Mathematics

Frontiers and Perspectives

Author: Vladimir Igorevich Arnolʹd

Publisher: American Mathematical Soc.

ISBN: 9780821826973

Category: Mathematics

Page: 459

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This remarkable book is a celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the volume was born as part of the activities observing the World Mathematical Year 2000. The volume consists of 30 articles written by some of the most influential mathematicians of our time. Authors of 15 contributions were recognized in various years by the IMU as recipients of the Fields Medal, from K. F. Roth (Fields Medalist, 1958) to W. T. Gowers (Fields Medalist, 1998). The articles offer valuable reflections about the amazing mathematical progress we have witnessed in this century and insightful speculations about the possible development of mathematics over the next century. Some articles formulate important problems, challenging future mathematicians. Others pay explicit homage to the famous set of Hilbert Problems posed one hundred years ago, giving enlightening commentary. Yet other papers offer a deeply personal perspective, allowing singular insight into the minds and hearts of people doing mathematics today. Mathematics: Frontiers and Perspectives is a unique volume that pertains to a broad mathematical audience of various backgrounds and levels of interest. It offers readers true and unequaled insight into the wonderful world of mathematics at this important juncture: the turn of the millennium. The work is one of those rare volumes that can be browsed, and if you do simply browse through it, you get a wonderful sense of mathematics today. Yet it also can be intensely studied on a detailed technical level for gaining insight into some of the great problems on which mathematicians are currently working. Editors Michael Atiyah and Peter Lax were winners of the famous Abel Prize awarded by The Norwegian Academy of Science and Letters for outstanding work in mathematics.

Theories of Mathematics Education

Seeking New Frontiers

Author: Bharath Sriraman,Lyn English

Publisher: Springer Science & Business Media

ISBN: 3642007422

Category: Education

Page: 668

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Advances in Mathematics Education is a new and innovative book series published by Springer that builds on the success and the rich history of ZDM—The Inter- tional Journal on Mathematics Education (formerly known as Zentralblatt für - daktik der Mathematik). One characteristic of ZDM since its inception in 1969 has been the publication of themed issues that aim to bring the state-of-the-art on c- tral sub-domains within mathematics education. The published issues include a rich variety of topics and contributions that continue to be of relevance today. The newly established monograph series aims to integrate, synthesize and extend papers from previously published themed issues of importance today, by orienting these issues towards the future state of the art. The main idea is to move the ?eld forward with a book series that looks to the future by building on the past by carefully choosing viable ideas that can fruitfully mutate and inspire the next generations. Taking ins- ration from Henri Poincaré (1854–1912), who said “To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority.

Modular Forms: A Classical Approach

Author: Henri Cohen,Fredrik Strömberg

Publisher: American Mathematical Soc.

ISBN: 0821849476

Category: Forms (Mathematics).

Page: 700

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The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.

The Symmetry Perspective

From Equilibrium to Chaos in Phase Space and Physical Space

Author: Martin Golubitsky,Ian Stewart

Publisher: Birkhäuser

ISBN: 3034881673

Category: Mathematics

Page: 325

View: 1934

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The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS

Vertex Operator Algebras in Mathematics and Physics

Author: Stephen Berman

Publisher: American Mathematical Soc.

ISBN: 0821828568

Category: Mathematics

Page: 249

View: 2892

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Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.

Introduction to Symplectic Topology

Author: Dusa McDuff,Dietmar Salamon

Publisher: Oxford University Press

ISBN: 0192514016

Category: Mathematics

Page: 632

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Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.

The Crest of the Peacock

Non-European Roots of Mathematics (Third Edition)

Author: George Gheverghese Joseph

Publisher: Princeton University Press

ISBN: 9780691135267

Category: Mathematics

Page: 561

View: 9489

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"Enthralling ... After reading it, we cannot see the past in the same comforting haze of age-old stories, faithfully and uncritically retold from teacher to pupil down the years ... Invaluable for mathematics teachers at all levels."--New Scientist.

