Mathematics Books
Princeton University Press Rigid Local Systems
Book SynopsisThe author introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise.Trade Review"It is clear that this book presents highly important new views and results on the classical theory of complex linear differential equations."--Zentralblatt fur MathematikTable of Contents* First results on rigid local systems * The theory of middle concolution * Fourier Transform and rigidity * Middle concolution: dependence on parameters * Structure of rigid local systems * Existence algorithms for rigids * Diophantine aspects of rigidity * rigids
£74.80
Princeton University Press Renormalization and 3Manifolds which Fiber over
Book SynopsisGives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity.Trade ReviewCurtis T. McMullen, Winner of the 1998 Fields Medal, International Congress of Mathematicians "A comprehensive study of a theory which brings into parallel two recent and very deep theorems, involving geometry and dynamics. These are Thurston's theorem on the existence of hyperbolic metrics on three-manifolds which fiber over the circle with pseudo-Anosov monodromy, and Sullivan's theorem on the convergence of the renormalization map for real quadratic mappings... The book is very dense in results and the style is superb."--Mathematical ReviewsTable of Contents1Introduction12Rigidity of hyperbolic manifolds113Three-manifolds which fiber over the circle414Quadratic maps and renormalization755Towers956Rigidity of towers1057Fixed points of renormalization1198Asymptotic structure in the Julia set1359Geometric limits in dynamics15110Conclusion175Appendix A. Quasiconformal maps and flows183Appendix B. Visual extension205Bibliography241Index251
£999.99
Princeton University Press Convex Analysis
Book SynopsisPresents readers with a coherent branch of nonlinear mathematical analysis that is suited to the study of optimization problems. This volume treats the topics such as: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, and more.Trade Review"This book should remain for some years as the standard reference for anyone interested in convex analysis."--J. D. Pryce, Edinburgh Mathematical SocietyTable of Contents*Frontmatter, pg. i*Preface, pg. vii*Contents, pg. ix*Introductory Remarks: A Guide Jar the Reader, pg. xi*Part I. Basic Concepts, pg. 1*Part II. Topological Properties, pg. 41*Part III. Duality Correspondences, pg. 93*Part IV. Representation and Inequalities, pg. 151*Part V. Differential Theory, pg. 211*Part VI. Constrained Extremum Problems, pg. 261*Part VII. Saddle-Functions and Minimax Theory, pg. 347*Part VIII. Convex Algebra, pg. 399*Comments and References, pg. 425*Bibliography, pg. 433*Index, pg. 447
£85.00
Princeton University Press Abelian Varieties with Complex Multiplication and
Book SynopsisReciprocity laws of various kinds play a central role in number theory. This book states several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. It also covers the zeta function of an abelian variety as a main theme.Trade Review"[This book] is a beautifully written, self-contained and complete treatment of a subject of which G. Shimura is a founding master, and is a fundamental reference for any researcher or student of the antimetric theory of abelian varieties and modular functions, and in particular of its applications to class field theory."--Bulletin of the London Mathematical SocietyTable of ContentsPreface Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory (1961) Notation and Terminology Ch. I. Preliminaries on Abelian Varieties Ch. II. Abelian Varieties with Complex Multiplication Ch. III. Reduction of Constant Fields Ch. IV. Construction of Class Fields Ch. V. The Zeta Function of an Abelian Variety with Complex Multiplication Ch. VI. Families of Abelian Varieties and Modular Functions Ch. VII. Theta Functions and Periods on Abelian Varieties Bibliography Supplementary References Index
£999.99
Princeton University Press Global Surgery Formula for the CassonWalker
Book SynopsisIt is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S3. This work describes a function F of framed links in S3 and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds.Table of ContentsCh. 1Introduction and statements of the results5Ch. 2The Alexander series of a link in a rational homology sphere and some of its properties21Ch. 3Invariance of the surgery formula under a twist homeomorphism35Ch. 4The formula for surgeries starting from rational homology spheres60Ch. 5The invariant [lambda] for 3-manifolds with nonzero rank81Ch. 6Applications and variants of the surgery formula95Appendix: More about the Alexander series117Bibliography147Index149
£63.75
