Groups and group theory Books

Book Synopsis1 Symmetries of the Tetrahedron.- 2 Axioms.- 3 Numbers.- 4 Dihedral Groups.- 5 Subgroups and Generators.- 6 Permutations.- 7 Isomorphisms.- 8 Plato's Solids and Cayley's Theorem.- 10 Products.- 11 Lagrange's Theorem.- 12 Partitions.- 13 Cauchy's Theorem.- 14 Conjugacy.- 15 Quotient Groups.- 16 Homomorphisms.- 17 Actions, Orbits, and Stabilizers.- 18 Counting Orbits.- 19 Groups.- 20 The Sylow Theorems.- 21 Finitely Generated Abelian Groups.- 22 Row and Column Operations.- 23 Automorphisms.- 24 The Euclidean Group.- 25 Lattices and Point Groups.- 26 Wallpaper Patterns.- 27 Free Groups and Presentations.- 28 Trees and the Nielsen-Schreier Theorem.Trade ReviewM.A. Armstrong Groups and Symmetry "This book is a gentle introductory text on group theory and its application to the measurement of symmetry. It covers most of the material that one might expect to see in an undergraduate course . . . The theory is amplified, exemplified and properly related to what this part of algebra is really for by discussion of a wide variety of geometrical phenomena in which groups measure symmetry. Overall, the author’s plan, to base his treatment on the premise that groups and symmetry go together, is a very good one, and the book deserves to succeed."—MATHEMATICAL REVIEWSTable of ContentsPreface. 1: Symmetries of the Tetrahedron. 2: Axioms. 3: Numbers. 4: Dihedral Groups. 5: Subgroups and Generators. 6: Permutations. 7: Isomorphisms. 8: Plato's Solids and Cayley's Theorem. 9: Matrix Groups. 10: Products. 11: Lagrange's Theorem. 12: Partitions. 13: Cauchy's Theorem. 14: Conjugacy. 15: Quotient Groups. 16: Homomorphisms. 17: Actions, Orbits, and Stabalizers. 18: Counting Orbits. 19: Finite Rotation Groups. 20: The Sylow Theorems. 21: Finitely Generated Abelian Groups. 22: Row and Column Operations. 23: Automorphisms. 24: The Euclidean Group. 25: Lattices and Point Groups. 26: Wallpaper Patterns. 27: Free Groups and Presentations. 28: Trees and the Nielsen-Schreier Theorem. Bibliography. Index.

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Book SynopsisWhy do we develop extreme attitudes to others? Can our personality contribute to our prejudices? How do we reduce prejudice and discrimination?The Psychology of Prejudice explores different forms of prejudice and discrimination, from racial jokes to genocide. It looks at what might cause our prejudiced attitudes, including our personalities, social influences, group identity, and evolutionary factors, and how prejudice can be reduced through education, campaigning, and consciousness raising.Offering insights into a topic of great public concern and debate, The Psychology of Prejudice shows us how we can confront our prejudiced attitudes and contribute to greater tolerance and understanding.Table of Contents1. What do we mean by ‘Prejudice’? 2. Prejudice within Biology, Psychology and Psychiatry 3. Prejudice and Personality 4. The Impact of Environmental Factors on Prejudice and Discrimination 5. The Influence of Group Membership 6. Reducing Prejudice and Discrimination

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Book SynopsisAlthough group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-coTrade ReviewHonorable Mention for the 2017 PROSE Award in Textbook/Best in Physical Sciences and Mathematics, Association of American Publishers "Another excellent entry in the 'Nutshell' series, Zee's latest has it all: broad scope, depth, thorough explanations, history, and an appealing sense of humor. The author's knowledge of mathematics and physics is encyclopedic, and he leavens the text generously with episodes and asides drawn from the life and work of the major figures in the development of group theory and its applications in physics."--Choice "In Group Theory in a Nutshell for Physicists, Anthony Zee ... combines clarity of presentation with mathematical detail at a level of rigor acceptable to physicists. The result is a tour de force that guides readers through the universe of group theory and leads them to recent particle physics, cosmology, and condensed matter. The book is unique in its laid-back presentation."--Physics Today "This book lives up to my high expectations and can stand shoulder to shoulder with Zee's other two Nutshell books."--Johannes Koelman, Science 2.0

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Book SynopsisThis book uses Big Allied and Dangerous (BAAD) as the dataset for a modern and comprehensive exploration of why insurgent groups attack civilians, even though their existence depends on public support. The book examines this phenomenon in specific contexts, including schools, news media, and nonmilitary/nongovernment spaces designed for the general public.Trade ReviewIn this compelling book, Asal, Phillips, and Rethemeyer provide a much-needed investigation into why armed militant organizations target civilians during conflicts. The authors use both original quantitative data and numerous case references to construct a comprehensive picture of militant group targeting behavior that considers group relations with civilians, state counter-insurgency strategy, inter-group competition, group criminal activity, group ideology and ethnic ties and a host of other factors. The end result is a book that will inform both scholarly and policy audiences alike. A must-read for anyone interested in insurgent group behavior. * James Piazza, Liberal Arts Professor of Political Science, The Pennsylvania State University *By honing in on relational explanations, this book makes a major contribution to our understanding of why insurgent organizations sometimes kill civilians and other times not. The concept of insurgent embeddedness provides a compelling and novel theoretical lens to explain this variation. Combined with a rich qualitative and quantitative empirical material, it generates profound insights that will inform and inspire students of insurgent violence in years to come. * Hanne Fjelde, Associate Professor, Uppsala University *Insurgent Terrorism is a thought-provoking, provocative investigation by three leading scholars on why insurgent groups may target civilians in pursuit of political goals. This is an important question of increasing relevance for sub-Saharan Africa and the Middle East and North Africa. The book supports its theses with data-driven, careful empirical analysis based on insurgent attacks, goals, and inter-organization linkages. * Todd Sandler, Emeritus Chair, University of Texas at Dallas *This book provides a fresh look at organizations' choices to engage in terrorist attacks against civilians. Advancing a theory of embeddedness, the authors examine complex relationships between insurgent organizations, the state, other insurgents, and the civilian population. They find a diverse set of factors impact different types of terrorism, advancing our understanding of this phenomena. * Kathleen Gallagher Cunningham, Cunningham, Professor, University of Maryland *Insurgent Terrorism is an important book that presents detailed cross-national data and analyses of civilian targeting by insurgent groups in civil conflict. Asal, Phillips, and Rethemeyer persuasively argue that the embeddedness of insurgent groups - that is, their relations with the state, the public, and each other - explains variation in civilian victimization. This relational account produces novel and intriguing findings, such as that both alignment and rivalry with other groups lead to more frequent civilian targeting. Marked by empirical richness, the book advances knowledge on the behavior of insurgent groups, civilian victimization, and civil conflict. * Ursula Daxecker, Associate Professor, University of Amsterdam *Table of ContentsSECTION I. Introduction, Theory, and Initial Testing Chapter 1. Introduction Chapter 2. The Embeddedness Theory of Civilian Targeting by Insurgent Groups Chapter 3. Describing the BAAD2 Insurgency Data and Other Data Sources Chapter 4. Testing Primary Hypotheses SECTION II. Empirical Extensions: Types of Civilian Targeting Chapter 5. Why Do Some Insurgent Groups Attack Schools? Chapter 6. Why Do Some Insurgent Groups Attack Journalists? Chapter 7. Why Do Some Insurgent Groups Mostly Attack the General Public? SECTION III. Further Analysis of Inter-Group Relationships Chapter 8. Longitudinal Modelling of Insurgent Alliances Chapter 9. Understanding Insurgent Rivalry Chapter 10. Conclusion

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Book SynopsisThis detailed yet accessible text introduces the advanced mathematical methods at the core of theoretical physics. Based on a course for senior undergraduate students of physics, it is written in a clear, pedagogical style and would also be valuable to students in other areas of science and engineering.Trade Review'The recent explosive development of topological quantum matter requires a deep systematic understanding of modern mathematics. Quantum many-body entanglement in topological quantum matter is a new phenomenon that requires new mathematical language to describe. This is a rare book that provides systematic and in-depth coverage of some of the most important mathematical concepts, such as groups, geometry, topology and algebra, among others. Many abstract mathematical notions are explained in an easy, explicit fashion. This is an in-depth, friendly book on modern mathematics. Very timely and highly recommended.' Xiao-Gang Wen, Massachusetts Institute of TechnologyTable of Contents1. Introduction; 2. Group theory; 3. Representation theory of groups; 4. Differentiable manifolds; 5. Riemannian geometry; 6. Semisimple Lie algebras and their unitary representations; Appendix A; References; Index.

