Mathematics Books
Princeton University Press Topology of 4Manifolds
Book SynopsisOne of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of tTable of Contents*FrontMatter, pg. i*Contents, pg. v*Introduction, pg. 3*CHAPTER 1. BASIC TOOLS, pg. 11*CHAPTER 2. CAPPED GROPES, pg. 30*CHAPTER 3. CAPPED TOWERS, pg. 48*CHAPTER 4. PARAMETERIZATION OF CONVERGENT TOWERS, pg. 62*CHAPTER 5. THE EMBEDDING THEOREMS, pg. 85*CHAPTER 6. EMBEDDING UP TO S-COBORDISM, pg. 92*INTRODUCTION, pg. 99*CHAPTER 7. h-COBORDISMS, pg. 101*CHAPTER 8. SMOOTH STRUCTURES, pg. 114*CHAPTER 9. HANDLEBODIES, NORMAL BUNDLES, AND TRANSVERSALITY, pg. 134*CHAPTER 10. CLASSIFICATIONS AND EMBEDDINGS, pg. 161*CHAPTER 11. SURGERY, pg. 195*CHAPTER 12. LINKS, AND REFORMULATIONS OF THE EMBEDDING PROBLEM, pg. 232*REFERENCES, pg. 249*Index of Notation, pg. 257*Index of Terminology, pg. 257
£40.80
Princeton University Press Abraham Robinson The Creation of Nonstandard
Book SynopsisOne of the most prominent mathematicians of the twentieth century, Abraham Robinson discovered and developed nonstandard analysis, a rigorous theory of infinitesimals that he used to unite mathematical logic with the larger body of historic and modern mathematics. In this first biography of Robinson, Joseph Dauben reveals the mathematician's personTrade ReviewJoseph Warren Dauben, Winner of the 2012 Albert Leon Whiteman Memorial Prize, American Mathematical Society "This masterpiece of scientific biography presents the eventful life and the pioneering work of a remarkable figure of twentieth-century pure and applied mathematics as well as symbolic logic. [A] well-written and most carefully researched text [that is] enlightening and delightful to read. Dauben alternates two narratives, biography and the progression of science, not omitting daily and academic life, and their background in general and cultural history, of the stations of Robinson's odyssey... The book is bound to become an indispensable source for future historical work."--Detlef Laugwitz, Mathematical Reviews "Robinson, who expressed a certain preference for 'glamour,' led a life that is interesting for its own sake. Dauben's account of it is engrossingly intimate."--Albert C. Lewis, IsisTable of ContentsForewordAcknowledgmentsCh. 1Family and Childhood: Germany 1918-19333Ch. 2Life in Palestine: 1933-193933Ch. 3Robinson in Paris: January-June 194059Ch. 4Robinson and the War: London 1940-194691Ch. 5Robinson after the War: London 1946-1951131Ch. 6The University of Toronto: 1951-1957185Ch. 7The Hebrew University: Jerusalem 1957-1962243Ch. 8UCLA and Nonstandard Analysis: 1962-1967305Ch. 9Robinson Joins the Ivy League: Yale University 1967-1974403Epilogue. Abraham Robinson: The Man and His Mathematics491Bibliography495Index537
£80.00
Princeton University Press The Global Nonlinear Stability of the Minkowski
Book SynopsisThe aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singulTrade ReviewWinner of the 1999 Bocher Memorial Prize, American Mathematical Association "This book presents the authors' theorem on the stability of Minkowski space, a landmark in the development of mathematical relativity. The book is quite self-contained... The book is not easy to read, due to the very technical nature of its contents, but under the circumstances the quality of the exposition is excellent."--Mathematical ReviewsTable of ContentsAcknowledgments1Introduction1IPreliminary Results in 2-and 3-Dimensional Riemannian Geometry2Generalized Hodge Systems in 2-D313General Results in 3-D Geometry534The Poisson Equation in 3-D785Curvature of an Initial Data Set1106Deformation of 2-Surfaces in 3-D121IIBianchi Equations in Space-Time7The Comparison Theorem1358The Error Estimates205IIIConstruction of Global Space-Times. Proof of the Main Theorem9Construction of the Optical Function26110Third Version of the Main Theorem28411Second Fundamental Form31112The Lapse Function34113Derivatives of the Optical Function35114The Last Slice41115The Matching44316The Rotation Vectorfields46617Conclusions491Bibliography513
£78.20
Princeton University Press Operator Techniques in Atomic Spectroscopy
Book SynopsisIn the 1920s, when quantum mechanics was in its infancy, chemists and solid state physicists had little choice but to manipulate unwieldy equations to determine the properties of even the simplest molecules. When mathematicians turned their attention to the equations of quantum mechanics, they discovered that these could be expressed in terms of grTrade Review"Throughout, I have had in mind the experimentalist who wishes to grasp the principles of the theory (of continuous groups) and learn how to apply them to physical problems."—From the introductionTable of ContentsPreface to the Paperback EditionPrefaceCh. 1Classical Methods1Ch. 2Crystal Fields25Ch. 3The n-j Symbols54Ch. 4Configurations of two Electrons76Ch. 5Continuous Groups95Ch. 6Seniority154Ch. 7Fractional Parentage Coefficients166Ch. 8Configurations of More than Two Equivalent Electrons193App. 1Radial Integrals for Hydrogenic Eigenfunctions225App. 2The Coefficients (UL\U'L' + f) and (WU\W'U' + f)227References233Index237
