The primary goal of the book is to present the ideas and research findings of active researchers such as physicists, economists, mathematicians and financial engineers working in the field of "Econophysics," who have undertaken the task of modeling and analyzing systemic risk, network dynamics and other topics.

Of primary interest in these studies is the aspect of systemic risk, which has long been identified as a potential scenario in which financial institutions trigger a dangerous contagion mechanism, spreading from the financial economy to the real economy.

This type of risk, long confined to the monetary market, has spread considerably in the recent past, culminating in the subprime crisis of 2008. As such, understanding and controlling systemic risk has become an extremely important societal and economic challenge. The Econophys-Kolkata VI conference proceedings are dedicated to addressing a number of key issues involved. Several leading researchers in these fields report on their recent work and also review contemporary literature on the subject.

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi

This is a research-based book that deals with a broad range of issues about mathematics teacher education. It examines teacher education programs from different societies and cultures as it develops an international perspective on mathematics teacher education. Practical situations that are associated with related theories are studied critically. It is intended for teacher educators, mathematics educators, graduate students in mathematics education, and mathematics teachers.

This is a fully revised edition of the successful text, Introductory Mathematics for Economists. Updated throughout, it covers the essential mathematics required by students of economics and business. The emphasis is on applying mathematics rather than providing theorems, and a wide range of applications are covered with detailed answers provided for many of the exercises.
The book is structured, and the material deliberately selected, to increase in difficulty as the book progresses. Subjects covered include: algebra; linear equations, with immediate applications in simple economic models of markets and the national economy; natural generalizations of elementary matrix algebra and non-linear equations; applications in finance; the groundwork for calculus; profit maximization for a firm, simple inventory models, and other applications of marginal concepts; integration covering both standard analytical techniques and numerical methods; partial differentiation; linear programming; and dynamic relationships in continuous terms and in discrete terms. Three appendices provide extensive treatment of trigonometric functions, an introduction to set theory, and detailed answers to all exercises provided.

Too often, the study of science, math, and technology is limited to the major successes of the Western world. Yet people all over the world have observed and explored nature and developed technologies to help them in their everyday lives.

From the creators of the national bestseller and Parent's Choice Book Award -- winner The Explorabook (over one million copies sold) comes Math and Science Across Cultures, designed to help teachers, parents, and youth-group leaders use hands-on activities to explore the math and science of different cultural traditions, and to make these subjects more relevant and approachable for children of all backgrounds. With instructions in this book, you can:
-- Construct a Brazilian carnival instrument and investigate the science of sound.
-- Play a peg solitaire game from Madagascar and learn about mathematical patterns.
-- Experiment with a traditionally prepared cup of Chinese tea and learn about energy flow.
-- Count like an Egyptian, decipher Mayan mathematical symbols, and decode the ancient Inca number system of knotted cords.

This book can be an invaluable instrument for overviewing the latest and newest issues in mathematical aspects of scientific computing, discovering new applications and the most recent developments in the old ones. Topics include applications like fluid dynamics, electromagnetism, structural mechanics, kinetic models, free boundary problems, and methodologies like a posteriori estimates, adaptivity, discontinuous Galerkin methods, domain decomposition techniques, and numerical linear algebra. ENUMATH Conferences provide a forum for discussing recent aspects of Numerical Mathematics, they convene leading experts and young scientists with a special emphasis on contributions from Europe. Readers will get an insight into the state of the art of Numerical Mathematics and, more generally, into the field of Advanced Applications.

This book, intended for mathematics education professionals and teachers of mathematics, is outstanding in that its contributions come from a broad range of countries and cultures; they are representative of different theoretical perspectives and classroom experiences. All contributors are concerned with helping teachers explore ways to develop children's mathematical understanding appropriate for the new millennium. The authors present complex ideas about mathematical understanding and provide readers with powerful classroom examples. Recommendations for changing the curriculum for young children are also suggested. The book comprehensively documents four years of development in the field. Among the emergent developments described is the importance of context to mathematical development - it is not only the physical context, but also the social context of the classroom and school that stimulate conceptual growth. The book also locates current theoretical perspectives in a broad framework. Finally the book is organized around four interconnected themes all related directly to teaching and learning mathematics.

This volume contains papers based on invited talks given at the 2005 IMA Summer Workshop on Wireless Communications, held at the Institute for Mathematics and Its Applications, University of Minnesota, June 22-July 1, 2005. The workshop provided a great opportunity to facilitate the communications between academia and the industry, and to bridge the mathematical sciences, engineering, information theory, and communication communities. The emphasis were on design and analysis of computationally efficient algorithms to better understand the behavior and to control the wireless telecommunication networks. As an achieve, this volume presents some of the highlights of the workshop, and collects papers covering a broad spectrum of important and pressing issues in wireless communications. All papers have been reviewed. One of the book's distinct features is highly multi-disciplinary. This book is useful for researchers and advanced graduate students working in communication networks, information theory, signal processing, and applied probability and stochastic processes, among others.

