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This work is a fresh presentation of the Ahlfors-Weyl theory of holomorphic curves that takes into account some recent developments in Nevanlinna theory and several complex variables. The treatment is differential geometric throughout, and assumes no previous acquaintance with the classical theory of Nevanlinna. The main emphasis is on holomorphic curves defined over Riemann surfaces, which admit a harmonic exhaustion, and the main theorems of the subject are proved for such surfaces. The author discusses several directions for further research.

This work offers a contribution in the geometric form of the theory of several complex variables. Since complex Grassmann manifolds serve as classifying spaces of complex vector bundles, the cohomology structure of a complex Grassmann manifold is of importance for the construction of Chern classes of complex vector bundles. The cohomology ring of a Grassmannian is therefore of interest in topology, differential geometry, algebraic geometry, and complex analysis. Wilhelm Stoll treats certain aspects of the complex analysis point of view.This work originated with questions in value distribution theory. Here analytic sets and differential forms rather than the corresponding homology and cohomology classes are considered. On the Grassmann manifold, the cohomology ring is isomorphic to the ring of differential forms invariant under the unitary group, and each cohomology class is determined by a family of analytic sets.

A practical guide to the art of theorizing in the social sciencesIn the social sciences today, students are taught theory by reading and analyzing the works of Karl Marx, Max Weber, and other foundational figures of the discipline. What they rarely learn, however, is how to actually theorize. The Art of Social Theory is a practical guide to doing just that.In this one-of-a-kind user's manual for social theorists, Richard Swedberg explains how theorizing occurs in what he calls the context of discovery, a process in which the researcher gathers preliminary data and thinks creatively about it using tools such as metaphor, analogy, and typology. He guides readers through each step of the theorist's art, from observation and naming to concept formation and explanation. To theorize well, you also need a sound knowledge of existing social theory. Swedberg introduces readers to the most important theories and concepts, and discusses how to go about mastering them. If you can think, you can also learn to theorize. This book shows you how.Concise and accessible, The Art of Social Theory features helpful examples throughout, and also provides practical exercises that enable readers to learn through doing.

Geometry of orthogonal spaces.

This book contains a valuable discussion of renormalization through the addition of counterterms to the Lagrangian, giving the first complete proof of the cancellation of all divergences in an arbitrary interaction. The author also introduces a new method of renormalizing an arbitrary Feynman amplitude, a method that is simpler than previous approaches and can be used to study the renormalized perturbation series in quantum field theory.

The description for this book, Degrees of Unsolvability. (AM-55), Volume 55, will be forthcoming.

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds.In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers.Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

In recent years, many disciplines have become interested in the scientific study of morality. However, a conceptual framework for this work is still lacking. In The Moral Background, Gabriel Abend develops just such a framework and uses it to investigate the history of business ethics in the United States from the 1850s to the 1930s.According to Abend, morality consists of three levels: moral and immoral behavior, or the behavioral level; moral understandings and norms, or the normative level; and the moral background, which includes what moral concepts exist in a society, what moral methods can be used, what reasons can be given, and what objects can be morally evaluated at all. This background underlies the behavioral and normative levels; it supports, facilitates, and enables them.Through this perspective, Abend historically examines the work of numerous business ethicists and organizations-such as Protestant ministers, business associations, and business schools-and identifies two types of moral background. "e;Standards of Practice"e; is characterized by its scientific worldview, moral relativism, and emphasis on individuals' actions and decisions. The "e;Christian Merchant"e; type is characterized by its Christian worldview, moral objectivism, and conception of a person's life as a unity.The Moral Background offers both an original account of the history of business ethics and a novel framework for understanding and investigating morality in general.

The English East India Company was one of the most powerful and enduring organizations in history. Between Monopoly and Free Trade locates the source of that success in the innovative policy by which the Company's Court of Directors granted employees the right to pursue their own commercial interests while in the firm's employ. Exploring trade network dynamics, decision-making processes, and ports and organizational context, Emily Erikson demonstrates why the English East India Company was a dominant force in the expansion of trade between Europe and Asia, and she sheds light on the related problems of why England experienced rapid economic development and how the relationship between Europe and Asia shifted in the eighteenth and nineteenth centuries.Though the Company held a monopoly on English overseas trade to Asia, the Court of Directors extended the right to trade in Asia to their employees, creating an unusual situation in which employees worked both for themselves and for the Company as overseas merchants. Building on the organizational infrastructure of the Company and the sophisticated commercial institutions of the markets of the East, employees constructed a cohesive internal network of peer communications that directed English trading ships during their voyages. This network integrated Company operations, encouraged innovation, and increased the Company's flexibility, adaptability, and responsiveness to local circumstance.Between Monopoly and Free Trade highlights the dynamic potential of social networks in the early modern era.

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring an abelian group K0 or K1 respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

This book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection cohomology, anddetailed information on representations of Weylgroups.

One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "e;The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master.? Milnor has published five books with Princeton University Press.

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "e;Fundamenta Nova"e; in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.

A comprehensive introduction to the statistical and econometric methods for analyzing high-frequency financial dataHigh-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis.Yacine Ait-Sahalia and Jean Jacod cover the mathematical foundations of stochastic processes, describe the primary characteristics of high-frequency financial data, and present the asymptotic concepts that their analysis relies on. Ait-Sahalia and Jacod also deal with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As they demonstrate, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes.Ait-Sahalia and Jacod approach high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet.Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.

Written and revised by D. B. A. Epstein.

