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Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
This book offers a biographical account of Henri Tajfel, one of the most influential European social psychologists of the twentieth century, offering unique insights into his ground-breaking work in the areas of social perception, social identity and intergroup relations. The author, Rupert Brown, paints a vivid and personal portrait of Tajfel's life, his academic career and its significance to social psychology, and the key ideas he developed. It traces Tajfel's life from his birth in Poland just after the end of World War I, his time as a prisoner-of-war in World War II, his work with Jewish orphans and other displaced persons after that war, and thence to his short but glittering academic career as a social psychologist. Based on a range of sources including interviews, archival material, correspondence, photographs, and scholarly output, Brown expertly weaves together Tajfel's personal narrative with his evolving intellectual interests and major scientific discoveries. Following a chronological structure with each chapter dedicated to a significant transition period in Tajfel's life, the book ends with an appraisal of two of his principal posthumous legacies: the European Association of Social Psychology, a project always close to Tajfel's heart and for which he worked tirelessly; and the 'social identity approach' to social psychology initiated by Tajfel over forty years ago and now one of the discipline's most important perspectives. This is fascinating reading for students, established scholars, and anyone interested in social psychology and the life and lasting contribution of this celebrated scholar.
This book offers a biographical account of Henri Tajfel, one of the most influential European social psychologists of the twentieth century, offering unique insights into his ground-breaking work in the areas of social perception, social identity and intergroup relations. The author, Rupert Brown, paints a vivid and personal portrait of Tajfel's life, his academic career and its significance to social psychology, and the key ideas he developed. It traces Tajfel's life from his birth in Poland just after the end of World War I, his time as a prisoner-of-war in World War II, his work with Jewish orphans and other displaced persons after that war, and thence to his short but glittering academic career as a social psychologist. Based on a range of sources including interviews, archival material, correspondence, photographs, and scholarly output, Brown expertly weaves together Tajfel's personal narrative with his evolving intellectual interests and major scientific discoveries. Following a chronological structure with each chapter dedicated to a significant transition period in Tajfel's life, the book ends with an appraisal of two of his principal posthumous legacies: the European Association of Social Psychology, a project always close to Tajfel's heart and for which he worked tirelessly; and the 'social identity approach' to social psychology initiated by Tajfel over forty years ago and now one of the discipline's most important perspectives. This is fascinating reading for students, established scholars, and anyone interested in social psychology and the life and lasting contribution of this celebrated scholar.
'Et moi, ..., si j'avait su comment en revenir, One service methematics has rendered the je n'y serais point aile.' human race. It has put common sense back JulesVerne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be seese'. able to do something with it. Eric T. Bell O.Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such state ments as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguable true. And all statements obtainable this .way form part of the raison d'etre of this series."
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 volume contains the proceedings of the Third International Conference on Non-Associative Algebra and Its Applications, held in Oviedo, Spain, July 12-17, 1993. The conference brought together specialists from all over the world who work in this field. All aspects of non-associative algebra are covered. Topics range from purely mathematical subjects to a wide spectrum of applications, and from state-of-the-art articles to overview papers. This collection should point the way for further research. The volume should be of interest to researchers in mathematics as well as those whose work involves the application of non-associative algebra in such areas as physics, biology and genetics.
This volume contains papers presented at the meeting Deformation Theory, Symplectic Geometry and Applications, held in Ascona, June 17-21, 1996. The contents touch upon many frontier domains of modern mathematics, mathematical physics and theoretical physics and include authoritative, state-of-the-art contributions by leading scientists. New and important developments in the fields of symplectic geometry, deformation quantization, noncommutative geometry (NCG) and Lie theory are presented. Among the subjects treated are: quantization of general Poisson manifolds; new deformations needed for the quantization of Nambu mechanics; quantization of intersection cardinalities; quantum shuffles; new types of quantum groups and applications; quantum cohomology; strong homotopy Lie algebras; finite- and infinite-dimensional Lie groups; and 2D field theories and applications of NCG to gravity coupled with the standard model. Audience: This book will be of interest to researchers and post-graduate students of mathematical physics, global analysis, analysis on manifolds, topological groups, nonassociative rings and algebras, and Lie algebras.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
History, Trauma and Shame provides an in-depth examination of the sustained dialogue about the past between children of Holocaust survivors and descendants of families whose parents were either directly or indirectly involved in Nazi crimes. Taking an autobiographical narrative perspective, the chapters in the book explore the intersection of history, trauma and shame, and how change and transformation unfolds over time. The analyses of the encounters described in the book provides a close examination of the process of dialogue among members of The Study Group on Intergenerational Consequences of the Holocaust (PAKH), exploring how Holocaust trauma lives in the 'everyday' lives of descendants of survivors. It goes to the heart of the issues at the forefront of contemporary transnational debates about building relationships of trust and reconciliation in societies with a history of genocide and mass political violence. This book will be great interest for academics, researchers and postgraduate students engaged in the study of social psychology, Holocaust or genocide studies, cultural studies, reconciliation studies, historical trauma and peacebuilding. It will also appeal to clinical psychologists, psychiatrists and psychoanalysts, as well as upper-level undergraduate students interested in the above areas.