Princeton University Press The Enjoyment of Math
Book SynopsisWhat is so special about the number 30? How many colors are needed to color a map? Do the prime numbers go on forever? And are there more whole numbers than even numbers? This title explores these and other mathematical puzzles. It leads the reader into some of the fundamental ideas of mathematics, the ideas that make the subject interesting.Trade Review"A thoroughly enjoyable sampler of fascinating mathematical problems and their solutions."--Science "Each chapter is a gem of mathematical exposition... [The book] will not only stretch the imagination of the amateur, but it will also give pleasure to the sophisticated mathematician."--American Mathematical MonthlyTable of ContentsPreface v Introduction 5 1. The Sequence of Prime Numbers 9 2. Traversing Nets of Curves 13 3. Some Maximum Problems 17 4. Incommensurable Segments and Irrational Numbers 22 5. A Minimum Property of the Pedal Triangle 27 6. A Second Proof of the Same Minimum Property 30 7. The Theory of Sets 34 8. Some Combinatorial Problems 43 9. On Waring's Problem 52 10. On Closed Self-Intersecting Curves 61 11. Is the Factorization of a Number into Prime Factors Unique?66 12. The Four-Color Problem 73 13. The Regular Polyhedrons 82 14. Pythagorean Numbers and Fermat's Theorem 88 15. The Theorem of the Arithmetic and Geometric Means 95 16. The Spanning Circle of a Finite Set of Points 103 17. Approximating Irrational Numbers by Means of Rational Numbers ill 18. Producing Rectilinear Motion by Means of Linkages 119 19. Perfect Numbers 129 20. Euler's Proof of the Infinitude of the Prime Numbers 135 21. Fundamental Principles of Maximum Problems 139 22. The Figure of Greatest Area with a Given Perimeter 142 23. Periodic Decimal Fractions 147 24. A Characteristic Property of the Circle 160 25. Curves of Constant Breadth 163 26. The Indispensability of the Compass for the Constructions of Elementary Geometry 177 27. A Property of the Number 30 187 28. An Improved Inequality 192 Notes and Remarks 197
£27.00
Princeton University Press Georg Cantor His Mathematics and Philosophy of
Book SynopsisOne of the greatest revolutions in mathematics occurred when Georg Cantor promulgated his theory of transfinite sets. His religious beliefs led him to expect paradoxes in any concept of the infinite. This work shows that these played an integral part in his understanding and defense of set theory.Trade ReviewJoseph Warren Dauben, Winner of the 2012 Albert Leon Whiteman Memorial Prize, American Mathematical Society "Historians of mathematics can only be grateful for the effort Professor Dauben has expended to create the synthesis of Cantor scholarship found in this book. But the book can, and I hope will, be read with profit by a far more extensive audience. Any student, mathematician, philosopher, theologian, or general historian with an interest in Georg Cantor and the wondrous revolution in mathematical and philosophical thought that his work did so much to precipitate will find this book of considerable interest."--Thomas Hawkins, Historia Mathematica
£59.50
Princeton University Press Mathematics and Plausible Reasoning Volume 1
Book SynopsisExplains how to become a 'good guesser'. This work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.Trade Review"Polya ... does a masterful job of showing just how plausible reasoning is used in mathematics... The material in both volumes is fresh and highly original; the presentation is stimulating, informal, and occasionally humorous; examples from science, legal reasoning, and daily life make the arguments clear even to a nonspecialist. Polya's book is a rare event."--Morris Kline, Scientific American "Professor Polya's beautifully written hook has become a classic."---A. 0. L. Atkin, The Mathematical Gazette "Professor Polya ... is interested in problem solving and the psychological aspects of mathematical discovery... [These books] should provide many entertaining hours for anyone who cares to pick up the challenge."--Carl Hammer, Journal of the Franklin Institute "Professor Polya presents a forceful argument for the teaching of intelligent guessing as well as proving... There are also very readable and enjoyable discussions of such concepts as the isoperimetric problem and 'chance, the ever-present rival of conjecture.' "--Bruce E. Meserve, The Mathematics Teacher
£31.50
Princeton University Press Combinatorics of Train Tracks
