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In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics. Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "e;My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."e; Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.

In a pluralistic society such as ours, tolerance is a virtue-but it doesn't always seem so. Some suspect that it entangles us in unacceptable moral compromises and inequalities of power, while others dismiss it as mere political correctness or doubt that it can safeguard the moral and political relationships we value. Tolerance among the Virtues provides a vigorous defense of tolerance against its many critics and shows why the virtue of tolerance involves exercising judgment across a variety of different circumstances and relationships-not simply applying a prescribed set of rules.Drawing inspiration from St. Paul, Aquinas, and Wittgenstein, John Bowlin offers a nuanced inquiry into tolerance as a virtue. He explains why the advocates and debunkers of toleration have reached an impasse, and he suggests a new way forward by distinguishing the virtue of tolerance from its false look-alikes, and from its sibling, forbearance. Some acts of toleration are right and good, while others amount to indifference, complicity, or condescension. Some persons are able to draw these distinctions well and to act in accord with their better judgment. When we praise them as tolerant, we are commending them as virtuous. Bowlin explores what that commendation means.Tolerance among the Virtues offers invaluable insights into how to live amid differences we cannot endorse-beliefs we consider false, actions we think are unjust, institutional arrangements we consider cruel or corrupt, and persons who embody what we oppose.

Originally published in 1960, The Edge of Objectivity helped to establish the history of science as a full-fledged academic discipline. In the mid-1950s, a young professor at Princeton named Charles Gillispie began teaching Humanities 304, one of the first undergraduate courses offered anywhere in the world on the history of science. From Galileo's analysis of motion to theories of evolution and relativity, Gillispie introduces key concepts, individuals, and themes. The Edge of Objectivity arose out of this course. It must have been a lively class. The Edge of Objectivity is pointed, opinionated, and selective. Even at six hundred pages, the book is, as the title suggests, an essay. Gillispie is unafraid to rate Mendel higher than Darwin, Maxwell above Faraday. Full of wry turns of phrase, the book effectively captures people and places. And throughout the book, Gillispie pushes an argument. He views science as the progressive development of more objective, detached, mathematical ways of viewing the world, and he orchestrates his characters and ideas around this theme. This edition of Charles Coulston Gillispie's landmark book introduces a new generation of readers to his provocative and enlightening account of the advancement of scientific thought over the course of four centuries. Since the original publication of The Edge of Objectivity, historians of science have focused increasingly on the social context of science rather than its internal dynamics, and they have frequently viewed science more as a threatening instance of power than as an accumulation of knowledge. Nevertheless, Gillispie's book remains a sophisticated, fast-moving, idiosyncratic account of the development of scientific ideas over four hundred years, by one of the founding intellects in the history of science.Featuring a new foreword by Theodore Porter, who places the work in its intellectual context and the development of the field, this edition of The Edge of Objectivity is a monumental work by one of the founding intellects of the history of science.

A close look at the evolution of American political alliances in Asia and their futureWhile the American alliance system in Asia has been fundamental to the region's security and prosperity for seven decades, today it encounters challenges from the growth of China-based regional organizations. How was the American alliance system originally established in Asia, and is it currently under threat? How are competing security designs being influenced by the United States and China? In Powerplay, Victor Cha draws from theories about alliances, unipolarity, and regime complexity to examine the evolution of the U.S. alliance system and the reasons for its continued importance in Asia and the world.Cha delves into the fears, motivations, and aspirations of the Truman and Eisenhower presidencies as they contemplated alliances with the Republic of China, Republic of Korea, and Japan at the outset of the Cold War. Their choice of a bilateral "e;hub and spokes"e; security design for Asia was entirely different from the system created in Europe, but it was essential for its time. Cha argues that the alliance system's innovations in the twenty-first century contribute to its resiliency in the face of China's increasing prominence, and that the task for the world is not to choose between American and Chinese institutions, but to maximize stability and economic progress amid Asia's increasingly complex political landscape.Exploring U.S. bilateral relations in Asia after World War II, Powerplay takes an original look at how global alliances are achieved and maintained.