New interest in modular forms of one complex variable has been caused chiefly by the work of Selberg and of Eichler. But there has been no introductory work covering the background of these developments. H. C. Gunning's book surveys techniques and problems; only the simpler cases are treated-modular forms of even weights without multipliers, the principal congruence subgroups, and the Hecke operators for the full modular group alone.

An in-depth look at America's changing gay neighborhoodsGay neighborhoods, like the legendary Castro District in San Francisco and New York's Greenwich Village, have long provided sexual minorities with safe havens in an often unsafe world. But as our society increasingly accepts gays and lesbians into the mainstream, are "e;gayborhoods"e; destined to disappear? Amin Ghaziani provides an incisive look at the origins of these unique cultural enclaves, the reasons why they are changing today, and their prospects for the future.Drawing on a wealth of evidence-including census data, opinion polls, hundreds of newspaper reports from across the United States, and more than one hundred original interviews with residents in Chicago, one of the most paradigmatic cities in America-There Goes the Gayborhood? argues that political gains and societal acceptance are allowing gays and lesbians to imagine expansive possibilities for a life beyond the gayborhood. The dawn of a new post-gay era is altering the character and composition of existing enclaves across the country, but the spirit of integration can coexist alongside the celebration of differences in subtle and sometimes surprising ways.Exploring the intimate relationship between sexuality and the city, this cutting-edge book reveals how gayborhoods, like the cities that surround them, are organic and continually evolving places. Gayborhoods have nurtured sexual minorities throughout the twentieth century and, despite the unstoppable forces of flux, will remain resonant and revelatory features of urban life.

A prehistory of today's humanities, from ancient Greece to the early twentieth centuryMany today do not recognize the word, but "e;philology"e; was for centuries nearly synonymous with humanistic intellectual life, encompassing not only the study of Greek and Roman literature and the Bible but also all other studies of language and literature, as well as history, culture, art, and more. In short, philology was the queen of the human sciences. How did it become little more than an archaic word?In Philology, the first history of Western humanistic learning as a connected whole ever published in English, James Turner tells the fascinating, forgotten story of how the study of languages and texts led to the modern humanities and the modern university. The humanities today face a crisis of relevance, if not of meaning and purpose. Understanding their common origins-and what they still share-has never been more urgent.

How the fear of a shortage in American science talent fuels cycles in the technical labor marketIs the United States falling behind in the global race for scientific and engineering talent? Are U.S. employers facing shortages of the skilled workers that they need to compete in a globalized world? Such claims from some employers and educators have been widely embraced by mainstream media and political leaders, and have figured prominently in recent policy debates about education, federal expenditures, tax policy, and immigration. Falling Behind? offers careful examinations of the existing evidence and of its use by those involved in these debates.These concerns are by no means a recent phenomenon. Examining historical precedent, Michael Teitelbaum highlights five episodes of alarm about "e;falling behind"e; that go back nearly seventy years to the end of World War II. In each of these episodes the political system responded by rapidly expanding the supply of scientists and engineers, but only a few years later political enthusiasm or economic demand waned. Booms turned to busts, leaving many of those who had been encouraged to pursue science and engineering careers facing disheartening career prospects. Their experiences deterred younger and equally talented students from following in their footsteps-thereby sowing the seeds of the next cycle of alarm, boom, and bust.Falling Behind? examines these repeated cycles up to the present, shedding new light on the adequacy of the science and engineering workforce for the current and future needs of the United States.

There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends.In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin.Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.

Since Poincare's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area.The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann problem for the Cauchy-Riemann complex and certain of its applications. The authors prove the main existence and regularity theorems in detail, assuming only a knowledge of the basic theory of differentiable manifolds and operators on Hilbert space. They discuss applications to the theory of several complex variables, examine the associated complex on the boundary, and outline other techniques relevant to these problems. In an appendix they develop the functional analysis of differential operators in terms of Sobolev spaces, to the extent it is required for the monograph.

This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry. Of particular interest are the discussions concerning the Adams Conjecture, K-theories of finite fields, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory, the author provides a new treatment of the foundations which is more general and more precise than previous versions.One purpose of this book is to offer the basic techniques and results of etale homotopy theory to topologists and algebraic geometers who may then apply the theory in their own work. With a view to such future applications, the author has introduced a number of new constructions (function complexes, relative homology and cohomology, generalized cohomology) which have immediately proved applicable to algebraic K-theory.

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology.In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems.Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "e;plats."e; Research problems are included in an appendix.

The description for this book, K-Theory of Forms. (AM-98), Volume 98, will be forthcoming.

Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.

Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.

Beginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators.

The last three decades have seen a massive expansion of China's visual culture industries, from architecture and graphic design to fine art and fashion. New ideologies of creativity and creative practices have reshaped the training of a new generation of art school graduates. Creativity Class is the first book to explore how Chinese art students develop, embody, and promote their own personalities and styles as they move from art school entrance test preparation, to art school, to work in the country's burgeoning culture industries. Lily Chumley shows the connections between this creative explosion and the Chinese government's explicit goal of cultivating creative human capital in a new "e;market socialist"e; economy where value is produced through innovation.Drawing on years of fieldwork in China's leading art academies and art test prep schools, Chumley combines ethnography and oral history with analyses of contemporary avant-garde and official art, popular media, and propaganda. Examining the rise of a Chinese artistic vanguard and creative knowledge-based economy, Creativity Class sheds light on an important facet of today's China.