Book SynopsisMeasured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a treatment of the combinatorial structure of the space of measured geodesic laminations in a fixed surface.Trade Review"The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician... [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area."--Zentralblatt for MathematikTable of ContentsPrefaceAcknowledgementsCh. 1The Basic Theory31.1Train Tracks41.2Multiple Curves and Dehn's Theorem101.3Recurrence and Transverse Recurrence181.4Genericity and Transverse Recurrence391.5Trainpaths and Transverse Recurrence601.6Laminations681.7Measured Laminations821.8Bounded Surfaces and Tracks with Stops102Ch. 2Combinatorial Equivalence1152.1Splitting, Shifting, and Carrying1162.2Equivalence of Birecurrent Train Tracks1242.3Splitting versus Shifting1272.4Equivalence versus Carrying1332.5Splitting and Efficiency1392.6The Standard Models1452.7Existence of the Standard Models1542.8Uniqueness of the Standard Models160Ch. 3The Structure of ML[subscript 0]1733.1The Topology of ML[subscript 0] and PL[subscript 0]1743.2The Symplectic Structure of ML[subscript 0]1823.3Topological Equivalence1883.4Duality and Tangential Coordinates191Epilogue204Addendum The Action of Mapping Classes on ML[subscript 0]210Bibliography214
£74.80
Princeton University Press An Extension of Cassons Invariant
Book SynopsisDescribes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case.Trade Review"[This is] a monograph describing Walker's extension of Casson's invariant to Q HS ... This is a fascinating subject and Walker's book is informative and well written ... it makes a rather pleasant introduction to a very active area in geometric topology."--Bulletin of the American Mathematical SocietyTable of Contents*Frontmatter, pg. i*Contents, pg. v*0. Introduction, pg. 1*1. Topology of Representation Spaces, pg. 6*2. Definition of lambda, pg. 27*3. Various Properties of lambda, pg. 41*4. The Dehn Surgery Formula, pg. 81*5. Combinatorial Definition of lambda, pg. 95*6. Consequences of the Dehn Surgery Formula, pg. 108*A. Dedekind Sums, pg. 113*B. Alexander Polynomials, pg. 122*Bibliography, pg. 129
£55.25
Princeton University Press Lectures on the Arithmetic RiemannRoch Theorem
Book SynopsisThe arithmetic Riemann-Roch Theorem has been shown by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. This book gives an introduction to the necessary techniques, and presents a simplified and extended version of the proof.Trade Review"This treatise provides a new approach to the arithmetic Riemann-Roch problem, and a widely algebraic-geometric method to solve it."--Zentralblatt fur MathematikTable of ContentsIntroductionList of SymbolsLecture 1Classical Riemann-Roch Theorem3Lecture 2Chern Classes of Arithmetic Vector Bundles15Lecture 3Laplacians and Heat Kernels29Lecture 4The Local Index Theorem for Dirac Operators44Lecture 5Number Operators and Direct Images62Lecture 6Arithmetic Riemann-Roch Theorem77Lecture 7The Theorem of Bismut-Vasserot93References99
£49.30
Princeton University Press Pseudorandomness and Cryptographic Applications
Book SynopsisA study of the pseudo-random generator, a basic primitive in crytography which is useful for constructing a private key cryptosystem that is secure against chosen plaintext attack. The author stresses rigorous definitions and proofs related to private key cryptography.Table of ContentsOverview and Usage Guide ix Mini-Courses xiii Acknowledgments xv Preliminaries 3 Introduction of some basic notation that is used in all subsequent lectures. Review of some computational complexity classes. Description of some useful probability facts. Lecture 1 Introduction to private key cryptosystems, pseudorandom generators, one-way functions. Introduction of some specific conjectured one-way functions. 13 Lecture 2 Discussions of security issues associated with the computing environment of a party, including the security parameter of a protocol. Definition of an adversary, the achievement ratio of an adversary for a protocol, and the security of a protocol. Definitions of one-way functions and one-way permutations, and cryptographic reduction. 21 Lecture 3 Definition of a weak one-way function. Reduction from a weak oneway function to a one-way function. More efficient security preserving reductions from a weak one-way permutation to a one-way permutation. 35 Lecture 4 Proof that the discrete log problem is either a one-way permutation or not even weak one-way permutation via random self-reducibility. Definition of a pseudorandom generator, the next bit test, and the proof that the two definitions are equivalent. Construction of a pseudorandom generator that stretches by a polynomial amount from a pseudorandom generator that stretches by one bit. 49 Lecture 5 Introduction of a two part paradigm for derandornizing probabilistic algorithms. Two problems are used to exemplify this approach: witness sampling and vertex partitioning. 