Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.

Peirce's Scientific Metaphysics is the first book devoted to understanding Charles Sanders Peirce's (1839-1914) metaphysics from the perspective of the scientific questions that motivated his thinking. Deftly situating Peirce's often original and pathbreaking ideas within their appropriate historical and scientific contexts, Reynolds traces his reliance upon the law of large numbers, which illustrated for Peirce the emergence of a stable order and regularity from a multitude of chance events, throughout his writings on late nineteenth-century physics, chemistry, biology, psychology, and cosmology. Along the way, Peirce's vision of an indeterministic and evolutionary cosmology is contrasted with the thought of other important late nineteenth-century scientists and philosophers, such as James Clerk Maxwell, Ludwig Boltzmann, William Thomson (Lord Kelvin), Herbert Spencer, Charles Darwin, and Ernst Haeckel. While offering a detailed account of the scientific ideas and theories essential for understanding Peirce's metaphysical system (e.g., the irreversibility of time and the reversibility of physical laws, the statistical law of large numbers), this book is written in a manner accessible to the non-specialist. This will make it especially attractive to students of Peirce's philosophy who lack familiarity with the scientific and mathematical ideas that are so central to his thought. Those with an interest in the history and philosophy of science, especially concerning the application of statistical and probabilistic thinking to physics, chemistry, biology, psychology, and cosmology, will find this discussion of Peirce's philosophy invaluable.

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.
Key Features
- Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
- Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
- Introduces each new topic with a clear, concise explanation.
- Includes numerous examples linking fundamental principles with applications.
- Solidifies the reader's understanding with numerous end-of-chapter problems.
-Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
-Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
-Introduces each new topic with a clear, concise explanation.
-Includes numerous examples linking fundamental principles with applications.
-Solidifies the reader's understanding with numerous end-of-chapter problems.

This book collects and coherently presents the research that has been undertaken since the author's previous book Module Theory (1998). In addition to some of the key results since 1995, it also discusses the development of much of the supporting material. In the twenty years following the publication of the Camps-Dicks theorem, the work of Facchini, Herbera, Shamsuddin, Puninski, Prihoda and others has established the study of serial modules and modules with semilocal endomorphism rings as one of the promising directions for module-theoretic research. Providing readers with insights into the directions in which the research in this field is moving, as well as a better understanding of how it interacts with other research areas, the book appeals to undergraduates and graduate students as well as researchers interested in algebra.

The Enhancing Diversity in Graduate Education (EDGE) Program began twenty years ago to provide support for women entering doctoral programs in the mathematical sciences. With a steadfast commitment to diversity among participants, faculty, and staff, EDGE initially alternated between Bryn Mawr and Spelman Colleges. In later years, EDGE has been hosted on campuses around the nation and expanded to offer support for women throughout their graduate school and professional careers. The refereed papers in A Celebration of the EDGE Program's Impact on the Mathematics Community and Beyond range from short memoirs, to pedagogical studies, to current mathematics research. All papers are written by former EDGE participants, mentors, instructors, directors, and others connected to EDGE. Together, these papers offer compelling testimony that EDGE has produced a diverse new generation of leaders in the mathematics community. This volume contains technical and non-technical works, and it is intended for a far-reaching audience, including mathematicians, mathematics teachers, diversity officers, university administrators, government employees writing educational or science policy, and mathematics students at the high school, college, and graduate levels. By highlighting the scope of the work done by those supported by EDGE, the volume offers strong evidence of the American Mathematical Society's recognition that EDGE is "a program that makes a difference." This volume offers unique testimony that a 20-year old summer program has expanded its reach beyond the summer experience to produce a diverse new generation of women leaders, nearly half of whom are underrepresented women. While some books with a women-in-math theme focus only on one topic such as research or work-life balance, this book's broad scope includes papers on mathematics research, teaching, outreach, and career paths.

This volume resulted from presentations given at the international "Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", that took place at the Instituto de Ciencias Matematicas (ICMAT) in Madrid, Spain. It combines overview and research articles on recent and ongoing developments, as well as new research directions. Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowned experts in numerical analysis of differential equations, provide a compelling answer to this question. After this introductory chapter a collection of high-quality research articles aim at exploring recent and ongoing developments, as well as new research directions in the areas of geometric integration methods for differential equations, nonlinear systems interconnections, and discrete mechanics. One of the highlights is the unfolding of modern algebraic and combinatorial structures common to those topics, which give rise to fruitful interactions between theoretical as well as applied and computational perspectives. The volume is aimed at researchers and graduate students interested in theoretical and computational problems in geometric integration theory, nonlinear control theory, and discrete mechanics.

This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.