£38.25
Princeton University Press Dynamical Chaos
Book SynopsisThe leading scientists who gave these papers under the sponsorship of the Royal Society in early 1987 provide reviews of facets of the subject of chaos ranging from the practical aspects of mirror machines for fusion power to the pure mathematics of geodesics on surfaces of negative curvature. The papers deal with systems in which chaotic conditionTable of Contents*FrontMatter, pg. i*Contents, pg. v*Chairman's introduction, pg. 3*Diagnosis of dynamical systems with fluctuating parameters, pg. 5*Nonlinear dynamics, chaos and complex cardiac arrhythmias, pg. 9*Chaos and the dynamics of biological populations, pg. 27*Fractal bifurcation sets, renormalization strange sets and their universal invariants, pg. 45*From chaos to turbulence in Benard convection, pg. 63*Dynamics of convection, pg. 71*Chaos: a mixed metaphor for turbulence, pg. 87*Arithmetical theory of Anosov diffeomorphisms, pg. 97*Chaotic behaviour in the Solar System, pg. 109*Chaos in hamiltonian systems, pg. 131*Particle confinement and adiabatic invariance, pg. 145*Semi-classical quantization, adiabatic invariants and classical chaos, pg. 157*Some geometrical models of chaotic dynamics, pg. 171*THE BAKERIAN LECTURE, 1 9 8 7 Quantum chaology, pg. 183
£34.00
Princeton University Press Fractals in the Natural Sciences
Book SynopsisIn the words of B. B. Mandelbrot's contribution to this important collection of original papers, fractal geometry is a new geometric language, which is geared towards the study of diverse aspects of diverse objects, either mathematical or natural, that are not smooth, but rough and fragmented to the same degree at all scales. This book will be ofTable of Contents*FrontMatter, pg. i*Contents, pg. 1*Fractal geometry: what is it, and what does it do ?, pg. 3*Fractals, phase transitions and criticality, pg. 17*Fractals and phase separation, pg. 35*Experiments on the structure and vibrations of fractal solids, pg. 55*Universality of fractal aggregates as probed by light scattering, pg. 71*Light-scattering studies of aggregation, pg. 89*Time-series analysis, pg. 103*Diffusion-controlled growth, pg. 123*Diffusion-limited aggregation, pg. 133*Electrodeposition in support: concentration gradients, an ohmic model and the genesis of branching fractals, pg. 149*Flow through porous media: limits of fractal patterns, pg. 159*Fractal BET and FHH theories of adsorption: a comparative study, pg. 169*Reactions in and on fractal media, pg. 189
£34.00
Princeton University Press HypoAnalytic Structures
Book SynopsisIn Hypo-Analytic Structures Franois Treves provides a systematic approach to the study of the differential structures on manifolds defined by systems of complex vector fields. Serving as his main examples are the elliptic complexes, among which the De Rham and Dolbeault are the best known, and the tangential Cauchy-Riemann operators. Basic geometriTable of ContentsPrefaceIFormally and Locally Integrable Structures. Basic Definitions3I.1Involutive systems of linear PDE defined by complex vector fields. Formally and locally integrable structures5I.2The characteristic set. Partial classification of formally integrable structures11I.3Strongly noncharacteristic, totally real, and maximally real submanifolds16I.4Noncharacteristic and totally characteristic submanifolds23I.5Local representations27I.6The associated differential complex32I.7Local representations in locally integrable structures39I.8The Levi form in a formally integrable structure46I.9The Levi form in a locally integrable structure49I.10Characteristics in real and in analytic structures56I.11Orbits and leaves. Involutive structures of finite type63I.12A model case: Tube structures68IILocal Approximation and Representation in Locally Integrable Structures73II.1The coarse local embedding76II.2The approximation formula81II.3Consequences and generalizations86II.4Analytic vectors94II.5Local structure of distribution solutions and of L-closed currents100II.6The approximate Poincare lemma104II.7Approximation and local structure of solutions based on the fine local embedding108II.8Unique continuation of solutions115IIIHypo-Analytic Structures. Hypocomplex Manifolds120III.1Hypo-analytic structures121III.2Properties of hypo-analytic functions128III.3Submanifolds compatible with the hypo-analytic structure130III.4Unique continuation of solutions in a hypo-analytic manifold137III.5Hypocomplex manifolds. Basic properties145III.6Two-dimensional hypocomplex manifolds152Appendix to Section III.6: Some lemmas about first-order differential operators159III.7A class of hypocomplex CR manifolds162IVIntegrable Formal Structures. Normal