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Book SynopsisAs the speed of globalization accelerates, world cultures are more closely connected to each other than ever before. But what exactly is culture? It seems to be involved in all psychological processes, but can its psychological consequences be studied scientifically? How can cultural differences be described without reifying culture and reinforcing cultural stereotypes? Culture and mind constitute each other, but how? Why do humans need culture? How did the evolution of the mind enable the development of human culture? How does participation in culture transform the mind, and how does the mind process and apply culture? How may culture become a resource for pursuing valued goals, and how does culture become part of the self? How do culture travelers navigate cultures and negotiate multiple cultural identities? The authors of this volume offer a refreshing theoretical perspective and organize seemingly disparate research evidence into a coherent body of psychological knowledge. With its accessible language and lively narrative, this volume engages its readers in an intellectual journey through the fascinating research literatures in psychology, anthropology, and the cognate disciplines. This book will make an ideal textbook for senior undergraduate and graduate courses on psychology and culture, cultural studies, cognitive anthropology, and intercultural communication. Trade Review “This superb account of the way culture and social psychology are interrelated uses a broad set of theoretical and applied perspectives. It is very much up-to-date, describing more recent experiments than even professional cultural psychologists are likely to know. Cultural psychology is a collaborative enterprise, and the inclusion of the biographies of the major researchers allows the reader to become, in a small way, a member of the team of researchers exploring the culture and social psychology link. Both professional psychologists and students will learn a great deal from it.” - Harry C. Triandis, Professor Emeritus, University of Illinois at Urbana-Champaign“This is truly a unique book. Written in a manner that is engaging and accessible to a broad audience, Social Psychology of Culture effectively weaves together theory and concrete illustrations of cultural influences on thought and behavior. The result is a comprehensive review that simultaneously advances our understanding of culture, and of social psychology. Kudos to the authors for a remarkable piece of scholarship.” - Marilynn B. Brewer, Ohio State University“Though the basic orientation of this book is social psychological, the perspective fromwhich the authors view cultural phenomena is unusually broad and integrative. I recommend this book to any psychologist who seeks entrée to this fascinating and burgeoning area of theory and research.” - Robert M. Krauss, Columbia University“This volume provides comprehensive coverage of fundamental issues and applicationsin a balanced and extremely readable manner. A definite must for any course on the social psychology of culture.” - Gün R. Semin, Free University Amsterdam'This superb account of the way culture and social psychology are interrelated uses a broad set of theoretical and applied perspectives. It is very much up-to-date, describing more recent experiments than even professional cultural psychologists are likely to know. Cultural psychology is a collaborative enterprise, and the inclusion of the biographies of the major researchers allows the reader to become, in a small way, a member of the team of researchers exploring the culture and social psychology link. Both professional psychologists and students will learn a great deal from it.'- Harry C. Triandis, Professor Emeritus, University of Illinois at Urbana-Champaign, USA'This is truly a unique book. Written in a manner that is engaging and accessible to a broad audience, Social Psychology of Culture effectively weaves together theory and concrete illustrations of cultural influences on thought and behavior. The result is a comprehensive review that simultaneously advances our understanding of culture, and of social psychology. Kudos to the authors for a remarkable piece of scholarship.'- Marilynn B. Brewer, Ohio State University, USA'Though the basic orientation of this book is social psychological, the perspective from which the authors view cultural phenomena is unusually broad and integrative. I recommend this book to any psychologist who seeks entrée to this fascinating and burgeoning area of theory and research.'- Robert M. Krauss, Columbia University, USA'This volume provides comprehensive coverage of fundamental issues and applications in a balanced and extremely readable manner. A definite must for any course on the social psychology of culture.'- Gün R. Semin, Free University Amsterdam, The NetherlandsTable of ContentsAbout the Authors. Preface. Chapter 1 What Is Culture? Culture in the News. The Concept of Culture in Historical Context. Categories of Culture. Definition of Culture. Organization of the Book. What is Social about Social Psychology of Culture? Chapter 2 Strategies for Describing Culture. Culture in the News … and Fairy Tales. Describing Cultural Variations. The Global Approach. The Focal Approach. Summary and Conclusion. Chapter 3 Psychological Foundation of Human Culture. Culture in the News. Ape Cultures. Human Cultures. Cognitive Foundation of Human Cultures. Social Psychological Foundation of Human Culture. Nature, Culture, and Mind. Chapter 4 What is Culture For? Fact or Hoax? Biological and Cultural Evolution. What Does Culture Do for the Survival of the Species? What Does Culture Do for a Society? What Does Culture Do for the Individual? Conclusion . Chapter 5 Culture as Mental Habits: Shared Unintended Thoughts. Culture Travelers’ Journal. Taxonomy of Knowledge. Interpretive Cautions. Mental Habits as Procedural Knowledge. The Linguistic Relativity Hypothesis. Conclusion. Chapter 6 Culture, Self, and Others: Who Am I and Who Are They? Culture and Architecture. Person Representations. Representations of Other People. Representations of the Self . Representations of Groups. Conclusion. Chapter 7 Events and Norms: How Events Unfold and What We Should Do. Cultural Psychology in Public Bathrooms. Event Representations. Norm Representations. Conclusion. Chapter 8 Organization and Application of Cultural Knowledge. Cultural Icons. Organization of Cultural Knowledge: Is Culture a Coherent Meaning System? Multiple Determinants of Cultural Behavior. Relative Influence of Different Determinants. The Context of Cultural Knowledge. Conclusion. Chapter 9 Reproduction of Culture and Cultural Change. Cultural Change across the Globe. Media of Cultural Transmission. How are Shared Representations Constructed and Reproduced? Cultural Change. Conclusion. Chapter 10 Intercultural Contacts: Implications for Cultural Competence. The Rice Storm and the Butterfly Effect. Nature of Cultural Competence. Psychological Benefits of Intercultural Contacts. Psychological Costs of Intercultural Contacts. Conclusion. Chapter 11 Globalization and Multicultural Identities. Tsunami and Globalization. Migration and Globalization. Will Globalization Lead to Homogenization of Cultures? Globalization and Cultural Diversity. Migration and Management of Multicultural. Identities. Colonization and Identity Negotiation. Conclusion. Chapter 12 Scientific Study of Cultural Processes. Studying Culture in Coffee Shops. Beyond Description of Cultural Differences. Explaining Cultures. Psychic Unity and Cultural Relativity. What is Social about Social Psychology of Culture? References. Author Index . Subject Index

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Book SynopsisFrom Crowd Psychology to the Dynamics of Large Groups offers transdisciplinary research on the history of the study of social formations, ranging from nineteenth-century crowd psychology in France and twentieth-century Freudian mass psychology, including the developments in critical theory, to the study of the psychodynamics of contemporary large groups.Carla Penna presents a unique combination of sociology, psychoanalysis, and group analysis in the study of social formations. This book revisits the epistemological basis of group analysis by introducing and discussing its historical path, especially in connection with the study of large groups and investigations of the social unconscious in persons, groups, and societies. It also explores early work on group relations and contemporary research on the basic-assumption group in England, particularly Hopperâs theory of Incohesion as a fourth basic assumption. From Crowd Psychology to the Dynamics of Large Groups Trade Review"Carla Penna takes us on a journey through centuries of thought about persons who are both social beings as well as sentient ones. Her book is more than a set of reflections, as it comprises a comprehensive survey of the political and sociological nature of groups, communities and societies. It then considers the various contemporary forms of therapy in groups. We are invited to see how social theorists such as Kurt Lewin or Norbert Elias contributed to therapeutic thinking, whilst therapeutic practice has informed sociological thinking. This multi-dimensional picture shows humans beings within the matrix of the societies which humans have created, and how that matrix can heal us as well as form us." - R.D. Hinshelwood, Psychiatrist, Psychoanalyst, Professor for Psychoanalysis, University of Essex"At last a helpful and scholarly account of the theoretical history of Large Group Theory. The book is to be recommended for forging a link between sociology, psychoanalysis and up to date group analysis. Readers are left in no doubt that large group phenomena can only be comprehended in an inter-disciplinary way and that there are more ways than one to look at human gatherings in large numbers." - Gerhard Wilke is a group analyst and an independent organizational consultant in London. He is an Associate of the Ashridge Business School"The Crowd is an essential addition to the literature on how to understand, and live with, the demands of our troubled times. Moving with great clarity and energy through the history of hordes, herds, masses, and crowds, and drawing from her deep understanding of group psychologies and group analysis, Carla Penna offers both a balanced and well-informed guide to group theory and a set of innovative ideas for confronting social and psychological reality." - Stephen Frosh, PhD, Professor of Psychosocial Studies, Birkbeck, University of London"Carla Penna's book From Crowd Psychology to the Dynamics of Large Groups: Historical, Theoretical and Practical Considerations is a monumental research project. The book is rich with facts and ideas, describing the development of the concept of the crowd, the birth of the work of Bion (the Tavistock Institute) and Foulkes (Group Analysis), the unstructured psychodynamic Large Group, Unconscious Social Processes, and Hopper's 4th Basic assumption of Incohesion. Penna integrates sociology, psychology, and group analysis in a very fluent and smooth way. Her historical research is broad and reveals many important facts from the end of the 19th century until today. This breadth is breathtaking. In today's world, at the beginning of the third decade of the 21th century, flooded by social conflicts, polarization, divisiveness, and mass impact of social media, this book is essential in order to understand the large social group unconscious processes. Its perspective allows the reader to take some distance from current political, sociological and cultural crises and to look at them from a wider angle. This book is highly recommended for sociologists, historians, psychologists, psychotherapists, group therapists, group analysts, and anyone who is interested in understanding more about unconscious social processes." - Haim Weinberg, PhD is a psychologist and group analyst in California and Israel. Past president of the Israeli Association for Group Psychotherapy. Former Director of International Programs at the Professional School of Psychology, California."Carla Penna puts at our disposition her encyclopedic knowledge on phenomena involving large numbers of persons. She approaches the context of masses with psychoanalytic and group analytic tools, first "mapping the field" of the unconscious life of crowds, illuminating the darkness of the twenty-first century crowds and masses." - Robi Friedman, PhD, group analyst, Past President of the Group Analytic Society International"This book represents an impressive tour de force. The author takes us on an exciting journey into a transdiciplinary analysis and investigation of the psychodynamics of the larger group starting with Durkheim and Le Bon over Freud to the Frankfurt School, the Northfield experiments, Bion and Foulkes ending up with Hopper’s 4th basic assumption of Incohesion. It is an outstanding achievement, and it is warmly recommended." - Gerda Winther, MA, is a psychologist. She is a former associate professor at the Faculty of Medicine, University of Copenhagen. Past President of the Group Analytic Society International. "Carla Penna’s particular view from Brazil, combined with her many years of experience as practitioner, teacher and academic of psychoanalysis and group analysis, enables a full study of where we are now in understanding large groups. She provides an expansive perspective with access to writers from Latin America and Europe often with her own translations." - Dr Jale Cilasun BM FRCPsych, Consultant Psychiatrist, Specialist in Medical Psychotherapy and Group Analyst. "This is a much-needed book - in time and on time. In a world where crowds take many different forms globally and virtually, transcending lives everywhere this transdisciplinary study investigates crowds as social and psychological phenomena historically and contemporary based on an impressive command of knowledge. However, the focus turns to the social unconscious as the most important tool for the understanding of the complicated and often incomprehensible processes that go on in the large groups that forms the crowds. The author is a psychoanalyst and group analyst and is drawing on theories and clinical experience of large group dynamics where the interaction in the social unconscious between the individual and the large group takes place." - Anne Lindhardt, psychiatrist, group analyst and trained group analyst. Former director of Mental Services in Copenhagen. Chairperson of Institute of Group Analysis Copenhagen."Carla Penna takes us on a journey through centuries of thought about persons who are both social beings as well as sentient ones. Her book is more than a set of reflections, as it comprises a comprehensive survey of the political and sociological nature of groups, communities, and societies. It then considers the various contemporary forms of therapy in groups. We are invited to see how social theorists such as Kurt Lewin or Norbert Elias contributed to therapeutic thinking, whilst therapeutic practice has informed sociological thinking. This multi-dimensional picture shows human beings within the matrix of the societies which humans have created, and how that matrix can heal us as well as form us." - R.D. Hinshelwood, psychiatrist, psychoanalyst, Professor of Psychoanalysis, University of Essex"At last a helpful and scholarly account of the theoretical history of Large Group Theory. The book is to be recommended for forging a link between sociology, psychoanalysis, and up to date group analysis. Readers are left in no doubt that large group phenomena can only be comprehended in an inter-disciplinary way and that there are more ways than one to look at human gatherings in large numbers." - Gerhard Wilke, group analyst, an independent organizational consultant in London, and an Associate of the Ashridge Business School"From Crowd Psychology to the Dynamics of Large Groups is an essential addition to the literature on how to understand, and live with, the demands of our troubled times. Moving with great clarity and energy through the history of hordes, herds, masses, and crowds, and drawing from her deep understanding of group psychologies and group analysis, Carla Penna offers both a balanced and well-informed guide to group theory and a set of innovative ideas for confronting social and psychological reality." - Stephen Frosh, PhD, Professor of Psychosocial Studies, Birkbeck, University of London"Carla Penna's book From Crowd Psychology to the Dynamics of Large Groups: Historical, Theoretical and Practical Considerations is a monumental research project. The book is rich with facts and ideas, describing the development of the concept of the crowd, the birth of the work of Bion (the Tavistock Institute) and Foulkes (Group Analysis), the unstructured psychodynamic Large Group, Unconscious Social Processes, and Hopper's fourth basic assumption of Incohesion. Penna integrates sociology, psychology, and group analysis in a very fluent and smooth way. Her historical research is broad and reveals many important facts from the end of the nineteenth century until today. This breadth is breathtaking. In today's world, at the beginning of the third decade of the twenty-first century, flooded by social conflicts, polarization, divisiveness, and mass impact of social media, this book is essential in order to understand the large social group unconscious processes. Its perspective allows the reader to take some distance from current political, sociological, and cultural crises and to look at them from a wider angle. This book is highly recommended for sociologists, historians, psychologists, psychotherapists, group therapists, group analysts, and anyone who is interested in understanding more about unconscious social processes." - Haim Weinberg, PhD, psychologist and group analyst in California and Israel, past President, Israeli Association for Group Psychotherapy, and former Director of International Programs, Professional School of Psychology, California"Carla Penna puts at our disposition her encyclopedic knowledge on phenomena involving large numbers of persons. She approaches the context of masses with psychoanalytic and group analytic tools, first 'mapping the field' of the unconscious life of crowds, illuminating the darkness of the twenty-first century crowds and masses." - Robi Friedman, PhD, group analyst, past President of the Group Analytic Society International"This book represents an impressive tour de force. The author takes us on an exciting journey into a transdiciplinary analysis and investigation of the psychodynamics of the larger group, starting with Durkheim and Le Bon over Freud to the Frankfurt School, the Northfield experiments, Bion and Foulkes, ending up with Hopper’s fourth basic assumption of Incohesion. It is an outstanding achievement and it is warmly recommended." - Gerda Winther, MA, psychologist, former Associate Professor at the Faculty of Medicine, University of Copenhagen , and past President of the Group Analytic Society International "Carla Penna’s particular view from Brazil, combined with her many years of experience as practitioner, teacher, and academic of psychoanalysis and group analysis, enables a full study of where we are now in understanding large groups. She provides an expansive perspective with access to writers from Latin America and Europe often with her own translations." - Dr Jale Cilasun, BM FRCPsych, consultant psychiatrist, specialist in medical psychotherapy and group analyst"This is a much-needed book – in time and on time. In a world where crowds take many different forms globally and virtually, transcending lives everywhere, this transdisciplinary study investigates crowds as social and psychological phenomena historically and contemporary based on an impressive command of knowledge. However, the focus turns to the social unconscious as the most important tool for the understanding of the complicated and often incomprehensible processes that go on in the large groups that forms the crowds. The author is a psychoanalyst and group analyst and is drawing on theories and clinical experience of large group dynamics where the interaction in the social unconscious between the individual and the large group takes place." - Anne Lindhardt, psychiatrist, trained group analyst, former Director of Mental Services, Copenhagen, and Chairperson of Institute of Group Analysis CopenhagenTable of ContentsAcknowledgmentsSeries Foreword by Earl HopperIntroductionCHAPTER ONENineteenth-century crowd psychologyCHAPTER TWOTwentieth-century Freudian mass psychologyCHAPTER THREETwentieth-century left-wing mass psychologyCHAPTER FOURReflections on a society of individuals CHAPTER FIVEThe Northfield experiments: the cradle of group work in EnglandCHAPTER SIXGroup relations and Bion’s legacyCHAPTER SEVENTowards new basic assumptions in groupsCHAPTER EIGHTFoulkes and group analysis: the development of the theory of the social unconsciousCHAPTER NINELarge-group psychodynamics in group analysisCHAPTER TENTraumatic experience in the unconscious life of social systems: Earl Hopper’s theory of the fourth basic assumption of Incohesion: Aggregation/Massification or (ba) I: A/MEpilogueReferencesIndex