Frontiers in Entrepreneurship

Author: Boris Urban

Publisher: Springer Science & Business Media

ISBN: 9783642045028

Category: Business & Economics

Page: 206

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Te series Perspectives in Entrepreneurship: A Research Companion provides an authoritative overview of specialised themes in entrepreneurship. Each of the four books presents the conceptual framework and foundations underlying a specialist feld of scholarship in entrepreneurship. Te series is inspired by the dearth of higher-level texts available in South Africa, failing to encapsulate the rigorous research evident in the growing feld of entrepreneurship internationally. Te content is driven by a judicious selection and interpretation of key knowledge set in context by introducing and delineating major topics previously not discussed in-depth in traditional entrepreneurial texts. A blend of theoretical and empirical evidence is presented that collectively demonstrates the convergence of thinking on a particular theme. Identifying and evaluating the most seminal and impactful scholarly research on diferent subject areas where entrepreneurship is at the core, serves to achieve this convergence. By applying a theoretical lens to central issues ‘about entrepreneurship’ rather than focusing on practical issues of ‘how to’, the series has a conceptual outlook with specialist areas in detailed narrative. Te book is deliberately structured to add value to learners who are undertaking secondary programmes in entrepreneurship by building on basic entrepreneurship principles and theory. Te series builds on fundamental entrepreneurial texts. Each book provides a valuable knowledge base for educators, third year and postgraduate students, researchers, policy makers, and service providers.

Perspectives on Organizational Fit

Author: Cheri Ostroff,Timothy A. Judge

Publisher: Psychology Press

ISBN: 1136679219

Category: Business & Economics

Page: 504

View: 3466

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This book concerns how employees consider their work lives, how well they fit their jobs, the work setting, other people, and what is important and valued in their organizations. Perspectives on Organizational Fit, a new book in SIOP's Organizational Frontiers Series, takes a scholarly look at fit in organizations: the relationship between individuals and the environments in which they find themselves. As the volume extends upon recent advances in fit theory, the contributors address how fit theory is used within selection, recruitment, diversity, and leadership teams. It also explores the integration of different fit perspectives, and clarifies the methodological and statistical issues that plague fit research. The burgeoning interest in fit issues makes this book especially timely. It is comprised of three parts that cover: new directions in fit processes, as well as micro and macro levels of analysis; methodological and statistics issues that pertain to conducting fit research; and reflections from the chapter authors and the continuing challenges of future research in fit theory. Perspectives on Organizational Fit is appropriate for researchers and professionals in the areas of human resource management, organizational behavior, and industrial organizational psychology.

Mathematics without Apologies

Portrait of a Problematic Vocation

Author: Michael Harris

Publisher: Princeton University Press

ISBN: 1400885523

Category: Mathematics

Page: 464

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What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

Mathematics for Industry

Challenges and Frontiers. A Process View: Practice and Theory

Author: David R. Ferguson,Thomas J. Peters,Society for Industrial and Applied Mathematics

Publisher: SIAM

ISBN: 9780898715989

Category: Mathematics

Page: 249

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The papers were elicited primarily from Mathematics for Industry: Challenges and Frontiers, a conference sponsored by SIAM in October, 2003.

Paul Dirac

The Man and His Work

Author: Abraham Pais,Maurice Jacob,David I. Olive,Michael F. Atiyah

Publisher: Cambridge University Press

ISBN: 9780521019538

Category: Biography & Autobiography

Page: 144

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Paul Adrien Maurice Dirac was one of the founders of quantum theory. He is numbered alongside Newton, Maxwell and Einstein as one of the greatest physicists of all time. Together the lectures in this volume, originally presented on the occasion of the dedication ceremony for a plaque honoring Dirac in Westminster Abbey, give a unique insight into the relationship between Dirac's character and his scientific achievements. The text begins with the dedication address given by Stephen Hawking at the ceremony. Then Abraham Pais describes Dirac as a person and his approach to his work. Maurice Jacob explains how Dirac was led to introduce the concept of antimatter, and its central role in modern particle physics and cosmology. This is followed by David Olive's account of the origin and enduring influence of Dirac's work on magnetic monopoles. Finally, Sir Michael Atiyah explains the deep and widespread significance of the Dirac equation in mathematics.

