Fundamentals of Group Theory provides a comprehensive account of the basic theory of groups. Both classic and unique topics in the field are covered, such as an historical look at how Galois viewed groups, a discussion of commutator and Sylow subgroups, and a presentation of Birkhoff's theorem. Written in a clear and accessible style, the work presents a solid introduction for students wishing to learn more about this widely applicable subject area.
This book will be suitable for graduate courses in group theory and abstract algebra, and will also have appeal to advanced undergraduates. In addition it will serve as a valuable resource for those pursuing independent study. Group Theory is a timely and fundamental addition to literature in the study of groups.

This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is easily accessible, even to those with limited knowledge of mathematics. Students will get a concise, but thorough introduction to numerical analysis. In addition the algorithmic principles are emphasized to encourage a deeper understanding of why an algorithm is suitable, and sometimes unsuitable, for a particular problem. A Concise Introduction to Numerical Analysis strikes a balance between being mathematically comprehensive, but not overwhelming with mathematical detail. In some places where further detail was felt to be out of scope of the book, the reader is referred to further reading. The book uses MATLAB (R) implementations to demonstrate the workings of the method and thus MATLAB's own implementations are avoided, unless they are used as building blocks of an algorithm. In some cases the listings are printed in the book, but all are available online on the book's page at www.crcpress.com. Most implementations are in the form of functions returning the outcome of the algorithm. Also, examples for the use of the functions are given. Exercises are included in line with the text where appropriate, and each chapter ends with a selection of revision exercises. Solutions to odd-numbered exercises are also provided on the book's page at www.crcpress.com. This textbook is also an ideal resource for graduate students coming from other subjects who will use numerical techniques extensively in their graduate studies.

This book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.

"Data Science Foundations is most welcome and, indeed, a piece of literature that the field is very much in need of...quite different from most data analytics texts which largely ignore foundational concepts and simply present a cookbook of methods...a very useful text and I would certainly use it in my teaching." - Mark Girolami, Warwick University Data Science encompasses the traditional disciplines of mathematics, statistics, data analysis, machine learning, and pattern recognition. This book is designed to provide a new framework for Data Science, based on a solid foundation in mathematics and computational science. It is written in an accessible style, for readers who are engaged with the subject but not necessarily experts in all aspects. It includes a wide range of case studies from diverse fields, and seeks to inspire and motivate the reader with respect to data, associated information, and derived knowledge.

Following an initiative of the late Hans Zassenhaus in 1965, the Departments of Mathematics at The Ohio State University and Denison University organize conferences in combinatorics, group theory, and ring theory. Between May 18-21, 2000, the 25th conference of this series was held. Usually, there are twenty to thirty invited 20-minute talks in each of the three main areas. However, at the 2000 meeting, the combinatorics part of the conference was extended, to honor the 65th birthday of Professor Dijen Ray-Chaudhuri. This volulme is the proceedings of this extension. Most of the papers are in coding theory and design theory, reflecting the major interest of Professor Ray-Chaudhuri, but there are articles on association schemes, algebraic graph theory, combinatorial geometry, and network flows as well. There are four surveys and seventeen research articles, and all of these went through a thorough refereeing process. The volume is primarily recommended for researchers and graduate students interested in new developments in coding theory and design theory.

The goal of Computer Algebra: Concepts and Techniques is to demystify computer algebra systems for a wide audience including students, faculty, and professionals in scientific fields such as computer science, mathematics, engineering, and physics. Unlike previous books, the only prerequisites are knowledge of first year calculus and a little programming experience - a background that can be assumed of the intended audience. The book is written in a lean and lively style, with numerous examples to illustrate the issues and techniques discussed. It presents the principal algorithms and data structures, while also discussing the inherent and practical limitations of these systems

This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.The format of the questions makes them suitable for teachers to use in quizzes and assigned homework. Some of the problems may provide excellent topics for presentation and discussions. Furthermore, answers are given for all odd-numbered exercises which will be extremely useful for self-directed learners. In each chapter, there is a short background section which includes important definitions and statements of theorems to provide context for the following exercises and problems.

This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.The format of the questions makes them suitable for teachers to use in quizzes and assigned homework. Some of the problems may provide excellent topics for presentation and discussions. Furthermore, answers are given for all odd-numbered exercises which will be extremely useful for self-directed learners. In each chapter, there is a short background section which includes important definitions and statements of theorems to provide context for the following exercises and problems.

This book examines the phenomenon of silence in relation to human behaviour from multiple perspectives, drawing on psychological and cultural-philosophical ideas to create new, surprising connections between silence, quiet and rest. Silence and being quiet are present in everyday life and in politics, but why do we talk about it so rarely? Silence can be cathartic and peaceful, but equally oppressive and unbearable. In the form of communication, we keep secrets to protect ourselves and others, but on the other hand subjects can be silenced with dictatorial posturing - a communicative display of power - and something can be literally 'hushed up' that needs to be disclosed. In unique and engaging style, Theodor Itten explores the multi-layered internal conversation on silence in relation to the self and emotions, demonstrating why it is sometimes necessary in our modern society. Describing and analyzing human behaviour in relation to silence, the book also draws on psychoanalytic ideas by outlining the power of silence in processing our emotions and relationships and hiding innermost feelings. With rich narrative signposts providing thought-provoking and amusing insights, and interpersonal communication examined in relation to everyday life, this is fascinating reading for students and academics in psychology, philosophy, cultural studies, and related areas.