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Book SynopsisCan a sense of belonging increase life satisfaction? Why do we sometimes feel lonely? How can we sustain lasting human connections?The Psychology of Belonging explores why feeling like we belong is so important throughout our lives, from childhood to old age, irrespective of culture, race or geography. With its virtues and shortcomings, belonging to groups such as families, social groups, schools, workplaces and communities is fundamental to our identity and wellbeing, even in a time when technology has changed the way we connect with each other.In a world where loneliness and social isolation is on the rise, The Psychology of Belonging shows how meaningful connections can build a sense of belonging for all of us. Table of Contents1. The beginnings of belonging 2. Belonging begins at birth 3. Belonging in adulthood 4. Rejection 5. Belonging in an age of technology 6. Belonging bad 7. Building belonging References

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Book SynopsisL-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.Trade Review'… a gentle introduction to this fascinating new subject. The presentation is very explicit and many examples are worked out with great detail … This book should be of great interest to students beginning with the theory of modular forms or for more advanced readers wanting to know about general L-functions.' Emmanuel P. Royer, Mathematical Reviews'This book, whose clear and sometimes simplified proofs make the basic theory of automorphic forms on GL(n) accessible to a wide audience, will be valuable for students. It nicely complements D. Bump's book (Automorphic Forms and Representations, Cambridge, 1997), which offers a greater emphasis on representation theory and a different selection of topics.' Zentralblatt MATH'Unfortunately, when n > 2 the GL(n) theory is not very accessible to the student of analytic number theory, yet it is increasing in importance. [This book] addresses this problem by developing a large part of the theory in a way that is carefully designed to make the field accessible … much of the literature is written in the adele language, and seeing how it translates into classical terms is both useful and enlightening … This is a unique and very welcome book, one that the student of automorphic forms will want to study, and also useful to experts.' Daniel Bump, SIAM ReviewTable of ContentsIntroduction; 1. Discrete group actions; 2. Invariant differential operators; 3. Automorphic forms and L-functions for SL(2,Z); 4. Existence of Maass forms; 5. Maass forms and Whittaker functions for SL(n,Z); 6. Automorphic forms and L-functions for SL(3,Z); 7. The Gelbert–Jacquet lift; 8. Bounds for L-functions and Siegel zeros; 9. The Godement–Jacquet L-function; 10. Langlands Eisenstein series; 11. Poincaré series and Kloosterman sums; 12. Rankin–Selberg convolutions; 13. Langlands conjectures; Appendix. The GL(n)pack manual; References.

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Book SynopsisThe field of random walks on groups is re-emerging with many new ideas and exciting research. This book contains a comprehensive introduction for researchers new to the field. Despite dealing with cutting-edge research, it is accessible even to new graduate students, with worked examples, exercises, and open problems all included.

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Book SynopsisThis volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.Table of ContentsPublications of Vyjayanthi Chari.- Students of Vyjayanthi Chari.- Part I: Courses.- String Diagrams and Categorification.- Quantum Affine Algebras and Cluster Algebras.- Part II: Surveys.- Work of Vyjayanthi Chari.- Steinberg Groups for Jordan Pairs - An Introduction with Open Problems.- On the Hecke-Algebraic Approach for General Linear Groups over a p-adic Field.- Part III: Papers.- Categorical Representations and Classical p-adic Groups.- Formulae of l-Divided Powers in Uq(sl2),II.- Longest Weyl Group Elements in Action.- Dual Kashiwara Functions for the B(∞) Crystal in the Bipartite Case.- Lusztig's t-Analogue of weight multiplicity via Crystals.- Conormal Varieties on the Cominuscule Grassmannian.- Evaluation Modules for Quantum Toroidal gln Algebras.- Dynamical Quantum Determinants and Pfaffians.

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Book SynopsisAlgebraic Topology is an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years. Each chapter, or lecture, corresponds to one day of class at SUMaC. The book begins with the preliminaries needed for the formal definition of a surface. Other topics covered in the book include the classification of surfaces, group theory, the fundamental group, and homology. This book assumes no background in abstract algebra or real analysis, and the material from those subjects is presented as needed in the text. This makes the book readable to undergraduates or high-school students who do not have the background typically assumed in an algebraic topology book or class. The book contains many examples and exercises, allowing it to be used for both self-study and for an introductory undergraduate topology course.Trade Review“Algebraic topology provides a self-contained introduction to the field … . the book thus provides a particularly well-organized, interesting, and smooth exposition of its subject. … This particular book unique is that it provides a clear, elementary, but mathematically solid introduction to algebraic topology that keeps the subject interesting throughout. … provides a clear, readable, and detailed treatment of the ideas and proofs in the subject … .” (Thomas Mack, Mathematical Reviews, July, 2022)“The book could easily be used in an undergraduate course or read by a bright high school student. It should certainly be in any high school library.” (Jonathan Hodgson, zbMATH 1481.55001, 2022)Table of ContentsIntroduction.- 1. Surface Preliminaries.- 2. Surfaces.- 3. The Euler Characteristic and Identification Spaces.- 4. Classification Theorem of Compact Surfaces.- 5. Introduction to Group Theory.- 6. Structure of Groups.- 7. Cosets, Normal Subgroups, and Quotient Groups.- 8. The Fundamental Group.- 9. Computing the Fundamental Group.- 10. Tools for Fundamental Groups.- 11. Applications of Fundamental Groups.- 12. The Seifert-Van Kampen Theorem.- 13. Introduction to Homology.- 14. The Mayer-Vietoris Sequence.- A. Topological Notions.- Bibliography.- Index.

