Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS). Recognizing young children's particular cognitive and developmental capabilities, this book powerfully argues for the importance of infusing algebraic thinking into early grade mathematics teaching and illustrates how this has been achieved by teachers in U.S. and Chinese contexts. Documenting best practice and students' responses to example-based instruction, the text demonstrates that this TEPS approach - which involves the use of worked examples, representations, and deep questions - helps students learn and master fundamental mathematical ideas, making it highly effective in developing algebraic readiness and mathematical understanding. This text will benefit post-graduate students, researchers, and academics in the fields of mathematics, STEM, and elementary education, as well as algebra research more broadly. Those interested in teacher education, classroom practice, and developmental and cognitive psychology will also find this volume of interest.

Linear Algebra: An Inquiry-based Approach is written to give instructors a tool to teach students to develop a mathematical concept from first principles. The Inquiry-based Approach is central to this development. The text is organized around and offers the standard topics expected in a first undergraduate course in linear algebra. In our approach, students begin with a problem and develop the mathematics necessary to describe, solve, and generalize it. Thus students learn a vital skill for the 21st century: the ability to create a solution to a problem. This text is offered to foster an environment that supports the creative process. The twin goals of this textbook are: *Providing opportunities to be creative, *Teaching "ways of thinking" that will make it easier for to be creative. To motivate the development of the concepts and techniques of linear algebra, we include more than two hundred activities on a wide range of problems, from purely mathematical questions, through applications in biology, computer science, cryptography, and more. Table of Contents Introduction and Features For the Student . . . and Teacher Prerequisites Suggested Sequences 1 Tuples and Vectors 2 Systems of Linear Equations 3 Transformations 4 Matrix Algebra 5 Vector Spaces 6 Determinants 7 Eigenvalues and Eigenvectors 8 Decomposition 9 Extras Bibliography Index Bibliography Jeff Suzuki is Associate Professor of Mathematics at Brooklyn College and holds a Ph.D. from Boston University. His research interests include mathematics education, history of mathematics, and the application of mathematics to society and technology. He is a two-time winner of the prestigious Carl B. Allendoerfer Award for expository writing. His publications have appeared in The College Mathematics Journals; Mathematics Magazine; Mathematics Teacher; and the American Mathematical Society's blog on teaching and learning mathematics. His YouTube channel (http://youtube.com/jeffsuzuki1) includes videos on mathematical subjects ranging from elementary arithmetic to linear algebra, cryptography, and differential equations.

This introduction to cryptography employs a programming-oriented approach to study the most important cryptographic schemes in current use and the main cryptanalytic attacks against them. Discussion of the theoretical aspects, emphasizing precise security definitions based on methodological tools such as complexity and randomness, and of the mathematical aspects, with emphasis on number-theoretic algorithms and their applications to cryptography and cryptanalysis, is integrated with the programming approach, thus providing implementations of the algorithms and schemes as well as examples of realistic size.

A distinctive feature of the author's approach is the use of Maple as a programming environment in which not just the cryptographic primitives but also the most important cryptographic schemes are implemented following the recommendations of standards bodies such as NIST, with many of the known cryptanalytic attacks implemented as well. The purpose of the Maple implementations is to let the reader experiment and learn, and for this reason the author includes numerous examples. The book discusses important recent subjects such as homomorphic encryption, identity-based cryptography and elliptic curve cryptography. The algorithms and schemes which are treated in detail and implemented in Maple include AES and modes of operation, CMAC, GCM/GMAC, SHA-256, HMAC, RSA, Rabin, Elgamal, Paillier, Cocks IBE, DSA and ECDSA. In addition, some recently introduced schemes enjoying strong security properties, such as RSA-OAEP, Rabin-SAEP, Cramer--Shoup, and PSS, are also discussed and implemented. On the cryptanalysis side, Maple implementations and examples are used to discuss many important algorithms, including birthday and man-in-the-middle attacks, integer factorization algorithms such as Pollard's rho and the quadratic sieve, and discrete log algorithms such as baby-step giant-step, Pollard's rho, Pohlig--Hellman and the index calculus method.