Forms167IV.1Integrable formal structures168IV.2Hormander numbers, multiplicities, weights. Normal forms174IV.3Lemmas about weights and vector fields178IV.4Existence of basic vector fields of weight - 1185IV.5Existence of normal forms. Pluriharmonic free normal forms. Rigid structures191IV.6Leading parts198VInvolutive Structures with Boundary201V.1Involutive structures with boundary202V.2The associated differential complex. The boundary complex209V.3Locally integrable structures with boundary. The Mayer-Vietoris sequence219V.4Approximation of classical solutions in locally integrable structures with boundary226V.5Distribution solutions in a manifold with totally characteristic boundary228V.6Distribution solutions in a manifold with noncharacteristic boundary235V.7Example: Domains in complex space246VILocal Integrability and Local Solvability in Elliptic Structures252VI.1The Bochner-Martinelli formulas253VI.2Homotopy formulas for [actual symbol not reproducible] in convex and bounded domains258VI.3Estimating the sup norms of the homotopy operators264VI.4Holder estimates for the homotopy operators in concentric balls269VI.5The Newlander-Nirenberg theorem281VI.6End of the proof of the Newlander-Nirenberg theorem287VI.7Local integrability and local solvability of elliptic structures. Levi flat structures291VI.8Partial local group structures297VI.9Involutive structures with transverse group action. Rigid structures. Tube structures303VIIExamples of Nonintegrability and of Nonsolvability312VII.1Mizohata structures314VII.2Nonsolvability and nonintegrability when the signature of the Levi form is |n - 2|319VII.3Mizohata structures on two-dimensional manifolds324VII.4Nonintegrability and nonsolvability when the cotangent structure bundle has rank one330VII.5Nonintegrability and nonsolvability in Lewy structures. The three-dimensional case337VII.6Nonintegrability in Lewy structures. The higher-dimensional case343VII.7Example of a CR structure that is not locally integrable but is locally integrable on one side348VIIINecessary Conditions for the Vanishing of the Cohomology. Local Solvability of a Single Vector Field352VIII.1Preliminary necessary conditions for exactness354VIII.2Exactness of top-degree forms358VIII.3A necessary condition for local exactness based on the Levi form364VIII.4A result about structures whose characteristic set has rank at most equal to one367VIII.5Proof of Theorem VIII.4.1373VIII.6Applications of Theorem VII
£70.40
Princeton University Press Topics in NonCommutative Geometry
Book SynopsisThere is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the applicationTrade Review"[This reviewer] like[s] the book a lot. First, because of the excellent mathematics it contains. But second, because of the truly enlightening way this mathematics gets conveyed to the reader."--Bulletin of the American Mathematical SocietyTable of Contents*FrontMatter, pg. i*CONTENTS, pg. v*PREFACE, pg. vii*CHAPTER 1 . AN OVERVIEW, pg. 3*CHAPTER 2. SUPERSYMMETRIC ALGEBRAIC CURVES, pg. 33*CHAPTER 3. FLAG SUPERSPACES AND SCHUBERT SUPERCELLS, pg. 96*CHAPTER 4. QUANTUM GROUPS AS SYMMETRIES OF, pg. 124*BIBLIOGRAPHY, pg. 157*INDEX, pg. 164
£28.80
Princeton University Press Plateaus Problem and the Calculus of Variations
Book SynopsisThis book is meant to give an account of recent developments in the theory of Plateau's problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and reTable of Contents*FrontMatter, pg. i*Contents, pg. vii*Preface, pg. ix*I. Existence of a solution, pg. 5*II. Unstable minimal surfaces, pg. 33*III. The existence of surfaces of prescribed constant mean curvature spanning a Jordan curve in IR3, pg. 91*IV. Unstable H-surfaces, pg. 111*References, pg. 141
£27.00
Princeton University Press Archimedes
Book SynopsisThis classic study by the eminent Dutch historian of science E. J. Dijksterhuis (1892-1965) presents the work of the Greek mathematician and mechanical engineer to the modern reader. With meticulous scholarship, Dijksterhuis surveys the whole range of evidence on Archimedes' life and the 2000-year history of the manuscripts and editions of the textTable of Contents*FrontMatter, pg. 1*Contents, pg. 5*Preface, pg. 7*Chapter I. The Life of Archimedes, pg. 9*Chapter II. The Works of Archimedes. Manuscripts and Edition, pg. 33*Chapter III. The Elements of the Work of Archimedes, pg. 49*Chapter IV. On the Sphere and Cylinder. Book 1, pg. 141*Chapter V. On the Sphere and Cylinder. Book II, pg. 188*Chapter VI. Measurement of a Circle, pg. 222*Chapter VII. On Conoids and Spheroids, pg. 240*Chapter VIII. On Spirals, pg. 264*Chapter IX. On the Equilibrium of Planes or Centres of Gravity of Planes. Book I, pg. 286*Chapter X. The Method of Mechanical Theorems, pg. 313*Chapter XI. Quadrature of the Parabola, pg. 336*Chapter XII. On the Equilibrium of Planes. Book II, pg. 346*Chapter XIII. The Sand-Reckoner, pg. 360*Chapter XIV. Floating Bodies, pg. 373*Chapter XV. Miscellaneous, pg. 398*Bibliography, pg. 417*Archimedes after Dijksterhuis: A Guide to Recent Studies, pg. 419*Index of Names, pg. 452*Errata, pg. 456
