Groups and group theory Books

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 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 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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Book SynopsisA Thorough But Understandable Introduction To Molecular Symmetry And Group Theory As Applied To Chemical Problems! In a friendly, easy--to--understand style, this new book invites the reader to discover by example the power of symmetry arguments for understanding theoretical problems in chemistry.Table of ContentsFundamental Concepts. Representations of Groups. Techniques and Relationships for Chemical Applications. Symmetry and Chemical Bonding. Equations for Wave Functions. Vibrational Spectroscopy. Transition Metal Complexes. Appendices. Index.

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Book SynopsisIn the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature.It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Table of ContentsIntroduction ; 1. What is symmetry? ; 2. Origins of symmetry ; 3. Types of symmetry ; 4. Structure of groups ; 5. Groups and games ; 6. Nature's patterns ; 7. Nature's laws ; 8. Atoms of symmetry ; Further reading ; References

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Book SynopsisThis book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.Trade ReviewFrom the reviews: "Serre’s book gives a fine introduction to representations for various audiences . . . As always with Serre, the exposition is clear and elegant, and the exercises contain a great deal of valuable information that is otherwise hard to find . . . it is highly recommended for specialists and nonspecialists alike." (Bulletin Of The American Mathematical Society)Table of ContentsPart I: Representations and Characters; 1. Generalities on Linear Representation; 2. Character Theory; 3. Subgroups, products, induced representations; 4. Compact Groups; 5. Examples; Bibliography Part I; Part II: Representation in Characteristic Zero; 6. The Group Algebra; 7. Induced Representations- Mackey's Criterion; 8. Examples of Induced Representations; 9. Artin's Theorem; 10. A Theorem of Brauer; 11. Applications of Brauer's Theorem; 12. Rationality Questions; 13. Rationality Questions: Examples; Bibliography Part II; Part III: Introduction to Brauer Theory; 14. The Groups Rk(G), Rk(G) and Pk(G); 15. The cde Triangle; 16. Theorems; 17. Proofs; 18. Modular Characters; 19. Application to Artin Representations; Appendix; Bibliography part III; Index of Notation; Index of Terminology.

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Book SynopsisThis solutions booklet is a supplement to the text book 'Group Theory in Physics' by Wu-Ki Tung. It will be useful to lecturers and students taking the subject as detailed solutions are given.

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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 book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in very recent years thanks to the introduction of new techniques, in particular the front tracking algorithm and the semigroup approach. These techniques provide a solution to the long standing open problems of uniqueness and stability of entropy weak solutions. This monograph is the first to present a comprehensive account of these new, fundamental advances, mainly obtained by the author together with several collaborators. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. The book is addressed to graduate students as well as researchers. Both the elementary and the more advanced material are carefully explained, helping the reader''s visual intuition withTrade ReviewAn excellent and self-contained treatment of the mathematical theory of hyperbolic systems of conservation laws ... written in a clear and self-contained way and will be of great value for graduate students and specialists in the field. * EMS *

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Book SynopsisThis concise introduction to the subject emphasizes the various classes of regular semigroups. More than 150 exercises, accompanied by references to the relevant research literature, direct readers to areas not explicitly covered in the text.Trade ReviewThe author succeeds admirably in his goal of providing an introduction to semigroup theory suitable for graduate students and non-specialists. At the same time, specialists will also find much to attract them. The book is highly readable, and the author takes pain to lead the reader gently through the longer proofs. I am sure that all specialists will want to own a copy of the book, that non-specialists will find it a most attractive and useful book for consulting, and that for many years to come research students will learn their subject from this book. * Bulletin of the London Mathematical Society *The book provides a useful survey of a rapidly developing topic and is suitable for specialists and as an introduction to the subject for non-specialists and graduate students. * Aslib Book Guide, vol.61, no.5, May 1996. *This book will still have its outstanding place as a general introduction to semigroup theory offering both an updated overview of the subject and a suitable entree for the graduate student * Monatshefte fur Mathematik Vol. 124 1997 *With this well-written and well-organised book I think the author has ensured that "Howie" will continue to be a byword for semigroup books * Edinburgh Mathematical Society 1997 *Table of Contents1. Introductory ideas ; 2. Green's equivalences; regular semigroups ; 3. 0-simple semigroups ; 4. Completely regular semigroups ; 5. Inverse semigroups ; 6. Other classes of regular semigroups ; 7. Free semigroups ; 8. Semigroup amalgams ; References ; List of symbols

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Book SynopsisThe book, which has grown out of a course given over the past ten years, provides an introduction to group theory and its application in subnuclear physics, particularly in multi-quark systems and hadron spectroscopy. A number of exercises, with solutions, are included.Trade ReviewThe book may be treated as a modern "practical introduction to concepts of group theory and some of their applications, especially in subnuclear physics"......In the text, the general statements and investigations are illustrated by many concrete examples given, as a rule, in explicit expanded mathematical form. A large number of tables (about 50) most of which are original forms an essential part of the book. * Zeitschrift fur Mathematik *Table of Contents1. Symmetries in quantum mechanics ; 2. Elements of group theory ; 3. Linear representations of a group ; 4. Permutation group Sn ; 5. Lie groups ; 6. The orthogonal group ; 7. The Poincare group and the Lorenz group ; 8. Unitary groups ; 9. Gauge groups ; 10. Multiquark systems ; Appendix A: Conservation Laws ; Appendix B: The rearrangement theorem, Schur's lemmas and the orthogonality theorem ; Appendix C: Invariant Integration ; Appendix D: Dimension of an SU(n) irrep

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Book SynopsisAn accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results.The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remTrade Review'The author's intention was to write a quick introduction to the area of algebraic groups of the Lie type over fields of positive characteristic and I think he was very successful. The first part of the book can be recommended as a very suitable text for undergraduate students at the beginning of their studies.' * EMS Newsletter *The style of exposition in the book is very reader-friendly ... The proofs are clear and complete. * Mathematical Reviews *Table of Contents1. Algebraic sets and algebraic groups ; 2. Affine varieties and finite morphisms ; 3. Algebraic representations and Borel subgroups ; 4. Frobenius maps and finite groups of Lie type ; Bibliography ; Index

