* Includes interdisciplinary contributions and brings together research on a range of extreme behaviors in one volume, by making theoretical links between different contexts * Explores the brain, hormones, and behaviour to offer insights into the mechanisms and processes that enable extremism to explain their occurrence and the conditions under which they may be likely to emerge * Ideal reading for high-level students taking courses on extremism, academics, and professionals dealing with extreme behavior

* Solid research basis, drawing on findings from a 4-year research project with in-depth interviews with judges, attorneys, and seasoned forensic neuropsychologists and psychologists as well as further interviews with professionals in other fields such as engineering, physics and economics. * Provides focused attention on how experts interact with judges, attorneys, and juries * Challenges experts to avoid the traps of professional jargon and traditional manners of presenting information/knowledge/opinions. * Provides a step-by-step approach to orienting the new academic to expert witnessing

Introduces a new web-based optimizer for Geometric algebra algorithms; Supports many programming languages as well as hardware; Covers the advantages of High-dimensional algebras; Includes geometrically intuitive support of quantum computing

This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.

Features: Suitable for PhD candidates and researchers. Requires prerequisites in set theory, general topology and abstract algebra, but is otherwise self-contained.

This proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018. Readers will find some of the latest research conducted by an international group of experts on affine and projective algebraic geometry. The topics covered include group actions and linearization, automorphism groups and their structure as infinite-dimensional varieties, invariant theory, the Cancellation Problem, the Embedding Problem, Mathieu spaces and the Jacobian Conjecture, the Dolgachev-Weisfeiler Conjecture, classification of curves and surfaces, real forms of complex varieties, and questions of rationality, unirationality, and birationality. These papers will be of interest to all researchers and graduate students working in the fields of affine and projective algebraic geometry, as well as on certain aspects of commutative algebra, Lie theory, symplectic geometry and Stein manifolds.

The Event of Psychopoetics overviews and investigates the notion of psychopoetics, a sociopsychological event that involves re-creative slips and that emerges under certain cultural conditions and power relations in the context of everyday interaction and through certain modes of dialoguing and conversing. This transdisciplinary text takes the reader through the thought processes of Deleuze, Guattari, Agamben, Maffesoli, Foucault, Butler, Haraway, and Braidotti, among others, addressing debates that are integral to the critique of psychology and its devices of subjectivization and normalization. Garcia takes a unique approach by reflecting on how psychopoetics contrasts institutionalized dialogues, while constantly emphasizing the generative and transformative potency of social worlds effectuated in the impetuous play of poetics. The book combines the rigor of academic research with the creative display of ideas that open diverse, suggestive lines of reflection on everyday interlocution and its possibilities of reinvention, modes of social existence, and the relation between subjectivity and the designs of power. A truly unique reading experience, this book is ideal for students, instructors, and researchers in the fields of philosophy, social psychology and sociological thought, discourse studies, literary theory, and cultural analysis.

The Event of Psychopoetics overviews and investigates the notion of psychopoetics, a sociopsychological event that involves re-creative slips and that emerges under certain cultural conditions and power relations in the context of everyday interaction and through certain modes of dialoguing and conversing. This transdisciplinary text takes the reader through the thought processes of Deleuze, Guattari, Agamben, Maffesoli, Foucault, Butler, Haraway, and Braidotti, among others, addressing debates that are integral to the critique of psychology and its devices of subjectivization and normalization. Garcia takes a unique approach by reflecting on how psychopoetics contrasts institutionalized dialogues, while constantly emphasizing the generative and transformative potency of social worlds effectuated in the impetuous play of poetics. The book combines the rigor of academic research with the creative display of ideas that open diverse, suggestive lines of reflection on everyday interlocution and its possibilities of reinvention, modes of social existence, and the relation between subjectivity and the designs of power. A truly unique reading experience, this book is ideal for students, instructors, and researchers in the fields of philosophy, social psychology and sociological thought, discourse studies, literary theory, and cultural analysis.

--Core textbook featuring accessible but advanced coverage of theory, research, and applications in nonverbal communication from renowned scholars --Usable for undergraduate and graduate courses in communication and psychology departments --Includes a new chapter on identity and impression management, as well as fully updated research coverage throughout --Online resources include an extensive instructor's manual and test bank

Features Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer science Every chapter consists of exercises with solution provided online at www.Routledge.com/9780367720292

This work is at the crossroads of a number of mathematical areas, including algebraic geometry, several complex variables, differential geometry, and representation theory. It is the first book to cover complex tori, among the simplest of complex manifolds, which are important to research in the above areas. The book gives a systematic approach to the theory, presents new results, and includes an up-to-date bibliography.

There has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth of new applications, ranging from number theory to geometry, physics to computer vision. This book provides readers with a self-contained introduction to the classical theory as well as modern developments and applications. The text concentrates on the study of binary forms (polynomials) in characteristic zero, and uses analytical as well as algebraic tools to study and classify invariants, symmetry, equivalence and canonical forms. A variety of innovations make this text of interest even to veterans of the subject; these include the use of differential operators and the transform approach to the symbolic method, extension of results to arbitrary functions, graphical methods for computing identities and Hilbert bases, complete systems of rationally and functionally independent covariants, introduction of Lie group and Lie algebra methods, as well as a new geometrical theory of moving frames and applications. Aimed at advanced undergraduate and graduate students the book includes many exercises and historical details, complete proofs of the fundamental theorems, and a lively and provocative exposition.

