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 is an extremely versatile and useful subject. It rewards those who study it with powerful computational tools, lessons about how mathematical theory is built, examples for later study in other classes, and much more. Functional Linear Algebra is a unique text written to address the need for a one-term linear algebra course where students have taken only calculus. It does not assume students have had a proofs course. The text offers the following approaches: More emphasis is placed on the idea of a linear function, which is used to motivate the study of matrices and their operations. This should seem natural to students after the central role of functions in calculus. Row reduction is moved further back in the semester and vector spaces are moved earlier to avoid an artificial feeling of separation between the computational and theoretical aspects of the course. Chapter 0 offers applications from engineering and the sciences to motivate students by revealing how linear algebra is used. Vector spaces are developed over R, but complex vector spaces are discussed in Appendix A.1. Computational techniques are discussed both by hand and using technology. A brief introduction to Mathematica is provided in Appendix A.2. As readers work through this book, it is important to understand the basic ideas, definitions, and computational skills. Plenty of examples and problems are provided to make sure readers can practice until the material is thoroughly grasped. Author Dr. Hannah Robbins is an associate professor of mathematics at Roanoke College, Salem, VA. Formerly a commutative algebraist, she now studies applications of linear algebra and assesses teaching practices in calculus. Outside the office, she enjoys hiking and playing bluegrass bass.

* The first book of its kind to approach the topic of humor from a social psychological perspective. * Includes contributions from leading international scholars to offer a broad, global overview of the social psychology of humor. * Focuses on current, cutting-edge research to provide future directions in the field for years to come.

By studying applications in radar, telecommunications and digital image restoration, this monograph discusses signal processing techniques based on bispectral methods. Improved robustness against different forms of noise as well as preservation of phase information render this method a valuable alternative to common power-spectrum analysis used in radar object recognition, digital wireless communications, and jitter removal in images.

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.

Scientific Computing with MATLAB (R), Second Edition improves students' ability to tackle mathematical problems. It helps students understand the mathematical background and find reliable and accurate solutions to mathematical problems with the use of MATLAB, avoiding the tedious and complex technical details of mathematics. This edition retains the structure of its predecessor while expanding and updating the content of each chapter. The book bridges the gap between problems and solutions through well-grouped topics and clear MATLAB example scripts and reproducible MATLAB-generated plots. Students can effortlessly experiment with the scripts for a deep, hands-on exploration. Each chapter also includes a set of problems to strengthen understanding of the material.

Originally published in 1992, Channeling is a comprehensive bibliography on the subject of channeling. The book defines channeling as any message received or conveyed from transcendent entities and covers material on the history of channeling, those that have claimed to transcend death, contact with UFOs and contemporary channeling groups. The book acts as a research guide and seeks to outline the historical roots of channeling, explaining its major teachings and considers its significance as a spiritual movement. It provides sources from books, booklets, articles, and ephemeral material and offers a comprehensive list of both primary and secondary materials related to channeling, the bibliography takes the most diverse and useful sources of the time. This volume although published almost 30 years ago, still provides a unique and insightful collection for academics of religion, in particular those researching spiritualism and the occult.

The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.

The book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by demonstrating how these techniques can be applied to investigate qualitative properties of the solutions of fractional systems. Since many applications have been included, the demonstrated techniques and models can be used in training students in mathematical modeling and in the study and development of fractional-order models.

This book presents a unified algebraic approach to stabilization problems of linear boundary control systems with no assumption on finite-dimensional approximations to the original systems, such as the existence of the associated Riesz basis. A new proof of the stabilization result for linear systems of finite dimension is also presented, leading to an explicit design of the feedback scheme. The problem of output stabilization is discussed, and some interesting results are developed when the observability or the controllability conditions are not satisfied.

A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.

"Taken together, the body of information contained in this book provides readers with a bird's-eye view of different aspects of exciting work at the convergence of disciplines that will ultimately lead to a future where we understand how immunity is regulated, and how we can harness this knowledge toward practical ends that reduce human suffering. I commend the editors for putting this volume together." -Arup K. Chakraborty, Robert T. Haslam Professor of Chemical Engineering, and Professor of Physics, Chemistry, and Biological Engineering, Massachusetts Institute of Technology, Cambridge, USA New experimental techniques in immunology have produced large and complex data sets that require quantitative modeling for analysis. This book provides a complete overview of computational immunology, from basic concepts to mathematical modeling at the single molecule, cellular, organism, and population levels. It showcases modern mechanistic models and their use in making predictions, designing experiments, and elucidating underlying biochemical processes. It begins with an introduction to data analysis, approximations, and assumptions used in model building. Core chapters address models and methods for studying immune responses, with fundamental concepts clearly defined. Readers from immunology, quantitative biology, and applied physics will benefit from the following: Fundamental principles of computational immunology and modern quantitative methods for studying immune response at the single molecule, cellular, organism, and population levels. An overview of basic concepts in modeling and data analysis. Coverage of topics where mechanistic modeling has contributed substantially to current understanding. Discussion of genetic diversity of the immune system, cell signaling in the immune system, immune response at the cell population scale, and ecology of host-pathogen interactions.

Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces and presents several applications and connections with fixed point theory. It contains an abundant and updated bibliography and provides comparisons between various investigations made in recent years in the field of computational nonlinear analysis. The book also provides recent advancements in the study of iterative procedures and can be used as a source to obtain the proper method to use in order to solve a problem. The book assumes a basic background in Mathematical Statistics, Linear Algebra and Numerical Analysis and may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences or Applied Sciences. Moreover, the newest techniques used to study the dynamics of iterative methods are described and used in the book and they are compared with the classical ones.

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 is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

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."

This book describes how, in the era of megamedia culture, aggression in communication constitutes a threat to the communication community. Based on the theoretical incorporation of transcendental pragmatics, the book explores how conceptualizing the phenomena of megamedia aggression from this perspective and diagnosing their destructive force are essential for: postulating the need for constructing a theory of media communication closely related to the model of discursive rationality, giving this theory a critical and normative character, and embedding it in the perspective of the project of social co-responsibility and in the plan for an ethics of co-responsibility. Combining key elements of media theory, the philosophy of communication, the concept of normative ethics and the fields of social psychology and social anthropology, this book will be of great interest to scholars and students in the areas of communication studies, philosophy, anthropology, psychology and psychoanalysis.

An authoritative, full-year course on both group theory and ordinary character theory—essential tools for mathematics and the physical sciences

One of the few treatments available combining both group theory and character theory, Groups and Characters is an effective general textbook on these two fundamentally connected subjects. Presuming only a basic knowledge of abstract algebra as in a first-year graduate course, the text opens with a review of background material and then guides readers carefully through several of the most important aspects of groups and characters, concentrating mainly on finite groups.

Challenging yet accessible, Groups and Characters features:

• An extensive collection of examples surveying many different types of groups, including Sylow subgroups of symmetric groups, affine groups of fields, the Mathieu groups, and symplectic groups
• A thorough, easy-to-follow discussion of Pólya-Redfield enumeration, with applications to combinatorics
• Inclusive explorations of the transfer function and normal complements, induction and restriction of characters, Clifford theory, characters of symmetric and alternating groups, Frobenius groups, and the Schur index
• Illuminating accounts of several computational aspects of group theory, such as the Schreier-Sims algorithm, Todd-Coxeter coset enumeration, and algorithms for generating character tables

As valuable as Groups and Characters will prove as a textbook for mathematicians, it has broader applications. With chapters suitable for use as independent review units, along with a full bibliography and index, it will be a dependable general reference for chemists, physicists, and crystallographers.

George Andrews is one of the most influential figures in number theory and combinatorics. In the theory of partitions and q-hypergeometric series and in the study of Ramanujan's work, he is the unquestioned leader. To suitably honor him during his 70th birthday year, an International Conference on Combinatory Analysis was held at The Pennsylvania State University during December 5-7, 2008. Three issues of the Ramanujan Journal comprising Volume 23 were published in 2010 as the refereed proceedings of that conference. The Ramanujan Journal was proud to bring out that volume honoring one of its Founding Editors. In view of the great interest that the mathematical community has in the influential work of Andrews, it was decided to republish Volume 23 of The Ramanujan Journal in this book form, so that the refereed proceedings are more readily available for those who do not subscribe to the journal but wish to possess this volume. As a fitting tribute to George Andrews, many speakers from the conference contributed research papers to this volume which deals with a broad range of areas that signify the research interests of George Andrews. In reproducing Volume 23 of The Ramanujan Journal in this book form, we have included two papers-one by Hei-Chi Chan and Shaun Cooper, and another by Ole Warnaar-which were intended for Volume 23 of The Ramanujan Journal, but appeared in other issues. The enormous productivity of George Andrews remains unabated in spite of the passage of time. His immensely fertile mind continues to pour forth seminal ideas year after year. He has two research papers in this volume. May his eternal youthfulness and his magnificent research output continue to inspire and influence researchers in the years ahead.

The continuous Hochschild cohomology of dual normal modules over a von Neumann algebra is the subject of this book. The necessary technical results are developed assuming a familiarity with basic C*-algebra and von Neumann algebra theory, including the decomposition into two types, but no prior knowledge of cohomology theory is required and the theory of completely bounded and multilinear operators is given fully. Central to this book are those cases when the continuous Hochschild cohomology H(superscript n)(M, M) of the von Neumann algebra M over itself is zero. The material in this book lies in the area common to Banach algebras, operator algebras and homological algebra, and will be of interest to researchers from these fields.

* The first book of its kind to approach the topic of humor from a social psychological perspective. * Includes contributions from leading international scholars to offer a broad, global overview of the social psychology of humor. * Focuses on current, cutting-edge research to provide future directions in the field for years to come.

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 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.

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 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.