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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 SynopsisAvailable for the first time in published form, Groups and Geometry presents the Oxford Mathematical Institute notes for undergraduates and first year postgraduates. The content is guided by the Oxford syllabus but includes much more material than is included on the syllabus. This book is about the measurement of symmetry: covering groups and geometry with the symbiotic relationship between the two more than justifying the union. A number of exercises are included in this sylish text to help the reader gain a full understanding of this branch of mathematics.Trade Review'develops a comprehensive group-theoretic approach to affine, projective and inversive geometry ... It ends with a fascinating chapter on the group theory behind the Rubik cube.' Ian Stewart, New Scientist'Both parts contain a number of exercises that will be invaluable to any reader wishing to gain a fuller understanding of this area of mathematics.' Extrait de L'Enseignement Mathematique, T. 40 1994The book can be recommended warmly for any interested reader. "Monatshefte fur Mathematik No.3 1996.delightful book ... The group theory is directed towards group actions, but all the basic material is there. * Mathematika, 41 (1994) *Table of Contents1. A survey of some group theory ; 2. A menagerie of groups ; 3. Actions of groups ; 4. A garden of G-spaces ; 5. Transitivity and orbits ; 6. The classification of transitive G-spaces ; 7. G-morphisms ; 8. Group actions in group theory ; 9. Actions count ; 10. Geometry: an introduction ; 11. The axiomatisation of geometry ; 12. Affine geometry ; 13. Projective geometry ; 14. Euclidean geometry ; 15. Finite groups of isometries ; 16. Complex numbers and quaternions ; 17. Inversive geometry ; 18. Topological considerations ; 19. The groups theory of Rubik's magic cube ; Index

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Book SynopsisThis book is an excellent and self-contained introduction to the theory of groups, covering all topics likely to be encountered in undergraduate courses. It aims to stimulate and encourage undergraduates to find out more about their subject. The book takes as its theme the various fundamental classification theorems in finite group theory, and the text is further explained in numerous examples and exercises, and summaries at the end of each chapter.Trade ReviewThe arguments are clear and full proofs are given. ... The whole text is actually built up around the idea of classification theorems. The inherent limitations of such an approach put aside, such glimpses of a distant horizon can do a lot towards stimulating the students to find more about the subject for themselves. * M Deaconescu, Zentralblatt fur Mathematik, Band 843/96. *Clear and fast moving, as you'd expect from this author. * New Scientist, Ian Stewart, September 1996, *Table of Contents1. Definitions and examples ; 2. Maps and relations on sets ; 3. Elementary consequences of the definitions ; 4. Subgroups ; 5. Cosets and Lagrange's Theorem ; 6. Error-correcting codes ; 7. Normal subgroups and quotient groups ; 8. The Homomorphism Theorem ; 9. Permutations ; 10. The Orbit-Stabilizer Theorem ; 11. The Sylow Theorems ; 12. Applications of Sylow Theorems ; 13. Direct products ; 14. The classification of finite abelian groups ; 15. The Jordan-Holder Theorem ; 16. Composition factors and chief factors ; 17. Soluble groups ; 18. Examples of soluble groups ; 19. Semi-direct products and wreath products ; 20. Extensions ; 21. Central and cyclic extensions ; 22. Groups with at most 31 elements ; 23. The projective special linear groups ; 24. The Mathieu groups ; 25. The classification of finite simple groups ; Appendix A Prerequisites from Number Theory and Linear Algebra ; Appendix B Groups of order < 32 ; Appendix C Solutions to Exercises ; Bibliography ; Index

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Book SynopsisThis work seeks to offer a concise introduction to geometric group theory - a method for studying infinite groups via their intrinsic geometry. Basic combinatorial and geometric group theory is presented, along with research on the growth of groups, and exercises and problems.

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Book SynopsisThis volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, Lie Algebras, the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, The Structure of Locally Compact Groups, deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.

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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 SynopsisThis unique textbook explores the complex topic of social class, explaining the many psychological nuances of class and classism in people's lives as subjective and phenomenological experiences.Social class can be a deeply personal, complicated topic that is often frustrating and uncomfortable to discuss, and as such has often been a blind spot in teaching and academic literature. For the first time, Noonan and Liu look to address this in one comprehensive text, using a combination of first-person narratives, academic approaches to class, and psychology's contributions to the subject. Across seven chapters, the book introduces a highly accessible theoretical model of the psychology of social class, Liu's own Social Class Worldview Model. Using vivid autobiographical texts to bring the theoretical model to life, the authors show how our worldviews develop through interactions with our social class and economic environment and provide a unique array of methods and skill Trade Review"If you’ve ever thought that the topic of social class sounded abstract or dry – or that it was barely relevant to the education of psychologists – this is the text for you. Anne Noonan and William Ming Liu have created a psychological perspective on social class that is comprehensive, scholarly, and politically-literate, but also accessible, spirited, personal, and contemporary. Students and other readers will find engaging essays and exercises throughout the book that invite them into the exploration as they see its connections to other social justice issues and to their development as psychologists and counselors. Highly recommended."Laura Smith, Teachers College, Columbia University, USA"Reading this wonderful book feels like you are in a conversation with the authors in their living rooms. This book is infused with warmth, intellectual rigor, fascinating narratives, and a call for readers to fully engage in the complex world of social class. The book will inspire many students who will resonate with the content and also will find their life stories represented in the narratives and text. In addition, the authors provided a very insightful perspective on the intersectionality of social identities, creating conceptual connections that are innovative and transformative. I strongly recommend this book for students, instructors, scholars, and interested readers who would like to engage with authors who share themselves and their fascinating ideas with compassion and creativity."David L. Blustein, Boston College, USA'If you’ve ever thought that the topic of social class sounded abstract or dry – or that it was barely relevant to the education of psychologists – this is the text for you. Anne Noonan and William Ming Liu have created a psychological perspective on social class that is comprehensive, scholarly, and politically-literate, but also accessible, spirited, personal, and contemporary. Students and other readers will find engaging essays and exercises throughout the book that invite them into the exploration as they see its connections to other social justice issues and to their development as psychologists and counselors. Highly recommended.'Laura Smith, Teachers College, Columbia University, USA'Reading this wonderful book feels like you are in a conversation with the authors in their living rooms. This book is infused with warmth, intellectual rigor, fascinating narratives, and a call for readers to fully engage in the complex world of social class. The book will inspire many students who will resonate with the content and also will find their life stories represented in the narratives and text. In addition, the authors provided a very insightful perspective on the intersectionality of social identities, creating conceptual connections that are innovative and transformative. I strongly recommend this book for students, instructors, scholars, and interested readers who would like to engage with authors who share themselves and their fascinating ideas with compassion and creativity.'David L. Blustein, Boston College, USATable of ContentsAcknowledgementsIntroduction: The Power of Story Social Class: It’s Complicated What Does a Psychology of Social Class Look Like?: Internalizing the Structural Accompanying Essay: The Breadwinner, William Ming Liu Economic Cultures, Capital Demands and Social Class: Component 1 of the SCWM-R Accompanying Essays: A Good School, J.D. Scrimgeour; Ghetto Fabulous, Tina Fakhrid-Deen Development of the Social Class Worldview (Lessons, Levels, and Lenses): Component 2 of the SCWM-R Accompanying Essays: Thanks, But No Thanks, Courtney Eldridge; Stink Tree, Anne E. Noonan Classism Means More Than You Might Think: Component 3 of the SCWM-R Accompanying Essays: The Poet and the Pauper, Meliza Bañales; Winter Coat, Terri Griffith Social Class, Race and Intersectionality: A Final Look Before We Go Appendix A