£62.40
Princeton University Press Programming as if People Mattered Friendly
Book SynopsisThrough a set of lively anecdotes and essays, Nathaniel Borenstein traces the divergence between the fields of software engineering and user-centered software design, and attempts to reconcile the needs of people in both camps. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make avaiTrade Review"This book is very easy to read, and is so entertaining that it is hard to put down... An excellent book, and a must-read for software professionals."--Choice "The book provides a stimulating read, with a fair sprinkling of controversial opinions from which intelligent readers ... will draw their own conclusions."--J. Dodd, Information and Science Technology "This book's great glory is the author's implicit, but pervasive, notion that the human interface extends through software; and that programs are just ways that people tell computers what they should be doing... [A] book filled with points to think about well before you start coding menus or screens."--UnixWorld "A witty look at the foibles of software engineering, based on real examples... This voice of experience offers a good dose of humility to arrogant young programmers."--American Mathematical MonthlyTable of Contents*FrontMatter, pg. i*Contents, pg. vii*Preface, pg. ix*Acknowledgments, pg. xiii*Introduction, pg. 3*Chapter 1. The Hostile Beast, pg. 5*Introduction, pg. 17*Chapter 2. Who Are AU These People?, pg. 19*Chapter 3. Stopwatches, Videotapes, and Human Nature, pg. 25*Chapter 4. That Reminds Me of the Time..., pg. 33*Chapter 5. The Quest for the Perfect Line Editor, pg. 39*Chapter 6. The Men in Suits, pg. 49*Chapter 7. Information Wants to Be Free, pg. 63*Introduction, pg. 67*Chapter 8. Never Underestimate Your Users, pg. 69*Chapter 9. Pretend That Small Is Beautiful, but Don't Believe It, pg. 75*Chapter 10. Tune Defaults to the Novice, pg. 83*Chapter 11. Don't Neglect the Experts, pg. 91*Chapter 12. Your Program Stinks, and So Do You, pg. 99*Chapter 13. Listen to Your Users, but Ignore What They Say, pg. 105*Chapter 14. Lie to Your Managers, pg. 111*Chapter 15. Cut Corners Proudly, pg. 115*Chapter 16. Remember Your Ignorance, pg. 123*Chapter 17. Dabble in Mysticism, pg. 129*Chapter 18. Break All the Rules, pg. 133*Introduction, pg. 137*Chapter 19. The Tools of the Trade, pg. 139*Chapter 20. The Ivory Tower, pg. 157*Chapter 21. People Are Perverse: Designing for the Fickle User, pg. 165*Epilogue: Programming, Humility, and the Eclipse of the Self, pg. 177*Further Reading, pg. 181*References, pg. 183
£34.00
Princeton University Press Shafarevich Maps and Automorphic Forms
Book SynopsisThe aim of this book is to study various geometric properties and algebraic invariants of smooth projective varieties with infinite fundamental groups. This approach allows for much interplay between methods of algebraic geometry, complex analysis, the theory of harmonic maps, and topology. Making systematic use of Shafarevich maps, a concept previTrade Review"I believe Kollar has written a powerful book, and not coincidentally, a fairly demanding one. However, the explanations are clear, and I think that more than half of it would be accessible to anyone who has mastered the basics of complex algebraic geometry... There are a number of sections ... which could be read independently of the rest of the book and would be of interest to almost any algebraic geometer. But to read only those sections would be a shame, because one would be missing a great deal of wonderful mathematics."--Bulletin of the American Mathematical SocietyTable of ContentsPrefaceAcknowledgmentsIntroduction3Ch. 1Lefschetz-Type Theorems for [pi][subscript 1]19Ch. 2Families of Algebraic Cycles27Ch. 3Shafarevich Maps and Variants36Ch. 4The Fundamental Group and the Classification of Algebraic Varieties49Ch. 5The Method of Poincare59Ch. 6The Method of Atiyah71Ch. 7Subjectivity of the Poincare Map81Ch. 8Ball Quotients92Ch. 9The Kodaira Vanishing Theorem105Ch. 10Generalizations of the Kodaira Vanishing Theorem115Ch. 11Vanishing of L[superscript 2]-Cohomologies127Ch. 12Rational Singularities and Hodge Theory133Ch. 13The Method of Gromov141Ch. 14Nonvanishing Theorems151Ch. 15Plurigenera in Etale Covers161Ch. 16Existence of Automorphic Forms167Ch. 17Applications to Abelian Varieties175Ch. 18Open Problems and Further Remarks183References191Index201
£34.00
Princeton University Press The Implementation of Prolog
