolutionary influences on human sociability, the role of psychological 'mindsets' in interpreting reality, and the use of attitude change techniques to promote adaptive behaviors. Part II explores the applications of social psychology to improve individual health and well-being, including managing aggression, eating disorders, and improving therapeutic interactions. Part III turns to the application of social psychology to improve interpersonal relations and communication, including attachment processes in social relationships, the role of parent-child interaction in preventing adolescent suicide, and analyzing social relations in legal settings and online social networks. Finally, Part IV addresses the question of how social psychology may improve our understanding of public affairs and political behavior. The book will be of interest to students and academics in social psychology, and professionals working in applied settings.
This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida s theory of p-adic modular forms and big Galois representations play a crucial part. Also a non-commutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan)."
This book provides an introduction to some key subjects in algebra and topology. It consists of comprehensive texts of some hours courses on the preliminaries for several advanced theories in (categorical) algebra and topology. Often, this kind of presentations is not so easy to find in the literature, where one begins articles by assuming a lot of knowledge in the field. This volume can both help young researchers to quickly get into the subject by offering a kind of " roadmap " and also help master students to be aware of the basics of other research directions in these fields before deciding to specialize in one of them. Furthermore, it can be used by established researchers who need a particular result for their own research and do not want to go through several research papers in order to understand a single proof. Although the chapters can be read as " self-contained " chapters, the authors have tried to coordinate the texts in order to make them complementary. The seven chapters of this volume correspond to the seven courses taught in two Summer Schools that took place in Louvain-la-Neuve in the frame of the project Fonds d'Appui a l'Internationalisation of the Universite catholique de Louvain to strengthen the collaborations with the universities of Coimbra, Padova and Poitiers, within the Coimbra Group.
Youth in Superdiverse Societies brings together theoretical, methodological and international approaches to the study of globalization, diversity, and acculturation in adolescence. It examines vital issues including migration, integration, cultural identities, ethnic minorities, and the interplay of ethnic and cultural diversity with experiences of growing up as an adolescent. This important volume focuses on understanding the experiences and consequences of multicultural societies and offers valuable new insights in the field of intergroup relations and the complexity of growingly heterogeneous societies. The book comprises four sections. The first includes fresh theoretical perspectives for studying youth development in multicultural societies, exploring topics such as superdiversity, globalization, bicultural identity development, polyculturalism, the interplay of acculturation and development, as well as developmental-ecological approaches. The second section highlights innovative methods in studying multicultural societies. It contains innovative dynamic concepts (e.g., experience-based sampling), methods for studying the nested structure of acculturative contexts, and suggestions for cross-comparative research to differentiate universal and context-specific processes. The third section examines social relations and social networks in diverse societies and features developmentally crucial contexts (e.g., family, peers, schools) and contributions on interethnic interactions in real-life contexts. The final section presents applications in natural settings and includes contributions on participatory action research and teachers dealings' with ethnic diversity. Each chapter provides a thorough overview of current research trends and findings, followed by detailed recommendations for future research, suggesting how the approaches can be cited, applied and improved. Youth in Superdiverse Societies is valuable reading for students studying adolescent acculturation and development in psychology, sociology, education, anthropology, linguistics and political science. It will also be of interest to scholars and researchers in social and developmental psychology, and related disciplines, as well as professionals in the field of migration.
This introduction to the representation theory of compact Lie groups follows Herman Weyl 's original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Thus, the presentation is more geometric and analytic than algebraic. It is a useful reference and a source of explicit computations. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.
With plenty of new material not found in other books, Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups. Offering a unified approach to theoretic concepts, this reference covers isomorphism, endomorphism, refinement, the Baer splitting property, Gabriel filters, and endomorphism modules. It shows how to effectively study a group G by considering finitely generated projective right End(G)-modules, the left End(G)-module G, and the ring E(G) = End(G)/N(End(G)). For instance, one of the naturally occurring properties considered is when E(G) is a commutative ring. Modern algebraic number theory provides results concerning the isomorphism of locally isomorphic rtffr groups, finitely faithful S-groups that are J-groups, and each rtffr L-group that is a J-group. The book concludes with useful appendices that contain background material and numerous examples.
Trust is a crucial facet of social functioning that feeds into our relationships with individuals, groups, and organizations. The Psychology of Interpersonal Trust: Theory and Research examines existing theories, frameworks, and models of trust as well as the methods and designs for examining it. To fully examine how interpersonal trust impacts our lives, Rotenberg reviews the many essential topics trust relates to, including close relationships, trust games, behavioural trust, and trust development. Designed to encourage researchers to recognize the links between different approaches to trust, this book begins with an overview of the different approaches to interpersonal trust and a description of the methods used to investigate it. Following on from this, each chapter introduces a new subtopic or context, including lying, adjustment, socialization, social media, politics, and health. Each subtopic begins with a short monologue (to provide a personal perspective) and covers basic theory and research. Rotenberg's applied focus demonstrates the relevance of interpersonal trust and highlights the issues and problems people face in contemporary society. This is essential reading for students, researchers, and academics in social psychology, especially those with a specific interest in the concept of trust.