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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 SynopsisGroups are arguably an essential and unavoidable part of our human livesâwhether we are part of families, work teams, therapy groups, organizational systems, social clubs, or larger communities. In Groups in Transactional Analysis, Object Relations, and Family Systems: Studying Ourselves in Collective Life, N. Michel Landaiche, III addresses the intense feelings and unexamined beliefs that exist in relation to groups, and explores how to enhance learning, development and growth within them.Landaicheâs multidisciplinary perspective is grounded in the traditions of Eric Berneâs transactional analysis, Wilfred Bionâs group-as-a-whole model, and Murray Bowenâs family systems theory. The book presents a practice of studying ourselves in collective life that utilizes a naturalistic method of observation, analysis of experiential data, and hypothesis formation, all of which are subject to further revision as we gather more data from our lived experiences. Drawing from his extTrade Review‘Mick Landaiche has done us all a great service in bringing together his excellent writing on living and learning through groups. For those not familiar with his work, Mick brings his understated style to exploring his longstanding experience of working with groups. Opening with a cautionary hesitation about being in group processes, Landaiche expertly navigates the complexity of group life that, in its unfolding, demonstrates that neither he, nor us as readers, can be anything other than immersed in the business of being together. Transactional analysis had its early history rooted in group work, which whilst innovative in its time, has at times, been overlooked as the central arena in which our practice and training takes place. In this much needed title, Landaiche resets the dial, reminding us of the enduring complexity and promise of what it is to be with others.’ - Giles Barrow, MA, MEd, PGCE, TSTA-Education, author and co-editor of Educational Transactional Analysis (Routledge)‘Perhaps the best treatise on the nature of collective life that I have ever read. Landaiche brilliantly integrates object relations and other psychoanalytic theories of the mind with Transactional Analysis, family systems theory and the author’s own unique perspectives honed over the course of a lifetime in and out of the treatment room. Indeed, it is the interweaving of personal and theoretical that makes this work unique and compelling, providing the reader with both an overview and deeply sophisticated understanding of the complex nature of groups. This book will be of great value to anyone with an interest in how we learn, lead and function in groups—psychotherapy, classroom, societal and the gamut.’ - Steven Kuchuck, DSW, President of IARPP, the International Association for Relational Psychoanalysis and Psychotherapy; editor of the Gradiva Award-winning Clinical Implications of the Psychoanalyst’s Life Experience: When the Personal Becomes Professional (Routledge)‘Michel Landaiche draws up the work of the "three B’s"—Berne, Bion, and Bowen—to offer an understanding of group cultures, group process, and the experience of learning in groups. Written in a voice both clear and humble, this book addresses the somatic, psychological, social, and spiritual aspects of group life and work. While the content is rich and stimulating, I found the ways in which Landaiche involves himself deeply and honestly into his own learning in and about groups, an exceptional demonstration of compassion and respect for the other. I hope this book will be translated into French, so that I will be able to recommend it to my students and clients.’ - Isabelle Crespelle, psychologist; psychotherapist; Teaching and Supervising Transactional Analyst-Psychotherapy; co-founder of the French School of TA; and co-founder and former VP of the French Federation for Psychoanalysis and Psychotherapy‘This in a timely compilation of thought and practice about groups and social systems. The author brings his wealth of experience and reflection on the many aspects of conscious and unconscious group process. A must-read for organizational consultants and for any professional who works with the notion that the direction for organizational transformation is already existing in the client organization, only covered by unconscious inhibitions.’ - Servaas van Beekum, Drs, TSTA-Organizations; winner of the 2015 Eric Berne Memorial Award‘A unique and honest contribution to the field of group work, which respectively integrates the wisdom of the masters with a spirit of contemporary enquiry. The openness, transparency and honesty of Landaiche’s writing reflects the very nature of the paradigm to which he introduces us - one which beautifully encapsulates his passion for and belief in groups, offering us a profound way of grappling with the complexities of being human and living in the world.’- Elana Leigh, BSc, MSc, TSTA-Psychotherapy, President of the International Transactional Analysis Association‘Mick Landaiche has done us all a great service in bringing together his excellent writing on living and learning through groups. For those not familiar with his work, Mick brings his understated style to exploring his longstanding experience of working with groups. Opening with a cautionary hesitation about being in group processes, Landaiche expertly navigates the complexity of group life that, in its unfolding, demonstrates that neither he, nor us as readers, can be anything other than immersed in the business of being together. Transactional analysis had its early history rooted in group work, which whilst innovative in its time, has at times, been overlooked as the central arena in which our practice and training takes place. In this much needed title, Landaiche resets the dial, reminding us of the enduring complexity and promise of what it is to be with others.’ - Giles Barrow, MA, MEd, PGCE, TSTA-Education, author and co-editor of Educational Transactional Analysis (Routledge)‘Perhaps the best treatise on the nature of collective life that I have ever read. Landaiche brilliantly integrates object relations and other psychoanalytic theories of the mind with Transactional Analysis, family systems theory and the author’s own unique perspectives honed over the course of a lifetime in and out of the treatment room. Indeed, it is the interweaving of personal and theoretical that makes this work unique and compelling, providing the reader with both an overview and deeply sophisticated understanding of the complex nature of groups. This book will be of great value to anyone with an interest in how we learn, lead and function in groups—psychotherapy, classroom, societal and the gamut.’ - Steven Kuchuck, DSW, President of IARPP, the International Association for Relational Psychoanalysis and Psychotherapy; editor of the Gradiva Award-winning Clinical Implications of the Psychoanalyst’s Life Experience: When the Personal Becomes Professional (Routledge)‘Michel Landaiche draws up the work of the "three B’s"—Berne, Bion, and Bowen—to offer an understanding of group cultures, group process, and the experience of learning in groups. Written in a voice both clear and humble, this book addresses the somatic, psychological, social, and spiritual aspects of group life and work. While the content is rich and stimulating, I found the ways in which Landaiche involves himself deeply and honestly into his own learning in and about groups, an exceptional demonstration of compassion and respect for the other. I hope this book will be translated into French, so that I will be able to recommend it to my students and clients.’ - Isabelle Crespelle, psychologist; psychotherapist; Teaching and Supervising Transactional Analyst-Psychotherapy; co-founder of the French School of TA; and co-founder and former VP of the French Federation for Psychoanalysis and Psychotherapy‘This in a timely compilation of thought and practice about groups and social systems. The author brings his wealth of experience and reflection on the many aspects of conscious and unconscious group process. A must-read for organizational consultants and for any professional who works with the notion that the direction for organizational transformation is already existing in the client organization, only covered by unconscious inhibitions.’ - Servaas van Beekum, Drs, TSTA-Organizations; winner of the 2015 Eric Berne Memorial Award‘A unique and honest contribution to the field of group work, which respectively integrates the wisdom of the masters with a spirit of contemporary enquiry. The openness, transparency and honesty of Landaiche’s writing reflects the very nature of the paradigm to which he introduces us - one which beautifully encapsulates his passion for and belief in groups, offering us a profound way of grappling with the complexities of being human and living in the world.’- Elana Leigh, BSc, MSc, TSTA-Psychotherapy, President of the International Transactional Analysis AssociationTable of ContentsIntroduction; 1. Engaged Research; 2. The Shared Bodymind; 3. Learning and Hating in Groups; 4. Social Pain Dynamics in Human Relations; 5. Looking for Trouble in Professional Development Groups; 6. Maturing as a Community Effort; 7. Groups That Learn and Groups That Don't; 8. The Learning Community; 9. Principles and Practices of Group Work; 10. Closing Reflections; References; 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 SynopsisWhen it comes to relationships, thereâs no shortage of advice from self-help âexpertsâ, pick-up artists, and glossy magazines. But modern-day myths of attraction often have no basis in fact or â worse â are rooted in little more than misogyny. Based on science rather than self-help clichÃs, psychologist Viren Swami debunks these myths and draws on cutting-edge research to provide a ground-breaking and evidence-based account of relationship formation. At the core of this book is a very simple idea: there are no âlaws of attractionâ, no fool-proof methods or strategies for getting someone to date you. But this isnât to say that thereâs nothing to be gained from studying attraction. Based on science rather than self-help clichÃs, Attraction Explained looks at how factors such as geography, physical appearance, reciprocity, and similarity affect who we fall for and why. With updated statistics, this second edition also includes new content on online dating, queer relationships, racism in dating, shyness, and individual differences. It remains an engaging and accessible introduction to attraction relationship formation for professionals, students, and general readers. Trade Review‘This is a much needed and timely book, covering everything you need to know about the science of relationship formation. It is beautifully written and scrupulously referenced. There is serious science in the study of how we form relationships and this book covers the ground superbly. It remains unputdownable.’– Prof Adrian Furnham, Professor of Psychology, broadcaster, and author‘I trusted this author at once because, unlike the psychobabblers, he says from the start that there are no "laws" of attraction and no fool-proof methods for getting someone to date you, let alone jump into bed with you. That isn’t to say there’s nothing to be gained from studying the processes involved in what draws us together. It’s just a lot trickier than most self-help books would suggest. But with precision and no small wit – I found myself frequently laughing out loud – he explores the four key factors that shape the formation of most relationships: proximity, appearance, reciprocity and similarity. As he shows, studying attraction or relationships scientifically, far from destroying the magic and mystery of it all, can actually be helpful, whether you aspire to be lover or friend. He also satisfyingly nails my biggest bête noire: that "treat ’em mean" is any sort of relationship advice and even more satisfyingly thrashes some of the so-called "experts" I abhor and think are downright dangerous in the "advice" they give. A great book. I’d buy it just for the laughs. But I’d recommend it – and do – to the many people who write to me as an agony aunt.’– Suzie Hayman, agony aunt, relationship counsellor, broadcaster, and author'This book provides a thoroughly compelling journey of over a century’s worth of research on the how, what, and why of human relationships and attraction. Swami’s exploration of key theories, stand-out studies, and new and exciting behavioural insights is a must read for anyone interested in understanding the science behind how we form relationships. Once you pick it up, you’ll struggle to put it down.'– Dr Daragh McDermott, Co-Editor-in-Chief of Psychology and Sexuality'On the whole, the book makes interesting reading, and offers numerous subtle intuitions into relationship formation. In continuity with his own previous analyses and reflections on related themes, the author arrives at a wise conclusion that no single factor can fully explain how and why two people enter into short-term or lasting relationships in the busy crossroads of life. Complex and mysterious as they are, human beings behave in a manner that evades every attempt to circumscribe it within predictive framework.' – Prof. Sahayadas Fernando, Marriage, Families & Spirituality, Volume 27‘This is a much needed and timely book, covering everything you need to know about the science of relationship formation. It is beautifully written and scrupulously referenced. There is serious science in the study of how we form relationships and this book covers the ground superbly. It remains unputdownable.’– Prof. Adrian Furnham, Professor of Psychology, broadcaster, and author‘I trusted this author at once because, unlike the psychobabblers, he says from the start that there are no "laws" of attraction and no fool-proof methods for getting someone to date you, let alone jump into bed with you. That isn’t to say there’s nothing to be gained from studying the processes involved in what draws us together. It’s just a lot trickier than most self-help books would suggest. But with precision and no small wit – I found myself frequently laughing out loud – he explores the four key factors that shape the formation of most relationships: proximity, appearance, reciprocity and similarity. As he shows, studying attraction or relationships scientifically, far from destroying the magic and mystery of it all, can actually be helpful, whether you aspire to be lover or friend. He also satisfyingly nails my biggest bête noire: that "treat ’em mean" is any sort of relationship advice and even more satisfyingly thrashes some of the so-called "experts" I abhor and think are downright dangerous in the "advice" they give. A great book. I’d buy it just for the laughs. But I’d recommend it – and do – to the many people who write to me as an agony aunt.’– Suzie Hayman, agony aunt, relationship counsellor, broadcaster, and author'This book provides a thoroughly compelling journey of over a century’s worth of research on the how, what, and why of human relationships and attraction. Swami’s exploration of key theories, stand-out studies, and new and exciting behavioural insights is a must read for anyone interested in understanding the science behind how we form relationships. Once you pick it up, you’ll struggle to put it down.'– Dr Daragh McDermott, Co-Editor-in-Chief of Psychology and Sexuality'On the whole, the book makes interesting reading, and offers numerous subtle intuitions into relationship formation. In continuity with his own previous analyses and reflections on related themes, the author arrives at a wise conclusion that no single factor can fully explain how and why two people enter into short-term or lasting relationships in the busy crossroads of life. Complex and mysterious as they are, human beings behave in a manner that evades every attempt to circumscribe it within predictive framework.' – Prof. Sahayadas Fernando, Marriage, Families & Spirituality, Volume 27Table of ContentsPreface to the Second Edition Cupid’s Arrow. Or, a brief history of attraction theories, why we need a science of relationship formation, and what this book is all about Getting up close and personal. Or, why geography matters, how the Internet is (and isn’t) changing how we form relationships, and a beauty-map of London Appearance matters. Or, how we judge books by their covers, how men aren’t from Mars and women aren’t from Venus, and why what is beautiful is good Appearance matters, part II. Or, how other things matter too, why nice guys don’t always finish last, and how love is sometimes blind Liking those who like us. Or how I like you because you like me, thirty-six questions that may (or may not) change your life, and why playing hard-to-get is… hard Birds of feather. Or why we like people who are similar to ourselves, how we match on attitudes (and other traits), and why opposites sometimes attract The end of the beginning. Or, why life outside the lab makes fools of all of us and, to conclude, some life-changing advice