This is the fi rst textbook leading coherently from classical character theory to the theory of lattices over orders and integral representations of fi nite groups. Character theory is developed in a highly pedagogical way including many examples and exercises covering at once the fi rst defi nitions up to Clifford theory, Brauer's induction theorem and the splitting fi eld theorem, as well as self-dual simple modules allowing bilinear forms. This latter part is done step by step using the approach given by Sin and Willems. Dirichlet characters and Dirichlet's result on primes in arithmetic progressions are given as an application. Examples of integral representations of fi nite groups are already detailed at a quite early stage where appropriate, so that the more systematic treatment of lattices over orders is natural. After that, the necessary number theory and homological algebra is developed as far as needed. Maximal as well as hereditary orders are introduced and the Auslander- Buchsbaum theorem is proved. The Jordan-Zassenhaus theorem on the fi niteness of lattices in a given vector space is fully proved. Then the development and properties of class groups of orders is a fi rst focus. As a further highlight Swan's example of a stably free but not free ideal over the integral group ring of the generalised quaternion group of order 32 is developed in great detail. A student friendly introduction to ordinary representation theory Many examples and exercises, including solutions for some of them, make the book well suited for self-study Leads coherently from ordinary character theory to the integral representation theory of lattices over orders Several topics appear for the fi rst time in a textbook, such as Sin-Willems' approach to self-dual simple modules and Swan's example of a stably free non free ideal.
--Core textbook featuring accessible but advanced coverage of theory, research, and applications in nonverbal communication from renowned scholars --Usable for undergraduate and graduate courses in communication and psychology departments --Includes a new chapter on identity and impression management, as well as fully updated research coverage throughout --Online resources include an extensive instructor's manual and test bank
Refers to topical and real-world political events including Trump, Brexit, the Arab Spring, and Gezi Park, as well as attitudes towards groups in society, such as immigrants, journalists, politicians, and bankers Explains the psychological underpinnings behind political participation, making this fascinating reading for students of psychology and politics, as well as anyone interested in politics and democracy Part of The Psychology of Everything series, which debunks the popular myths and pseudo-science surrounding some of life's biggest questions
This updated edition of this classic book is devoted to ordinary representation theory and is addressed to finite group theorists intending to study and apply character theory. It contains many exercises and examples, and the list of problems contains a number of open questions.
In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof of the Feit-Thompson theorem. Simpler, more detailed proofs are provided for some intermediate theorems. Recent results are used to shorten other proofs. The book will make the first half of this remarkable proof accessible to readers familiar with just the rudiments of group theory.
Insurgent groups consist of individuals willing to organize and commit acts of terror to achieve their goals. By nature, they depend on public support, yet they sometimes target private civilians in addition to military personnel and government officials. This book examines insurgent embeddedness-the extent to which an insurgent group is enmeshed in relationships with the state, other insurgents, and the public-in order to understand why they attack civilians. Using Big Allied and Dangerous (BAAD) as the dataset, this book drills into civilian attacks in specific contexts, including schools, news media, and nonmilitary/nongovernment spaces designed for the general public. This book goes one step further, presenting in-depth analyses of intergroup alliances and rivalries, their changes and determinants over time, and the implications for several types of bloodshed against civilians. Insurgent Terrorism offers a comprehensive, modern approach for academics, students, and policy practitioners who seek to understand interorganizational relationships between insurgent organizations.
This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications. It also includes the most recent developments on other areas of mathematics including algebra and geometry. Lie group representation theory and harmonic analysis on Lie groups and on their homogeneous spaces form a significant and important area of mathematical research. These areas are interrelated with various other mathematical fields such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics. Keeping up with the fast development of this exciting area of research, Ali Baklouti (University of Sfax) and Takaaki Nomura (Kyushu University) launched a series of seminars on the topic, the first of which took place on November 2009 in Kerkennah Islands, the second in Sousse on December 2011, and the third in Hammamet on December 2013. The last seminar, which took place December 18th to 23rd 2015 in Monastir, Tunisia, has promoted further research in all the fields where the main focus was in the area of Analysis, algebra and geometry and on topics of joint collaboration of many teams in several corners. Many experts from both countries have been involved.