Mapping Scientific Frontiers

The Quest for Knowledge Visualization

Author: Chaomei Chen

Publisher: Springer Science & Business Media

ISBN: 1447151283

Category: Computers

Page: 344

View: 9978

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This is an examination of the history and the state of the art of the quest for visualizing scientific knowledge and the dynamics of its development. Through an interdisciplinary perspective this book presents profound visions, pivotal advances, and insightful contributions made by generations of researchers and professionals, which portrays a holistic view of the underlying principles and mechanisms of the development of science. This updated and extended second edition: highlights the latest advances in mapping scientific frontiers examines the foundations of strategies, principles, and design patterns provides an integrated and holistic account of major developments across disciplinary boundaries “Anyone who tries to follow the exponential growth of the literature on citation analysis and scientometrics knows how difficult it is to keep pace. Chaomei Chen has identified the significant methods and applications in visual graphics and made them clear to the uninitiated. Derek Price would have loved this book which not only pays homage to him but also to the key players in information science and a wide variety of others in the sociology and history of science.” – Eugene Garfield “This is a wide ranging book on information visualization, with a specific focus on science mapping. Science mapping is still in its infancy and many intellectual challenges remain to be investigated and many of which are outlined in the final chapter. In this new edition Chaomei Chen has provided an essential text, useful both as a primer for new entrants and as a comprehensive overview of recent developments for the seasoned practitioner.” – Henry Small Chaomei Chen is a Professor in the College of Information Science and Technology at Drexel University, Philadelphia, USA, and a ChangJiang Scholar at Dalian University of Technology, Dalian, China. He is the Editor-in-Chief of Information Visualization and the author of Turning Points: The Nature of Creativity (Springer, 2012) and Information Visualization: Beyond the Horizon (Springer, 2004, 2006).

Mathematics Applied in Information Systems

Author: Mangey Ram

Publisher: Frontiers in Information Syste

ISBN: 9781681087146

Category: Computers

Page: 298

View: 2718

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Recent developments in information science and technology have been possible due to original and timely research contributions containing new results in various fields of applied mathematics. It is also true that advances in information science create opportunities for developing mathematical models further. Mathematics Applied in Information Systems presents a series of reviews of mathematical methods applied to information systems. Readers will find, in this volume, chapters that cover mathematics applied in various vistas of information systems: - software reliability modeling and optimizations, - software release control, - natural language processing and social network analysis, - food safety systems, - soil scattering models, - digital imaging processing, - supply chain management systems This volume is essential reading for software engineering students and IT managers working in academia and industry (geosciences, supply chain management, software development, forensics, transportation etc.).

Encyclopedia of Library and Information Science, Second Edition -

Author: Miriam Drake

Publisher: CRC Press

ISBN: 9780824720797

Category: Language Arts & Disciplines

Page: 800

View: 6528

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A revitalized version of the popular classic, the Encyclopedia of Library and Information Science, Second Edition targets new and dynamic movements in the distribution, acquisition, and development of print and online media-compiling articles from more than 450 information specialists on topics including program planning in the digital era, recruitment, information management, advances in digital technology and encoding, intellectual property, and hardware, software, database selection and design, competitive intelligence, electronic records preservation, decision support systems, ethical issues in information, online library instruction, telecommuting, and digital library projects.

Team Effectiveness In Complex Organizations

Cross-Disciplinary Perspectives and Approaches

Author: Eduardo Salas,Pegasus Professor and University Trustee Chair Department of Psychology Eduardo Salas, PhD,Gerald F. Goodwin,C. Shawn Burke

Publisher: Routledge

ISBN: 1135596565

Category: Business & Economics

Page: 624

View: 8289

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Over the past 40 years, there has been a growing trend toward the utilization of teams for accomplishing work in organizations. Project teams, self-managed work teams and top management teams, among others have become a regular element in the corporation or military. This volume is intended to provide an overview of the current state of the art research on team effectiveness.

Weapons of Math Destruction

How Big Data Increases Inequality and Threatens Democracy

Author: Cathy O'Neil

Publisher: Crown Books

ISBN: 0553418815

Category: Big data

Page: 259

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"A former Wall Street quantitative analyst sounds an alarm on mathematical modeling, a pervasive new force in society that threatens to undermine democracy and widen inequality, "--NoveList.

Analysis and Mathematical Physics

Author: Bjorn Gustafsson,Alexander Vasiliev

Publisher: Springer Science & Business Media

ISBN: 9783764399061

Category: Mathematics

Page: 514

View: 7037

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Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.

Mathematics Unlimited - 2001 and Beyond

Author: Björn Engquist,Wilfried Schmid

Publisher: Springer

ISBN: 364256478X

Category: Mathematics

Page: 1236

View: 3641

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This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.