Examining creativity in Chinese societies from both a personal and contextual standpoint, this ground-breaking book offers readers a unique insight into the Chinese mind. It provides a review of the nature, origins, and consequences of creativity, deriving from empirical evidence in the Chinese context. Specifically, the book unravels the conceptualization of creativity and its relationships with various demographic and dispositional factors in Chinese societies. The book proceeds to give readers an understanding of how creativity maintains reciprocal relationships with various forms of well-being. The content of the book brings together empirical evidence and theory grounded on Chinese societies to offer researchers and students a unique realistic view of the nature of creativity there. This book will be a must read for any researcher or practitioner interested in this fascinating topic.
The aim of this monograph is to give an overview of various classes of in?ni- dimensional Lie groups and their applications, mostly in Hamiltonian - chanics, ?uid dynamics, integrable systems, and complex geometry. We have chosen to present the unifying ideas of the theory by concentrating on speci?c typesandexamplesofin?nite-dimensionalLiegroups. Ofcourse, theselection of the topics is largely in?uenced by the taste of the authors, but we hope thatthisselectioniswideenoughtodescribevariousphenomenaarisinginthe geometry of in?nite-dimensional Lie groups and to convince the reader that they are appealing objects to study from both purely mathematical and more applied points of view. This book can be thought of as complementary to the existing more algebraic treatments, in particular, those covering the str- ture and representation theory of in?nite-dimensional Lie algebras, as well as to more analytic ones developing calculus on in?nite-dimensional manifolds. This monograph originated from advanced graduate courses and mi- courses on in?nite-dimensional groups and gauge theory given by the ?rst author at the University of Toronto, at the CIRM in Marseille, and at the Ecole Polytechnique in Paris in 2001-2004. It is based on various classical and recentresultsthathaveshapedthisnewlyemergedpartofin?nite-dimensional geometry and group theory. Our intention was to make the book concise, relatively self-contained, and useful in a graduate course. For this reason, throughout the text, we have included a large number of problems, ranging from simple exercises to open questions
"Numerical Semigroups" is the first monograph devoted exclusively to the development of the theory of numerical semigroups. This concise, self-contained text is accessible to first year graduate students, giving the full background needed for readers unfamiliar with the topic. Researchers will find the tools presented useful in producing examples and counterexamples in other fields such as algebraic geometry, number theory, and linear programming.
Originally published in 1982, Time Resources, Society and Ecology examines and seeks to examine the time dimension in terms of the ecology, technology, social organization and spatial structure of the human habitat. Approaches to time resources - sociological time-budget studies, anthropological activity analysis, and economic analysis of money allocation - have been limited by their sectoral scope or their failure to relate effectively to the processes of social interaction, technological change and environmental structure. In this book, the book's articulation of time resources is developed in a general theoretical framework of action and interaction in time and space. The book examines constraints and possibilities facing preindustrial societies and throws light on the impact of technology on modern societies. Basic models of time allocation are presented, and, finally, a cross-cultural comparison is made of the mobilization of time resources in preindustrial societies. Geographers, social anthropologists and human ecologists should find this work directly relevant to their interest in understanding the interactions between man and environment.
This volume brings together research on cyberbullying across contexts, age groups, and cultures to gain a fuller perspective of the prevalence and impact of electronic mistreatment on individual, group, and organizational outcomes. This is the first book to integrate research on cyberbullying across three contexts: schools, workplaces, and romantic relationships, providing a unique synthesis of lifespan contexts. For each context, the expert chapter authors bring together three different 'lenses': existing research on the predictors and outcomes of cyberbullying within that context; a cross-cultural review across national borders and cultural boundaries; and a developmental perspective that examines age-related differences in cyberbullying within that context. The book closes by drawing commonalities across these different contexts leading to a richer understanding of cyberbullying as a whole and some possible avenues for future research and practice. This is fascinating reading for researchers and upper-level students in social psychology, counseling, school psychology, industrial-organizational psychology, and developmental psychology, as well as educators and administrators.
Originally published in 1992, Channeling is a comprehensive bibliography on the subject of channeling. The book defines channeling as any message received or conveyed from transcendent entities and covers material on the history of channeling, those that have claimed to transcend death, contact with UFOs and contemporary channeling groups. The book acts as a research guide and seeks to outline the historical roots of channeling, explaining its major teachings and considers its significance as a spiritual movement. It provides sources from books, booklets, articles, and ephemeral material and offers a comprehensive list of both primary and secondary materials related to channeling, the bibliography takes the most diverse and useful sources of the time. This volume although published almost 30 years ago, still provides a unique and insightful collection for academics of religion, in particular those researching spiritualism and the occult.
