The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications. In order to keep the presentation reasonably self-contained, Professor Sarnak begins by developing the necessary background material in modular forms. He then considers the solution of three problems: the Ruziewicz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs: 'expander graphs' and 'Ramanujan graphs'; and the Linnik problem concerning the distribution of integers that represent a given large integer as a sum of three squares. These applications are carried out in detail. The book therefore should be accessible to a wide audience of graduate students and researchers in mathematics
"The Afterlife of Stars moved me more than any other novel I've read in recent memory." --Tim O'BrienWhen Russian tanks roll into the public squares of Budapest to crush the Hungarian Revolution, brot
This volume examines the painting, sculpture, decorative arts, and architecture produced in nine important court cities of Italy during the course of the fourteenth, fifteenth, and sixteenth centuries. Although each chapter represents a separate study of a particular geographical locale, many common themes emerge. This volume gives a multifaceted consideration of the art created for princes, prelates, confraternities, and civic authorities – works displayed in public squares, private palaces, churches, and town halls. Including six essays specially commissioned that explore the interaction of artists and their civic and/or courtly patrons within the context of prevailing cultural, political, and religious circumstances, The Court Cities of Northern Italy provides a rich supplement to traditional accounts of the artistic heritage of the Italian Renaissance, which has traditionally focused on the Florentine, Venetian, and Roman traditions. The book includes 35 color plates and 221 black
Paradoxes and paper-folding, Moebius variations and mnemonics, fallacies, magic squares, topological curiosities, parlor tricks, and games ancient and modern, from Polyominoes, Nim, Hex, and the Tower of Hanoi to four-dimensional ticktacktoe. These mathematical recreations, clearly and cleverly presented by Martin Gardner, delight and perplex while demonstrating principles of logic, probability, geometry, and other fields of mathematics. Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi is the inaugural volume in Martin Gardner's New Mathematical Library. This book of the earliest of Gardner's enormously popular Scientific American columns and puzzles continues to challenge and fascinate readers. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries.
Martin Gardner continues to delight. He introduces readers to the Generalized Ham Sandwich Theorem, origami, digital roots, magic squares, the mathematics of cooling coffee, the induction game of Eleusis, Dudeney puzzles, the maze at Hampton Court Palace, and many more mathematical puzzles and principles. Origami, Eleusis, and the Soma Cube is the second volume in Martin Gardner's New Mathematical Library, based on his enormously popular Scientific American columns. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries, to challenge and fascinate a new generation of readers.
This book explains how and why Berlin became the symbolic capital of the Cold War. It brings the history of the Cold War down to earth by focusing on the messy accounts of daily struggles to survive rather than seamless narratives of diplomatic exchange. By following Berliners as they made their way from ration offices to the black markets, from allied occupation bureaus to the physical and symbolic battles for the city's streets and squares, Paul Steege anchors his account of this emerging global conflict in the fractured terrain of a city literally shattered by World War II. In this history of everyday life, he claims for Berliners a vital role in making possible Berlin's iconic Cold War status. The world saw an absolutely divided city, but everyday Berliners crossed its many boundaries, and these transgressive practices brought into focus the stark oppositions of the Cold War.
Max Reinhardt (1873–1943), one of the major theatre figures of the twentieth century, was among the first to establish the importance of the director in modern theatre. His fame outside Germany rests somewhat unfairly on his distorted image as producer of giant, Gothic spectacles staged in vast auditoria or cathedral squares. In this book Professor Styan is concerned to illustrate Reinhardt's astonishing versatility as director of more than six hundred productions, which together cover almost all the dramatic genres and all the major theatrical movements of the time. Professor Styan explains Reinhardt's place in the history of Austrian and German culture and world theatrical movements. Using contemporary reviews and the Regiebuch, or director's promptbook, he describes in detail the organization, performance and impact of some of the director's major productions: his symbolist interpretation of Ghosts and Salome; the expressionist experiment with plays by Wedekind, Strindberg, Sorge an
Bath is the home of America's oldest county fair. The commmunity was planned as western New York's "Queen City," a great metropolis, with broad tree-lined boulevards and spacious squares. Airplanes an
These notes present an investigation of a condition similar to Euclid's parallel axiom for subsets of finite sets. The background material to the theory of parallelisms is introduced and the author then describes the links this theory has with other topics from the whole range of combinatorial theory and permutation groups. These include network flows, perfect codes, Latin squares, block designs and multiply-transitive permutation groups, and long and detailed appendices are provided to serve as introductions to these various subjects. Many of the results are published for the first time.
Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.
Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to suppo
Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduction of a powerful new method into elementary number theory. This book provides a gentle introduction to this method, explaining it in a clear and straightforward manner. The many applications provided include applications to sums of squares, sums of triangular numbers, recurrence relations for divisor functions, convolution sums involving the divisor functions, and many others. All of the topics discussed have a rich history dating back to Euler, Jacobi, Dirichlet, Ramanujan and others, and they continue to be the subject of current mathematical research. Williams places the results in their historical and contemporary contexts, making the connection between Liouville's ideas and modern theory. This is the only book in English entirely devoted to the subject and is thus an extremely valuable resource for both students and researchers alike.
Originally published in 1996, this is a presentation of some complex problems of discrete mathematics in a simple and unified form using an original, general combinatorial scheme. The author's aim is not always to present the most general results, but rather to focus attention on ones that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived. Professor Sachkov begins with a discussion of block designs and Latin squares before proceeding to treat transversals, devoting much attention to enumerative problems. The main role in these problems is played by generating functions, which are considered in Chapter 3. The general combinatorial scheme is then introduced and in the last chapter Polya's enumerative theory is discussed. This is an important book, describing many ideas not previously available in English; the author has taken the chance to update the text and references where appropriate.
In 1865, when San Francisco's Daily Evening Bulletin asked its readers if it were not time for the city to finally establish a public park, residents had only private gardens and small urban squares w
The new edition adds a chapter on multiple linear regression in biomedical research, with sections including the multiple linear regressions model and least squares; the ANOVA table, parameter estimat
Originally published in 1996, this is a presentation of some complex problems of discrete mathematics in a simple and unified form using an original, general combinatorial scheme. The author's aim is not always to present the most general results, but rather to focus attention on ones that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived. Professor Sachkov begins with a discussion of block designs and Latin squares before proceeding to treat transversals, devoting much attention to enumerative problems. The main role in these problems is played by generating functions, which are considered in Chapter 3. The general combinatorial scheme is then introduced and in the last chapter Polya's enumerative theory is discussed. This is an important book, describing many ideas not previously available in English; the author has taken the chance to update the text and references where appropriate.
Using real-life applications, this graduate-level textbook introduces different mathematical methods of scientific computation to solve minimization problems using examples ranging from locating an aircraft, finding the best time to replace a computer, analyzing developments on the stock market, and constructing phylogenetic trees. The textbook focuses on several methods, including nonlinear least squares with confidence analysis, singular value decomposition, best basis, dynamic programming, linear programming, and various optimization procedures. Each chapter solves several realistic problems, introducing the modelling optimization techniques and simulation as required. This allows readers to see how the methods are put to use, making it easier to grasp the basic ideas. There are also worked examples, practical notes, and background materials to help the reader understand the topics covered. Interactive exercises are available at www.cambridge.org/9780521849890.
The Supreme Court has emphasized that expressive liberties require 'breathing space' in which to thrive. At a minimum, speakers need places in which to assemble, speak, and petition government. This book is a comprehensive examination of First Amendment rights in public places. It shows that the literal ground beneath speakers' feet has been steadily eroding, from personal spaces to college campuses and to once vast and important inscribed places, such as public parks and public squares. Through the study of 'expressive topography', this book considers a variety of contemporary speech contests including restrictions on abortion clinic sidewalk counselors, protests at military funerals, and restrictions on assembly and speech at political conventions. Countering or reversing these forces will require a focused and sustained effort by public officials, courts, and, of course, the people themselves.
The story of the American Quilt Trail, featuring the colorful patterns of quilt squares writ large on barns throughout North America, is the story of one of the fastest-growing grassroots public arts
