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Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
This ground-breaking new volume reviews and extends theory and
research on the psychology of justice in social contexts, exploring
the dynamics of fairness judgments and their consequences.
Perceptions of fairness, and the factors that cause and are caused
by fairness perceptions, have long been an important part of social
psychology. Featuring work from leading scholars on psychological
processes involved in reactions to fairness, as well as the
applications of justice research to government institutions,
policing, medical care and the development of radical and extremist
behavior, the book expertly brings together two traditionally
distinct branches of social psychology: social cognition and
interpersonal relations. Examining how people judge whether the
treatment they experience from others is fair and how this effects
their attitudes and behaviors, this essential collection draws on
theory and research from multiple disciplines as it explores the
dynamics of fairness judgments and their consequences. Integrating
theory on interpersonal relations and social cognition, and
featuring innovative biological research, this is the ideal
companion for senior undergraduates and graduates, as well as
researchers and scholars interested in the social psychology of
justice.
Based on research focusing on the experience of having confused
speech and being with confused speakers, this book begins with
everyday, commonly understood ideas such as "talking too much" and
examines how confused speech is "brought off" as a collaborative
activity by the people involved. The author became involved in this
project because she was interested in how "confusion" seemed to be
something that everyone is not only involved in but also recognizes
as part of ordinary life. At the same time, "confusion" is a word
that is used somewhat as a blanket category for some people
considered permanently incompetent and "set apart" from ordinary
members of society. Her study analyzes how talk between confused
and normal speakers throws light on this tension.
Originally published in 1963, this book was one of the first to
explore group process and working with groups. The introductory
chapter tells us that working with groups requires three skills:
and understanding of theory, a knowledge of its application, and
trained experience in its use. It goes on to discuss these points,
helping the reader towards an understanding of group processes and
making decisions in groups. This title is an early example of
author's explorations of groups and group work, which were to be a
major factor in the establishment of group-work practice in Britain
over the following years.
The aim of this book is to provide a systematic and practical
account of methods of integration of ordinary and partial
differential equations based on invariance under continuous (Lie)
groups of trans formations. The goal of these methods is the
expression of a solution in terms of quadrature in the case of
ordinary differential equations of first order and a reduction in
order for higher order equations. For partial differential
equations at least a reduction in the number of independent
variables is sought and in favorable cases a reduction to ordinary
differential equations with special solutions or quadrature. In the
last century, approximately one hundred years ago, Sophus Lie tried
to construct a general integration theory, in the above sense, for
ordinary differential equations. Following Abel's approach for
algebraic equations he studied the invariance of ordinary
differential equations under transformations. In particular, Lie
introduced the study of continuous groups of transformations of
ordinary differential equations, based on the infinitesimal
properties of the group. In a sense the theory was completely
successful. It was shown how for a first-order differential
equation the knowledge of a group leads immediately to quadrature,
and for a higher order equation (or system) to a reduction in
order. In another sense this theory is somewhat disappointing in
that for a first-order differ ential equation essentially no
systematic way can be given for finding the groups or showing that
they do not exist for a first-order differential equation."
The Social Psychology of Everyday Politics examines the ways in
which politics permeates everyday life, from the ordinary
interactions we have with others to the sense of belonging and
identity developed within social groups and communities.
Discrimination, prejudice, inclusion and social change, politics is
an on-going process that is not solely the domain of the elected
and the powerful. Using a social and political psychological lens
to examine how politics is enacted in contemporary societies, the
book takes an explicitly critical approach that places political
activity within collective processes rather than individual
behaviors. While the studies covered in the book do not ignore the
importance of the individual, they underscore the need to examine
the role of culture, history, ideology and social context as
integral to psychological processes. Individuals act, but they do
not act in isolation from the groups and societies in which they
belong. Drawing on extensive international research, with
contributions from leaders in the field as well as emerging
scholars, the book is divided into three interrelated parts which
cover: The politics of intercultural relations Political agency and
social change Political discourse and practice Offering insights
into how psychology can be applied to some of the most pressing
social issues we face, this will be fascinating reading for
students of psychology, political science, sociology and cultural
studies, as well as anyone working in the area of public policy.
The central concept in this monograph is that of a soluable group -
a group which is built up from abelian groups by repeatedly forming
group extenstions. It covers all the major areas, including
finitely generated soluble groups, soluble groups of finite rank,
modules over group rings, algorithmic problems, applications of
cohomology, and finitely presented groups, while remaining failry
strictly within the boundaries of soluable group theory. An
up-to-date survey of the area aimed at research students and
academic algebraists and group theorists, it is a compendium of
information that will be especially useful as a reference work for
researchers in the field.
In the middle of the last century, after hearing a talk of Mostow
on one of his rigidity theorems, Borel conjectured in a letter to
Serre a purely topological version of rigidity for aspherical
manifolds (i.e. manifolds with contractible universal covers). The
Borel conjecture is now one of the central problems of topology
with many implications for manifolds that need not be aspherical.
Since then, the theory of rigidity has vastly expanded in both
precision and scope. This book rethinks the implications of
accepting his heuristic as a source of ideas. Doing so leads to
many variants of the original conjecture - some true, some false,
and some that remain conjectural. The author explores this
collection of ideas, following them where they lead whether into
rigidity theory in its differential geometric and representation
theoretic forms, or geometric group theory, metric geometry, global
analysis, algebraic geometry, K-theory, or controlled topology.
This book provides an introduction to the role of diversity in
complex adaptive systems. A complex system--such as an economy or a
tropical ecosystem--consists of interacting adaptive entities that
produce dynamic patterns and structures. Diversity plays a
different role in a complex system than it does in an equilibrium
system, where it often merely produces variation around the mean
for performance measures. In complex adaptive systems, diversity
makes fundamental contributions to system performance.
Scott Page gives a concise primer on how diversity happens, how
it is maintained, and how it affects complex systems. He explains
how diversity underpins system level robustness, allowing for
multiple responses to external shocks and internal adaptations; how
it provides the seeds for large events by creating outliers that
fuel tipping points; and how it drives novelty and innovation. Page
looks at the different kinds of diversity--variations within and
across types, and distinct community compositions and interaction
structures--and covers the evolution of diversity within complex
systems and the factors that determine the amount of maintained
diversity within a system.Provides a concise and accessible
introduction Shows how diversity underpins robustness and fuels
tipping points Covers all types of diversity The essential primer
on diversity in complex adaptive systems
This book introduces the theory of enveloping semigroups-an
important tool in the field of topological dynamics-introduced by
Robert Ellis. The book deals with the basic theory of topological
dynamics and touches on the advanced concepts of the dynamics of
induced systems and their enveloping semigroups. All the chapters
in the book are well organized and systematically dealing with
introductory topics through advanced research topics. The basic
concepts give the motivation to begin with, then the theory, and
finally the new research-oriented topics. The results are presented
with detailed proof, plenty of examples and several open questions
are put forward to motivate for future research. Some of the
results, related to the enveloping semigroup, are new to the
existing literature. The enveloping semigroups of the induced
systems is considered for the first time in the literature, and
some new results are obtained. The book has a research-oriented
flavour in the field of topological dynamics.
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