The first book on the central importance of literary sources in the paintings of Cy TwomblyMany of Cy Twombly's paintings and drawings include handwritten words and phrases-naming or quoting poets ranging from Sappho, Homer, and Virgil to Mallarme, Rilke, and Cavafy. Enigmatic and sometimes hard to decipher, these inscriptions are a distinctive feature of his work. Reading Cy Twombly poses both literary and art historical questions. How does poetic reference in largely abstract works affect their interpretation?Reading Cy Twombly is the first book to focus specifically on the artist's use of poetry. Twombly's library formed an extension of his studio and he sometimes painted with a book open in front of him. Drawing on original research in an archive that includes his paint-stained and annotated books, Mary Jacobus's account-richly illustrated with more than 125 color and black-and-white images-unlocks an important aspect of Twombly's practice.Jacobus shows that poetry was an indispensable source of reference throughout Twombly's career; as he said, he "e;never really separated painting and literature."e; Among much else, she explores the influence of Ezra Pound and Charles Olson; Twombly's fondness for Greek pastoral poetry and Virgil's Eclogues; the inspiration of the Iliad and Ovid's Metamorphoses; and Twombly's love of Keats and his collaboration with Octavio Paz.Twombly's art reveals both his distinctive relationship to poetry and his use of quotation to solve formal problems. A modern painter, he belongs in a critical tradition that goes back, by way of Roland Barthes, to Baudelaire. Reading Cy Twombly opens up fascinating new readings of some of the most important paintings and drawings of the twentieth century.

A groundbreaking book that examines all aspects of male aging through an evolutionary lensWhile the health of aging men has been a focus of biomedical research for years, evolutionary biology has not been part of the conversation-until now. How Men Age is the first book to explore how natural selection has shaped male aging, how evolutionary theory can inform our understanding of male health and well-being, and how older men may have contributed to the evolution of some of the very traits that make us human.In this informative and entertaining book, renowned biological anthropologist Richard Bribiescas looks at all aspects of male aging through an evolutionary lens. He describes how the challenges males faced in their evolutionary past influenced how they age today, and shows how this unique evolutionary history helps explain common aspects of male aging such as prostate disease, loss of muscle mass, changes in testosterone levels, increases in fat, erectile dysfunction, baldness, and shorter life spans than women. Bribiescas reveals how many of the physical and behavioral changes that we negatively associate with male aging may have actually facilitated the emergence of positive traits that have helped make humans so successful as a species, including parenting, long life spans, and high fertility.Popular science at its most compelling, How Men Age provides new perspectives on the aging process in men and how we became human, and also explores future challenges for human evolution-and the important role older men might play in them.

A remarkable sequence of sonnets that reflect contemporary daily life in New York CityScaffolding is a sequence of eighty-two sonnets written over the course of a year, dated and arranged in roughly chronological order, and vividly reflecting life in New York City. In this, her third book of poetry, Elena Rivera uses the English sonnet as a scaffold to explore daily events, observations, conversations, thoughts, words, and memories-and to reflect on the work of earlier poets and the relationship between life and literature.Guided by formal and syllabic constraints, the poems become in part an exploration of how form affects content and how other poets have approached the sonnet. The poems, which are very attentive to rhythm and sound, are often in conversation with historical, philosophical, artistic, and literary sources. But at the same time they engage directly with the present moment. Like the construction scaffolding that year after year goes up around buildings all over New York, these poems build on one another and change the way we see what was there before.

