This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique.
Applied statisticians often need to perform analyses of multivariate data; for these they will typically use one of the statistical software packages, S-Plus or R. This book sets out how to use these packages for these analyses in a concise and easy-to-use way, and will save users having to buy two books for the job. The author is well-known for this kind of book, and so buyers will trust that he’s got it right.
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
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
Object Oriented Data Analysis is a framework that facilitates inter-disciplinary research through new terminology for discussing the often many possible approaches to the analysis of complex data. Such data are naturally arising in a wide variety of areas. This book aims to provide ways of thinking that enable the making of sensible choices. The main points are illustrated with many real data examples, based on the authors' personal experiences, which have motivated the invention of a wide array of analytic methods. While the mathematics go far beyond the usual in statistics (including differential geometry and even topology), the book is aimed at accessibility by graduate students. There is deliberate focus on ideas over mathematical formulas. J. S. Marron is the Amos Hawley Distinguished Professor of Statistics, Professor of Biostatistics, Adjunct Professor of Computer Science, Faculty Member of the Bioinformatics and Computational Biology Curriculum and Research Member of the Lineberger Cancer Center and the Computational Medicine Program, at the University of North Carolina, Chapel Hill. Ian L. Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami, has served as Head of School of Mathematical Sciences at the University of Nottingham, and is joint author of the acclaimed book Statistical Shape Analysis.
Experimenting with Ethnography collects twenty-one essays that open new paths for doing ethnographic analysis. The contributors—who come from a variety of intellectual and methodological traditions—enliven analysis by refusing to take it as an abstract, disembodied exercise. Rather, they frame it as a concrete mode of action and a creative practice. Encompassing topics ranging from language and the body to technology and modes of collaboration, the essays invite readers to focus on the imaginative work that needs to be performed prior to completing an argument. Whether exchanging objects, showing how to use drawn images as a way to analyze data, or working with smartphones, sound recordings, and social media as analytic devices, the contributors explore the deliberate processes for pursuing experimental thinking through ethnography. Practical and broad in theoretical scope, Experimenting with Ethnography is an indispensable companion for all ethnographers. Contributors. Patricia Alvarez Astacio, Andrea Ballestero, Ivan da Costa Marques, Steffen Dalsgaard, Endre Dányi, Marisol de la Cadena, Marianne de Laet, Carolina Domínguez Guzmán, Rachel Douglas-Jones, Clément Dréano, Joseph Dumit, Melanie Ford Lemus, Elaine Gan, Oliver Human, Alberto Corsín Jiménez, Graham M. Jones, Trine Mygind Korsby, Justine Laurent, James Maguire, George E. Marcus, Annemarie Mol, Sarah Pink, Els Roding, Markus Rudolfi, Ulrike Scholtes, Anthony Stavrianakis, Lucy Suchman, Katie Ulrich, Helen Verran, Else Vogel, Antonia Walford, Karen Waltorp, Laura Watts, Brit Ross Winthereik
Interpersonal phenomena such as attachment, conflict, person perception, learning, and influence have traditionally been studied by examining individuals in isolation, which falls short of capturing their truly interpersonal nature. This book offers state-of-the-art solutions to this age-old problem by presenting methodological and data-analytic approaches useful in investigating processes that take place among dyads: couples, coworkers, parent and child, teacher and student, or doctor and patient, to name just a few. Rich examples from psychology and across the behavioral and social sciences help build the researcher's ability to conceptualize relationship processes; model and test for actor effects, partner effects, and relationship effects; and model and control for the statistical interdependence that can exist between partners. The companion website provides clarifications, elaborations, corrections, and data and files for each chapter.
‘Econometric Analysis of Panel Data’ has become established as the leading textbook for postgraduate courses in panel data. This book is intended as a companion to the main text. The prerequisites include a good background in mathematical statistics and econometrics. The companion guide will add value to the existing textbooks on panel data by solving exercises in a logical and pedagogical manner, helping the reader understand, learn and teach panel data. These exercises are based upon those in Baltagi (2008) and are complementary to that text even though they are stand alone material and the reader can learn the basic material as they go through these exercises. The exercises in this book start by providing some background material on partitioned regressions and the Frisch-Waugh-Lovell theorem, showing the reader some applications of this material that are useful in practice. Then it goes through the basic material on fixed and random effects models in a one-way and two-way error components models, following the same outline as in Baltagi (2008). The book also provides some empirical illustrations and examples using Stata and EViews that the reader can replicate. The data sets are available on the Wiley web site (www.wileyeurope.com/college/baltagi).
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
"Pollock and Edwards explain the nuts-and-bolts of research design and data analysis in a clear and concise style. The Essential of Political Analysis is an intuitive introduction to complex material, replete with examples from the political science literature that add relevance to statistical concepts. This text offers students an excellent balance between the technical and the practical." —Francis Neely, San Francisco State University Gain the skills you need to conduct political analysis and critically assess statistical research. In this Sixth Edition of The Essentials of Political Science, bestselling authors Philip H. Pollock III and Barry C. Edwards build students’ analytic abilities and develop their statistical reasoning with new data, fresh exercises, and accessible examples. This brief, accessible guide walks students through the essentials—measuring concepts, formulating and testing hypotheses, describing variables—while using key terms, chapter-opening objectives, over 80 tables and figures, and practical exercises to get them using and applying their new skills. Using SPSS, STATA or R? Discounted package deals available with Philip H. Pollock’s companion workbooks. . Give your students the SAGE edge! SAGE edge offers a robust online environment featuring an impressive array of free tools and resources for review, study, and further exploration, keeping both instructors and students on the cutting edge of teaching and learning.