Spatializing Social Media charts the theoretical and methodological challenges in analyzing and visualizing social media data mapped to geographic areas. It introduces the reader to concepts, theories, and methods that sit at the crossroads between spatial and social network analysis to unpack the conceptual differences between online and face-to-face social networks and the nonlinear effects triggered by social activity that overlaps online and offline. The book is divided into four sections, with the first accounting for the differences between space (the geometrical arrangements that structure and enable forms of interaction) and place (the mechanisms through which social meanings are attached to physical locations). The second section covers the rationale of social network analysis and the ontological differences, stating that relationships, more than individual and independent attributes, are key to understanding of social behavior. The third section covers a range of case studies that successfully mapped social media activity to geographically situated areas and considers the inflection of homophilous dependencies across online and offline social networks. The fourth and last section of the book explores a range of networks and discusses methods for and approaches to plotting a social network graph onto a map, including the purpose-built R package Spatial Social Media. The book takes a non-mathematical approach to social networks and spatial statistics suitable for postgraduate students in sociology, psychology and the social sciences.

This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.

This book is a conference proceedings based on the 1996 Durham Symposium on "Galois representations in arithmetic algebraic geometry". The title was interpreted loosely and the symposium covered recent developments on the interface between algebraic number theory and arithmetic algebraic geometry. The book reflects this and contains a mixture of articles. Some are expositions of subjects that have received substantial recent attention: Erez on geometric trends in Galois module theory; Mazur on rational points on curves and varieties; Moonen on Shimura varieties in mixed characteristics; Rubin and Scholl on the work of Kato on the Birch-Swinnerton-Dyer conjecture; and Schneider on rigid geometry. Some are research papers by: Coleman and Mazur, Goncharov, Gross, Serre.

This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.

This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.

This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic. The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material, then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields, and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry. About the Author Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published several papers in number theory. For hobbies, he likes to travel and hike. His book, Fundamentals of Linear Algebra, is also published by CRC Press.

This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications. The approach is novel, and the book can be used in undergraduate courses, for example, following a first course in linear algebra, but is also suitable for use in graduate level courses. The book will benefit anyone with a basic background in linear algebra. It defines fundamental concepts in signal processing and wavelet theory, assuming only a familiarity with elementary linear algebra. No background in signal processing is needed. Additionally, the book demonstrates in detail why linear algebra is often the best way to go. Those with only a signal processing background are also introduced to the world of linear algebra, although a full course is recommended. The book comes in two versions: one based on MATLAB, and one on Python, demonstrating the feasibility and applications of both approaches. Most of the code is available interactively. The applications mainly involve sound and images. The book also includes a rich set of exercises, many of which are of a computational nature.

This volume offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inverses and the applications. The book is as self-contained as possible, assuming no prior knowledge of matrix theory and linear algebra. The book first addresses the basic definitions and concepts of an arbitrary generalized matrix inverse with special reference to the calculation of {i,j,...,k} inverse and the Moore-Penrose inverse. Then, the results of LDL* decomposition of the full rank polynomial matrix are introduced, along with numerical examples. Methods for calculating the Moore-Penrose's inverse of rational matrix are presented, which are based on LDL* and QDR decompositions of the matrix. A method for calculating the A(2)T;S inverse using LDL* decomposition using methods is derived as well as the symbolic calculation of A(2)T;S inverses using QDR factorization. The text then offers several ways on how the introduced theoretical concepts can be applied in restoring blurred images and linear regression methods, along with the well-known application in linear systems. The book also explains how the computation of generalized inverses of matrices with constant values is performed. It covers several methods, such as methods based on full-rank factorization, Leverrier-Faddeev method, method of Zhukovski, and variations of the partitioning method.

Based on and enriched by the long-term teaching experience of the authors, this volume covers the major themes of mathematics in engineering and technical specialties. The book addresses the elements of linear algebra and analytic geometry, differential calculus of a function of one variable, and elements of higher algebra. On each theme the authors first present short theoretical overviews and then go on to give problems to be solved. The authors provide the solutions to some typical, relatively difficult problems and guidelines for solving them. The authors consider the development of the self-dependent thinking ability of students in the construction of problems and indicate which problems are relatively difficult. The book is geared so that some of the problems presented can be solved in class, and others are meant to be solved independently. An extensive, explanatory solution of at least one typical problem is included, with emphasis on applications, formulas, and rules. This volume is primarily addressed to advanced students of engineering and technical specialties as well as to engineers/technicians and instructors of mathematics. Key features: Presents the theoretical background necessary for solving problems, including definitions, rules, formulas, and theorems on the particular theme Provides an extended solution of at least one problem on every theme and guidelines for solving some difficult problems Selects problems for independent study as well as those for classroom time, taking into account the similarity of both sets of problems Differentiates relatively difficult problems from others for those who want to study mathematics more deeply Provides answers to the problems within the text rather than at the back of the book, enabling more direct verification of problem solutions Presents a selection of problems and solutions that are very interesting not only for the students but also for professor-teacher staff

Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB(R), and Maple(TM) to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.

Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first few chapters cover foundational topics, including the importance of proofs and a discussion of the properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solutions of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra. New to the second edition Several updated chapters, plus an all-new chapter discussing the construction of the real numbers by means of approximations by rational numbers Includes fifteen short 'essays' that are accessible to undergraduate readers, but which direct interested students to more advanced developments of the material Expanded references Contains chapter exercises with solutions provided online at www.routledge.com/9780367563035

Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first few chapters cover foundational topics, including the importance of proofs and a discussion of the properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solutions of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra. New to the second edition Several updated chapters, plus an all-new chapter discussing the construction of the real numbers by means of approximations by rational numbers Includes fifteen short 'essays' that are accessible to undergraduate readers, but which direct interested students to more advanced developments of the material Expanded references Contains chapter exercises with solutions provided online at www.routledge.com/9780367563035

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."