The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index
The ultimate mathematics reference book This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries—written especially for this book by some of the world's leading mathematicians—that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music—and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors include: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, and Doron Zeilberger
The first encyclopedic reference to Atlantic history Between the fifteenth and nineteenth centuries, the connections among Africa, the Americas, and Europe transformed world history—through maritime exploration, commercial engagements, human migrations and settlements, political realignments and upheavals, cultural exchanges, and more. This book, the first encyclopedic reference work on Atlantic history, takes an integrated, multicontinental approach that emphasizes the dynamics of change and the perspectives and motivations of the peoples who made it happen. The entries—all specially commissioned for this volume from an international team of leading scholars—synthesize the latest scholarship on central themes, including economics, migration, politics, war, technologies and science, the physical environment, and culture. Part one features five major essays that trace the changes distinctive to each chronological phase of Atlantic history. Part two includes more than 125 entries on key topics, from the seemingly familiar viewed in unfamiliar and provocative ways (the Seven Years' War, trading companies) to less conventional subjects (family networks, canon law, utopias). This is an indispensable resource for students, researchers, and scholars in a range of fields, from early American, African, Latin American, and European history to the histories of economics, religion, and science. The first encyclopedic reference on Atlantic history Features five major essays and more than 125 alphabetical entries Provides essential context on major areas of change: Economies (for example, the slave trade, marine resources, commodities, specie, trading companies) Populations (emigrations, Native American removals, blended communities) Politics and law (the law of nations, royal liberties, paramount chiefdoms, independence struggles in Haiti, the Hispanic Americas, the United States, and France) Military actions (the African and Napoleonic wars, the Seven Years' War, wars of conquest) Technologies and science (cartography, nautical science, geography, healing practices) The physical environment (climate and weather, forest resources, agricultural production, food and diets, disease) Cultures and communities (captivity narratives, religions and religious practices) Includes original contributions from Sven Beckert, Holly Brewer, Peter A. Coclanis, Seymour Drescher, Eliga H. Gould, David S. Jones, Wim Klooster, Mark Peterson, Steven Pincus, Richard Price and Sophia Rosenfeld, and many more Contains illustrations, maps, and bibliographies
The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.
"Information technology shapes nearly every part of modern life, and debates about information--its meaning, effects, and applications--are central to a range of fields, from economics, technology, and politics to library science, media studies, and cultural studies. This rich, unique resource traces the history of information with an approach designed to draw connections across fields and perspectives, and provide essential context for our current age of information. Clear, accessible, and authoritative, the book opens with a series of articles that provide a narrative history of information from premodern practices to twenty-first-century information culture. This section focuses on major developments in the creation, storage, search, exchange, management, and manipulation of information, as well as the many meanings and uses of information over time. Coverage spans Europe, North America, and many other places and periods, including the medieval Islamic world and early modern East Asia, as well as the emergence of global networks. A second, alphabetical section includes more than 100 concise articles that cover specific concepts (e.g., data, intellectual property, privacy); formats and genres (books, databases, maps, newspapers, scrolls, social media); people (archivists, diplomats and spies, readers, secretaries, teachers); practices (censorship, forecasting, learning, surveilling, translating); processes (digitization, quantification, storage and search); systems (bureaucracy, platforms, telecommunications); technologies (algorithms, cameras, computers), and much more. The book concludes with an informative glossary, defining terms from "analog/digital" to "World Wide Web.""--
Jonathan Edwards (1703–1758) is widely recognized as one of the greatest philosopher-theologians America has ever produced, and recent years have seen a remarkable increase in research on his writings. To date, however, there has been no single authoritative volume that introduces and interprets the key aspects of Edwards' thought as a whole. The Princeton Companion to Jonathan Edwards provides just such a concise and comprehensive work, one that will be invaluable to students and scholars of American religion and theology as well as of literature, philosophy, and history. Comprising twenty essays by leading scholars on Edwards, the book will inform and challenge readers on subjects ranging from Edwards' understanding of the Trinity, God and the world, Christ, and salvation, as well as of history, typology, the church, and mission to Native Americans. It also includes a chronology of Edwards' life and writings that incorporates current research. Those familiar with Edwards' writings will find in these essays succinct expositions as well as bold new interpretations, and others will find an accessible, authoritative, up-to-date orientation to his multifaceted thought. The essays are by Robert E. Brown, Allen C. Guezlo, Robert W. Jenson, Wilson H. Kimnach, Janice Knight, Sang Hyun Lee, Gerald R. McDermott, Kenneth P. Minkema, Mark Noll, Richard R. Niebuhr, Amy Plantinga Pauw, John E. Smith, Stephen J. Stein, Harry S. Stout, Douglas A. Sweeney, Peter J. Thuesen, and John F. Wilson.
The acclaimed guide to the ecology and natural history of the American tropics—now fully updated and expanded The New Neotropical Companion is the completely revised and expanded edition of a book that has helped thousands of people to understand the complex ecology and natural history of the most species-rich area on Earth, the American tropics. Featuring stunning color photos throughout, it is a sweeping and cutting-edge account of tropical ecology that includes not only tropical rain forests but also other ecosystems such as cloud forests, rivers, savannas, and mountains. This is the only guide to the American tropics that is all-inclusive, encompassing the entire region's ecology and the amazing relationships among species rather than focusing just on species identification. The New Neotropical Companion is a book unlike any other. Here, you will learn how to recognize distinctive ecological patterns of rain forests and other habitats and to interpret how these remarkable ecosystems function—everything is explained in clear and engaging prose free of jargon. You will also be introduced to the region's astonishing plant and animal life. Informative and entertaining, The New Neotropical Companion is a pleasurable escape for armchair naturalists, and visitors to the American tropics will want to refer to this book before, during, and after their trip. Covers all of tropical America Describes the species and habitats most likely to be observed by visitors Includes every major ecosystem, from lowland rain forests to the high Andes Features a wealth of color photos of habitats, plants, and animals
An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.
