There is good reason to be excited about Linear Algebra. With the world becoming increasingly digital, Linear Algebra is gaining more and more importance. When we send texts, share video, do internet searches, there are Linear Algebra algorithms in the background that make it work. This concise introduction to Linear Algebra is authored by a leading researcher presents a book that covers all the requisite material for a first course on the topic in a more practical way. The book focuses on the development of the mathematical theory and presents many applications to assist instructors and students to master the material and apply it to their areas of interest, whether it be to further their studies in mathematics, science, engineering, statistics, economics, or other disciplines. Linear Algebra has very appealing features: *It is a solid axiomatic based mathematical theory that is accessible to a large variety of students. *It has a multitude of applications from many different fields, ranging from traditional science and engineering applications to more 'daily life' applications. *It easily allows for numerical experimentation through the use of a variety of readily available software (both commercial and open source). Several suggestions of different software are made. While MATLAB is certainly still a favorite choice, open-source programs such as Sage (especially among algebraists) and the Python libraries are increasingly popular. This text guides the student to try out different programs by providing specific commands.

The Psychology of Political Polarization was inspired by the notion that, to understand the momentum of radical political movements, it is important to understand the attitudes of individual citizens who support such movements. Leading political psychologists have contributed to this important book, in which they share their latest ideas about political polarization - a complex phenomenon that cannot be traced back to a single cause, and that is associated with intolerance, overconfidence, and irrational beliefs. The book explores the basis of political polarization as being how citizens think and feel about people with a different worldview, how they perceive minority groups, and how much they trust leaders and experts on pressing societal issues such as climate change, health, international relations, and poverty. The chapters are organized into two sections that examine what psychological processes and what social factors contribute to polarization among regular citizens. The book also describes practical strategies and interventions to depolarize people. The book offers a state-of-the-art introduction to the psychology of political polarization which will appeal to the academic market and political professionals.

The recent rise of populist politics represent a major challenge for liberal democracies. This important book explores the psychological reasons for the rise of populism, featuring contributions from leading international researchers in the fields of psychology and political science. Unlike liberal democracy based on the Enlightenment values of individual freedom, autonomy and rationality, both right-wing and left-wing populism offer collectivist, autocratic formulations reminiscent of the evolutionary history and tribal instincts of our species. The book offers a comprehensive overview of the psychology of populism, covering such phenomena as identity seeking, anger and fear, collective narcissism, grievance, norms, perceptions of powerlessness and deprivation, authoritarianism, nationalism, radicalism, propaganda and persuasion, ethnocentrism, xenophobia and the effects of globalization. The book is divided into four parts. Part I deals with the motivational and emotional factors that attract voters to populist causes, and the human needs and values that populist movements satisfy. Part II analyzes the cognitive features of populist appeals, especially their emphasis on simplicity, epistemic certainty and moral absolutism. Part III turns to one of the defining features of populism: its offer of a powerful tribal identity and collectivist ideology that provide meaning and personal significance to its followers. Finally, in Part IV, the propaganda tactics used by populist movements are analysed, including the role of charismatic leadership, authoritarianism, and nationalism and the use of conspiracy narratives and persuasive strategies. This is fascinating reading on a highly topical issue. The book will be of interest to students, researchers, and applied professionals in all areas of psychology and the social sciences as a textbook or reference book, and to anyone interested in the global rise of populism. Please follow this link for an insightful interview by one of the editors of the book - Joseph P. Forgas: https://www.routledge.com/blog/article/editor-interview-the-psychology-of-populism We have also created a short promotional video for the book here - https://www.youtube.com/watch?v=iK1BEF8WyMA.

The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.

Imparts a self--contained development of the algebraic theory of Kac--Moody algebras, their representations and close relatives----the Virasoro and Heisenberg algebras. Focuses on developing the theory of triangular decompositions and part of the Kac--Moody theory not specific to the affine case. Also covers lattices, and finite root systems, infinite--dimensional theory, Weyl groups and conjugacy theorems.

When it comes to relationships, there's no shortage of advice from self-help 'experts', pick-up artists, and glossy magazines. But modern-day myths of attraction often have no basis in fact or - worse - are rooted in little more than misogyny. Based on science rather than self-help cliches, 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 'laws of attraction', no fool-proof methods or strategies for getting someone to date you. But this isn't to say that there's nothing to be gained from studying attraction. Based on science rather than self-help cliches, 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.