56 Lecture 6 Definition of inner product bit for a function and what it means to be a hidden bit. Description and proof of the Hidden Bit Theorem that shows the inner product bit is hidden for a one-way function. Lecture 7 Definitions of statistical measures of distance between probability distributions and the analogous computational measures. Restatement of the, Hidden Bit Theorem in these terms and application of this theorem to construct a pseudorandom generator from a one-way permutation. Description and proof of the Many Hidden Bits Theorem that shows many inner product bit are hidden for a one-way function. Lecture 8 Definitions of various notions of statistical entropy, computational entropy and pseudoentropy generators. Definition of universal hash Functions. Description and proof of the Smoothing Entropy Theorem. 79 Lecture 9 Reduction from a one-way one-to-one function to a pseudorandom generator using the Smoothing Entropy Theorem and the Hidden Bit Theorem. Reduction from a one-way regular function to a pseudorandom generator using the Smoothing Entropy Theorem and Many Hidden Bits Theorem. 88 Lecture 10 Definition of a false entropy generator. Construction and proof of a pseudorandom generator from a false entropy generator. Construction and proof of a false entropy generator from any one-way function in the non- uniform sense. 95 Lecture 11 Definition of a stream private key cryptosystem, definitions of several notions of security, including passive attack and chosen plaintext. attack, and design of a stream private key cryptosystern that is secure against these attacks based on a pseudorandom generator. 105 Lecture 12 Definitions and motivation for a block cryptosystern and security against chosen plaintext attack. Definition and construction of a pseudorandom function generator from a pseudorandom generator. Construction of a block private key cryptosystern secure against chosen plaintext attack based on a pseudorandom function generator. 117 Lecture 13 Discussion of the Data Encryption Standard. Definition of a pseudorandom invertible permutation generator and discussion of applications to the construction of a block private key cryptosystern secure against chosen plaintext attack. Construction of a perfect random permutation based on a perfect random function. 128 Lecture 14 Construction of a pseudorandom invertible permutation generator from a pseudorandom function generator. Definition and construction of a super pseudorandom invertible permutation generator. Applications to block private key cryptosystems. 138 Lecture 15 Definition of trapdoor one-way functions, specific examples, and construction of cryptosystems without initial communication using a private line. 146 Lecture 16 Definition and construction of a universal one-way hash function. 154 Lecture 17 Definition and construction of secure one bit and many bit signature schemes. 162 Lecture 18 Definition of interactive proofs IP and the zero knowledge restriction of this class ZKIP. Definition and construction of a hidden bit commitment scheme based on a one-way function. Construction of a ZKIP for all NP based on a hidden bit commitment scheme. 174 List of Exercises and Research Problems 185 List of Primary Results 195 Credits and History 199 References 211 Notation 221 Index 225
£74.80
Princeton University Press Laws of the Game
Book SynopsisUsing game theory and examples of actual games people play, this work shows how the elements of chance and rules underlie all that happens in the universe, from genetic behavior through economic growth to the composition of music. It also presents games derived from scientific models for equilibrium, selection, growth, and the composition of RNA.Trade Review"Fascinating ... has the character of the deepest sort of discussion among brilliant friends."--The New Yorker "Remarkable, fascinating, and very profound."--The New York Times Book ReviewTable of ContentsTranslators' NoteAcknowledgmentsForewordForeword to the English Edition1The Taming of Chance11The Origin of Play32Games People Play63Microcosm - Macrocosm194Statistical Bead Games305Darwin and Molecules492Games in Time and Space676Structure, Pattern, Shape697Symmetry1038Metamorphoses of Order1313The Limits of the Game - The Limits of Humanity1739The Parable of the Physicists17510Of Self-Reproducing Automata and Thinking Machines17811"From One Make Ten..."19912Limited Space and Resources21613From Ecosystem to Industrial Society2364In the Realm of Ideas24914Popper's Three Worlds25115From Symbol to Language25916Memory and Complex Reality28317The Art of Asking the Right Question29818Playing with Beauty306List of References331Index339
£35.70
Princeton University Press Nilpotence and Periodicity in Stable Homotopy
