928 pages | 90 line illustrations, 57 halftones | 246x171mm
978-019-960319-0 | Paperback | January 2011 (estimated)
A high quality overview of current research trends
Covers 5000 years of mathematics across all key mathematical cultures
Editors and contributors are academics of excellent reputation
Engagingly written with numerous illustrations
This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood.
The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.
Readership: Graduates and researchers in mathematics, historians of science, and general historians.
Oxford Statistical Science Series 36
536 pages | 150 black and white line drawings, 10 black and white half tones | 234x156mm
978-0-19-953302-2 | Hardback | April 2011 (estimated)
Unifies several seemingly disparate model formulations
Considers both full and empirical Bayes inference
Up-to-date treatment of longitudinal, spatial and event history data in a regression context
Applications from diverse fields such as forestry, development economics, medicine, and marketing
Offers a balance between theory and its applications
Worked examples of all methods covered in book
Accompanying website containing codes and some of the data sets used in the book
Several recent advances in smoothing and semiparametric regression are presented in this book from a unifying, Bayesian perspective. Simulation-based full Bayesian Markov chain Monte Carlo (MCMC) inference, as well as empirical Bayes procedures closely related to penalized likelihood estimation and mixed models, are considered here. Throughout, the focus is on semiparametric regression and smoothing based on basis expansions of unknown functions and effects in combination with smoothness priors for the basis coefficients.
Beginning with a review of basic methods for smoothing and mixed models, longitudinal data, spatial data and event history data are treated in separate chapters. Worked examples from various fields such as forestry, development economics, medicine and marketing are used to illustrate the statistical methods covered in this book. Most of these examples have been analysed using implementations in the Bayesian software, BayesX, and some with R Codes. These, as well as some of the data sets, are made publicly available on the website accompanying this book.
Readership: Suitable for graduates, PhD students and their lecturers as a basis, or as additional material, for courses in statistics, biostatistics and econometrics. Also suitable for researchers in applied statistics, quantitative economics, the social sciences and the life sciences.
208 pages | 82 line illustrations, 4 colour plates | 234x153mm
978-0-19-954318-2 | Hardback |
978-0-19-954319-9 | Paperback
August 2011 (estimated)
Statistical methods embedded in real scientific settings
Problem-oriented rather than technique-oriented
Emphasis on statistics as integral part of scientific method
No knowledge of mathematics needed beyond school level
Full details of worked examples provided with data and source code in R
Most introductory statistics text-books are written either in a highly mathematical style for an intended readership of mathematics undergraduate students, or in a recipe-book style for an intended audience of non-mathematically inclined undergraduate or postgraduate students, typically in a single discipline; hence, "statistics for biologists", "statistics for psychologists", and so on.
An antidote to technique-oriented service courses, this book is different. It studiously avoids the recipe-book style and keeps algebraic details of specific statistical methods to the minimum extent necessary to understand the underlying concepts. Instead, the text aims to give the reader a clear understanding of how core statistical ideas of experimental design, modelling and data analysis are integral to the scientific method.
Aimed primarily at beginning postgraduate students across a range of scientific disciplines (albeit with a bias towards the biological, environmental and health sciences), it therefore assumes some maturity of understanding of scientific method, but does not require any prior knowledge of statistics, or any mathematical knowledge beyond basic algebra and a willingness to come to terms with mathematical notation.
Any statistical analysis of a realistically sized data-set requires the use of specially written computer software. An Appendix introduces the reader to our open-source software of choice, R, whilst the book's web-page includes downloadable data and R code that enables the reader to reproduce all of the analyses in the book and, with easy modifications, to adapt the code to analyse their own data if they wish. However, the book is not intended to be a textbook on statistical computing, and all of the material in the book can be understood without using either R or any other computer software.
Readership: Suitable for postgraduate students in science and health, quantitative researchers and final-year statistics students
Cloth | May 2011
280 pp. | 7 x 10 | 182 color illus. 4 line illus. 7 tables.
ISBN: 978-1-4008-3898-1
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.
This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincare conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems.
The essential introduction to discrete and computational geometry
Covers traditional topics as well as new and advanced material
Features numerous full-color illustrations, exercises, and unsolved problems
Suitable for sophomores in mathematics, computer science, engineering, or physics
Rigorous but accessible
An online solutions manual is available (for teachers only). To obtain access, please e-mail: Vickie_Kearn@press.princeton.edu
Satyan L. Devadoss is associate professor of mathematics at Williams College. Joseph O'Rourke is the Olin Professor of Computer Science and professor of mathematics at Smith College. His books include Geometric Folding Algorithms: Linkages, Origami, Polyhedra.
"This book is ideal for people who want to learn about the topic without wading too deeply into technical details. I really like the figures, and the writing style is very nice for students, with frequent jumps into exercises. The book favors topics that are intuitive, engaging, and easily grasped. It could form the basis of an excellent undergraduate-level course for students in computer science, applied mathematics, and pure mathematics."--Samir Khuller, University of Maryland
"I thoroughly enjoyed reading this book. It covers an incredibly diverse set of topics, ranging from elementary objects to deep mathematical concepts and important computational problems. Devadoss and O'Rourke have done a remarkable job of showing off the rich interplay between pure mathematics and computing that drives our research community. There really is nothing else like this on the market."--Jeff Erickson, University of Illinois, Urbana-Champaign
Annals of Mathematics Studies, 175
Paper | June 2011 ISBN13: 978-0-691-15066-6
Cloth | June 2011 ISBN13: 978-0-691-15065-9
184 pp. | 6 x 9 | 168 line illus.
Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics.
These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished.
The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.
Ben Brubaker is assistant professor of mathematics at Massachusetts Institute of Technology. Daniel Bump is professor of mathematics at Stanford University. Solomon Friedberg is professor of mathematics at Boston College.
Annals of Mathematics Studies, 176
Paper | July 2011 | ISBN13: 978-0-691-14202-9
Cloth | July 2011 | ISBN13: 978-0-691-14201-2
440 pp. | 6 x 9 | 6 line illus.
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program.
The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields.
The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
Bas Edixhoven is professor of mathematics at the University of Leiden. Jean-Marc Couveignes is professor of mathematics at the University of Toulouse le Mirail. Robin de Jong is assistant professor at the University of Leiden. Franz Merkl is professor of applied mathematics at the University of Munich. Johan Bosman is a postdoctoral researcher at the Institut fur Experimentelle Mathematik in Essen, Germany.