When it comes to relationships, there's no shortage of advice from self-help 'experts', pick-up artists, and glossy magazines. But modern-day myths of attraction often have no basis in fact or - worse - are rooted in little more than misogyny. Based on science rather than self-help cliches, 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 'laws of attraction', no fool-proof methods or strategies for getting someone to date you. But this isn't to say that there's nothing to be gained from studying attraction. Based on science rather than self-help cliches, 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.

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.

Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.

Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.

Recently, many books on multiobjective programming have been published. However, only a few books have been published, in which multiobjective programming under the randomness and the fuzziness are investigated. On the other hand, several books on multilevel programming have been published, in which multiple decision makers are involved in hierarchical decision situations. In this book, we introduce the latest advances in the field of multiobjective programming and multilevel programming under uncertainty. The reader can immediately use proposed methods to solve multiobjective programming and multilevel programming, which are based on linear programming or convex programming technique. Organization of each capter is summarized as follows. In Chapter 2, multiobjective programming problems with random variables are formulated, and the corresponding interactive algorithms are developed to obtain a satisfactory solution, in which the fuzziness of human's subjective judgment for permission levels are considered. In Chapter 3, multiobjective programming problems with fuzzy random variables are formulated, and the corresponding interactive algorithms are developed to obtain a satisfactory solution, in which not only the uncertainty of fuzzy random variables but also the fuzziness of human's subjective judgment for permission levels are considered. In Chapter 4, multiobjective multilevel programming is discussed, and the interactive algorithms are developed to obtain a satisfactory solution, in which the hierarchical decision structure of multiple decision makers is reflected. In Chapter 5, two kinds of farm planning problems are solved by applying the proposed method, in which cost coefficients of crops are expressed by random variables.

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.

In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems.

But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether's achievements were remembered, and sometimes figure in quick historical accounts of the time.

This book carries a translation of Noether's original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether's results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins."

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.

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.

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.

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.

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 set of notes is an activity-oriented introduction to linear and multilinear algebra. The great majority of the most elementary results in these subjects are straightforward and can be verified by the thoughtful student. Indeed, that is the main point of these notes - to convince the beginner that the subject is accessible. In the material that follows there are numerous indicators that suggest activity on the part of the reader: words such as 'proposition', 'example', 'theorem', 'exercise', and 'corollary', if not followed by a proof (and proofs here are very rare) or a reference to a proof, are invitations to verify the assertions made.These notes are intended to accompany an (academic) year-long course at the advanced undergraduate or beginning graduate level. (With judicious pruning most of the material can be covered in a two-term sequence.) The text is also suitable for a lecture-style class, the instructor proving some of the results while leaving others as exercises for the students.This book has tried to keep the facts about vector spaces and those about inner product spaces separate. Many beginning linear algebra texts conflate the material on these two vastly different subjects.

This book explains how people can be radically manipulated by extreme groups and leaders to engage in incomprehensible and often dangerous acts through psychologically isolating situations of extreme social influence. These methods are used in totalitarian states, terrorist groups and cults, as well as in controlling personal relationships. Illustrated with compelling stories from a range of cults and totalitarian systems, Stein's book defines and analyses the common identifiable traits that underlie these groups, emphasizing the importance of maintaining open yet supportive personal networks. Using original attachment theory-based research this book highlights the dangers of closed, isolating relationships and the closed belief systems that justify them, and demonstrates the psychological impact of these environments, ending with evidence-based recommendations to support an educational approach to awareness and prevention. Featuring a foreword by John Horgan, the new edition has been fully updated to include recent work on political extremism and radicalization and totalitarian systems, as well as the recent highly publicized NXIVM case. Terror, Love and Brainwashing, second edition is essential reading for professionals, policy makers, legal professionals, educators and cult survivors and their families themselves.

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.

Basic Algebra is the first volume of a new and revised edition of P.M. Cohn's classic three-volume text Algebra which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two self-contained, companion volumes, covering advanced topics in algebra for second- and third-year undergraduate and postgraduate research students. In this first volume, the author covers the important results of algebra; the companion volume, Further Algebra and Applications, brings more advanced topics and focuses on the applications. Readers should have some knowledge of linear algebra and have met groups and fields before, although all the essential facts and definitions are recalled. The coverage is comprehensive and includes topics such as: - Groups - lattices and categories - rings, modules and algebras - fields The author gives a clear account, supported by worked examples, with full proofs. There are numerous exercises with occasional hints, and some historical remarks.

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