Book SynopsisA semantically well-defined programming language widely used in artificial intelligence, Prolog has greatly influenced other programming languages since its introduction in the late 1970s. A user may find Prolog deceptively easy, however, and there are a number of different implementations. In this book Patrice Boizumault draws from his extensive eTable of ContentsForewordAcknowledgmentsIntroductionPt. IFundamental Principles of the LanguageCh. 1UnificationCh. 2Resolution and Prolog ControlCh. 3Improving Prolog ControlPt. IIPrinciples and Techniques of ImplementationCh. 4Control and Stack(s) ManagementCh. 5Representation of TermsCh. 6Deterministic Call ReturnsCh. 7Last-Call OptimizationCh. 8Clause IndexingCh. 9Compilation of PrologCh. 10The dif and freeze Predicates of Prolog-IIPt. IIIImplementationsCh. 11Mini-CPrologCh. 12Mini-WAMCh. 13Mini-Prolog-IICh. 14Built-In PredicatesConclusionAppendix A: Mini-CPrologAppendix B: Mini-WAMAppendix C: Mini-Prolog-IIAppendix D: Common PartBibliographyIndex
£46.40
Princeton University Press Matrices and Society Matrix Algebra and Its
Book SynopsisMatrices offer some of the most powerful techniques in modem mathematics. In the social sciences they provide fresh insights into an astonishing variety of topics. Dominance matrices can show how power struggles in offices or committees develop; Markov chains predict how fast news or gossip will spread in a village; permutation matrices illuminateTable of Contents*FrontMatter, pg. 1*Contents, pg. 5*Preface, pg. 7*1. Matrices and How to Manipulate Them, pg. 13*2. Matrix Inversion, pg. 30*3. The Ins and Outs of Economic Planning, pg. 42*4. Matrices and Matrimony in Tribal Societies, pg. 61*5. Dominance in Coops and Courts, pg. 79*6. The Simple Mathematics of Markov Chains, pg. 92*7. Models of Mobility, pg. 106*8. The Mathematics of Absorbing Markov Chains, pg. 122*9 'Everywhere Man Is in Chains', pg. 130*10. The Seven Ages of Man and Population Problems, pg. 149*11. Playing Games in Theory, pg. 173*12. Magic, Fishing and Farming - Some Applications of Constant-sum Games Theory, pg. 194*13. Conflict or Co-operation, pg. 207*Epilogue and Further Reading, pg. 231
£36.00
Princeton University Press Predicative Arithmetic
Book SynopsisThis book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton LegacyTable of Contents*FrontMatter, pg. i*Acknowledgments, pg. v*Table of Contents, pg. vii*Chapter 1. The impredicativity of induction, pg. 1*Chapter 2. Logical terminology, pg. 3*Chapter 3. The axioms of arithmetic, pg. 8*Chapter 4. Order, pg. 10*Chapter 5. Induction by relativization, pg. 12*Chapter 6. Interpretability in Robinson's theory, pg. 16*Chapter 7. Bounded induction, pg. 23*Chapter 8. The bounded least number principle, pg. 29*Chapter 9. The euclidean algorithm, pg. 32*Chapter 10. Encoding, pg. 36*Chapter 11. Bounded separation and minimum, pg. 43*Chapter 12. Sets and functions, pg. 46*Chapter 13. Exponential functions, pg. 51*Chapter 14. Exponentiation, pg. 54*Chapter 15. A stronger relativization scheme, pg. 60*Chapter 16. Bounds on exponential functions, pg. 64*Chapter 17. Bounded replacement, pg. 70*Chapter 18. An impassable barrier, pg. 73*Chapter 19. Sequences, pg. 82*Chapter 20. Cardinality, pg. 90*Chapter 21. Existence of sets, pg. 95*Chapter 22. Semibounded Replacement, pg. 98*Chapter 23. Formulas, pg. 101*Chapter 24. Proofs, pg. 111*Chapter 25. Derived rules of inference, pg. 115*Chapter 26. Special constants, pg. 134*Chapter 27. Extensions by definition, pg. 136*Chapter 28. Interpretations, pg. 152*Chapter 29. The arithmetization of arithmetic, pg. 157*Chapter 30. The consistency theorem, pg. 162*Chapter 31. Is exponentiation total?, pg. 173*Chapter 32. A modified Hilbert program, pg. 178*Bibliography, pg. 181*General index, pg. 183*Index of defining axioms, pg. 186
£35.00
Princeton University Press A Source Book in Mathematics 12001800
Book SynopsisThese selected mathematical writings cover the years when the foundations were laid for the theory of numbers, analytic geometry, and the calculus. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of PrincetonTable of Contents*FrontMatter, pg. i*ERRATA ET ADDENDA, pg. vii*PREFACE, pg. ix*CONTENTS, pg. xi*ABBREVIATIONS OF TITLES, pg. xiv*CHAPTER I ARITHMETIC, pg. 1*CHAPTER II. ALGEBRA, pg. 55*CHAPTER III. GEOMETRY, pg. 133*CHAPTER IV. ANALYSIS BEFORE NEWTON AND LEIBNIZ, pg. 188*CHAPTER V. NEWTON, LEIBNIZ, AND THEIR SCHOOL, pg. 270*INDEX, pg. 421
£63.75
Princeton University Press Introduction to Harmonic Analysis on Reductive P
Book SynopsisBased on a series of lectures given by Harish-Chandra at the Institute for Advanced Study in 1971-1973, this book provides an introduction to the theory of harmonic analysis on reductive p-adic groups. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-prTable of Contents*Frontmatter, pg. i*FOREWORD. ACKNOWLEDGMENTS, pg. iii*TABLE OF CONTENTS, pg. iv*Chapter 0. On the Structure of Reductive p-adic Groups, pg. 1*Chapter 1. Generalities Concerning Totally Disconnected Groups and Their Representations, pg. 14*Chapter 2. Jacquet's Theory, Bruhat's Theory, the Elementary Theory of the Constant Term, pg. 78*Chapter 3. Exponents and the Maass-Selberg Relations, pg. 116*Chapter 4. The Schwartz Spaces, pg. 147*Chapter 5. The Eisenstein Integral and Applications, pg. 221*References, pg. 362*SELECTED TERMINOLOGY, pg. 365*SELECTED NOTATIONS, pg. 370