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Book SynopsisThis book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike.Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.Trade Review“Adhikari’s work is an excellent resource for any individual seeking to learn more about algebraic topology. By no means will this text feel like an introduction to algebraic topology, but it does offer much for both beginners and experts. … the text will be a valuable reference on the bookshelf of any reader with an interest in algebraic topology. Summing Up: Recommended. Upper-division undergraduates and above; researchers and faculty.” (A. Misseldine, Choice, Vol. 54 (9), May, 2017)“I am pretty enthusiastic about this book. … it shows very good taste on the author’s part as far as what he’s chosen to do and how he’s chosen to do it. … Wow! What a nice book. I’m glad I have a copy.” (Michael Berg, MAA Reviews, maa.org, February, 2017)“This is a comprehensive textbook on algebraic topology. … accessible to students of all levels of mathematics, so suitable for anyone wanting and needing to learn about algebraic topology. It can also offer a valuable resource for advanced students with a specialized knowledge in other areas who want to pursue their interest in this area. … further readings are provided at the end of each of them, which also enables students to study the subject discussed therein in more depth.” (Haruo Minami, zbMATH 1354.55001, 2017)Table of ContentsPrerequisite Concepts and Notations.- Basic Homotopy.- The Fundamental Groups.-Covering Spaces.- Fibre Bundles, Vector Bundles and K-theory.- Geometry of Simplicial Complexes and Fundamental Groups.- Higher Homotopy Groups.- Products in Higher Homotopy Groups.- CW-complexes and Homotopy.- Eilenberg-MacLane Spaces.- Homology and Cohomology Theories.- Eilenberg-Steenrod Axioms for Homology and Cohomology Theories.- Consequences of the Eilenberg-Steenrod Axioms.- Some Applications of Homology Theory.- Spectral Homology and Cohomology Theories.- Obstruction Theory.- More Relations Between Homotopy and Homology Groups.- A Brief Historical Note.

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Book SynopsisThe development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest.

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Book SynopsisGroups and subgroups.- Normal subgroups.- Finite groups.- Series groups.

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Book SynopsisFeaturing strategies for solving the puzzles and computations illustrated using the SAGE open-source computer algebra system, the second edition of Adventures in Group Theory is perfect for mathematics enthusiasts and for use as a supplementary textbook.Trade Review"Adventures in Group Theory is a tour through the algebra of several 'permutation puzzles'... If you like puzzles, this is a somewhat fun book. If you like algebra, this is a fun book. If you like puzzles and algebra, this is a really fun book." - MAA Online "Joyner has collated all the Rubik lore and integrated it with a self-contained introduction to group theory that equals or, more likely, exceeds what is available in typical dedicated elementary texts." - Choice "Joyner does convey some of the excitement and adventure in picking up knowledge of group theory by trying to understand Rubik's Cube. Enthusiastic students will learn a lot of mathematics from this book." - American Scientist"Table of ContentsPrefaceAcknowledgmentsWhere to Begin...1. Elementary, my dear Watson2. 'And you do addition?'3. Bell ringing and other permutations4. A procession of permutation puzzles5. What's commutative and purple?6. Welcome to the machine7. 'God's algorithm' and graphs8. Symmetry and the Platonic solids9. The illegal cube group10. Words which move11. The (legal) Rubik's Cube group12. Squares, two-faces, and other subgroups13. Other Rubik-like puzzle groups14. Crossing the Rubicon15. Some solution strategies16. Coda: Questions and other directionsBibliographyIndex

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Book SynopsisThe principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning. This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment.Table of ContentsMotivation.- I Euclidean and Inversive Geometry.- Euclidean Isometries and Similarities.- Inversive Geometry.- Applications of Inversive Geometry.- II Non-Euclidean Geometry.- Spherical Geometry.- Appendix: Set Theory.

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Book Synopsis'Oxford Logic Guide provides comprehensive coverage of a new research area in algebra and model theory. Model theoretical and group theoretical notions are explained in detail, and almost all the known results in the area are included. Aimed at the needs of the graduate student, there are many exercises (with hints) and carefully chosen examples.Table of Contents1. Basic Group Theory ; 2. Definability ; 3. Interpretability ; 4. Ranked Universe ; 5. Basic Properties ; 6. Nilpotent Groups ; 7. Semisimple Groups ; 8. Fields and Rings ; 9. Solvable Groups ; 10. 2-Sylow Theory ; 11. Permutation Groups ; 12. Gepometrics ; 13. bad Groups ; 14. CN and CIT-Groups ; A. Miscellaneous Results ; B. Open Problems ; C. Link with Model Theory ; D. Hints to the Exercises ; Bibliography ; Index

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Book Synopsis1 Introduction to Lie Groups.- 1.1. Manifolds.- 1.2. Lie Groups.- 1.3. Vector Fields.- 1.4. Lie Algebras.- 1.5. Differential Forms.- Notes.- Exercises.- 2 Symmetry Groups of Differential Equations.- 2.1. Symmetries of Algebraic Equations.- 2.2. Groups and Differential Equations.- 2.3. Prolongation.- 2.4. Calculation of Symmetry Groups.- 2.5. Integration of Ordinary Differential Equations.- 2.6. Nondegeneracy Conditions for Differential Equations.- Notes.- Exercises.- 3 Group-Invariant Solutions.- 3.1. Construction of Group-Invariant Solutions.- 3.2. Examples of Group-Invariant Solutions.- 3.3. Classification of Group-Invariant Solutions.- 3.4. Quotient Manifolds.- 3.5. Group-Invariant Prolongations and Reduction.- Notes.- Exercises.- 4 Symmetry Groups and Conservation Laws.- 4.1. The Calculus of Variations.- 4.2. Variational Symmetries.- 4.3. Conservation Laws.- 4.4. Noether's Theorem.- Notes.- Exercises.- 5 Generalized Symmetries.- 5.1. Generalized Symmetries of Differential Equations.- 5.2. Récursion Operators, Master Symmetries and Formal Symmetries.- 5.3. Generalized Symmetries and Conservation Laws.- 5.4. The Variational Complex.- Notes.- Exercises.- 6 Finite-Dimensional Hamiltonian Systems.- 6.1. Poisson Brackets.- 6.2. Symplectic Structures and Foliations.- 6.3. Symmetries, First Integrals and Reduction of Order.- Notes.- Exercises.- 7 Hamiltonian Methods for Evolution Equations.- 7.1. Poisson Brackets.- 7.2. Symmetries and Conservation Laws.- 7.3. Bi-Hamiltonian Systems.- Notes.- Exercises.- References.- Symbol Index.- Author Index.Table of Contents1 Introduction to Lie Groups.- 1.1. Manifolds.- Change of Coordinates.- Maps Between Manifolds.- The Maximal Rank Condition.- Submanifolds.- Regular Submanifolds.- Implicit Submanifolds.- Curves and Connectedness.- 1.2. Lie Groups.- Lie Subgroups.- Local Lie Groups.- Local Transformation Groups.- Orbits.- 1.3. Vector Fields.- Flows.- Action on Functions.- Differentials.- Lie Brackets.- Tangent Spaces and Vectors Fields on Submanifolds.- Frobenius’ Theorem.- 1.4. Lie Algebras.- One-Parameter Subgroups.- Subalgebras.- The Exponential Map.- Lie Algebras of Local Lie Groups.- Structure Constants.- Commutator Tables.- Infinitesimal Group Actions.- 1.5. Differential Forms.- Pull-Back and Change of Coordinates.- Interior Products.- The Differential.- The de Rham Complex.- Lie Derivatives.- Homotopy Operators.- Integration and Stokes’ Theorem.- Notes.- Exercises.- 2 Symmetry Groups of Differential Equations.- 2.1. Symmetries of Algebraic Equations.- Invariant Subsets.- Invariant Functions.- Infinitesimal Invariance.- Local Invariance.- Invariants and Functional Dependence.- Methods for Constructing Invariants.- 2.2. Groups and Differential Equations.- 2.3. Prolongation.- Systems of Differential Equations.- Prolongation of Group Actions.- Invariance of Differential Equations.- Prolongation of Vector Fields.- Infinitesimal Invariance.- The Prolongation Formula.- Total Derivatives.- The General Prolongation Formula.- Properties of Prolonged Vector Fields.- Characteristics of Symmetries.- 2.4. Calculation of Symmetry Groups.- 2.5. Integration of Ordinary Differential Equations.- First Order Equations.- Higher Order Equations.- Differential Invariants.- Multi-parameter Symmetry Groups.- Solvable Groups.- Systems of Ordinary Differential Equations.- 2.6. Nondegeneracy Conditions for Differential Equations.- Local Solvability.- In variance Criteria.- The Cauchy—Kovalevskaya Theorem.- Characteristics.- Normal Systems.- Prolongation of Differential Equations.- Notes.- Exercises.- 3 Group-Invariant Solutions.- 3.1. Construction of Group-Invariant Solutions.- 3.2. Examples of Group-Invariant Solutions.- 3.3. Classification of Group-Invariant Solutions.- The Adjoint Representation.- Classification of Subgroups and Subalgebras.- Classification of Group-Invariant Solutions.- 3.4. Quotient Manifolds.- Dimensional Analysis.- 3.5. Group-Invariant Prolongations and Reduction.- Extended Jet Bundles.- Differential Equations.- Group Actions.- The Invariant Jet Space.- Connection with the Quotient Manifold.- The Reduced Equation.- Local Coordinates.- Notes.- Exercises.- 4 Symmetry Groups and Conservation Laws.- 4.1. The Calculus of Variations.- The Variational Derivative.- Null Lagrangians and Divergences.- Invariance of the Euler Operator.- 4.2. Variational Symmetries.- Infinitesimal Criterion of Invariance.- Symmetries of the Euler—Lagrange Equations.- Reduction of Order.- 4.3. Conservation Laws.- Trivial Conservation Laws.- Characteristics of Conservation Laws.- 4.4. Noether’s Theorem.- Divergence Symmetries.- Notes.- Exercises.- 5 Generalized Symmetries.- 5.1. Generalized Symmetries of Differential Equations.- Differential Functions.- Generalized Vector Fields.- Evolutionary Vector Fields.- Equivalence and Trivial Symmetries.- Computation of Generalized Symmetries.- Group Transformations.- Symmetries and Prolongations.- The Lie Bracket.- Evolution Equations.- 5.2. Récursion Operators, Master Symmetries and Formal Symmetries.- Frechet Derivatives.- Lie Derivatives of Differential Operators.- Criteria for Recursion Operators.- The Korteweg—de Vries Equation.- Master Symmetries.- Pseudo-differential Operators.- Formal Symmetries.- 5.3. Generalized Symmetries and Conservation Laws.- Adjoints of Differential Operators.- Characteristics of Conservation Laws.- Variational Symmetries.- Group Transformations.- Noether’s Theorem.- Self-adjoint Linear Systems.- Action of Symmetries on Conservation Laws.- Abnormal Systems and Noether’s Second Theorem.- Formal Symmetries and Conservation Laws.- 5.4. The Variational Complex.- The D-Complex.- Vertical Forms.- Total Derivatives of Vertical Forms.- Functionals and Functional Forms.- The Variational Differential.- Higher Euler Operators.- The Total Homotopy Operator.- Notes.- Exercises.- 6 Finite-Dimensional Hamiltonian Systems.- 6.1. Poisson Brackets.- Hamiltonian Vector Fields.- The Structure Functions.- The Lie-Poisson Structure.- 6.2. Symplectic Structures and Foliations.- The Correspondence Between One-Forms and Vector Fields.- Rank of a Poisson Structure.- Symplectic Manifolds.- Maps Between Poisson Manifolds.- Poisson Submanifolds.- Darboux’ Theorem.- The Co-adjoint Representation.- 6.3. Symmetries, First Integrals and Reduction of Order.- First Integrals.- Hamiltonian Symmetry Groups.- Reduction of Order in Hamiltonian Systems.- Reduction Using Multi-parameter Groups.- Hamiltonian Transformation Groups.- The Momentum Map.- Notes.- Exercises.- 7 Hamiltonian Methods for Evolution Equations.- 7.1. Poisson Brackets.- The Jacobi Identity.- Functional Multi-vectors.- 7.2. Symmetries and Conservation Laws.- Distinguished Functionals.- Lie Brackets.- Conservation Laws.- 7.3. Bi-Hamiltonian Systems.- Recursion Operators.- Notes.- Exercises.- References.- Symbol Index.- Author Index.