Book SynopsisDescribes some major advances made in algebraic topology, centering on the nilpotence and periodicity theorems. This book begins with some elementary concepts of homotopy theory that are needed to state the problem. The latter portion provides specialists with a coherent and rigorous account of the proofs.Trade Review"Familiarity with the material of this book is essential for any a serious homotopy theorist... [The author's] important role in the developments will ensure that [this book] will remain an important source for some time."--Bulletin of the London Mathematical SocietyTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*Introduction, pg. xiii*Chapter 1. The main theorems, pg. 1*Chapter 2. Homotopy groups and the chromatic filtration, pg. 11*Chapter 3. MU-theory and formal group laws, pg. 25*Chapter 4. Morava's orbit picture and Morava stabilizer groups, pg. 37*Chapter 5. The thick subcategory theorem, pg. 45*Chapter 6. The periodicity theorem, pg. 53*Chapter 7. Bousfield localization and equivalence, pg. 69*Chapter 8. The proofs of the localization, smash product and chromatic convergence theorems, pg. 81*Chapter 9. The proof of the nilpotence theorem, pg. 99*Appendix A. Some tools from homotopy theory, pg. 119*Appendix B. Complex bordism and BP-theory, pg. 145*Appendix C. Some idempotents associated with the symmetric group, pg. 183*Bibliography, pg. 195*Index, pg. 205
£78.20
Princeton University Press The SeibergWitten Equations and Applications to
Book SynopsisThe introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. This book serves as an introduction to the Seiberg-Witten invariants. It also includes a review of the classical material on Spin c structures and their associated Dirac operators.Trade Review"This book provides an excellent introduction to the recently discovered Seilberg-Witten invariants for smooth closed oriented 4-mainifolds."--Mathematical ReviewsTable of Contents1Introduction12Clifford Algebras and Spin Groups53Spin Bundles and the Dirac Operator234The Seiberg-Witten Moduli Space555Curvature Identities and Bounds696The Seiberg-Witten Invariant877Invariants of Kahler Surfaces109Bibliography127
£51.00
Princeton University Press Lectures on the Theory of Games
Book SynopsisOffers an introduction to the mathematical discipline known as the Theory of Games. This book opens by addressing 'matrix games'. It continues with a treatment of games in extensive form and also deals with games that have an infinite number of pure strategies for the two players. It features examples and exercises, and various historical notes.Table of ContentsAuthor's Note vii Preface ix Chapter 1. What Is the Theory of Games? 1 Notes 3 Chapter 2. Matrix Games 5 2.1 Two Examples 5 2.2 The Definition of a Matrix Game 9 2.3 The Fundamental Theorem for 2 x 2 Matrix Games 10 2.4 The Geometry of Convex Sets 12 2.5 Fundamental Theorem for All Matrix Games 21 2.6 A Graphical Method of Solution 24 2.7 An Algorithm for Solving All Matrix Games 28 2.8 Simplified Poker 36 Notes 45 Appendix 48 Chapter 3. Extensive Games 59 3.1 Some Preliminary Restrictions 59 3.2 The Axiom System 59 3.3 Pure and Mixed Strategies 64 3.4 Games with Perfect Information 66 3.5 A Reduction of the Game Matrix 67 3.6 An Instructive Example 70 3.7 Behavior Strategies and Perfect Recall 72 3.8 Simplified Poker Reconsidered 77 Notes 78 Chapter 4. Infinite Games 81 4.1 Some Preliminary Restrictions 81 4.2 An Illuminating Example 81 4.3 Mixed Strategies and Expectation 83 4.4 The Battle of the Maxmin versus Supinf 88 4.5 The Fundamental Theorem 92 4.6 The Solution of Games on the Unit Square 94 Notes 103 Index 105
£49.30
Princeton University Press Mathematical Foundations of Quantum Mechanics
Book SynopsisShows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. This title presents the theory of Hermitean operators and Hilbert spaces.Trade Review"It remains indispensable to those who desire a rigorous presentation of the foundations of the subject."--Quarterly of Applied Mathematics "The translator and publisher have performed a service in making the classic available to a wider circle of English-speaking readers. It remains indispensable to those who desire a rigorous presentation of the foundations of the subject."--A. F. Stevenson, Quarterly of Applied Mathematics
£999.99
Princeton University Press The Garden in the Machine The Emerging Science