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When it comes to relationships, there’s no shortage of advice from self-help ‘experts’, pick-up artists, and glossy magazines. Based on science rather than self-help clichés, psychologist Viren Swami debunks these myths and draws on cutting-edge research to provide a ground-breaking and evidence-based account of relationship formation.

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Book SynopsisGeometry of complex numbers and quaternions.- Groups.- Generalized rotation groups.- The exponential map.- The tangent space.- Structure of Lie algebras.- The matrix logarithm.- Topology.- Simply connected Lie groups.Trade ReviewFrom the reviews:“An excellent read. In just 200 pages the author explains what Lie groups and algebras actually are. … An undergraduate who has taken the calculus series, had a course in linear algebra that discusses matrices, has some knowledge of complex variables and some understanding of group theory should easily follow the material to this point. … the best book to get you going.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)“There are several aspects of Stillwell’s book that I particularly appreciate. He keeps the sections very short and straightforward, with a few exercises at the end of each to cement understanding. The theory is built up in small bites. He develops an intuition for what is happening by starting with very simple examples and building toward more complicated groups. … In short, if you want to teach an undergraduate course on Lie theory, I recommend Stillwell.”(David Bressoud, The UMAP Journal, Vol. 31 (4), 2010)"Lie theory, basically the study of continuous symmetry, certainly occupies a central position in modern mathematics … . In Naive Lie Theory, Stillwell (Univ. of San Franciso) concentrates on the simplest examples and stops short of representation theory … . Summing Up: Recommended. Upper-division undergraduates and graduate students." (D. V. Feldman, Choice, Vol. 46 (9), May, 2009)"This book provides an introduction to Lie groups and Lie algebras suitable for undergraduates having no more background than calculus and linear algebra. … Each chapter concludes with a lively and informative account of the history behind the mathematics in it. The author writes in a clear and engaging style … . The book is a welcome addition to the literature in representation theory." (William M. McGovern, Mathematical Reviews, Issue 2009 g)"This is a beautifully clear exposition of the main points of Lie theory, aimed at undergraduates who have … calculus and linear algebra. … The book is well equipped with examples … . The book has a very strong geometric flavor, both in the use of rotation groups and in the connection between Lie algebras and Lie groups." (Allen Stenger, The Mathematical Association of America, October, 2008)Table of ContentsGeometry of complex numbers and quaternions.- Groups.- Generalized rotation groups.- The exponential map.- The tangent space.- Structure of Lie algebras.- The matrix logarithm.- Topology.- Simply connected Lie groups.

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Book SynopsisThis book treats Jacques Tit's beautiful theory of buildings, making that theory accessible to readers with minimal background.Trade ReviewFrom the reviews:American Mathematical Society Mathematical Reviews MR2439729:"The book under review ... is the first encyclopedic treatment of buildings made available in the literature, so that with writing this book the authors manage to close a serious gap in the mathematical literature: the non-existence of an easily accessible reference for buildings beyond an introduction.In their introduction the authors state that it is their ``goal in this book to treat buildings from all three ... points of view [via the simplicial, the combinatorial, and the metric approach]. The various approaches complement one another and are useful. On the other hand, [the authors] recognize that some readers may prefer one particular viewpoint. [The authors] have therefore tried to create more than one path through the book so that, for example, the reader interested only in the combinatorial approach can learn the basics without having to spend too much time studying buildings as simplicial complexes.'' In the reviewer's opinion, the authors perfectly reach this goal and, moreover, manage to show that the theory of buildings and their applications are active, thriving, exciting and beautiful areas of mathematics. This book is very well written. The reviewer is sure that it will become a standard reference for buildings and remain one for a very long time.... The main advantages of the combinatorial approach to buildings are that it is elementary and abstract and, hence, easily accessible. Since the simplicial and combinatorial approaches are equivalent..., one can always work with the one which is more suitable for one's own problems or more appealing to one's own taste. It is indeed one of the great achievements of this book to introduce both concepts simultaneously and to combine them in a natural way.... Chapter 8 is extremely valuable for students and researchers interested in the theory of twin buildings, as it makes the theory ... easily accessible. It is particularly important for the mathematical community that the folklore Theorem 8.27 has finally been recorded.... Altogether, the book under review is a wonderful piece of work that will have many enthusiastic readers."“This book is the first one which presents all of the different approaches to buildings alongside one another, and it does so in an accessible yet thorough manner which should prove extremely useful to anyone wishing to learn more about this interesting area of mathematics. The goal of presenting this introductory material in one place would be laudable enough. … this book is an extremely valuable addition to the mathematical literature. … it should also be an essential resource for experts in the area.” (Michael Bate, Zentralblatt MATH, Vol. 1214, 2011)Table of ContentsPreface.- Introduction.- Finite Reflection Groups.- Coxeter Groups.- Coxeter Complexes.- Buildings as Chamber Complexes.- Buildings as W-Metric Spaces.- Buildings and Groups.- Root Groups and the Moufang Property.- Moufang Twin Buildings and RGD-Systems.- The Classification of Spherical Buildings.- Euclidean and Hyperbolic Reflection Groups.- Euclidean Buildings.- Buildings as Metric Spaces.- Applications to the Cohomology of Groups.- Other Applications.- Cell Complexes.- Root Systems.- Algebraic Groups.