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Book SynopsisThis book presents a new version of the local analysis section of the Feit–Thompson theorem. It includes a recent (1991) significant improvement by Feit and Thompson and a short revision by T. Peterfalvi of the separate final section of the second half of the proof.Trade Review'This book is written well … the authors have succeeded both in simplifying the proof of the Odd Order Theorem and in making it accessible to a wider audience.' Paul Flavell, Bulletin of the London Mathematical SocietyTable of ContentsPart I. Preliminary Results: 1. Notation and elementary properties of solvable groups; 2. General results on representations; 3. Actions of Frobenius groups and related results; 4. p-Groups of small rank; 5. Narrow p-groups; 6. Additional results; Part II. The Uniqueness Theorem: 7. The transitivity theorem; 8. The fitting subgroup of a maximal subgroup; 9. The uniqueness theorem; Part III. Maximal Subgroups: 10. The subgroups Ma and Me; 11. Exceptional maximal subgroups; 12. The subgroup E; 13. Prime action; Part IV. The Family of All Maximal Subgroups of G: 14. Maximal subgroups of type p and counting arguments; 15. The subgroup Mf; 16. The main results; Appendix; Prerequisites and p-stability.

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Book SynopsisConsiders the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. This book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension.Trade Review"Zannier's book is well written and a pleasure to read... [T]he author always makes an effort to point out key ideas and key steps, so a reader who wants to read and understand the complete proofs in this technically demanding field will find this monograph to be an extremely helpful entree into the subject... [T]he reviewer highly recommends Zannier's book as an excellent survey of and introduction to the important and hot topic of unlikely intersections in arithmetic geometry."--Joseph H. Silverman, Bulletin of the AMS "This book is indeed a great source of knowledge and inspiration for everybody interested in the unlikely intersection problems. The author must be commended for doing this job, and doing it so well."--Yuri Bilu, Mathematical Reviews ClippingsTable of Contents*FrontMatter, pg. i*Contents, pg. v*Preface, pg. ix*Notation and Conventions, pg. xi*Introduction: An Overview of Some Problems of Unlikely Intersections, pg. 1*Chapter 1: Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture, pg. 15*Chapter 2: An Arithmetical Analogue, pg. 43*Chapter 3 Unlikely Intersections in Elliptic Surfaces and Problems of Masser, pg. 62*Chapter 4: About the Andre-Oort Conjecture, pg. 96*Appendix A: Distribution of Rational Points on Subanalytic Surfaces, pg. 128*Appendix B: Uniformity in Unlikely Intersections: An Example for Lines in Three Dimensions, pg. 136*Appendix C: Silverman's Bounded Height Theorem for Elliptic Curves: A Direct Proof, pg. 138*Appendix D: Lower Bounds for Degrees of Torsion Points: The Transcendence Approach, pg. 140*Appendix E: A Transcendence Measure for a Quotient of Periods, pg. 143*Appendix F: Counting Rational Points on Analytic Curves: A Transcendence Approach, pg. 145*Appendix G: Mixed Problems: Another Approach, pg. 147*Bibliography, pg. 149*Index, pg. 159

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Book SynopsisPeople Skills for Behavior Analysts provides a much-needed introduction to the people skills needed to succeed as a behavior analyst.Divided into two primary parts Foundational Skills and Specialized Skills this book addresses an impressive breadth of people skills, focusing on intrapersonal and interpersonal skills, collaboration, consultation and training, leadership, and resource development. Relying on recent evidence-based practices and relevant literature tailored to meet the new BACB Task List, Professional & Ethical Compliance Code, and Supervised Independent Fieldwork requirements, the text includes contributions from leading figures from a wide variety of applied behavior analysis subfields to provide a truly balanced overview. The book delves into the literature from fields related to behavior analysis, such as counselling, psychology, graphic design, management and education, and applies these perspectives to behavioral theories and principles to provide Table of ContentsPart I: Foundational Skills Chapter 1: Intrapersonal Skills 1.1 The Importance of Intrapersonal Skills for Behavior Analysts 1.2 The Discerning ABA Practitioner 1.3 Self-Care for Behavior Analysts: A guide to eating fewer doughnuts and taking more naps Chapter 2: Interpersonal Skills 2.1 20 Key Behaviors for Rapport Building 2.2 Cultural Competence in Communication 2.3 A Critical Look at Autism 2.4 Accepting Feedback Makes the World Go ‘Round: From Student to Practitioner 2.5 How to Teach Rapport Building Skills to Behavior Analysts Chapter 3: Collaboration 3.1 No More “Train And Train More”: A Functional, Contextual Approach to Collaboration with Families 3.2 Playing Nicely in the Interdisciplinary Sandbox: A How to Guide on Effective Collaboration with Various Professionals 3.3 Whose the King of the Castle? Collaborating with Educators and Schools as a Behavior Analyst 3.4 Overcoming the Aversive: Handling Difficult Conversations with Professionalism and Compassion 3.5 Running Efficient and Effective Meetings with Collaboration and Compassion Part 2: Specialized Skills Chapter 4: Consultation & Training 4.1 Don’t Blame the Mediator: Keeping Applied Behavior Analysis Doable for Best Possible Outcomes 4.2 Beyond the PowerPoint: Becoming an Engaging Presenter 4.3 Behavior Analyst as Changemaker: Science, Advocacy and Activism in Practice 4.4 Using Movement Education, Motor Learning, and Phenomenology to Inform Teaching Strategies in Other Professional Contexts Chapter 5: Leadership 5.1 It’s Not You, It’s Us: Fostering a Behavior Analytical Supervisor/Supervisee Relationship 5.2 People Skills for Behavior Analysis: Putting the Super in Your Supervisory Relationships 5.3 Giving Performance Feedback that Makes a Difference 5.4 Interviewing Strategies: Integrating Practices from Industrial/Organizational Psychology into Behavior Analysis for Successful Hiring Chapter 6: Innovative, Creative Ways to use ABA 6.1 Making Applied Behavior Analysis Accessible to Consumers 6.2 Telehealth to Implement Applied Behavior Analysis 6.3 You’re on mute! People skills behind the screens and behind the scenes 6.4 Making a Document People will Actually Read 6.5 A Trauma-Informed Approach to Behavior Analysis 6.6 Behavior analysts' skills for co-developing virtual reality game-based technologies as applied behavior analysis programs for autistic adults

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Book SynopsisThis fascinating book explores the concept of slow living, offering a philosophical and psychological exploration of the need for a slower pace of life. It advocates for reclaiming and rediscovering more natural and human ways of being.In a digital age, which is dominated by an increasingly tyrannical trinity of speed, efficiency and productivity, the author challenges the pernicious ideal of instant gratification, perpetuated by modern consumer culture. This book examines alternative ways of being through re-examining the Wisdom Traditions of Hinduism, Buddhism, Daoism and Judaism through an ongoing and engaging dialogue with psychology and psychotherapy, including insights from environmental psychology, ecopsychology and cyberpsychology. The book argues against the trend for personal responsibility, adaptability and resilience, and the idea that stress is the new normal.' Instead, it proposes a radical shift in paradigm, promoting not for collectively rising up and ove

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The Handbook of Communication Skills is recognised as one of the core texts in the field of communication, offering a state-of-the-art overview of this rapidly evolving field of study.The fifth edition of this bestselling book situates communication in a range of different contexts, from interacting in groups to the counselling interview. It covers topics such as non-verbal behaviour, listening, negotiation, interacting in groups, and mentoring. This new edition has been fully revised and updated, and includes a brand new chapter on digitally mediated communications in social and working environments, as well as newly written chapters on humour and laughter in communication, and persuasion. Based on the core tenet that interpersonal communication can be conceptualised as a form of skilled activity, the book looks at core communication skills and how these can be applied in specific contexts, expertly combining theory with practice.This handbook provides a rich m

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Book SynopsisHow do we find the courage to act together against the climate crisis? This book weaves together real-life findings and examples from the socio-ecological movement with psychological research to show how motivation for collective climate action can be built.The book addresses two key questions: how can individuals be motivated to participate in collective climate action, and how can climate groups become resilient and effective? Specifically, it explores how individuals can foster their identification with climate action groups and the belief in their joint efficacy. It touches on a wide range of topics, covering anger, moral considerations, activist burnout, and the perception of protests, as well as general theories of socio-ecological change.This book is for anyone who is seeking the courage to act together and is curious about psychological insights. It will be essential reading for climate and environmental practitioners, climate activists and campaigners, climate change communicators, and anyone involved in socio-ecological change. It will also be of interest to students and researchers in the fields of environmental psychology, climate change, collective action, and political psychology.The Open Access version of this book, available at http://www.taylorfrancis.com, has been made available under a Creative Commons (CC BY) 4.0 license.