A fully updated and expanded new edition of the acclaimed, bestselling dinosaur field guideThe bestselling Princeton Field Guide to Dinosaurs remains the must-have book for anyone who loves dinosaurs, from amateur enthusiasts to professional paleontologists. Now extensively revised and expanded, this dazzlingly illustrated large-format edition features some 100 new dinosaur species and 200 new and updated illustrations, bringing readers up to the minute on the latest discoveries and research that are radically transforming what we know about dinosaurs and their world.Written and illustrated by acclaimed dinosaur expert Gregory Paul, this stunningly beautiful book includes detailed species accounts of all the major dinosaur groups as well as nearly 700 color and black-and-white images-skeletal drawings, "e;life"e; studies, scenic views, and other illustrations that depict the full range of dinosaurs, from small feathered creatures to whale-sized supersauropods. Paul's extensively revised introduction delves into dinosaur history and biology, the extinction of nonavian dinosaurs, the origin of birds, and the history of dinosaur paleontology, as well as giving a taste of what it might be like to travel back in time to the era when dinosaurs roamed the earth.Now extensively revised and expandedCovers nearly 750 dinosaur species, including scores of newly discovered onesProvides startling new perspectives on the famed Brontosaurus and TyrannosaurusFeatures nearly 700 color and black-and-white drawings and figures, including life studies, scenic views, and skull and muscle drawingsIncludes color paleo-distribution maps and a color time lineDescribes anatomy, physiology, locomotion, reproduction, and growth of dinosaurs, as well as the origin of birds and the extinction of nonavian dinosaurs

The ideal introductory textbook to the politics of the policymaking processThis textbook uses modern political economy to introduce students of political science, government, economics, and public policy to the politics of the policymaking process. The book's distinct political economy approach has two virtues. By developing general principles for thinking about policymaking, it can be applied across a range of issue areas. It also unifies the policy curriculum, offering coherence to standard methods for teaching economics and statistics, and drawing connections between fields.The book begins by exploring the normative foundations of policymaking-political theory, social choice theory, and the Paretian and utilitarian underpinnings of policy analysis. It then introduces game theoretic models of social dilemmas-externalities, coordination problems, and commitment problems-that create opportunities for policy to improve social welfare. Finally, it shows how the political process creates technological and incentive constraints on government that shape policy outcomes. Throughout, concepts and models are illustrated and reinforced with discussions of empirical evidence and case studies.This textbook is essential for all students of public policy and for anyone interested in the most current methods influencing policymaking today.Comprehensive approach to politics and policy suitable for advanced undergraduates and graduate studentsModels unify policy curriculum through methodological coherenceExercises at the end of every chapterSelf-contained appendices cover necessary game theoryExtensive discussion of cases and applications

Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non-zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, Andre, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G -series is again a G -series. This book will be indispensable for those wishing to study the work of Bombieri and Andre on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations.

Democracy for Realists assails the romantic folk-theory at the heart of contemporary thinking about democratic politics and government, and offers a provocative alternative view grounded in the actual human nature of democratic citizens.Christopher Achen and Larry Bartels deploy a wealth of social-scientific evidence, including ingenious original analyses of topics ranging from abortion politics and budget deficits to the Great Depression and shark attacks, to show that the familiar ideal of thoughtful citizens steering the ship of state from the voting booth is fundamentally misguided. They demonstrate that voterseven those who are well informed and politically engagedmostly choose parties and candidates on the basis of social identities and partisan loyalties, not political issues. They also show that voters adjust their policy views and even their perceptions of basic matters of fact to match those loyalties. When parties are roughly evenly matched, elections often turn on irrelevant or misleading considerations such as economic spurts or downturns beyond the incumbents' control; the outcomes are essentially random. Thus, voters do not control the course of public policy, even indirectly.Achen and Bartels argue that democratic theory needs to be founded on identity groups and political parties, not on the preferences of individual voters. Democracy for Realists provides a powerful challenge to conventional thinking, pointing the way toward a fundamentally different understanding of the realities and potential of democratic government.

The subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose light-like geodesics are periodic? A surprising fact is that such manifolds exist in abundance in (2 + 1)-dimensions (though in higher dimensions they are quite rare). This book is concerned with the deformation theory of M2,1 (which furnishes almost all the known examples of these objects). It also has a section describing conformal invariants of these objects, the most interesting being the determinant of a two dimensional "e;Floquet operator,"e; invented by Paneitz and Segal.