Anyone who has studied "abstract algebra" and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of the clarity of presentation that was the hallmark of the previous editions.The first six chapters provide ample material for a first course: beginning with the basic properties of groups and homomorphisms, topics covered include Lagrange's theorem, the Noether isomorphism theorems, symmetric groups, G-sets, the Sylow theorems, finite Abelian groups, the Krull-Schmidt theorem, solvable and nilpotent groups, and the Jordan-Holder theorem.The middle portion of the book uses the Jordan-Holder theorem to organize the discussion of extensions (automorphism groups, semidirect products, the Schur-Zassenhaus lemma, Schur multipliers) and simple groups (simplicity of projective unimodular groups and, after a return to G-sets, a construction of the sporadic Mathieu groups).
Edward Conze's The Psychology of Mass Propaganda presents a commentary on the psychology of propaganda and the rise of fascism in Europe in the 1930s. Completed in 1939, during the period of Conze's own inflection from Marxist philosophy to Buddhist studies, the original manuscript was never published and is now in print for the first time. Presenting a unique historical perspective, while also appealing to an acutely topical interest in the conditions under which autocracy and fascism arise, the book examines the psychology of mass propaganda through copious contemporary and historical examples. Conze focuses especially on recent news articles and the statements of the propagandists of many of the governments that would go on to participate in the Second World War, including Germany, Italy, the USSR, USA and UK, all of which he interprets through the lens of recent psychological and historical research. The book has been edited and includes a new introduction by Richard N. Levine and Nathan H. Levine, also featuring a foreword by American legal scholar Laurence H. Tribe, and an afterword by actor, director, writer, and Buddhist priest Peter Coyote. This is a fascinating opportunity for scholars across several disciplines, including political scientists and psychologists, historians and sociologists, to access one of Conze's previously unpublished works. It will also be of importance to those interested in Conze's work on Buddhist philosophy, and in the psychology of propaganda more broadly.
This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.
Originally published in 1964 The Experience of Higher Education reports the findings of about 400 intensive interviews with final year undergraduates at three universities - Cambridge, Leeds and Southampton - and a College of Advanced Technology in London. The discussion concentrates upon the aims and expectations with which students enter higher education; the relationship between teacher and pupil; the influence of residential patterns; and the students sense of the relevance of their education in a wider social context. The final chapter is a more personal reflection, in the light of the enquiry, upon the ideals and purposes of higher education.
Starting from an undergraduate level, this book systematically develops the basics of * Calculus on manifolds, vector bundles, vector fields and differential forms, * Lie groups and Lie group actions, * Linear symplectic algebra and symplectic geometry, * Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen. We learn how the bechamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng's work on category theory, a cutting-edge "mathematics of mathematics," that is about figuring out how math works. Combined with her infectious enthusiasm for cooking and true zest for life, Cheng's perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let's look for the answer in the kitchen.
The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to the questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory. Due to this feature, the book will be useful and interesting to readers with very different background in mathematics, from undergraduate students to researchers.
Multi-body Kinematics and Dynamics with Lie Groups explores the use of Lie groups in the kinematics and dynamics of rigid body systems. The first chapter reveals the formal properties of Lie groups on the examples of rotation and Euclidean displacement groups. Chapters 2 and 3 show the specific algebraic properties of the displacement group, explaining why dual numbers play a role in kinematics (in the so-called screw theory). Chapters 4 to 7 make use of those mathematical tools to expound the kinematics of rigid body systems and in particular the kinematics of open and closed kinematical chains. A complete classification of their singularities demonstrates the efficiency of the method. Dynamics of multibody systems leads to very big computations. Chapter 8 shows how Lie groups make it possible to put them in the most compact possible form, useful for the design of software, and expands the example of tree-structured systems. This book is accessible to all interested readers as no previous knowledge of the general theory is required.
This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applicationsmake the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry."
A revised and expanded second edition of Reiter's classic text, this book deals with various developments in analysis centring around the fundamental work of Wiener, Carleman, and Weil. It starts with the classical theory of Fourier transforms in euclidean space, continues with a study of certain general function algebras, and then discusses functions defined on locally compact groups. The book gives a systematic introduction to these topics and endeavours to provide tools for further research. The new edition contains relevent material that was unavailable when the first edition was published.
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.
Originally published in 1973, this work takes a hard look at the claims made for the small group as a learning medium (lecture, structured discussion, 'sensitivity', training groups etc.). Various theories of group dynamics, leadership function and learning process are looked at critically on the basis of actual research findings. It was intended for students of social psychology and anyone teaching or training to teach at Further Education level at the time, and will still be of interest in its historical context today. |
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