£56.00
Princeton University Press The Motion of a Surface by Its Mean Curvature
Book SynopsisKenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity. He formulates his study in terms of varifold surfaces and uses the methods of geometric measure theory to develop a mathematical description of the motion ofTable of Contents*Frontmatter, pg. i*Table of Contents, pg. iii*1. Introduction, pg. 1*2. Preliminaries, pg. 6*3. Motion by mean curvature, pg. 18*4. Existence of varifolds moving by their mean curvature, pg. 33*5. Perpendicularity of mean curvature, pg. 121*6. Regularity, pg. 161*Appendix A: Grain growth in metals, pg. 224*Appendix B: Curves in R2, pg. 229*Appendix C: Curves of constant shape, pg. 235*Appendix D: Density bounds and rectiflability, pg. 238*Figure captions, pg. 240*Figures, pg. 241*References, pg. 251
£38.25
Princeton University Press Lectures on Exponential Decay of Solutions of
Book SynopsisMathematical Notes, 29 Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperTable of Contents*FrontMatter, pg. i*Table of Contents, pg. 1*Introduction, pg. 3*Chapter 0. Preliminaries, pg. 8*Chapter 1. The Main Theorem, pg. 11*Chapter 2. Geometric Spectral Analysis, pg. 32*Chapter 3. SeU-Adjointness, pg. 41*Chapter 4. L2 Exponenttal Decay Applications to eigenfunctions of N-body Schrodmger Operators, pg. 52*Chapter 5. Pointwise Exponential Bounds, pg. 83*Appendix 1. Approximallon of Metrics and Completeness, pg. 99*Appendix 2. Proof of Lemma 1.2, pg. 102*Appenduc 3. Proof of Lemma 2.2, pg. 104*Appendix 4. Proof of Lemma 5.7, pg. 110*Bibliographical Comments, pg. 112*References, pg. 115
£27.00
Princeton University Press Existence and Regularity of Minimal Surfaces on
Book SynopsisMathematical No/ex, 27 Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperTable of Contents*FrontMatter, pg. i*CONTENTS, pg. iv*INTRODUCTION, pg. 1*CHAPTER 1. NONTECHNICAL SYSTEMIC DESCRIPTION AND ILLUSTRATIVE EXAMPLES, pg. 12*CHAPTER 2. PRELIMINARIES, pg. 48*CHAPTER 3. ALMOST MINIMIZING VARIFOLDS, pg. 91*CHAPTER 4. EXISTENCE OF ALMOST MINIMIZING VARIFOLDS, pg. 138*CHAPTER 5. POINTWISE CURVATURE ESTIMATES FOR STABLE HYPERSURFACES, pg. 178*CHAPTER 6. DECOMPOSITION THEOREM FOR STABLE HYPERSURFACES, pg. 224*CHAPTER 7. REGULARITY, pg. 288*REFERENCES, pg. 327
£54.00
Princeton University Press Recurrence in Ergodic Theory and Combinatorial
Book SynopsisTopological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again makeTable of Contents*FrontMatter, pg. i*CONTENTS, pg. v*Foreword from the Porter Lectures Committee, pg. ix*Preface, pg. xi*Introduction, pg. 1*Chapter 1. Recurrence and Uniform Recurrence in Compact Spaces, pg. 19*Chapter 2. Van der Waerden's Theorem, pg. 40*Chapter 3. Invariant Measures on Compact Spaces, pg. 59*Chapter 4. Some Special Ergodic Theorems, pg. 79*Chapter 5. Measure Theoretic Preliminaries, pg. 98*Chapter 6. Structure of Measure Preserving Systems, pg. 117*Chapter 7. The Multiple Recurrence Theorem, pg. 140*Chapter 8. Proximality in Dynamical Systems and the Theorems of Hindman and Rado, pg. 157*Chapter 9. The Fine Structure of Recurrence and Mixing, pg. 175*Bibliography, pg. 195*Index, pg. 201
£34.00
Princeton University Press Algebraic Structures of Symmetric Domains
Book SynopsisThis book is a comprehensive treatment of the general (algebraic) theory of symmetric domains. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the originTable of Contents*FrontMatter, pg. i*Preface, pg. vii*Contents, pg. ix*Instructions to the Reader, pg. xi*List of Symbols, pg. xv*Chapter I. Algebraic Preliminaries, pg. 1*Chapter II. Basic Concepts on Symmetric Domains, pg. 44*Chapter III. Unbounded Realizations of Symmetric Domains. (Theory of Wolf -Koranyi), pg. 89*Chapter IV. Equivariant Holomorphic Maps of a Symmetric Domain into a Siegel Space, pg. 165*Chapter V. Infinitesimal Automorphisms of Symmetric Siegel Domains, pg. 209*Appendix: Classical Domains, pg. 267*References, pg. 291*Index, pg. 319
£51.00
Princeton University Press An Introduction to Combinatorial Analysis
Book SynopsisThis book introduces combinatorial analysis to the beginning student. The author begins with the theory of permutation and combinations and their applications to generating functions. In subsequent chapters, he presents Bell polynomials; the principle of inclusion and exclusion; the enumeration of permutations in cyclic representation; the theory oTable of Contents*FrontMatter, pg. i*Preface, pg. vii*Contents, pg. xi*Errata, pg. xii*CHAPTER 1. Permutations and Combinations, pg. 1*CHAPTER 2. Generating Functions, pg. 19*CHAPTER 3. The Principle of Inclusion and Exclusion, pg. 50*CHAPTER 4. The Cycles of Permutations, pg. 66*CHAPTER 5. Distributions: Occupancy, pg. 90*CHAPTER 6. Partitions, Compositions, Trees, and Networks, pg. 107*CHAPTER 7. Permutations with Restricted Position I, pg. 163*CHAPTER 8. Permutations with Restricted Position II, pg. 195*Index, pg. 239