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Book SynopsisThis book is a significant reworking of an earlier work by the authors. It offers a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that includes a broader range of applications.Trade ReviewFrom the reviews:"This is a terrific book, succeeding in its considerable ambitions, and doing so in the remarkable style … . Symmetry, Representations, and Invariants is indeed capable of instructing the reader in the three themes given in its title, taking him from elementary and foundational notions to very advanced material … . Symmetry, Representations, and Invariants promises to be a graduate text of major importance." (Michael Berg, The Mathematical Association of America, August, 2009)“The book under review is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups. … can be used as a source for various kinds of courses. … supported by the rich collections of exercises (mostly with detailed hints for solutions) accompanying each section. Local reading is well supported by the structure of the book. The book can be recommended for a … wide audience of readers: for graduate and postgraduate students as well as for researchers as a reference work.” (Sergei Platonov, Zentralblatt MATH, Vol. 1173, 2009)“The book under review is a substantial rewriting and extension of the authors’ previous work ‘Representations and Invariants of the Classical Groups’. It is a thorough and comprehensive treatment of the geometry of Lie and algebraic group actions. … More than 350 exercises are presented. This monograph is written with great care and provides an excellent basis for a variety of courses from this field.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 163 (1), May, 2011)“The book will serve as a useful reference for a broad range of mathematicians, as well as physicists seeking a rigorous, systematic development of the representation theory underlying much of modern quantum mechanics. Detailed and careful statements of definitions, theorems, and proofs are provided, as well as over 350 exercises, many of them substantial. … can be used as the basis for graduate-level courses in Lie groups and algebraic groups, representation theory, invariant theory, and a variety of applications.” (Peter J. Olver, SIAM Review, Vol. 53 (3), 2011)“This volume is clearly a labour of love on the part of the authors, who have obviously thought very carefully about the best way to explain and motivate this often sophisticated material. … The authors have taken great pains to make this book a textbook as well as a useful reference. … It should be in the library of every university with a graduate mathematics program, as well as on the shelf of every lecturer teaching, or with research interests in, the material covered here.” (Mark Hunacek, The Mathematical Gazette, Vol. 96 (536), July, 2012)Table of ContentsLie Groups and Algebraic Groups.- Structure of Classical Groups.- Highest-Weight Theory.- Algebras and Representations.- Classical Invariant Theory.- Spinors.- Character Formulas.- Branching Laws.- Tensor Representations of GL(V).- Tensor Representations of O(V) and Sp(V).- Algebraic Groups and Homogeneous Spaces.- Representations on Spaces of Regular Functions.

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Book SynopsisFoundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds.Table of Contents1 Manifolds.- 2 Tensors and Differential Forms.- 3 Lie Groups.- 4 Integration on Manifolds.- 5 Sheaves, Cohomology, and the de Rham Theorem.- 6 The Hodge Theorem.- Supplement to the Bibliography.- Index of Notation.

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Book SynopsisThis is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics.Trade ReviewD. Eisenbud Commutative Algebra with a View Toward Algebraic Geometry "This text has personality—Those familiar with Eisenbud"s own research will recognize its traces in his choice of topics and manner of approach. The book conveys infectious enthusiasm and the conviction that research in the field is active and yet accessible."—MATHEMATICAL REVIEWSTable of ContentsIntroduction; 0. Elementary Definitions; I. Basic Constructions; 1. Roots and Commutative Algebra; 2. Localization; 3. Associated Primes and Primary Decomposition; 4. Integral Dependence and the Nullstellensatz; 5. Filtrations and the Artin-Rees Lemma; 6. Flat Families; 7. Completions and Hensel's Lemma; II. Dimension Theory; 8. Introduction to Dimension Theory; 9. Fundamental Definitions of Dimension Theory; 10. The Principal Ideal Theorem and Systems of Parameters; 11. Dimension and Codimension One; 12. Dimension and Hilbert- Samuel Polynomials; 13. Dimension of Affine Rings; 14. Elimination Theory, Generic Freeness and the Dimension of Fibers; 15. Grobner Bases; 16. Modules of Differentials; III. Homological Methods; 17. Regular Sequence and the Koszul Complex; 18. Depth, Codimension and Cohen-Macaulay Rings; 19. Homological Theory of Regular Local Rings; 20. Free Resolutions and Fitting Invariants; 21. Duality, Canonical Modules and Gorenstein Rings; Appendix 1. Field Theory; Appendix 2. Multilinear Algebra; Appendix 3. Homological Algebra; Appendix 4. A Sketch of Local Cohomology; Appendix 5. Category Theory; Appendix 6. Limits and Colimits; Appendix 7. Where Next?; Hints and Solutions for Selected Exercises; References; Index of Notations; Index