This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles. Lie groups are a special class of groups that are studied using differential and integral calculus methods. As a mathematical structure, a Lie group combines the algebraic group structure and the differentiable variety structure. Studies of such groups began around 1870 as groups of symmetries of differential equations and the various geometries that had emerged. Since that time, there have been major advances in Lie theory, with ramifications for diverse areas of mathematics and its applications. Each chapter of the book begins with a general, straightforward introduction to the concepts covered; then the formal definitions are presented; and end-of-chapter exercises help to check and reinforce comprehension. Graduate and advanced undergraduate students alike will find in this book a solid yet approachable guide that will help them continue their studies with confidence.

Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. The array of articles devoted to this topic is enormous, and there are many monographs concerned with matrix groups, ranging from old, classical texts to ones published more recently. However, in the case when the dimension is infinite (and such cases arise quite often), the reality is quite different. The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups, in the transition from the study of finite groups to the study of infinite groups which appeared about one hundred years ago. It is well known that this transition was extremely efficient and led to the development of a rich and central branch of algebra: Infinite group theory. The hope is that this book can be part of a similar transition in the field of linear groups. Features This is the first book dedicated to infinite-dimensional linear groups This is written for experts and graduate students specializing in algebra and parallel disciplines This book discusses a very new theory and accumulates many important and useful results

This ground-breaking book is designed to raise awareness of human rights implications in psychology, and provide knowledge and tools enabling psychologists to put a human rights perspective into practice. Psychologists have always been deeply engaged in alleviating the harmful consequences human rights violations have on individuals. However, despite the fundamental role that human rights play for professional psychology and psychologists, human rights education is underdeveloped in psychologists' academic and vocational training. This book, the first of its kind, looks to change this, by: raising awareness among professional psychologists, university teachers and psychology students about their role as human rights promoters and protectors providing knowledge and tools enabling them to put a human rights perspective into practice providing texts and methods for teaching human rights. Featuring chapters from leading scholars in the field, spanning 18 countries and six continents, the book identifies how psychologists can ensure they are practising in a responsible way, as well as contributing to wider society with a clear knowledge of human rights issues in relation to culture, gender, organisations and more. Including hands-on recommendations, case studies and discussion points, this is essential reading for professional psychologists as part of continuing professional development and those in training and taking psychology courses. For additional electronic resources for students and teachers, see the support material tab on the Routledge book page: https://www.routledge.com/Human-Rights-Education-for-Psychologists/Hagenaars-Plavsic-Sveaass-Wagner-Wainwright/p/book/9780367222963

This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. ." . . far more readable than most . . . it is also much more complete." Olivier Debarre in Mathematical Reviews, 1994.

This book is a translation from Russian of Part I of the book Mathematics Through Problems: From Olympiads and Math Circles to Profession. The other two parts, Geometry and Combinatorics, will be published soon. The main goal of this book is to develop important parts of mathematics through problems. The author tries to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover and recreate much of elementary mathematics and start edging into the sophisticated world of topics such as group theory, Galois theory, and so on, thus building a bridge (by showing that there is no gap) between standard high school exercises and more intricate and abstract concepts in mathematics. Definitions and/or references for material that is not standard in the school curriculum are included. However, many topics in the book are difficult when you start learning them from scratch. To help with this, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions. The book is based on classes taught by the author at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Published in honor of his 70th birthday, this volume explores and celebrates the work of G.W. (Pete) Stewart, a world-renowned expert in computational linear algebra. This volume includes: forty-four of Stewart's most influential research papers in two subject areas: matrix algorithms, and rounding and perturbation theory; a biography of Stewart; a complete list of his publications, students, and honors; selected photographs; and commentaries on his works in collaboration with leading experts in the field. G.W. Stewart: Selected Works with Commentaries will appeal to graduate students, practitioners, and researchers in computational linear algebra and the history of mathematics.

Praise for the first edition

"This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and computer science libraries."
-CHOICE

As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing-with extensive use in computing science, physics, chemistry, and data communications as well as in areas of mathematics such as combinatorics.

Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject-effectively holding your interest and creating a more seamless method of instruction.

Incorporating the applications of modern algebra throughout its authoritative treatment of the subject, this book covers the full complement of group, ring, and field theory typically contained in a standard modern algebra course. Numerous examples are included in each chapter, and answers to odd-numbered exercises are appended in the back of the text.