£38.25
Princeton University Press Estimates of the Neumann Problem
Book SynopsisThe ?? Neumann problem is probably the most important and natural example of a non-elliptic boundary value problem, arising as it does from the Cauchy-Riemann equations. It has been known for some time how to prove solvability and regularity by the use of L2 methods. In this monograph the authors apply recent methods involving the Heisenberg groupTable of Contents*Frontmatter, pg. i*Preface, pg. iii*Table of Contents, pg. v*Introduction, pg. 1*Part I. Analysis on the Heisenberg group, pg. 10*Part II. Parametrix for the -Neumann problem, pg. 44*Part III. The Estimates, pg. 130*Principal notations, pg. 190*References, pg. 192
£34.00
Princeton University Press Optimization A Theory of Necessary Conditions
Book SynopsisThis book presents a comprehensive treatment of necessary conditions for general optimization problems. The presentation is carried out in the context of a general theory for extremal problems in a topological vector space setting. Following a brief summary of the required background, generalized Lagrange multiplier rules are derived for optimizatiTable of Contents*Frontmatter, pg. i*CONTENTS, pg. vii*PREFACE, pg. ix*SUMMARY OF NOTATION, pg. xiii*CHAPTER I. Mathematical Preliminaries, pg. 1*CHAPTER II. A Basic Optimization Problem in Simplified Form, pg. 63*CHAPTER III. A General Multiplier Rule, pg. 96*CHAPTER IV. Optimization with Operator Equation Restrictions, pg. 144*CHAPTER V. Optimal Control Problems with Ordinary Differential Equation Constraints, pg. 212*CHAPTER VI. Optimal Control Problems with Parameters and Related Problems, pg. 263*CHAPTER VII. Miscellaneous Optimal Control Problems, pg. 315*APPENDIX. Volterra-Type Operators, pg. 361*NOTES AND HISTORICAL COMMENTS, pg. 384*REFERENCES, pg. 413*SUBJECT INDEX, pg. 422
£55.25
Princeton University Press Kunihiko Kodaira Volume I Collected Works
Book SynopsisKunihiko Kodaira's influence in mathematics has been fundamental and international, and his efforts have helped lay the foundations of modern complex analysis. These three volumes contain Kodaira's written contributions, published in a large number of journals and books between 1937 and 1971. The volumes cover chronologically the major periods of KTable of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. xv*( 1 ) Tiber Die Struktur Des Endlichen, Vollstandig Primaren Ringes Mit Verschwindendem Radikalquadrat, pg. 1*( 2 ) Tiber Den Allgemeinen Zellenbegriti und die Zellenzer Spaltungen der Komplexe, pg. 8*( 3 ) Eine Bemerkung zur Dimensionstheorie, pg. 12*( 4 ) On Some Fundamental Theorems in the Theory of Operators in Hilbert Space, pg. 15*( 5 ) On the theory of almost periodic functions in a group, pg. 19*( 6 ) Uiber die DitIerenzierbarkeit der einparametrigen Untergruppe Liescher Gruppen, pg. 24*( 7 ) Uber zusammenhangende kompakte abelsche Gruppen, pg. 26*( 8 ) Die Kuratowskische Abbildung und der Hopfsche Erweiterungssatz, pg. 32*( 9 ) Uber die Gruppe der messbaren Abbildungen, pg. 40*( 10 ) Uber die Beziehung zwischen den Massen und den Topologien in einer Gruppe, pg. 46*( 11 ) Normed ring of a locally compact abelian group, pg. 99*( 12 ) Uber die Harmonischen Tensorfelder in Riemannschen Mannigfaltigkeiten, (I), (II), (III), pg. 105*( 13 ) Uber die Rand- und Eigenwertprobleme der linearen elliptischen Differentialgleichungen zweiter Ordnung, pg. 129*( 14 ) Uber das Haarsche Mass in der lokal bikompakten Gruppe, pg. 136*( 15 ) Relations between harmonic fields in Riemannian manifolds, pg. 143*( 16 ) On the existence of analytic functions on closed analytic surface, pg. 161*( 17 ) Harmonic fields in Riemannian manifolds (generalized potential theory), pg. 172*( 18 ) The eigenvalue problem for ordinary differential equations of the second order and Heisenberg's theory of S-matrices, pg. 251*( 19 ) On ordinary differential equations of any even order and the corresponding eigenfunction expansions, pg. 276*( 20 ) A non-separable translation invariant extension of the Lebesgue measure space, pg. 319*( 21 ) Harmonic integrals, Part II, pg. 325*( 22 ) The theorem of Riemann-Roch on compact analytic surfaces, pg. 339*( 23 ) Green's forms and meromorphic functions on compact analytic varieties, pg. 402*( 24 ) The theorem of Riemann-Roch for adjoint systems on 3-dimensional algebraic varieties, pg. 423*( 25 ) On analytic surfaces with two independent meromorphic functions (collaborated with W.-L. Chow), pg. 468*( 26 ) On the theorem of Riemann-Roch for adjoint systems on Kiihlerian varieties, pg. 475*( 27 ) Arithmetic genera of algebraic varieties, pg. 481*( 28 ) The theory of harmonic integrals and their applications to algebraic geometry, pg. 488*( 29 ) The theorem of Riemann-Roch for adjoint systems on Kiihlerian varieties, pg. 583*( 30 ) Some results in the transcendental theory of algebraic varieties, pg. 599