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Book Synopsis1 Groups and Homomorphisms.- Permutations.- Cycles.- Factorization into Disjoint Cycles.- Even and Odd Permutations.- Semigroups.- Groups.- Homomorphisms.- 2 The Isomorphism Theorems.- Subgroups.- Lagrange's Theorem.- Cyclic Groups.- Normal Subgroups.- Quotient Groups.- The Isomorphism Theorems.- Correspondence Theorem.- Direct Products.- 3 Symmetric Groups and G-Sets.- Conjugates.- Symmetric Groups.- The Simplicity of An.- Some Representation Theorems.- G-Sets.- Counting Orbits.- Some Geometry.- 4 The Sylow Theorems.- p-Groups.- The Sylow Theorems.- Groups of Small Order.- 5 Normal Series.- Some Galois Theory.- The Jordan-Hölder Theorem.- Solvable Groups.- Two Theorems of P. Hall.- Central Series and Nilpotent Groups.- p-Groups.- 6 Finite Direct Products.- The Basis Theorem.- The Fundamental Theorem of Finite Abelian Groups.- Canonical Forms; Existence.- Canonical Forms; Uniqueness.- The KrullSchmidt Theorem.- Operator Groups.- 7 Extensions and Cohomology.- The Extension Problem.- Automorphism Groups.- Semidirect Products.- Wreath Products.- Factor Sets.- Theorems of Schur-Zassenhaus and Gaschütz.- Transfer and Burnside's Theorem.- Projective Representations and the Schur Multiplier.- Derivations.- 8 Some Simple Linear Groups.- Finite Fields.- The General Linear Group.- PSL(2, K).- PSL(m, K).- Classical Groups.- 9 Permutations and the Mathieu Groups.- Multiple Transitivity.- Primitive G-Sets.- Simplicity Criteria.- Affine Geometry.- Projective Geometry.- Sharply 3-Transitivc Groups.- Mathieu Groups.- Steiner Systems.- 10 Abelian Groups.- Basics.- Free Abelian Groups.- Finitely Generated Abelian Groups.- Divisible and Reduced Groups.- Torsion Groups.- Subgroups of ?.- Character Groups.- 11 Free Groups and Free Products.- Generators and Relations.- SemigroupInterlude.- Coset Enumeration.- Presentations and the Schur Multiplier.- Fundamental Groups of Complexes.- Tietze's Theorem.- Covering Complexes.- The Nielscn-Schreier Theorem.- Free Products.- The Kurosh Theorem.- The van Kampen Theorem.- Amalgams.- HNN Extensions.- 12 The Word Problem.- Turing Machines.- The MarkovPost Theorem.- The NovikovBooneBritton Theorem: Sufficiency of Boone's Lemma.- Cancellation Diagrams.- The NovikovBooneBritton Theorem: Necessity of Boone's Lemma.- The Higman Imbedding Theorem.- Some Applications.- Epilogue.- Appendix I Some Major Algebraic Systems.- Appendix II Equivalence Relations and Equivalence Classes.- Appendix III Functions.- APPENDIX IV Zorn's Lemma.- APPENDIX V Countability.- APPENDIX VI Commutative Rings.- Notation.Trade ReviewFourth Edition J.J. Rotman An Introduction to the Theory of Groups "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route."—MATHEMATICAL REVIEWSTable of Contents1 Groups and Homomorphisms.- Permutations.- Cycles.- Factorization into Disjoint Cycles.- Even and Odd Permutations.- Semigroups.- Groups.- Homomorphisms.- 2 The Isomorphism Theorems.- Subgroups.- Lagrange’s Theorem.- Cyclic Groups.- Normal Subgroups.- Quotient Groups.- The Isomorphism Theorems.- Correspondence Theorem.- Direct Products.- 3 Symmetric Groups and G-Sets.- Conjugates.- Symmetric Groups.- The Simplicity of An.- Some Representation Theorems.- G-Sets.- Counting Orbits.- Some Geometry.- 4 The Sylow Theorems.- p-Groups.- The Sylow Theorems.- Groups of Small Order.- 5 Normal Series.- Some Galois Theory.- The Jordan-Hölder Theorem.- Solvable Groups.- Two Theorems of P. Hall.- Central Series and Nilpotent Groups.- p-Groups.- 6 Finite Direct Products.- The Basis Theorem.- The Fundamental Theorem of Finite Abelian Groups.- Canonical Forms; Existence.- Canonical Forms; Uniqueness.- The Krull—Schmidt Theorem.- Operator Groups.- 7 Extensions and Cohomology.- The Extension Problem.- Automorphism Groups.- Semidirect Products.- Wreath Products.- Factor Sets.- Theorems of Schur-Zassenhaus and Gaschütz.- Transfer and Burnside’s Theorem.- Projective Representations and the Schur Multiplier.- Derivations.- 8 Some Simple Linear Groups.- Finite Fields.- The General Linear Group.- PSL(2, K).- PSL(m, K).- Classical Groups.- 9 Permutations and the Mathieu Groups.- Multiple Transitivity.- Primitive G-Sets.- Simplicity Criteria.- Affine Geometry.- Projective Geometry.- Sharply 3-Transitivc Groups.- Mathieu Groups.- Steiner Systems.- 10 Abelian Groups.- Basics.- Free Abelian Groups.- Finitely Generated Abelian Groups.- Divisible and Reduced Groups.- Torsion Groups.- Subgroups of ?.- Character Groups.- 11 Free Groups and Free Products.- Generators and Relations.- Semigroup Interlude.- Coset Enumeration.- Presentations and the Schur Multiplier.- Fundamental Groups of Complexes.- Tietze’s Theorem.- Covering Complexes.- The Nielscn-Schreier Theorem.- Free Products.- The Kurosh Theorem.- The van Kampen Theorem.- Amalgams.- HNN Extensions.- 12 The Word Problem.- Turing Machines.- The Markov—Post Theorem.- The Novikov—Boone—Britton Theorem: Sufficiency of Boone’s Lemma.- Cancellation Diagrams.- The Novikov—Boone—Britton Theorem: Necessity of Boone’s Lemma.- The Higman Imbedding Theorem.- Some Applications.- Epilogue.- Appendix I Some Major Algebraic Systems.- Appendix II Equivalence Relations and Equivalence Classes.- Appendix III Functions.- APPENDIX IV Zorn’s Lemma.- APPENDIX V Countability.- APPENDIX VI Commutative Rings.- Notation.

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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 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 SynopsisI: Finite Groups.- 1. Representations of Finite Groups.- Table of ContentsI: Finite Groups.-

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Book Synopsis1 Sphere Packings and Kissing Numbers.- 2 Coverings, Lattices and Quantizers.- 3 Codes, Designs and Groups.- 4 Certain Important Lattices and Their Properties.- 5 Sphere Packing and Error-Correcting Codes.- 6 Laminated Lattices.- 7 Further Connections Between Codes and Lattices.- 8 Algebraic Constructions for Lattices.- 9 Bounds for Codes and Sphere Packings.- 10 Three Lectures on Exceptional Groups.- 11 The Golay Codes and the Mathieu Groups.- 12 A Characterization of the Leech Lattice.- 13 Bounds on Kissing Numbers.- 14 Uniqueness of Certain Spherical Codes.- 15 On the Classification of Integral Quadratic Forms.- 16 Enumeration of Unimodular Lattices.- 17 The 24-Dimensional Odd Unimodular Lattices.- 18 Even Unimodular 24-Dimensional Lattices.- 19 Enumeration of Extremal Self-Dual Lattices.- 20 Finding the Closest Lattice Point.- 21 Voronoi Cells of Lattices and Quantization Errors.- 22 A Bound for the Covering Radius of the Leech Lattice.- 23 The Covering Radius of the Leech Lattice.- 24 Twenty-Three Constructions for the Leech Lattice.- 25 The Cellular Structure of the Leech Lattice.- 26 Lorentzian Forms for the Leech Lattice.- 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice.- 28 Leech Roots and Vinberg Groups.- 29 The Monster Group and its 196884-Dimensional Space.- 30 A Monster Lie Algebra?.- Supplementary Bibliography.Trade ReviewThird Edition J.H. Conway and N.J.A. Sloane Sphere Packings, Lattices and Groups "This is the third edition of this reference work in the literature on sphere packings and related subjects. In addition to the content of the preceding editions, the present edition provides in its preface a detailed survey on recent developments in the field, and an exhaustive supplementary bibliography for 1988-1998. A few chapters in the main text have also been revised."—MATHEMATICAL REVIEWSTable of Contents1 Sphere Packings and Kissing Numbers.- 2 Coverings, Lattices and Quantizers.- 3 Codes, Designs and Groups.- 4 Certain Important Lattices and Their Properties.- 5 Sphere Packing and Error-Correcting Codes.- 6 Laminated Lattices.- 7 Further Connections Between Codes and Lattices.- 8 Algebraic Constructions for Lattices.- 9 Bounds for Codes and Sphere Packings.- 10 Three Lectures on Exceptional Groups.- 11 The Golay Codes and the Mathieu Groups.- 12 A Characterization of the Leech Lattice.- 13 Bounds on Kissing Numbers.- 14 Uniqueness of Certain Spherical Codes.- 15 On the Classification of Integral Quadratic Forms.- 16 Enumeration of Unimodular Lattices.- 17 The 24-Dimensional Odd Unimodular Lattices.- 18 Even Unimodular 24-Dimensional Lattices.- 19 Enumeration of Extremal Self-Dual Lattices.- 20 Finding the Closest Lattice Point.- 21 Voronoi Cells of Lattices and Quantization Errors.- 22 A Bound for the Covering Radius of the Leech Lattice.- 23 The Covering Radius of the Leech Lattice.- 24 Twenty-Three Constructions for the Leech Lattice.- 25 The Cellular Structure of the Leech Lattice.- 26 Lorentzian Forms for the Leech Lattice.- 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice.- 28 Leech Roots and Vinberg Groups.- 29 The Monster Group and its 196884-Dimensional Space.- 30 A Monster Lie Algebra?.- Supplementary Bibliography.