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Book SynopsisFourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course Trade Review'[Fourier Analysis: Volume l - Theory is] fabulous … Constantin structures his exercise sets beautifully, I think: they are abundant and long, covering a spectrum of levels of difficulty; each set is followed immediately by a section of hints (in one-one correspondence); finally the hints sections are followed by very detailed and well-written solutions (also bijectively). Can there be any clearer homage to the maxim that to learn mathematics one has to get one's hands really dirty? To boot, attention to detail is ubiquitous: it's everywhere in Constantin's presentation of proofs and arguments, as well as examples, all throughout the narrative itself. The entire presentation is very much to the point and the student who works through this book will come out knowing some real mathematics very well.' Michael Berg, MAA ReviewsTable of Contents1. Introduction; 2. The Lebesgue measure and integral; 3. Elements of functional analysis; 4. Convergence results for Fourier series; 5. Fourier transforms; 6. Multi-dimensional Fourier analysis; 7. A glance at some advanced topics; Appendix: historical notes; References; Index.

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Book SynopsisBusiness Psychology and Organizational Behaviour introduces principles and concepts in psychology and organizational behaviour with emphasis on relevance and applications. Well organised and clearly written, it draws on a sound theoretical and applied base, and utilizes real-life examples, theories, and research findings of relevance to the world of business and work. The new edition of this best-selling textbook has been revised and updated with expanded and new material, including: proactive personality and situational theory in personality; theory of purposeful work behaviour; emotional and social anxiety in communication; decision biases and errors; and right brain activity and creativity, to name a few. There are numerous helpful features such as learning outcomes, chapter summaries, review questions, a glossary, and a comprehensive bibliography. Illustrations of practice and relevant theory and research also take the reader through individual, group, andTrade Review"This new up-to-date edition of Eugene McKenna’s highly respected textbook exceeds expectations. It is my book of choice both for teaching and for reference on business psychology and organizational behavior. It brings together relevant insights from past and present research, and it clarifies how the contributions of psychology relate to those of other disciplines. What may appear to be a formidably comprehensive book is actually easy to read due to its clear style and the many summaries and examples provided." - John Child, D.Sc., FBA, Professor of Commerce, Birmingham Business School, University of Birmingham, UK"This new edition of Business Psychology and Organizational Behaviour is outstanding. Not only does it cover thoroughly and up-to-date all the areas of business psychology and OB, but also develops new ones as well (e.g., business ethics). The standout for me are the international case studies, and particularly practitioner perspectives. A must-buy textbook in the field of OB by a renowned author and scholar." — Sir Cary Cooper, CBE, 50th Anniversary Professor of Organizational Psychology & Health at the ALLIANCE Manchester Business School, University of Manchester, UKPraise for the Fifth Edition: "The content of the book covers all the usual areas of business psychology. McKenna’s approach is scholarly, presenting research evidence for and against controversial topics before arriving at well-considered conclusions. A text such as this earns its place on the bookshelf of psychology undergraduates as a comprehensive core text." – Anne Kearns, Chartered Psychologist, The Psychologist "This new edition of Business Psychology and Organizational Behaviour is outstanding. Not only does it cover thoroughly and up-to-date all the areas of business psychology and OB, but also develops new ones as well (e.g., business ethics). The standout for me are the international case studies, and particularly practitioner perspectives. A must-buy textbook in the field of OB by a renowned author and scholar." — Sir Cary Cooper, CBE, 50th Anniversary Professor of Organizational Psychology & Health at the ALLIANCE Manchester Business School, University of Manchester, UK"This new up-to-date edition of Eugene McKenna’s highly respected textbook exceeds expectations. It is my book of choice both for teaching and for reference on business psychology and organizational behavior. It brings together relevant insights from past and present research, and it clarifies how the contributions of psychology relate to those of other disciplines. What may appear to be a formidably comprehensive book is actually easy to read due to its clear style and the many summaries and examples provided." - John Child, D.Sc., FBA, Professor of Commerce, Birmingham Business School, University of Birmingham, UK Praise for the Fifth Edition: "The content of the book covers all the usual areas of business psychology. McKenna’s approach is scholarly, presenting research evidence for and against controversial topics before arriving at well-considered conclusions. A text such as this earns its place on the bookshelf of psychology undergraduates as a comprehensive core text." – Anne Kearns, Chartered Psychologist, The PsychologistTable of ContentsAcknowledgments Preface PART I PERSPECTIVES AND ENQUIRY1. Historical Influences and Research MethodologyPART II THE INDIVIDUAL2. Personality and Intelligence3. Psychological Testing, Selection and Appraisal4. Motivation, Job Design and Extrinsic Rewards5. Perception and Communication6. Learning, Memory and Training7. Individual Decision Making and Creativity8. Attitudes, Values, Job Satisfaction, and CommitmentPART III THE GROUP9. Groups10. Teambuilding11. Leadership and Management Style12. Power, Politics, and ConflictPART IV THE ORGANIZATION13. Organizational Structure and Design14. Organizational Culture15. Organizational Change and Development16. Health and Work: StressGlossaryReferencesAuthor IndexSubject Index

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Book SynopsisWritten for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.Trade Review'The whole of theoretical physics, and our general picture of the world, are based on symmetries. This book is devoted to symmetries and their manifestations in nature, and it allows students to develop a theoretical and experimental understanding of the fundamental properties of the Universe. This path is carefully paved by the authors.' Professor Vladimir Zelevinsky, Michigan State UniversityTable of ContentsPreface; Part I. Symmetry Groups and Algebras: 1. Introduction; 2. Some properties of groups; 3. Introduction to lie groups; 4. Permutation groups; 5. Electrons on periodic lattices; 6. The rotation group; 7. Classification of lie algebras; 8. Unitary and special unitary groups; 9. SU(3) flavor symmetry; 10. Harmonic oscillators and SU(3); 11. SU(3) matrix elements; 12. Introduction to non-compact groups; 13. The Lorentz group; 14. Lorentz covariant fields; 15. Poincaré invariance; 16. Gauge invariance; Part II. Broken Symmetry: 17. Spontaneous symmetry breaking; 18. The Higgs mechanism; 19. The standard model; 20. Dynamical symmetry; 21. Generalized coherent states; 22. Restoring symmetry by projection; 23. Quantum phase transitions; Part III. Topology and Geometry: 24. Topology, manifolds, and metrics; 25. Topological solitons; 26. Geometry and gauge theories; 27. Geometrical phases; 28. Topology of the quantum Hall effect; 29. Topological matter; Part IV. A Variety of Physical Applications: 30. Angular momentum recoupling; 31. Nuclear fermion dynamical symmetry; 32. Superconductivity and superfluidity; 33. Current algebra; 34. Grand unified theories; Appendix A. Second quantization; Appendix B. Natural units; Appendix C. Angular momentum tables; Appendix D. Lie algebras; References; Index.

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Book SynopsisRepresentation theory studies maps from groups into the general linear group of a finite-dimensional vector space.Trade ReviewFrom the reviews: "The book under review is an introduction to the modular representation theory of finite groups with a somehow balanced approach to the subject. ... the book is almost self-contained. It has the lightness of a gentle-paced lecture course and could be used with profit for an introduction to the methods of representation theory of finite groups, either in a formal course or for self-study." (Felipe Zaldivar, MAA Reviews, May, 2013)Table of ContentsPrerequisites in module theory.- The Cartan{Brauer triangle.- The Brauer character.- Green's theory of indecomposable modules.- Blocks.

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Book SynopsisPeople interact and perform in group settings in all areas of life. Organizations and businesses are increasingly structuring work around groups and teams. Every day, we work in groups such as families, friendship groups, societies and sports teams, to make decisions and plans, solve problems, perform physical tasks, generate creative ideas, and more.Group Performance outlines the current state of social psychological theories and findings concerning the performance of groups. It explores the basic theories surrounding group interaction and development and investigates how groups affect their members. Bernard A. Nijstad discusses these issues in relation to the many different tasks that groups may perform, including physical tasks, idea generation and brainstorming, decision-making, problem-solving, and making judgments and estimates. Finally, the book closes with an in-depth discussion of teamwork and the context in which groups interact and perform.Offering an integrated approach, with particular emphasis on the interplay between group members, the group task, interaction processes and context, this book provides a state-of-the-art overview of social psychological theory and research. It will be highly valuable to undergraduates, graduates and researchers in social psychology, organizational behavior and business.Trade Review"Bernard Nijstad is one of the 'young lions' of this field and has made substantial contributions to a number of the content areas covered in the book. Group Performance handles the conceptual and empirical material very well, leaving the reader with a good sense of what we currently know about the psychology of behavior in and by groups.Overall an excellent introduction to the area." - R. Scott Tindale, Loyola University, Chicago, USA"Bernard Nijstad, a brilliant and enthusiastic researcher, provides a comprehensive, cutting-edge perspective on a fascinating area of social psychology. This textbook will be a classic. I seriously could not stop reading it until the very last page. Highly recommended!" - Andreas Mojzisch, Institute of Psychology, University of Goettingen, Germany"Professor Nijstad does a fantastic job integrating both classic and contemporary research on group performance. I was particularly impressed with Nijstad’s ability to translate this literature in a well-organized and proficient manner. Nijstad’s enthusiasm for this work should help generate excitement in students reading about this topic for the first time." - Robert B. Lount, Jr., The Ohio State University, USA"Bernard Nijstad is one of the 'young lions' of this field and has made substantial contributions to a number of the content areas covered in the book. Group Performance handles the conceptual and empirical material very well, leaving the reader with a good sense of what we currently know about the psychology of behavior in and by groups.Overall an excellent introduction to the area." - R. Scott Tindale, Loyola University, Chicago, USA"Bernard Nijstad, a brilliant and enthusiastic researcher, provides a comprehensive, cutting-edge perspective on a fascinating area of social psychology. This textbook will be a classic. I seriously could not stop reading it until the very last page. Highly recommended!" - Andreas Mojzisch, Institute of Psychology, University of Goettingen, Germany"Professor Nijstad does a fantastic job integrating both classic and contemporary research on group performance. I was particularly impressed with Nijstad’s ability to translate this literature in a well-organized and proficient manner. Nijstad’s enthusiasm for this work should help generate excitement in students reading about this topic for the first time." - Robert B. Lount, Jr., The Ohio State University, USATable of ContentsStudying Small Groups. Group Processes and Social Influence. A Theoretical Framework. Audience and Co-action Effects. Motivation and Group Performance: Individual Effort on Collective Tasks. Group Idea Generation and Creativity. Group Decision-Making. Group Problem-Solving and Group Judgment. Teamwork and Leadership. Groups in Context. Groups and Technology.