This book features a selection of articles based on the XXXV Bialowieza Workshop on Geometric Methods in Physics, 2016. The series of Bialowieza workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Bialowieza Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.
The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that time, both P. Conrad and P. Cohn had showed that a group admits a total right ordering if and only if the group is a group of automor phisms of a totally ordered set. (In a right ordered group, the order is required to be preserved by all right translations, unlike a (two-sided) ordered group, where both right and left translations must preserve the order."
This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others. This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin's lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka-Krein formalism, which further strengthens Manin's approach to symmetry and moduli-objects in noncommutative geometry.
This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.
This volume collects the proceedings of the conference 'Topological methods in group theory', held at Ohio State University in 2014 in honor of Ross Geoghegan's 70th birthday. It consists of eleven peer-reviewed papers on some of the most recent developments at the interface of topology and geometric group theory. The authors have given particular attention to clear exposition, making this volume especially useful for graduate students and for mathematicians in other areas interested in gaining a taste of this rich and active field. A wide cross-section of topics in geometric group theory and topology are represented, including left-orderable groups, groups defined by automata, connectivity properties and -invariants of groups, amenability and non-amenability problems, and boundaries of certain groups. Also included are topics that are more geometric or topological in nature, such as the geometry of simplices, decomposition complexity of certain groups, and problems in shape theory.
Analyzing Group Interactions gives a comprehensive overview of the use of different methods for the analysis of group interactions. International experts from a range of different disciplines within the social sciences illustrate their step-by-step procedures of how they analyze interactions within groups and explain what kind of data and skills are needed to get started. Each method is discussed in the same, structured manner, focusing on each method's strengths and weaknesses, its applicability and requirements, and the precise workflow to "follow along" when analyzing group interactions with the respective method. The analyzing strategies covered in this book include ethnographical approaches, phenomenology, content analysis, documentary method, discourse analysis, grounded theory, social network analysis, quantitative ratings, and several triangulative and mixed-method research designs. This volume is recommended for researchers at all levels that need guidance with the complex task of analyzing group interactions. The unified structure throughout the book facilitates comparison across the different methods and helps with deciding on the approach to be taken.
This ground-breaking book is designed to raise awareness of human rights implications in psychology, and provide knowledge and tools enabling psychologists to put a human rights perspective into practice. Psychologists have always been deeply engaged in alleviating the harmful consequences human rights violations have on individuals. However, despite the fundamental role that human rights play for professional psychology and psychologists, human rights education is underdeveloped in psychologists' academic and vocational training. This book, the first of its kind, looks to change this, by: raising awareness among professional psychologists, university teachers and psychology students about their role as human rights promoters and protectors providing knowledge and tools enabling them to put a human rights perspective into practice providing texts and methods for teaching human rights. Featuring chapters from leading scholars in the field, spanning 18 countries and six continents, the book identifies how psychologists can ensure they are practising in a responsible way, as well as contributing to wider society with a clear knowledge of human rights issues in relation to culture, gender, organisations and more. Including hands-on recommendations, case studies and discussion points, this is essential reading for professional psychologists as part of continuing professional development and those in training and taking psychology courses. For additional electronic resources for students and teachers, see the support material tab on the Routledge book page: https://www.routledge.com/Human-Rights-Education-for-Psychologists/Hagenaars-Plavsic-Sveaass-Wagner-Wainwright/p/book/9780367222963
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
The Mathieu groups have many fascinating and unusual characteristics and have been studied at length since their discovery. This book provides a unique, geometric perspective on these groups. The amalgam method is explained and used to construct M24, enabling readers to learn the method through its application to a familiar example. The same method is then used to construct, among others, the octad graph, the Witt design and the Golay code. This book also provides a systematic account of 'small groups', and serves as a useful reference for the Mathieu groups. The material is presented in such a way that it guides the reader smoothly and intuitively through the process, leading to a deeper understanding of the topic.
Permutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nan-Scott theory are presented not only for primitive permutation groups but also for the larger families of quasiprimitive and innately transitive groups, including several classes of infinite permutation groups. Their precision is sharpened by the introduction of a cartesian decomposition concept. This facilitates reduction arguments for primitive groups analogous to those, using orbits and partitions, that reduce problems about general permutation groups to primitive groups. The results are particularly powerful for finite groups, where the finite simple group classification is invoked. Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures. Students and researchers with an interest in mathematical symmetry will find the book enjoyable and useful. |
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