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Book SynopsisSpecific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering.Trade Review"The book is self-contained.It remains a good and solid introduction to this subject."Nieuw Archief voor Wiskunde, March 2001 "... This book takes the reader on one of the greatest journeys in modern mathematics that has as its roots a subject that is more than 300 years old. Armed with this knowledge a reader is ready to pursue numerous topics of active mathematical research, from the more pure domains of symplectic geometry and topology to the geometric analysis of the limitless supply of examples from mechanics."Newsletter of the Newzealand Mathematical Society, No. 81, April 2001 Second Edition J.E. Marsden and T.S. Ratiu Introduction to Mechanics and Symmetry A Basic Exposition of Classical Mechanical Systems "As the name of the book implies, a consistent theme running through the book is that of symmetry. Indeed the latter half of the book focuses on Poisson manifolds, momentum maps, Lie-Poisson reduction, co-adjoint orbits and the integrability of the rigid body. The discussion of reduction must be the most comprehensive yet given. A pleasant feature of the book is that most of the theory that relates to finite-dimensional mechanical systems is illustrated concretely in terms of local coordinates, thereby making the book accessible even to beginners in the field."—MATHEMATICAL REVIEWSTable of ContentsPreface * About the Authors * 1 Introduction and Overview * 2 Hamiltonian Systems on Linear Symplectic Spaces * 3 An Introduction to Infinite-Dimensional Systems * 4 Manifolds, Vector Fields, and Differential Forms * 5 Hamiltonian Systems on Symplectic Manifolds * 6 Cotangent Bundles * 7 Lagrangian Mechanics * 8 Variational Principles, Constraints, and Rotating Systems * 9 An Introduction to Lie Groups * 10 Poisson Manifolds * 11 Momentum Maps *12 Computation and Properties of Momentum Maps * 13 Lie-Poisson and Euler-Poincare Reduction * 14 Coadjoint Orbits * 15 The Free Rigid Body * References

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Book SynopsisThis book presents ordinary differential equations based on Lie group analysis and related invariance principles. The author provides students and teachers with a text for one-semester undergraduate and graduate courses that spans a variety of topics, from the basic theory through to applications.Trade Review"…this is the first self-contained university text on ordinary differential equations…" (Zentralblatt Math, Vol.1047, No.22, 2004)Table of ContentsIntroduction to Differential Equations. Transformation Groups. Lie Group Analysis of Ordinary Differential Equations. Brief on Lie Algebras. First Order Differential Equations. Integration of Second Order Equations. Basic Theory of Linear Equations. Nonlinear Second Order Equations. Integration of Third Order Equations. Nonlinear Superposition Principle. Index.

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Book SynopsisAs algebra becomes more widely used in a variety of applications and computers are developed to allow efficient calculations in the field, so there becomes a need for new techniques to further this area of research. Grobner Bases is one topic which has recently become a very popular and important area of modern algebra.Table of ContentsRings. Fields, and Ideals. Monomial Ideals. Gröbner Bases. Algebraic Sets. Primary Decomposition of Ideals. Solving Systems of Polynomial Equations. Applications of Gröbner Bases. Homogeneous Algebras. Projective Varieties. The Associated Graded Ring. Hilbert Series. Variations of Gröbner Bases. Improvements to Buchberger's Algorithm. Software. Hints to Some Exercises. Answers to Exercises. Bibliography. Index.

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Book SynopsisOriginally published in 1989, this is an advanced text and research monograph on groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the topology becomes graph theory. Two-dimensional topics include the characterization of Poincare duality groups and accessibility of almost finitely presented groups. The main three-dimensional topics are the equivariant loop and sphere theorems. The prerequisites grow as the book progresses up the dimensions. A familiarity with group theory is sufficient background for at least the first third of the book, while the later chapters occasionally state without proof and then apply various facts which require knowledge of homological algebra and algebraic topology. This book is essential reading for anyone contemplating working in the subject.Table of ContentsPreface; Conventions; 1. Groups and graphs; 2. Cutting graphs and building trees; 3. The almost stability theorem; 4. Applications of the almost stability theorem; 5. Poincaré duality; 6. Two-dimensional complexes and three-dimensional manifolds; Bibliography and author index; Symbol index; Subject index.

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Book SynopsisThe particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S. J. Patterson for Fuchsian groups, and later extended and refined by Sullivan.Table of Contents1. Preliminaries; 2. The limit set; 3. A measure of the limit set; 4. Conformal densities; 5. Hyperbolically harmonic functions; 6. The sphere at infinity; 7. Elementary ergodic theory; 8. The geodesic flow; 9. Geometrically finite groups; 10. Fuchsian groups.

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Book SynopsisThe aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in maTrade Review'… a beautifully written book. Anyone wishing to learn the fundamental facts of Brauer's theory of blocks cannot do better than to begin his study with this text.' Bulletin of the London Mathematical SocietyTable of ContentsPreface; Part I. Semi-Simple Modules: Part II. Projective Modules: Part III. Modules and Subgroups: Part IV. Blocks: Part V. Cyclic Blocks.

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