Book SynopsisWhat is life? Is it just the biologically familiar - birds, trees, snails, people - or is it an infinitely complex set of patterns that a computer could simulate? This book outlines many of the challenges and controversies involved in the dynamic and curious science of artificial life.Trade Review"Emmeche's account goes beyond describing (with appropriate awe) the accomplishments of computer biology to raise the crucial question of whether the new metaphor of the machine can be extended ... to the whole of nature."--Times Literary Supplement "A serious, sensible introduction to an exciting new field. It is not every day that one can see science fiction clash with natural philosophy in such a civilized fashion."--Karl Sigmund, Science "Can life be synthesized? Emmeche suggests in his fascinating book an approach to this question by means of computer simulation of living processes ... [and] tackles the posed questions with great insight."--Borje Ekstig, The Quarterly Review of BiologyTable of ContentsPrefaceAcknowledgementsCh. 1The Game of Life3Ch. 2What Is Life?23Ch. 3The Logic of Self-Reproduction47Ch. 4Artificial Growth and Evolution71Ch. 5The Ecology of Computation110Ch. 6The Biology of the Impossible134Ch. 7Simulating Life: Postmodern Science156Notes167Index189
£23.75
Princeton University Press Introduction to Mathematical Logic
Book SynopsisLogic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church's contributions to number theory and theories of algorithms and computability laid the theoretical foundations of computer science. This book is a basic source for understanding formal logic.Trade Review"This volume ... is a reprint of the revised 1956 version of this notable title first published in 1944 in the Annals of Mathematics Studies. Quite a pedigree ... [I]t is fitting that the release of this inexpensive reprint should make his masterly treatise available to everyone with an interest in the subject."--Australian & New Zealand PhysicistTable of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Introduction, pg. 1*I. The Propositional Calculus, pg. 69*II. The Propositional Calculus (Continued), pg. 119*III. Functional Calculi of First Order, pg. 168*IV. The Pure Functional Calculus of First Order, pg. 218*V. Functional Calculi of Second Order, pg. 295*Index of Definitions, pg. 357*Index of Authors, pg. 373*Errata, pg. 377
£999.99
Princeton University Press The Ecological Detective Confronting Models with
Book SynopsisHow do we make the field and laboratory coherent? How do we use statistics to help experimentation? How do we integrate modeling and statistics? This book answers these questions. It makes liberal use of computer programming for the generation of hypotheses, exploration of data, and the comparison of different models.Table of ContentsPreface: Beyond the Null Hypothesis1An Ecological Scenario and the Tools of the Ecological Detective32Alternative Views of the Scientific Method and of Modeling123Probability and Probability Models: Know Your Data394Incidental Catch in Fisheries: Seabirds in the New Zealand Squid Trawl Fishery945The Confrontation: Sum of Squares1066The Evolutionary Ecology of Insect Oviposition Behavior1187The Confrontation: Likelihood and Maximum Likelihood1318Conservation Biology of Wildebeest in the Serengeti1809The Confrontation: Bayesian Goodness of Fit20310Management of Hake Fisheries in Namibia Motivation23511The Confrontation: Understanding How the Best Fit Is Found263Appendix"The Method of Multiple Working Hypotheses"281References295Index309
£69.70
Princeton University Press An Introduction to GFunctions
Book SynopsisWritten 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. Its main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K.Trade Review"[This book] is well suited for a graduate course, its value as a textbook being enhanced by working out several concrete examples and counterexamples of the phenomena studied in the book."--Mathematical ReviewsTable of ContentsPREFACE INTRODUCTION xiii LIST OF SYMBOLS xix CHAPTER I Valued Fields 1. Valuations 3 2. Complete Valued Fields 6 3. Normed Vector Spaces 8 4. Hensel's Lemma 10 5. Extensions of Valuations 17 6. Newton Polygons 24 7. The y-intercept Method 28 8. Ramification Theory 30 9. Totally Ramified Extensions 33 CHAPTER II Zeta Functions 1. Logarithms 38 2. Newton Polygons for Power Series 41 3. Newton Polygons for Laurent Series 46 4. The Binomial and Exponential Series 49 5. Dieudonne's Theorem 53 6. Analytic Representation of Additive Characters 56 7. Meromorphy of the Zeta Function of a Variety 61 8. Condition for Rationality 71 9. Rationality of the Zeta Function 74 Appendix to Chapter II 76 CHAPTER III Differential Equations 1. Differential Equations in Characteristic p 77 2. Nilpotent Differential Operators. Katz-Honda Theorem 81 3. Differential Systems 86 4. The Theorem of the Cyclic Vector 89 5. The Generic Disk. Radius of Convergence 92 6. Global Nilpotence. Katz's Theorem 98 7. Regular