The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n). The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometric-like functions by their exponents at the divisors "e;at infinity"e; permits one to prove generalizations in n-variables of the Kummer identities for n-1 involving quadratic and cubic changes of the variable.

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.

On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial.Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.

The description for this book, Calculus on Heisenberg Manifolds. (AM-119), Volume 119, will be forthcoming.

A new group of contributions to the development of this theory by leading experts in the field. The contributors include L. D. Berkovitz, L. E. Dubins, H. Everett, W. H. Fleming, D. Gale, D. Gillette, S. Karlin, J. G. Kemeny, R. Restrepo, H. E. Scarf, M. Sion, G. L. Thompson, P. Wolfe, and others.

The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.

The description for this book, Linear Inequalities and Related Systems. (AM-38), Volume 38, will be forthcoming.

The description for this book, Contributions to Fourier Analysis. (AM-25), will be forthcoming.

The description for this book, Lectures on Differential Equations. (AM-14), Volume 14, will be forthcoming.

A survey, thorough and timely, of the singularities of two-dimensional normal complex analytic varieties, the volume summarizes the results obtained since Hirzebruch's thesis (1953) and presents new contributions. First, the singularity is resolved and shown to be classified by its resolution; then, resolutions are classed by the use of spaces with nilpotents; finally, the spaces with nilpotents are determined by means of the local ring structure of the singularity.

The description for this book, The Calculi of Lambda Conversion. (AM-6), Volume 6, will be forthcoming.

In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes.The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2-1)...(qn-1-1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq).

Kurt Godel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Godel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Gottingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty. His 1940 book, better known by its short title, The Consistency of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Godel set forth his proof for this problem. In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond.

In this monograph the authors redevelop the theory systematically using two different approaches. A general mechanism for the deformation of structures on manifolds was developed by Donald Spencer ten years ago. A new version of that theory, based on the differential calculus in the analytic spaces of Grothendieck, was recently given by B. Malgrange. The first approach adopts Malgrange's idea in defining jet sheaves and linear operators, although the brackets and the non-linear theory arc treated in an essentially different manner. The second approach is based on the theory of derivations, and its relationship to the first is clearly explained. The introduction describes examples of Lie equations and known integrability theorems, and gives applications of the theory to be developed in the following chapters and in the subsequent volume.

The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.

This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory.TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Over baseball history, which park has been the best for run scoring?1 Which player would lose the most home runs after adjustments for ballpark effect?2 Which player claims four of the top five places for best individual seasons ever played, based on all-around offensive performance.3 (See answers, below). These are only three of the intriguing questions Michael Schell addresses in Baseball's All-Time Best Sluggers, a lively examination of the game of baseball using the most sophisticated statistical tools available. The book provides an in-depth evaluation of every major offensive event in baseball history, and identifies the players with the 100 best seasons and most productive careers. For the first time ever, ballpark effects across baseball history are presented for doubles, triples, right- and left-handed home-run hitting, and strikeouts. The book culminates with a ranking of the game's best all-around batters. Using a brisk conversational style, Schell brings to the plate the two most important credentials essential to producing a book of this kind: an encyclopedic knowledge of baseball and a professional background in statistics. Building on the traditions of renowned baseball historians Pete Palmer and Bill James, he has analyzed the most important factors impacting the sport, including the relative difficulty of hitting in different ballparks, the length of hitters' careers, the talent pool from which players are drawn, player aging, and changes in the game that have raised or lowered major-league batting averages. Schell's book finally levels the playing field, giving new credit to hitters who played in adverse conditions, and downgrading others who faced fewer obstacles. It also provides rankings based on players' positions. For example, Derek Jeter ranks 295th out of 1,140 on the best batters list, but jumps to 103rd in the position-adjusted list, reflecting his offensive prowess among shortstops. Replete with dozens of never-before reported stories and statistics, Baseball's All-Time Best Sluggers will forever shape the way baseball fans view the greatest heroes of America's national pastime. Answers: 1. Coors Field 2. Mel Ott 3. Barry Bonds, 2001-2004 seasons