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Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields studied in every university maths course, through Lie groups to cohomology and category theory, the author shows how the origins of each concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Required reading for mathematicians, from beginners to experts.
Aimed at researchers, graduate students and undergraduates alike, this book presents a unified exposition of all the main areas and methods of the theory of Kleinian groups and the theory of uniformization of manifolds. The past 20 years have seen a rejuvenation of the field, due to the development of powerful new methods in topology, the theory of functions of several complex variables, and the theory of quasiconformal mappings. Thus this new book should provide a valuable resource, listing the basic facts regarding Kleinian groups and serving as a general guide to the primary literature, particularly the Russian literature in the field. In addition, the book includes a large number of examples, problems, and unsolved problems, many of them presented for the first time.
Varieties of algebras are equationally defined classes of algebras, or "primitive classes" in MAL'CEV'S terminology. They made their first explicit appearance in the 1930's, in Garrett BIRKHOFF'S paper on "The structure of abstract algebras" and B. H. NEUMANN'S paper "Identical relations in groups I". For quite some time after this, there is little published evidence that the subject remained alive. In fact, however, as part of "universal algebra", it aroused great interest amongst those who had access, directly or indirectly, to PHILIP HALL'S lectures given at Cambridge late in the 1940's. More recently, category theory has provided a general setting since varieties, suitably interpreted, are very special examples of categories. Whether their relevance to category theory goes beyond this, I do not know. And I doubt that the category theoretical approach to varieties will be more than a fringe benefit to group theory. Whether or not my doubts have substance, the present volume owes its existence not to the fact that varieties fit into a vastly more general pattern, but to the benefit group theory has derived from the classification of groups by varietal properties. It is this aspect of the study of varieties that seems to have caused its reappearance in the literature in the 1950's.
This study of ethnic violence in the United States from 1877 to 1914 reveals that not all ethnic groups were equally likely to be victims of violence; the author seeks the reasons for this historical record. This analysis of the causes of urban racial and ethnic strife in large American cities at the turn of the century should comprise important empirical and theoretical reference material for social scientists and historians alike.
Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians.
Learn the Ansible automation technology with some real-life examples. Every successful IT department needs automation nowadays for bare metal servers, virtual machines, could, containers, and edge computing. Automate your IT journey with Ansible automation technology. I'm going to teach you example by example how to manage users and groups in Linux and macOS operation systems are the most common System Administrator tasks. Each of the 20+ lessons summarizes a specific scenario about user and groups management: creating a user, creating a new pair of a suitable SSH key and a home directory, changing a password and specifying the encryption cipher, removing the home directory and the mailbox, or assigning a special `nologin` shell for temporarily disabled users. Another user scenario that happens very often is when you need only to temporarily disable and enable a user. Another useful administrator tool is group management to assign permission to resources to a bunch of users. You could easily customize the example code with your username and use it in your everyday journey without any additional effort. There are some Ansible codes usable in all the Linux systems, battle-tested for RedHat-like and Debian-like systems. Are you ready to automate your day with Ansible? Examples in the book are tested with the latest version of Ansible 2.9+ and Ansible Core 2.11+.
The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.
Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects. Provides a wealth of exercises and problems to support self-study. Additional online resources on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.
The Dietary Reference Intakes (DRIs) are quantitative estimates of nutrient intakes to be used for planning and assessing diets for apparently healthy people. This volume is the second of two reports in the DRI series aimed at providing specific guidance on the appropriate uses of the DRIs. The first report provided guidance on appropriate methods for using DRIs in dietary assessment. This volume builds on the statistical foundations of the assessment report to provide specific guidance on how to use the appropriate DRIs in planning diets for individuals and for groups. Dietary planning, whether for an individual or a group, involves developing a diet that is nutritionally adequate without being excessive. The planning goal for individuals is to achieve recommended and adequate nutrient intakes using food-based guides. For group planning, the report presents a new approach based on considering the entire distribution of usual nutrient intakes rather than focusing on the mean intake of the group. The report stresses that dietary planning using the DRIs is a cyclical activity that involves assessment, planning, implementation, and reassessment. Nutrition and public health researchers, dietitians and nutritionists responsible for the education of the next generation of practitioners, and government professionals involved in the development and implementation of national diet and health assessments, public education efforts and food assistance programs will find this volume indispensable for setting intake goals for individuals and groups.