Singularities. Fuchs' Theorem 100 8. Formal Fuchsian Theory 102 CHAPTER IV Effective Bounds. Ordinary Disks 1. p-adic Analytic Functions 114 2. Effective Bounds. The Dwork-Robba Theorem 119 3. Effective Bounds for Systems 126 4. Analytic Elements 128 5. Some Transfer Theorems 133 6. Logarithms 138 7. The Binomial Series 140 8. The Hypergeometric Function of Euler and Gauss 150 CHAPTER V Effective Bounds. Singular Disks 1. The Dwork-Frobenius Theorem 155 2. Effective Bounds for Solutions in a Singular Disk: the Case of Nilpotent Monodromy. The Christol-Dwork Theorem: Outline of the Proof 159 3. Proof of Step V 168 4. Proof of Step IV. The Shearing Transformation 169 5. Proof of Step III. Removing Apparent Singularities 170 6. The Operators (CHARACTER O w/ slash through it) and (CHARACTER U w/ slash through it) 173 7. Proof of Step I. Construction of Frobenius 176 8. Proof of Step II. Effective Form of the Cyclic Vector 180 9. Effective Bounds. The Case of Unipotent Monodromy 189 CHAPTER VI Transfer Theorems into Disks with One Singularity 1. The Type of a Number 199 2. Transfer into Disks with One Singularity: a First Estimate 203 3. The Theorem of Transfer of Radii of Convergence 212 CHAPTER VII Differential Equations of Arithmetic Type 1. The Height 222 2. The Theorem of Bombieri-Andre 226 3. Transfer Theorems for Differential Equations of Arithmetic Type 234 4. Size of Local Solution Bounded by its Global Inverse Radius 243 5. Generic Global Inverse Radius Bounded by the Global Inverse Radius of a Local Solution Matrix 254 CHAPTER VIII G-Series. The Theorem of Chudnovsky 1. Definition of G-Series- Statement of Chudnovsky's Theorem 263 2. Preparatory Results 267 3. Siegel's Lemma 284 4. Conclusion of the Proof of Chudnovsky's Theorem 289 Appendix to Chapter VIII 300 APPENDIX I Convergence Polygon for Differential Equations 301 APPENDIX II Archimedean Estimates 307 APPENDIX III Cauchy's Theorem 310 BIBLIOGRAPHY 317 INDEX 321
£85.00
Princeton University Press Introduction to the Numerical Solution of Markov
Book SynopsisOffers a systematic and detailed treatment of the numerical solution of Markov chains. This book explores various aspects of numerically computing solutions of Markov chains, especially when the state is huge. It examines many different numerical computing methods - direct, single-and multi-vector iterative, and projection methods.Trade Review"The book contains very rich material which is the result of long-term research in this field. No other book is known to the reviewer that treats this subject in such detail... The book excellently reflects the great experience that the author has in the theory of Markov chains, matrix algebra, numerics and informatics. He ... richly illustrates the book with numerous examples, flow-charts, pictures and even computer screen copies."--Mathematical ReviewsTable of Contents* Markov Chains * Direct Methods * Iterative Methods * Projection Methods * Block Hessenberg Matrices * Decompositional Methods * LI-Cyclic Markov Chains * Transient Solutions * Stochastic Automata Networks * Software
£117.30
Princeton University Press Quantization of Gauge Systems
Book SynopsisStarts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. This book is a systematic study of the classical and quantum theories of gauge systems. It discusses reducible gauge systems, and explains the relationship between BRST cohomology and gauge invariance.Trade Review"A useful reference for those interested in the formal aspects of constrained (i.e. gauge invariant) systems."--Physics WorldTable of ContentsPrefaceAcknowledgmentsNotationsCh. 1Constrained Hamiltonian Systems3Ch. 2Geometry of the Constraint Surface48Ch. 3Gauge Invariance of the Action65Ch. 4Generally Covariant Systems102Ch. 5First-Class Constraints: Further Developments112Ch. 6Fermi Degrees of Freedom: Classical Mechanics over a Grassmann Algebra134Ch. 7Constrained Systems with Fermi Variables156Ch. 8Graded Differential Algebras - Algebraic Structure of the BRST Symmetry165Ch. 9BRST Construction in the Irreducible Case187Ch. 10BRST Construction in the Reducible Case205Ch. 11Dynamics of the Ghosts - Gauge-Fixed Action234Ch. 12The BRST Transformation in Field Theory253Ch. 13Quantum Mechanics of Constrained Systems: Standard Operator Methods272Ch. 14BRST Operator Method - Quantum BRST Cohomology296Ch. 15Path Integral for Unconstrained Systems333Ch. 16Path Integral for Constrained Systems380Ch. 17Antifield Formalism: Classical Theory407Ch. 18Antifield Formalism and Path Integral428Ch. 19Free Maxwell Theory. Abelian Two-Form Gauge Field455Ch. 20Complementary Material481Bibliography503Index515
£103.70
Princeton University Press Introduction to Partial Differential Equations