Protein informatics is a newer name for an already existing discipline. It encompasses the techniques used in bioinformatics and molecular modeling that are related to proteins. While bioinformatics is mainly concerned with the collection, organization, and analysis of biological data, molecular modeling is devoted to representation and manipulation of the structure of proteins.

Protein informatics requires substantial prerequisites on computer science, mathematics, and molecular biology. The approach chosen here, allows a direct and rapid grasp on the subject starting from basic knowledge of algorithm design, calculus, linear algebra, and probability theory.

An Introduction to Protein Informatics, a professional monograph will provide the reader a comprehensive introduction to the field of protein informatics. The text emphasizes mathematical and computational methods to tackle the central problems of alignment, phylogenetic reconstruction, and prediction and sampling of protein structure.

An Introduction to Protein Informatics is designed for a professional audience, composed of researchers and practitioners within bioinformatics, molecular modeling, algorithm design, optimization, and pattern recognition. This book is also suitable as a graduate-level text for students in computer science, mathematics, and biomedicine.

This volume presents a collection of some of the seminal articles of Professor K. S. Shukla who made immense contributions to our understanding of the history and development of mathematics and astronomy in India. It consists of six parts: Part I constitutes introductory articles which give an overview of the life and work of Prof. Shukla, including details of his publications, reminiscences from his former students, and an analysis of his monumental contributions. Part II is a collection of important articles penned by Prof. Shukla related to various aspects of Indian mathematics. Part III consists of articles by Bibhutibhusan Datta and Avadhesh Narayan Singh-which together constitute the third unpublished part of their History of Hindu Mathematics-that were revised and updated by Prof. Shukla. Parts IV and V consist of a number of important articles of Prof. Shukla on different aspects of Indian astronomy. Part VI includes some important reviews authored by him and a few reviews of his work. Given the sheer range and depth of Prof. Shukla's scholarship, this volume is essential reading for scholars seeking to deepen their understanding of the rich and varied contributions made by Indian mathematicians and astronomers.

Closely matched to the latest A-Level Edexcel Maths specification, these brilliant CGP Practice Papers are the most realistic way for students to prepare for the tough exams! This pack contains two complete sets of exam-style tests (six papers in total) - plus a formula booklet with all the formulas and statistics tables students will need for their exams. We've also included detailed answers with step-by-step solutions and full mark schemes to make marking easy. For even more practice, don't miss CGP's Exam Practice Workbook for both years of A-Level Edexcel Maths (9781782947400).

Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.

This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.

Contents: Equations-solving and Theorems-proving Zero-set Formulation and Ideal Formulation (W-T Wu); Theory of Computation and Complex Analytic Dynamics (C T Chong); Affine Geometry in Complex Function Spaces and Algebras (A J Ellis); Some Results on Chromatically Unique Graphs (K M Koh & C P Teo); On the Decomposition of 0-Simple Dual Semigroups (C K Lai & K P Shum); On the Geometry of Infinite Dimensional Teichmuller Spaces (Z Li); Analytic Functionals and Their Transformations (M Morimoto); Groups and Designs (C E Praeger); Global Small Solutions to Nonlinear Evolution Equations (R Racke); and other papers;

This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines.Gottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege's enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has recieved extensive attention and discussion, the present volume is unique in presenting a thorough going examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns). Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut - or cauchy-sequence-related abstraction principles...

Lesson play is a novel construct in research and teachers' professional development in mathematics education. Lesson play refers to a lesson or part of a lesson presented in dialogue form-inspired in part by Lakatos's evocative Proofs and Refutations-featuring imagined interactions between a teacher and her/his students. We have been using and refining our use of this tool for a number of years and using it in a variety of situations involving mathematics thinking and learning. The goal of this proposed book is to offer a comprehensive survey of the affordances of the tool, the results of our studies-particularly in the area of pre-service teacher education, and the reasons that the tool offers such productive possibilities for both researchers and teacher educators.

The provocative contributions to Opening the Research Text reflect current interest in the political and cultural underpinnings of mathematics education. With 22 contributors including both established researchers and newcomers, this innovative research-oriented volume challenges traditional theories and "comforting narratives" of pedagogy through realistic, non-linear scenarios reflecting the ambiguities and power relationships of the classroom. By alternating research chapters with inventive responses (including poetry, concept mapping, graphic novel, and collage), the editors present theoretical as well as practice-based possibilities in areas as diverse as arts-based inquiry and social justice pedagogy, all in relation to mathematics education. These multiple calls to action will inspire readers to:

• Rethink the accessibility and impact of their classroom work.
• Consider the value of poststructuralist strategies to curriculum theory.
• Explore alternate research paradigms in mathematics education.
• Trace the intersections of power, economics and mathematics.
• Critically examine the discourse of school mathematics and policy documents.
• Engage in self-study, writing their own stories of insight and in(ter)vention.

Opening the Research Text asks teachers, researchers and scholars to add to the dialogue that is transforming the mathematics education field, and leads new educators toward insights into their careers and the students and communities they serve. Additionally, the book can be a primary graduate or supplementary undergraduate text in education ormathematics education.