£104.00
Princeton University Press Kunihiko Kodaira Volume II Collected Works
Book SynopsisKunihiko Kodaira's influence in mathematics has been fundamental and international, and his efforts have helped lay the foundations of modern complex analysis. These three volumes contain Kodaira's written contributions, published in a large number of journals and books between 1937 and 1971. The volumes cover chronologically the major periods of KTable of Contents*Frontmatter, pg. i*CONTENTS, pg. v*31. On arithmetic genera of algebraic varieties, pg. 648*32. On cohomology groups of compact analytic varieties with coefficients in some analytic faisceaux, pg. 657*33. Groups of complex line bundles over compact Kahler varieties, pg. 661*34. Divisor class groups on algebraic varieties, pg. 665*35. On a differential-geometric method in the theory of analytic stacks, pg. 671*36. On a theorem of Lefschetz and the lemma of Enriques- Severi-Zariski, pg. 677*37. On Kahler Varieties of Restricted Type, pg. 683*38. On Kahler Varieties of Restricted Type (An Intrinsic Characterization of Algebraic Varieties), pg. 687*39. Some Results in the Transcendental Theory of Algebraic Varieties, pg. 708*40. Characteristic Linear Systems of Complete Continuous Systems, pg. 715*41. On The Complex: Projective Spaces, pg. 744*42. On The Variation of Almost-Complex Structure, pg. 760*43. On Deformations of Complex Analytic Structures, I, pg. 772*44. On The Existence of Deformations of Complex Analytic Structures, pg. 910*45. A Theorem of Completeness for Complex Analytic Fibre Spaces, pg. 920*46. Existence of Complex Structure on a Differentiable Family of Deformations of Compact Complex Manifolds, pg. 934*47. A Theorem of Completeness of Characteristic Systems of Complete Continuous Systems, pg. 956*48. On deformations of complex analytic structures, III, Stability theorems for complex structures, pg. 980*49. On deformations of some complex pseudo-group structures, pg. 1014*50. Multifoliate structures, pg. 1093
£73.60
Princeton University Press Kunihiko Kodaira Volume III Collected Works
Book SynopsisKunihiko Kodaira's influence in mathematics has been fundamental and international, and his efforts have helped lay the foundations of modern complex analysis. These three volumes contain Kodaira's written contributions, published in a large number of journals and books between 1937 and 1971. The volumes cover chronologically the major periods of KTable of Contents*Frontmatter, pg. i*Contents, pg. v*On Compact Analytic Surfaces, pg. 1142*On Compact Complex Analytic Surfaces, pg. 1157*A Theorem Of Completeness For Analytic Systems Of Surfaces, With Ordinary Singularities, pg. 1199*A Theorem Of Completeness Of Characteristic Systems For Analytic Families Of Compact Submanifolds Of Complex Manifolds, pg. 1236*On Stability Of Compact Submanifolds Of Complex Manifolds, pg. 1253*On Compact Analytic Surfaces, II-III, pg. 1269*On The Structure Of Compact Complex Analytic Surfaces, pg. 1373*On The Structure Of Compact Complex Analytic Surfaces, pg. 1382*On The Structure Of Compact Complex Analytic Surfaces, I, pg. 1389*On Characteristic Systems Of Families Of Surfaces With Ordinary Singularities In A Projective Space, pg. 1437*Complex structures on S1x S3, pg. 1467*On The Structure Of Compact Complex Analytic Surfaces, II, pg. 1471*A Certain Type Of Irregular Algebraic Surfaces, pg. 1511*Pluricanonical Systems On Algebraic Surfaces Of General Type, pg. 1520*On The Structure Of Compact Complex Analytic Surfaces, III, pg. 1525*Pluricanonical Systems On Algebraic Surfaces Of General Type, pg. 1554*On The Structure Of Complex Analytic Surfaces, IV., pg. 1577*On Homotopy K3 Surfaces, pg. 1596*Holomorphic Mappings Of Polydiscs Into Compact Complex Manifolds, pg. 1608
£63.75
Princeton University Press Fourier Analysis on Local Fields
Book SynopsisThis book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the aTable of Contents*Frontmatter, pg. i*Preface, pg. v*Introduction, pg. vii*Table of Contents, pg. xi*Chapter I: Introduction to local fields, pg. 1*Chapter II: Fourier analysis on K, the one-dimension case, pg. 20*Chapter III. Fourier analysis on Kn., pg. 115*Chapter IV. Regularization and the theory of regular and sub-regular functions, pg. 168*Chapter V. The Littlewood-Paley function and some applications, pg. 195*Chapter VI. Multipliers and singular integral operators, pg. 217*Chapter VII. Conjugate systems of regular functions and an F. and M. Riesz theorem, pg. 241*Chapter VIII. Almost everywhere convergence of Fourier series, pg. 262*Bibliography, pg. 286
£49.50