Chapter topics include:

• Boolean Algebras
• Polynomial and Euclidean Rings
• Groups
• Quotient Rings
• Quotient Groups
• Field Extensions
• Symmetry Groups in Three Dimensions
• Latin Squares
• Polya--Burnside Method of Enumeration
• Geometrical Constructions
• Monoids and Machines
• Error-Correcting Codes
• Rings and Fields

In addition to improvements in exposition, this fully updated Second Edition also contains new material on order of an element and cyclic groups, more details about the lattice of divisors of an integer, and new historical notes.

Filled with in-depth insights and over 600 exercises of varying difficulty, Modern Algebra with Applications, Second Edition can help anyone appreciate and understand this subject.

The H control has been one of the important robust control approaches since the 1980s. This book extends the area to nonlinear stochastic H2/H control, and studies more complex and practically useful mixed H2/H controller synthesis rather than the pure H control. Different from the commonly used convex optimization method, this book applies the Nash game approach to give necessary and sufficient conditions for the existence and uniqueness of the mixed H2/H control. Researchers will benefit from our detailed exposition of the stochastic mixed H2/H control theory, while practitioners can apply our efficient algorithms to address their practical problems.

This book examines engineering and mathematical models for documenting and approving mechanical and environmental discharges. The author emphasizes engineering design considerations as well as applications to waste water and atmospheric discharges. Chapters discuss: the fundamentals of turbulent jet mixing, dilution concepts, and mixing zone concepts diffuser configurations and head loss calculations different modeling techniques and accepted models - discussed in detail with theoretical background, restrictions, input, output, and examples Lagrangian and the EPA UM 2-dimensional diffuser model the PLUMES interface Eulerian integral methods, EPA UDKHG 3-dimensional diffuser model, and PDSG surface discharge model empirical techniques, RSB diffuser model, the CORMIX family of models for both diffusers and surface discharge numerical methods with a discussion of shelf commercial models Gaussian atmospheric plume models Fundamentals of Environmental Discharge Modeling includes numerous case studies and examples for each model and problem.

The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon

The authors examine topics in modern physics and offer a unitary and original treatment of the fundamental problems of the dynamics of physical systems, as well as a description of the nuclear matter within a framework of general relativity. They show that some physical phenomena studied at two different resolution scales (e.g. microscale, cosmological scale), apparently with no connection between them, become compatible by means of the operational procedures, acting either as some "hidden" symmetries, or harmonic-type mappings. The book is addressed to the students, researchers and university/high school teachers working in the fields of mathematics, physics, and chemistry.

Groups are arguably an essential and unavoidable part of our human lives-whether 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. Landaiche's multidisciplinary perspective is grounded in the traditions of Eric Berne's transactional analysis, Wilfred Bion's group-as-a-whole model, and Murray Bowen's 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 extensive professional experience of group work in a range of contexts, Landaiche deftly explores topics including group culture, social pain, learning and language, and presents key principles which enhance and facilitate learning in groups. With a style that is both deeply personal and theoretically grounded in a diverse range of studies, Groups in Transactional Analysis, Object Relations, and Family Systems presents a contemporary assessment of how we operate collectively, and how modern life has changed our outlook. It will be essential reading for transactional analysts in practice and in training, as well as other professionals working with groups. It will also be of value to academics and students of psychology, psychotherapy, and group dynamics, and anyone seeking to understand their role within a group. See the below link to an interview about the book with Tess Elliott: https://vimeo.com/510266467

A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.

This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are considered and some new approaches and research methods are described - e.g., the F-hypercenter of groups, X-permutable subgroups, subgroup functors, generalized supplementary subgroups, quasi-F-group, and F-cohypercenter for Fitting classes. At the end of each chapter, we provide relevant supplementary information and introduce readers to selected open problems.

The volume is introduced with a schedule of the conference sessions held in May 1998 in Moscow, and a vita of Kurosh (1908-1971), a forefather of modern algebra affiliated with Moscow State U. The names of the six sessions offer a sense of the diversity of participant interests: group theory; theory of rings and modules, homological algebra, and K-theory; Lie groups and Lie algebras, invariant theory, and algebraic groups; algebraic geometry, algebraic number theory, commutative algebra; algebraic systems; and computer algebra, and algorithmic problems. A sampling of the 32 titles by the international contributors includes: Strictly stratified algebras; Randomness: algebraic, statistical and complexity theory aspects; Codimension growth and graded identities; Birational correspondences of a double cone; Modular Lie algebras: new trends; and Some notes on universal algebraic geometry. Lacks an index.

The book contains seven refereed research papers on locally compact quantum groups and groupoids by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg from February 21 to February 23, 2002. Topics covered are: various constructions of locally compact quantum groups and their multiplicative unitaries; duality theory for locally compact quantum groups; combinatorial quantization of flat connections associated with SL(2,c); quantum groupoids, especially coming from Depth 2 Extensions of von Neumann algebras, C*-algebras and Rings. Many mathematical results are motivated by problems in theoretical physics. Historical remarks set the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research in which great progress has been achieved in the last few years, with new ties to many other areas of mathematics and physics.