This book contains nine refereed research papers in various areas, from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme. Topics covered are irregular connections, summability of solutions and rank reduction of differential systems, asymptotic behaviour of divergent series, integrability of Hamiltonian systems, multiple zeta values, quasi polynomial formalism, Pade approximants related to analytic integrability, hybrid systems. The volume as a whole gives a presentation of productive interactions between ideas stemming from computer algebra and questions arising in dynamical systems or combinatorics. As such, it should be useful for both mathematicians and theoretical physicists who are interested in effective computation."

This text examines how multiobjective evolutionary algorithms and related techniques can be used to solve problems, particularly in the disciplines of science and engineering. Contributions by leading researchers show how the concept of multiobjective optimization can be used to reformulate and resolve problems in areas such as constrained optimization, co-evolution, classification, inverse modeling, and design.

This book is intended to be self-contained, giving the theory of absolute (equivalent to Lebesgue) and non-absolute (equivalent to Denjoy-Perron) integration by using a simple extension of the Riemann integral. A useful tool for mathematicians and scientists needing advanced integration theory would be a method combining the ideas of the calculus of indefinite integral and Riemann definite integral in such a way that Lebesgue properties can be proved easily.Three important results that have not appeared in any other book distinguish this book from the rest. First a result on limits of sequences under the integral sign, secondly the necessary and sufficient conditions for the various limits under the integral sign and thirdly the application of these results to ordinary differential equations. The present book will give non-absolute integration theory just as easily as the absolute theory, and Stieltjes-type integration too.

STATISTICAL THEORY The Relationship of Probability Credibility and. Error LANCELOT HOGBEN, F. R. S Statistical Theory The Relationship of PROBABILITY, CREDIBILITY AND ERROR AN EXAMINATION OF THE CONTEMPORARY CRISIS IN STATISTICAL THEORY FROM A BEHAVIOURIST VIEWPOINT V-W-NORTON COMPANY INC Publishers New York CONTENTS Foreword page 7 1 The Contemporary Crisis or the Uncertainties of Uncertain Inference 13 PART I. THE FOUNDING FATHERS 2 The Founding Fathers and the Natural History of Gambling 33 3 Randomness and the Relevance of the Rule 59 4 Division of the Stakes and the Lottery of Life and Death 83 5 The Backward Look and the Balance Sheet of Thomas Bayes no 6 The Place of Laplace and the Grand Climacteric of the Classical Tradition 133 PART II. THE CALCULUS OF ERROR AND THE CALCULUS OF EXPLORATION 7 The Normal Law comes into the Picture 159 8 The Method of Least Squares and the Concept of Point Estimation 182 9 Error, Variation and Natural Law 210 10 Stochastic Models for Simple Regression 232 11 The Impasse of Factor Analysis 257 PART III. THE CALCULUS OF AGGREGATES 12 Maxwell and the Urn of Mature 279 13 Mendelism and the Two Meanings of Probability 297 PART IV. THE CALCULUS OF JUDGMENTS 14 Statistical Prudence and Statistical Inference 319 1 5 Decision Indecision and Sample Economy 345 1 6 Induction and Design, Stochastic and Non-stochastic 370 1 7 Recipe and Rule in Stochastic Induction 399 1 8 The Confidence Controversy and the Fifth Canon 433 1 9 Epilogue 454 Appendix I 477 Appendix II 480 Appendix III 485 Appendix IV 7 Index 07 FOREWORD THE USE of the word behaviourist in my sub-title calls for clari fication. It came into current usage chiefly through the writings of J. B.Watson, in the first fine flush of enthusiasm following the reception of Pavlovs work on conditioned reflexes. Watson conveyed the impression that all forms of animal including human behaviour are ultimately explicable in terms of neural or humoral co-ordination of receptors and effectors. Neither this proposition nor its denial is susceptible of proof. A comet may destroy the earth before we have completed a research programme of such magnitude as the operative adverb ultimately suggests. Many years ago, and in what now seems to me a very im mature volume of essays written as a counter-irritant to the mystique of Eddingtons Nature of the Physical World, I suggested a more restricted definition of the term and offered an alter native which seemingly did not commend itself to my con temporaries. By behaviourist in this context I mean what Ryle means in the concluding section of his recent book The Concept of Mind. What Ryle speaks of as the behaviourist viewpoint and what I had previously preferred to call the publicist outlook has no concern with structure and mechanism. Our common approach to the problem of cognition is not at the ontological level. The class of questions we regard as profitable topics of enquiry in this context arise at the level of epistemology, or, better still, what G. P. Meredith calls epistemics. If one wishes to discuss with any hope of reaching agreement what one means by knowledge or preferably knowing the two main topics of the agenda for our public symposium will be recognition and communication and we shall discuss them as different facets of the same problem, neither meaningful in isolation. A simple illustration will suffice to make clear, both at theemotive level of non-communicable private conviction and at the public or communicable level of observable be haviour, the difference between knowing, conceived as a process, and knowledge, conceived as a static repository. The Nature of Living Matter 1930. 7 STATISTICAL THEORY We shall suppose that B is colour-blind to differences in the red and green regions of the visible spectrum, A being normal in the customary sense of the term in the relevant context...