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 articles in these two volumes arose from papers given at the 1991 International Symposium on Geometric Group Theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. This second volume contains solely a ground breaking paper by Gromov, which provides a fascinating look at finitely generated groups. For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.

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 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.

In the Psychological Insights for Understanding COVID-19 series, international experts introduce important themes in psychological science that engage with people's unprecedented experience of the pandemic, drawing together chapters as they originally appeared before COVID-19 descended on the world. This book explores how COVID-19 has impacted society, and chapters examine a range of societal issues including leadership and politics, community, social status, welfare, social exclusion and accountability. Addressing the social and psychological processes that structure, and are structured by, our social contexts, it shows not only how groups and individuals can come together to manage global crises, but also how these crises can expose weaknesses in our society. The volume also reflects on how we can work together to rebuild society in the aftermath of the pandemic, by cultivating a shared sense of responsibility through social integration and responsible leadership. Showcasing theory and research on key topics germane to the global pandemic, the Psychological Insights for Understanding COVID-19 series offers thought-provoking reading for professionals, students, academics and policy makers concerned with the psychological consequences of COVID-19 for individuals, families and society.

This is the first book to contain a rigorous construction and uniqueness proof for the largest and most famous sporadic simple group, the Monster. The author provides a systematic exposition of the theory of the Monster group, which remains largely unpublished despite great interest from both mathematicians and physicists due to its intrinsic connection with various areas in mathematics, including reflection groups, modular forms and conformal field theory. Through construction via the Monster amalgam - one of the most promising in the modern theory of finite groups - the author observes some important properties of the action of the Monster on its minimal module, which are axiomatized under the name of Majorana involutions. Development of the theory of the groups generated by Majorana involutions leads the author to the conjecture that Monster is the largest group generated by the Majorana involutions.

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.

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.

This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.

Multivariable Calculus with Mathematica is a textbook addressing the calculus of several variables. Instead of just using Mathematica to directly solve problems, the students are encouraged to learn the syntax and to write their own code to solve problems. This not only encourages scientific computing skills but at the same time stresses the complete understanding of the mathematics. Questions are provided at the end of the chapters to test the student's theoretical understanding of the mathematics, and there are also computer algebra questions which test the student's ability to apply their knowledge in non-trivial ways. Features Ensures that students are not just using the package to directly solve problems, but learning the syntax to write their own code to solve problems Suitable as a main textbook for a Calculus III course, and as a supplementary text for topics scientific computing, engineering, and mathematical physics Written in a style that engages the students' interest and encourages the understanding of the mathematical ideas

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.

In this groundbreaking volume, Vezzali and Stathi present their research program within the larger contact literature, examining classic theories and current empirical findings, to show how they can be used to reduce prejudice and negative attitudes. The contact hypothesis (Allport, 1954) posits that in an environment of equality, cooperation, and normative support, contact between members of distinct groups can reduce prejudice. Whilst considerable research supports this hypothesis, how theory can be tested in the field remains relatively unexplored. In this innovative book, Vezzali and Stathi discuss why relying solely on advancing theory without considering applied aspects integral to contact may limit the scope of contact theory and restrict our understanding of complex social phenomena. Exploring fascinating topics such as the role of contact in reducing implicit prejudice and fostering collective action, applying indirect contact, and promoting positive interactions among survivors of natural disasters, Vezzali and Stathi explain how contact theory can be implemented and enhance the societal impact of intergroup contact research. Featuring extensive discussion on intergroup contact literature, future directions, and the necessity of applied research, this book will be essential reading for both students and academics of social and behavioral psychology.

In this groundbreaking volume, Vezzali and Stathi present their research program within the larger contact literature, examining classic theories and current empirical findings, to show how they can be used to reduce prejudice and negative attitudes. The contact hypothesis (Allport, 1954) posits that in an environment of equality, cooperation, and normative support, contact between members of distinct groups can reduce prejudice. Whilst considerable research supports this hypothesis, how theory can be tested in the field remains relatively unexplored. In this innovative book, Vezzali and Stathi discuss why relying solely on advancing theory without considering applied aspects integral to contact may limit the scope of contact theory and restrict our understanding of complex social phenomena. Exploring fascinating topics such as the role of contact in reducing implicit prejudice and fostering collective action, applying indirect contact, and promoting positive interactions among survivors of natural disasters, Vezzali and Stathi explain how contact theory can be implemented and enhance the societal impact of intergroup contact research. Featuring extensive discussion on intergroup contact literature, future directions, and the necessity of applied research, this book will be essential reading for both students and academics of social and behavioral psychology.