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Book SynopsisThis textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition.The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory.Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.Trade Review “This book can be also used by incoming graduate students to refresh their knowledge of Algebra before taking graduate courses. I highly recommend this book for a standard undergraduate algebra course, as well as to students interested in independent study.” (Louisa Catalano, MAA Reviews, July 21, 2019)Table of Contents

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Book SynopsisThis book provides an organized exposition of the current state of the theory of commutative semigroup cohomology, a theory which was originated by the author and has matured in the past few years. The work contains a fundamental scientific study of questions in the theory. The various approaches to commutative semigroup cohomology are compared. The problems arising from definitions in higher dimensions are addressed. Computational methods are reviewed. The main application is the computation of extensions of commutative semigroups and their classification.Previously the components of the theory were scattered among a number of research articles. This work combines all parts conveniently in one volume. It will be a valuable resource for future students of and researchers in commutative semigroup cohomology and related areas. Table of Contents- 1. The Beginning. - 2. Beck Cohomology. - 3. Symmetric Cohomology. - 4. Calvo-Cegarra Cohomology. - 5. The Third Cohomology Group. - 6. The Overpath Method. - 7. Symmetric Chains. - 8. Inheritance. - 9. Appendixes.

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Book SynopsisThis book develops a new theory in convex geometry, generalizing positive bases and related to Carathéordory’s Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra)This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization. While factorization into irreducibles, called atoms, generally fails to be unique, there are various measures of how badly this can fail. Among the most important is the elasticity, which measures the ratio between the maximum and minimum number of atoms in any factorization. Having finite elasticity is a key indicator that factorization, while not unique, is not completely wild. Via the developed material in convex geometry, we characterize when finite elasticity holds for any Krull domain with finitely generated class group $G$, with the results extending more generally to transfer Krull monoids. This book is aimed at researchers in the field but is written to also be accessible for graduate students and general mathematicians.Table of Contents- 1. Introduction. - 2. Preliminaries and General Notation. - 3. Asymptotically Filtered Sequences, Encasement and Boundedness. - 4. Elementary Atoms, Positive Bases and Reay Systems. - 5. Oriented Reay Systems. - 6. Virtual Reay Systems. - 7. Finitary Sets. - 8. Factorization Theory.

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Book SynopsisThis book systematically develops the theory of continuous representations on p-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductive p-adic groups on p-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras, p-adic measures and distributions, p-adic functional analysis, reductive groups, and smooth and algebraic representations. Part 1 culminates with the duality between Banach space representations and Iwasawa modules. This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces.This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.Trade Review“This is a book on the representation theory of p-adic groups on p-adic Banach spaces whose foundations were laid by Schneider and Teitelbaum. It explains their duality theory and demonstrates its applications to continuous principal series. ... It could also be of an interest to mathematicians who are working in the representation theory on complex vector spaces.” (Barbara Bošnjak, zbMATH 1523.22001, 2023)Table of ContentsPart I : Banach space representations of p-adic Lie groupsChapter 1. Iwasawa algebras: The purpose of the chapter is to define Iwasawa algebras and study their properties. As a preparation, we first cover projective limits of topological spaces, finite groups, and linear-topological modules. After that, we explain in detail Iwasawa algebras and their topology.Chapter 2. Distributions: We review basic definitions and properties of locally convex vector spaces. We study the algebra of continuous distributions and establish an isomorphism with the corresponding Iwasawa algebra. We discuss different topologies on the algebra of continuous distributions, among them the weak topology and the bounded-weak topology.Chapter 3. Banach space representations: We prove some fundamental theorems in nonarchimedean functional analysis and introduce Banach space representations. We give an overview of the Schikhof duality between p-adic Banach spaces and compactoids. Then, we present the theory of admissible Banach space representations by Schneider and Teitelbaum and their duality theory.Part II: Principal series representations of reductive groupsChapter 4. Reductive Groups: In this chapter, we give an overview of the structure theory of split reductive Z-groups, with no proofs. The purpose of this chapter is to help a learner navigate through the literature and to explain different objects we need in Chapters 6 and 7, such as roots, unipotent subgroups, and Iwahori subgroups. We also review important structural results, such as Bruhat decomposition, Iwasawa decomposition, and Iwahori factorization.Chapter 5. Algebraic and smooth representations: In our study of Banach space representations, we also encounter algebraic and smooth representations. Namely, continuous principal series representations may contain finite dimensional algebraic representations or smooth principal series representations. In this chapter, we review some basic properties of these representations.Chapter 6. Continuous principal series: We establish some basic properties of the continuous principal series representations. In particular, we prove that they are Banach. After that, we work on the dual side and study the corresponding Iwasawa modules.Chapter 7. Intertwining operators: In this chapter, we present the main results and proofs from a recent joint work with Joseph Hundley. The purpose is to describe the space of continuous intertwining operators between principal series representations. As before, we apply the Schneider-Teitelbaum duality and work with the corresponding Iwasawa modules.

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Book SynopsisIn recent years cube complexes have become a cornerstone topic of geometric group theory and have proven to be a powerful tool in other areas, such as low dimensional topology, phylogenetic trees or in the context of optimization problems.This book covers a wide variety of algebraic and geometric properties of cube complexes and the groups acting on them. The content ranges from basic properties of metric spaces, notions of non-positive curvature, Gromov's link condition and the Švarc–Milnor theorem to advanced material such as the cubulation of half-space systems and the Roller boundary, the construction of cube complexes associated with Coxeter groups, and the Tits alternative for cubical groups.Being the first self-contained, comprehensive introduction to cube complexes this book serves as an entry point for researchers interested in the subject. The material is accessible to advanced undergraduate and graduate students. The text is illustrated with many figures and examples and comes with a large collection of exercises.Table of Contents- 1. Introduction. - 2. Metric Spaces Meet Groups. - 3. Non-positive Curvature. - 4. Cube Complexes and Gromov’s Link Condition. - 5. Hyperplanes and Half-Spaces. - 6. Cubulating Coxeter Groups. - 7. A Panoramic Tour.

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Book SynopsisThe 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 Ceará, Fortaleza, BrasilWalter D. Neumann, Columbia University, New York, USAMarkus J. Pflaum, University of Colorado, Boulder, USADierk Schleicher, Aix-Marseille Université, FranceKatrin Wendland, Trinity College Dublin, Dublin, Ireland 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 Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021) Table of ContentsNotations and results from group theory; representations and representation-modules; simple and semisimple modules; orthogonality relations; the group algebra; characters of abelian groups; degrees of irreducible representations; characters of some small groups; products of representation and characters; on the number of solutions gm =1 in a group; a theorem of A. Hurwitz on multiplicative sums of squares ; permutation representations and characters; the class number; real characters and real representations; Coprime action; groups pa qb; Fronebius groups; induced characters; Brauer's permutation lemma and Glauberman's character correspondence; Clifford theory 1; projective representations; Clifford theory 2; extension of characters; Degree pattern and group structure; monomial groups; representation of wreath products; characters of p-groups; groups with a small number of character degrees; linear groups; the degree graph; groups all of whose character degrees are primes; two special degree problems; lengths of conjugacy classes; R. Brauer's theorem on the character ring; applications of Brauer's theorems; Artin's induction theorem; splitting fields; the Schur index; integral representations; three arithmetical applications; small kernels and faithful irreducible characters; TI-sets; involutions; groups whose Sylow-2-subgroups are generalized quaternion groups; perfect Fronebius complements. (Part contents).

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Book SynopsisThis textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.Review of the first edition:This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.— The Mathematical GazetteTrade Review“The first edition of this book was very good; the second is even better, and more versatile. This text remains one of the most attractive sources available from which to learn elementary Lie group theory, and is highly recommended.” (Mark Hunacek, The Mathematical Gazette, Vol. 101 (551), July, 2017)Table of ContentsPart I: General Theory.-Matrix Lie Groups.- The Matrix Exponential.- Lie Algebras.- Basic Representation Theory.- The Baker–Campbell–Hausdorff Formula and its Consequences.- Part II: Semisimple Lie Algebras.- The Representations of sl(3;C).-Semisimple Lie Algebras.- Root Systems.- Representations of Semisimple Lie Algebras.- Further Properties of the Representations.- Part III: Compact lie Groups.- Compact Lie Groups and Maximal Tori.- The Compact Group Approach to Representation Theory.- Fundamental Groups of Compact Lie Groups.- Appendices.

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Book SynopsisThis lecture note provides a tutorial review of non-Abelian discrete groups and presents applications to particle physics where discrete symmetries constitute an important principle for model building. While Abelian discrete symmetries are often imposed in order to control couplings for particle physics—particularly model building beyond the standard model—non-Abelian discrete symmetries have been applied particularly to understand the three-generation flavor structure. The non-Abelian discrete symmetries are indeed considered to be the most attractive choice for a flavor sector: Model builders have tried to derive experimental values of quark and lepton masses, mixing angles and CP phases on the assumption of non-Abelian discrete flavor symmetries of quarks and leptons, yet lepton mixing has already been intensively discussed in this context as well. Possible origins of the non-Abelian discrete symmetry for flavors are another topic of interest, as they can arise from an underlying theory, e.g., the string theory or compactification via orbifolding as geometrical symmetries such as modular symmetries, thereby providing a possible bridge between the underlying theory and corresponding low-energy sector of particle physics. The book offers explicit introduction to the group theoretical aspects of many concrete groups, and readers learn how to derive conjugacy classes, characters, representations, tensor products, and automorphisms for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest. Further, CP symmetry and modular symmetry are also presented.Table of ContentsIntroduction.- Basics of Finite Groups.- SN.- AN.- 5 T ′.- DN.- QN.- QD2N.- Σ(2N ).- Δ (3N2).- TN.- Σ(3N3).- Δ(6N2).- Subgroups and Decompositions of Multiplets.- Anomalies.- Non-Abelian Discrete Symmetry in Quark/Lepton Flavor Models.- Modular Group.- CP Symmetry.- Appendices.

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Book Synopsis

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Book SynopsisThe book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras.