This textbook is suitable for advanced undergraduate and graduate students of computer science, engineering and mathematics, satisfying the requirements of various types of courses: a basic introductory course; a theoretically oriented course whose focus is on the precise definition of security concepts and on cryptographic schemes with reductionist security proofs; a practice-oriented course requiring little mathematical background and with an emphasis on applications; or a mathematically advanced course addressed to students with a stronger mathematical background. The main prerequisite is a basic knowledge of linear algebra and elementary calculus, and while some knowledge of probability and abstract algebra would be helpful, it is not essential because the book includes the necessary background from these subjects and, furthermore, explores the number-theoretic material in detail. The book is also a comprehensive reference and is suitable for self-study by practitioners and programmers."

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

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.

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.

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.

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.

After being an open question for sixty years the Tarski conjecture was answered in the affirmative by Olga Kharlampovich and Alexei Myasnikov and independently by Zlil Sela. Both proofs involve long and complicated applications of algebraic geometry over free groups as well as an extension of methods to solve equations in free groups originally developed by Razborov. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. This material includes a complete exposition of the theory of fully residually free groups or limit groups as well a complete description of the algebraic geometry of free groups. Also included are introductory material on combinatorial and geometric group theory and first-order logic. There is then a short outline of the proof of the Tarski conjectures in the manner of Kharlampovich and Myasnikov.

Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design.

Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations, tabulations, and easy-to-follow algebraic proofs.

The book includes many worked examples to show how the algebra works in practice and is essential reading for anyone involved in designing 3D geometric algorithms.

This book is an updated and extended version of Completely Positive Matrices (Abraham Berman and Naomi Shaked-Monderer, World Scientific 2003). It contains new sections on the cone of copositive matrices, which is the dual of the cone of completely positive matrices, and new results on both copositive matrices and completely positive matrices.The book is an up to date comprehensive resource for researchers in Matrix Theory and Optimization. It can also serve as a textbook for an advanced undergraduate or graduate course.

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

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.

With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies

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.

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.

Why do we develop extreme attitudes to others? Can our personality contribute to our prejudices? How do we reduce prejudice and discrimination? The Psychology of Prejudice explores different forms of prejudice and discrimination, from racial jokes to genocide. It looks at what might cause our prejudiced attitudes, including our personalities, social influences, group identity, and evolutionary factors, and how prejudice can be reduced through education, campaigning, and consciousness raising. Offering insights into a topic of great public concern and debate, The Psychology of Prejudice shows us how we can confront our prejudiced attitudes and contribute to greater tolerance and understanding.

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.

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.

Praise is perhaps the most widely used technique to influence others. When used appropriately, praise can motivate people, make them feel better, and improve their social relationships. Often, however, praise fails to work as intended and may even cause harm. Psychological Perspectives on Praise reviews and integrates psychological theory and research to provide an overarching perspective on praise. With contributions from leading scholars in the field, this book amalgamates diverse theoretical and empirical perspectives on praise. The book starts with providing an overview of prominent theories that seek to explain the effects of praise, including self-enhancement theory, self-verification theory, attribution theory, and self-determination theory. It then discusses several lines of empirical research on how praise impacts competence and motivation, self-perceptions (e.g., self-esteem and narcissism), and social relationships. It does so in a range of contexts, including children's learning at school, employees' commitment at work, and people's behavior within romantic relationships. The book concludes by showing how praise can be understood in its developmental and cultural context. Revealing that praise is a message rich in information about ourselves and our social environments, this book will be of interest to social, organizational, personality, developmental, and educational psychologists; students in psychology and related disciplines; and practitioners including teachers, managers, and counselors who use praise in their daily practice.

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.

From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras." The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K."

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

The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications. It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications. In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here. The book also includes generalization of Lie symmetries for fractional integro differential equations. Features Provides a solid basis for understanding fractional calculus, before going on to explore in detail Lie Symmetries and their applications Useful for PhD and postdoc graduates, as well as for all mathematicians and applied researchers who use the powerful concept of Lie symmetries Filled with various examples to aid understanding of the topics