Linear Algebra, James R. Kirkwood and Bessie H. Kirkwood, 978-1-4987-7685-1, K29751 Shelving Guide: Mathematics This text has a major focus on demonstrating facts and techniques of linear systems that will be invaluable in higher mathematics and related fields. A linear algebra course has two major audiences that it must satisfy. It provides an important theoretical and computational tool for nearly every discipline that uses mathematics. It also provides an introduction to abstract mathematics. This book has two parts. Chapters 1-7 are written as an introduction. Two primary goals of these chapters are to enable students to become adept at computations and to develop an understanding of the theory of basic topics including linear transformations. Important applications are presented. Part two, which consists of Chapters 8-14, is at a higher level. It includes topics not usually taught in a first course, such as a detailed justification of the Jordan canonical form, properties of the determinant derived from axioms, the Perron-Frobenius theorem and bilinear and quadratic forms. Though users will want to make use of technology for many of the computations, topics are explained in the text in a way that will enable students to do these computations by hand if that is desired. Key features include: Chapters 1-7 may be used for a first course relying on applications Chapters 8-14 offer a more advanced, theoretical course Definitions are highlighted throughout MATLAB (R) and R Project tutorials in the appendices Exercises span a range from simple computations to fairly direct abstract exercises Historical notes motivate the presentation

Making an Impact on Policing and Crime: Psychological Research, Policy and Practice applies a range of case studies and examples of psychological research by international, leading researchers to tackle real-world issues within the field of crime and policing. Making an Impact on Policing and Crime documents the application of cutting-edge research to real-world policing and explains how psychologists' insights have been adapted and developed to offer effective solutions across the criminal justice system. The experts featured in this collection cover a range of psychological topics surrounding the field, including the prevention and reduction of sexual offending and reoffending, the use of CCTV and 'super-recognisers', forensic questioning of vulnerable witnesses, the accuracy of nonverbal and verbal lie detection interview techniques, psychological 'drivers' of political violence, theoretical models of police-community relations, and the social and political significance of urban 'riots'. This collection is a vital resource for practitioners in policing fields and the court system and professionals working with offenders, as well as students and researchers in related disciplines.

Making an Impact on Policing and Crime: Psychological Research, Policy and Practice applies a range of case studies and examples of psychological research by international, leading researchers to tackle real-world issues within the field of crime and policing. Making an Impact on Policing and Crime documents the application of cutting-edge research to real-world policing and explains how psychologists' insights have been adapted and developed to offer effective solutions across the criminal justice system. The experts featured in this collection cover a range of psychological topics surrounding the field, including the prevention and reduction of sexual offending and reoffending, the use of CCTV and 'super-recognisers', forensic questioning of vulnerable witnesses, the accuracy of nonverbal and verbal lie detection interview techniques, psychological 'drivers' of political violence, theoretical models of police-community relations, and the social and political significance of urban 'riots'. This collection is a vital resource for practitioners in policing fields and the court system and professionals working with offenders, as well as students and researchers in related disciplines.

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.

Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on the topic.

The present book is devoted to one of the newest branches of variety theory: varieties of group representations. In addition to its intrinsic value, it has numerous connections with varieties of groups, rings and Lie algebras, polynomial identities, group rings, etc., and provides results, methods and ideas that are of interest to a broad algebraic audience. The book presents a clear and detailed exposition of several central topics in the field, leading from initial definitions and problems to the most current advances and developments. Among the topics treated are stable and unipotent varieties, locally finite-dimensional varieties, the finite basis problem, connections with varieties of groups and associative algebras and their applications.

This book draws on research in psychology and behavioral economics to show how striving to live up to our identity claims profoundly affects our daily lives. The author argues the claims we make about who we are and what we stand for powerfully influence us, and our social world. Asking questions such as: Why do people resist the temptation to cheat when cheating would benefit them greatly and no one would find out? Why do people express different beliefs about climate change when they are first reminded of their political affiliation? Why do people prefer to be compensated for donating blood with cholesterol screening than with money? Miller puts forth a novel and compelling argument regarding how strongly our identity claims affect our daily lives. The book provides explanations for many forms of puzzling behavior, such as why people sometimes act against their economic self-interest, how they avoid situations that test their moral identities, and how they respond to failures to live up to their moral identities. It paints an intriguing picture of people's investment in their identity claims by showing how they seek opportunities to demonstrate their validity, avoid actions and circumstances that challenge their legitimacy, and employ psychological defenses when others challenge their legitimacy. Based on extensive research in the fields of psychology, economics, and political science, this book is fascinating reading for students and academics interested in identity and the self. It also provides an expanded tool kit for those who seek behavioral change in their organization or community.

This book draws on research in psychology and behavioral economics to show how striving to live up to our identity claims profoundly affects our daily lives. The author argues the claims we make about who we are and what we stand for powerfully influence us, and our social world. Asking questions such as: Why do people resist the temptation to cheat when cheating would benefit them greatly and no one would find out? Why do people express different beliefs about climate change when they are first reminded of their political affiliation? Why do people prefer to be compensated for donating blood with cholesterol screening than with money? Miller puts forth a novel and compelling argument regarding how strongly our identity claims affect our daily lives. The book provides explanations for many forms of puzzling behavior, such as why people sometimes act against their economic self-interest, how they avoid situations that test their moral identities, and how they respond to failures to live up to their moral identities. It paints an intriguing picture of people's investment in their identity claims by showing how they seek opportunities to demonstrate their validity, avoid actions and circumstances that challenge their legitimacy, and employ psychological defenses when others challenge their legitimacy. Based on extensive research in the fields of psychology, economics, and political science, this book is fascinating reading for students and academics interested in identity and the self. It also provides an expanded tool kit for those who seek behavioral change in their organization or community.

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.

This is the second of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure. Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely generated. The final three papers in this volume investigate factorization in a broad sense. The first paper by Celikbas and Eubanks-Turner discusses the partially ordered set of prime ideals of the projective line over the integers. The editors have also included a paper on zero divisor graphs by Coykendall, Sather-Wagstaff, Sheppardson and Spiroff. The final paper, by Chapman and Krause, concerns non-unique factorization.