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Book SynopsisExplores an important aspect of number theory - the theory of exponential sums over finite fields and their Mellin transforms - from a categorical point of view. This book presents fundamentally important results and a plethora of examples, opening up new directions in the subject.Trade Review"The book is written in a clear and enlightening style. The author provides the reader with many examples that are developed throughout a dozen chapters. These examples help understand and clarify the depth and the variety of applications of the beautiful main equidistribution statement that relies on rather complicated and subtle algebrageometric arguments."--Florent Jouve, Mathematical Reviews Clippings "The book provides the reader with much material around the question of the equidistribution of the angles if one fixes f and varies over the multiplicative character x. More than one hundred pages of examples provide the reader with great insight in the different applications of the main theorem. This turns the book into a very good basis for research in this area."--Manfred G. Madritsch, Zentralblatt MATH "Once a certain basic understanding is reached, this book, like the others written by N. Katz, reveals itself to be very precisely and sharply written, and to be full of riches. And finally, this theory shows spectacularly how some of the most abstract ideas of algebra and algebraic geometry may be essential to solving extremely concrete problems."--Emmanuel Kowalski, Bulletin of the American Mathematical SocietyTable of Contents*FrontMatter, pg. i*Contents, pg. vi*Introduction, pg. 1*CHAPTER 1. Overview, pg. 7*CHAPTER 2. Convolution of Perverse Sheaves, pg. 19*CHAPTER 3. Fibre Functors, pg. 21*CHAPTER 4. The Situation over a Finite Field, pg. 25*CHAPTER 5. Frobenius Conjugacy Classes, pg. 31*CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith, pg. 33*CHAPTER 7. The Main Theorem, pg. 39*CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility, pg. 45*CHAPTER 9. Autodualities and Signs, pg. 49*CHAPTER 10. A First Construction of Autodual Objects, pg. 53*CHAPTER 11. A Second Construction of Autodual Objects, pg. 55*CHAPTER 12. The Previous Construction in the Nonsplit Case, pg. 61*CHAPTER 13. Results of Goursat-Kolchin-Ribet Type, pg. 63*CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick, pg. 67*CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family, pg. 73*CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith, pg. 77*CHAPTER 17. GL(n) Examples, pg. 81*CHAPTER 18. Symplectic Examples, pg. 89*CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples, pg. 103*CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples, pg. 113*CHAPTER 21. SL(n) Examples, for n an Odd Prime, pg. 125*CHAPTER 22. SL(n) Examples with Slightly Composite n, pg. 135*CHAPTER 23. Other SL(n) Examples, pg. 141*CHAPTER 24. An O(2n) Example, pg. 145*CHAPTER 25. G2 Examples: the Overall Strategy, pg. 147*CHAPTER 26. G2 Examples: Construction in Characteristic Two, pg. 155*CHAPTER 27. G2 Examples: Construction in Odd Characteristic, pg. 163*CHAPTER 28. The Situation over Z: Results, pg. 173*CHAPTER 29. The Situation over Z: Questions, pg. 181*CHAPTER 30. Appendix: Deligne's Fibre Functor, pg. 187*Bibliography, pg. 193*Index, pg. 197

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Book SynopsisThis book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included.These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms.Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.Table of Contents- 1. Introduction. - 2. The Lie Group SU(2,1) and Subgroups. - 3. Fourier Term Modules. - 4. Submodule Structure. - 5. Application to Automorphic Forms.

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Book SynopsisNetworks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. This book offers a comprehensive introduction to social and economic networks, drawing on the findings in economics, sociology, computer science, physics, and mathematics.Trade ReviewHonorable Mention for the 2008 PROSE Award in Economics, Association of American Publishers "Jackson's review of diffusion models is excellent, as tight an overview of these models as I have seen anywhere... Social and Economic Networks is a must-read for all those steeped in the traditional social network analysis paradigm. Economists will find Jackson offers them a superb and accessible introduction to network questions and models. And for others from any social science background curious about social networks, I recommend a careful read of the book."--David Krackhardt, Science "This book deserves the highest recommendations for all readers interested in networks and interdependence. It is written clearly, and could be used both as a starting textbook for a journey to the world of networks and also as an expert guide for scientists studying social and economic networks."--Karoly Takacs, Journal of Artificial Societies and Social Simulation "I strongly recommend this book to any scholar or student interested in networks, not only in economics but in any connected field such as sociology, physics, and applied mathematics. Matthew Jackson's guided tour of the literature on economic and social networks is superb."--Joan de Marti Beltran, Regional Science and Urban Economics "[T]his is a valuable book that raises crucial questions for today's sociologist interested in social networks."--Paola Tubaro, SociologyTable of ContentsPreface xi PART I: BACKGROUND AND FUNDAMENTALS OF NETWORK ANALYSIS Chapter 1 Introduction 3 1.1 Why Model Networks? 3 1.2 A Set of Examples 4 1.3 Exercises 17 Chapter 2: Representing and Measuring Networks 20 2.1 Representing Networks 20 2.2 Some Summary Statistics and Characteristics of Networks 30 2.3 Appendix: Basic Graph Theory 43 2.4 Appendix: Eigenvectors and Eigenvalues 49 2.5 Exercises 51 Chapter 3: Empirical Background on Social and Economic Networks 54 3.1 The Prevalence of Social Networks 55 3.2 Observations on the Structure of Networks 56 PART II: MODELS OF NETWORK FORMATION Chapter 4: Random-Graph Models of Networks 77 4.1 Static Random-Graph Models of Random Networks 78 4.2 Properties of Random Networks 86 4.3 An Application: Contagion and Diffusion 105 4.4 Distribution of Component Sizes 107 4.5 Appendix: Useful Facts, Tools, and Theorems 110 4.6 Exercises 121 Chapter 5: Growing Random Networks 124 5.1 Uniform Randomness: An Exponential Degree Distribution 125 5.2 Preferential Attachment 130 5.3 Hybrid Models 134 5.4 Small Worlds, Clustering, and Assortativity 141 5.5 Exercises 150 Chapter 6: Strategic Network Formation 153 6.1 Pairwise Stability 154 6.2 Efficient Networks 157 6.3 Distance-Based Utility 159 6.4 A Coauthor Model and Negative Externalities 166 6.5 Small Worlds in an Islands-Connections Model 170 6.6 A General Tension between Stability and Efficiency 173 6.7 Exercises 179 PART III: IMPLICATIONS OF NETWORK STRUCTURE Chapter 7: Diffusion through Networks 185 7.1 Background: The Bass Model 187 7.2 Spread of Information and Disease 189 7.3 Search and Navigation on Networks 209 7.4 Exercises 221 Chapter 8: Learning and Networks 223 8.1 Early Theory and Opinion Leaders 224 8.2 Bayesian and Observational Learning 225 8.3 Imitation and Social Influence Models: The DeGroot Model 228 8.4 Exercises 253 Chapter 9: Decisions, Behavior, and Games on Networks 257 9.1 Decisions and Social Interaction 258 9.2 Graphical Games 269 9.3 Semi-Anonymous Graphical Games 273 9.4 Randomly Chosen Neighbors and Network Games 279 9.5 Richer Action Spaces 286 9.6 Dynamic Behavior and Contagion 293 9.7 Multiple Equilibria and Diffusion in Network Games 297 9.8 Computing Equilibria 304 9.9 Appendix: A Primer on Noncooperative Game Theory 308 9.10 Exercises 319 Chapter 10: Networked Markets 327 10.1 Social Embeddedness of Markets and Exchange 328 10.2 Networks in Labor Markets 334 10.3 Models of Networked Markets 353 10.4 Concluding Remarks 365 10.5 Exercises 366 PART IV: METHODS, TOOLS, AND EMPIRICAL ANALYSES Chapter 11: Game-Theoretic Modeling of Network Formation 371 11.1 Defining Stability and Equilibrium 372 11.2 The Existence of Stable Networks 377 11.3 Directed Networks 383 11.4 Stochastic Strategic Models of Network Formation 388 11.5 Farsighted Network Formation 395 11.6 Transfers and Network Formation 399 11.7 Weighted Network Formation 402 11.8 Agent-Based Modeling 406 11.9 Exercises 407 Chapter 12: Allocation Rules, Networks, and Cooperative Games 411 12.1 Cooperative Game Theory 412 12.2 Communication Games 416 12.3 Networks and Allocation Rules 419 12.4 Allocation Rules When Networks Are Formed 425 12.5 Concluding Remarks 430 12.6 Exercises 430 Chapter 13: Observing and Measuring Social Interaction 434 13.1 Specification and Identification 435 13.2 Community Structures, Block Models, and Latent Spaces 443 13.3 Exercises 457 Afterword 459 Bibliography 461 Index 491

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Book SynopsisContemporary Abstract Algebra, Tenth EditionFor more than three decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.The author presents the concepts and methodologies of contemporary abstract algebra as used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop but rarely do. Applications are included to illustrate the utility of the abstract concepts.Examples and exercises are the heart of the book. Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The Trade Review"It has now been 35 years since Gallian's classic textbook Contemporary Abstract Algebra was first published. The book is deservedly popular with instructors of abstract algebra courses. It is written at an appropriate level for junior and senior undergraduates, has lucid coverage of all of the standard topics and several nonstandard ones (Frieze Groups and Crystallographic Groups, Coding Theory, Greek Geometric Construction Problems, etc), is example-driven, and contains thousands of exercises at various levels of difficulty. Moreover, every chapter begins with an interesting quote or two (by as diverse a group of people as Einstein, Miguel de Cervantes, Ralph Waldo Emerson, Bob Dylan, etc) and most conclude with a mini- biography of a mathematician whose work relates to the chapter's content. This is an interesting book that is a pleasure to read. According to the Preface, changes made for the tenth edition include: 1. Approximately 200 new exercises2. Many new examples3. New quotes4. A freshening of the discussion portions"- Benjamin Linowitz, Oberlin College, Published in MAATable of Contents1 Introduction to Groups 2 Groups 3 Finite Groups; Subgroups 4 Cyclic Groups 5 Permutation Groups 6 Ismorphisms 7 Cosets and Lagrange's Theorem 8 External Direct Products 9 Normal Subgroups and Factor Groups 10 Group Homomorphisms 11 Fundamental Theorem of Finite Abelian Groups 12 Introduction to Rings 13 Integral Domains 14 Ideals and Factor Rings 15 Ring Homomorphisms 16 Polynomial Rings 17 Factorization of Polynomials 18 Divisibilty in Integral Domains 19 Extension Fields 20 Algebraic Extensions 21 Finite Fields 22 Geometric Constructions 23 Sylow Theorems 24 Finite Simple Groups 25 Generators and Relations 26 Symmetry Groups 27 Symmetry and Counting 28 Cayley Digraphs of Groups 29 Introduction to Algebraic Coding Theory 30 An Introduction to Galois Theory 31 Cyclotomic Extensions

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