New 2017 Cambridge A Level Maths and Further Maths resources to help students with learning and revision. Written for the OCR AS/A Level Further Mathematics specification for first teaching from 2017, this print Student Book covers the Mechanics content for AS and A Level. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with an emphasis on skills development and the synoptic nature of the course. Includes answers to aid independent study.

In Pi ( ) in Nature, Art, and Culture Marcel Danesi revisits the importance of as a pattern in the structure of reality, fitting in with the Pythagorean view of Order. Pi has cropped up in formulas that describe natural and physical structures which, on the surface, seem to have nothing to do with a circle, but might harbor the archetype of circularity as a principle. Through , this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science,' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.

Fundamentals of Calculus for Teachers helps readers connect the dots between key calculus concepts and the mathematics content taught in the middle grades, namely fourth through eighth grade in the United States. The text prepares future instructors to fully understand the mathematical content taught in lower and higher grades, build upon the knowledge their students will bring to the classroom, and prepare students for study of more advanced topics. The book focuses on broad concepts rather than detailed techniques. Over the course of five targeted chapters, students are introduced to key calculus concepts that relate to limits, derivatives, and integrals. Each chapter begins with a description of prerequisite knowledge and brief warmup exercises to prepare the reader for forthcoming content. Students are guided through a set of exercises that demonstrate the concepts in action, with distinct opportunities for input from their instructor and the use of technology (graphing calculators, spreadsheets, etc.) to encourage practical application. Designed to help students sharpen their conceptual knowledge of calculus concepts, Fundamentals of Calculus for Teachers is an ideal resource for courses that prepare future instructors to teach classes in middle-grades mathematics.

Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.

International authorities from Canada, Denmark, England, Germany, Russia and South Africa focus on research on fractal geometry and the best practices in software, theoretical mathematical algorithms, and analysis. They address the rich panoply of manifold applications of fractal geometry available for study and research in science and industry: i.e., remote sensing, mapping, texture creations, pattern recognition, image compression, aeromechanical systems, cryptography and financial analysis. Economically priced, this important and authoritative reference source for research and study cites over 230 references to the literature, copiously illustrated with over 320 diagrams and photographs. The book is published for The Institute of Mathematics and its Applications, co-sponsored with The Institute of Physics and The Institution of Electrical Engineers.
Outlines research on fractal geometry and the best practices in software, theoretical mathematical algorithms, and analysisInternational authorities from around the world address the rich panoply of manifold applications of fractal geometry available for study and research in science and industryAddresses applications in key research fields of remote sensing, mapping, texture creations, pattern recognition, image compression, aeromechanical systems, cryptography and financial analysis

This book focuses on the spatial distribution of landslide hazards of the Darjeeling Himalayas. Knowledge driven methods and statistical techniques such as frequency ratio model (FRM), information value model (IVM), logistic regression model (LRM), index overlay model (IOM), certainty factor model (CFM), analytical hierarchy process (AHP), artificial neural network model (ANN), and fuzzy logic have been adopted to identify landslide susceptibility. In addition, a comparison between various statistical models were made using success rate cure (SRC) and it was found that artificial neural network model (ANN), certainty factor model (CFM) and frequency ratio based fuzzy logic approach are the most reliable statistical techniques in the assessment and prediction of landslide susceptibility in the Darjeeling Himalayas. The study identified very high, high, moderate, low and very low landslide susceptibility locations to take site-specific management options as well as to ensure developmental activities in theDarjeeling Himalayas. Particular attention is given to the assessment of various geomorphic, geotectonic and geohydrologic attributes that help to understand the role of different factors and corresponding classes in landslides, to apply different models, and to monitor and predict landslides. The use of various statistical and physical models to estimate landslide susceptibility is also discussed. The causes, mechanisms and types of landslides and their destructive character are elaborated in the book. Researchers interested in applying statistical tools for hazard zonation purposes will find the book appealing.

This is the third volume of the "Handbook of Game Theory with Economic Applications." Since the publication of multi-Volume 1 a decade ago, game theory has continued to develop at a furious pace, and today it is the dominant tool in economic theory. The three volumes together cover the fundamental theoretical aspects, a wide range of applications to economics, several chapters on applications to political science and individual chapters on applications to disciplines as diverse as evolutionary biology, computer science, law, psychology and ethics. The authors are the most eminent practitioners in the field, including three Nobel Prize winners.

The topics covered in the present volume include strategic ("Nash") equilibrium; incomplete information; two-person non-zero-sum games; noncooperative games with a continuum of players; stochastic games; industrial organization; bargaining, inspection; economic history; the Shapley value and its applications to perfectly competitive economies, to taxation, to public goods and to fixed prices; political science; law mechanism design; and game experimentation.