Book SynopsisServes as a text for mathematics students at the intermediate graduate level. This book aims to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers.Trade Review"The first edition of Folland's text on PDEs used to be my favorite source for a course on DPEs. The new edition includes many more exercises and offers a new chapter on pseudodifferential operators. ... This text book is a pleasant compromise between the modern abstract theory and the concrete classical examples and applications."--Monatshefte fur MathematikTable of Contents* Local Existence Theory * The Laplace Operator * Layer Potentials * The Heat Operator * The Wave Operator * The L2 Theory of Derivatives * Elliptic Boundary Value Problems * Pseudodifferential Operators
£92.65
Princeton University Press Modern Methods in Complex Analysis
Book SynopsisIncludes fifteen articles which focus on the developments in complex analysis. This work covers a spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. It covers topics that include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, and more.Table of ContentsPrefaceList of ParticipantsProgram of the ConferenceThe Scientific Work of Robert C. Gunning3The Scientific Work of Joseph J. Kohn16On Invariants of Manifolds29Remarks on Analytic Hypoellipticity of [actual symbol not reproducible]41Finite Type Conditions and Subelliptic Estimates63Characterization of Certain Holomorphic Geodesic Cycles on Hermitian Locally Symmetric Manifolds of the Noncompact Type79On Kohn's Microlocalization of [actual symbol not reproducible] Problems119Complex Dynamics in Higher Dimension. II135Set Theoretical Real Analytic Spaces183An Isoperimetric Estimate for the Ricci Flow on the Two-Sphere191Isoperimetric Estimates for the Curve Shrinking Flow in the Plane201The Abel-Radon Transform and Several Complex Variables223On the Absence of Periodic Points for the Ricci Curvature Operator Acting on the Space of Kahler Metrics277The Maximum Principle and Related Topics283Very Ampleness Criterion of Double Adjoints of Ample Line Bundles291Integrability of Elliptic Overdetermined Systems of Nonlinear First-Order Complex PDE319The Holomorphic Contact Geometry of a Real Hypersurface327
£80.75
Princeton University Press Cycles Transfers and Motivic Homology Theories
Book SynopsisAims to construct "motivic cohomology theory," whose existence was conjectured by A Beilinson and S Lichtenbaum. This is achieved in the book's fourth paper, using results of the other papers whose additional role is to contribute to our understanding of various properties of algebraic cycles.Table of ContentsChapter I Introduction Eric M. Friedlander, A. Suslin, and V. Voevodsky 3 Chapter 2 Relative Cycles and Chow Sheaves Andrei Suslin and Vladimir Voevodsky 10 Chapter 3 Cohomological Theory of Presheaves with Transfers Vladimir Voevodsky 87 Chapter 4 Bivariant Cycle Cohomology Eric M. Friedlander and Vladimir Voevodsky 138 Chapter 5 Triangulated Categories of Motives Over a Field Vladimir Voevodsky 188 Chapter 6 Higher Chow Groups and Etale Cohomology Andrei A. Suslin 239
£999.99
Princeton University Press Surveys on Surgery Theory Volume 1
Book SynopsisSurgery theory is the basis for the classification theory of manifolds. There have been extraordinary accomplishments in that time, which have led to varied interactions with algebra, analysis, and geometry. This work is of interest to those interested in topology, not only graduate students and mathematicians, but also mathematical physicists.Table of ContentsThe Editors Preface vii The Editors C. T. C. Wall's contributions to the topology of manifolds 3 C. T. C. Wall's publication list 17 J. Milnor Classification of (n - l)-connected 2n-dimensional manifolds and the discovery of exotic spheres 25 S. Novikov Surgery in the 1960's 31 W. Browder Differential topology of higher dimensional manifolds 41 T. Lance Differentiable structures on manifolds 73 E. Brown The Kervaire invariant and surgery theory 105 A Kreck A guide to the classification of manifolds 121 J. Klein Poincare duality spaces 135 A Davis Poincare duality groups 167 J. Davis Manifold aspects of the Novikov Conjecture 195 I. Hambleton and L. Taylor A guide to the calculation of the surgery obstruction groups for finite groups 225 C. Stark Surgery theory and infinite fundamental groups 275 E. Pedersen Continuously controlled surgery theory 307 W. Mio Homology manifolds 323 J. Levine and K. Orr A survey of applications of surgery to knot and link theory 345 J. Roe Surgery and C*-algebras 365 R. J. Milgram The classification of Aloff-Wallach manifolds and their generalizations 379 C. Thomas Elliptic cohomology 409
£92.65
Princeton University Press The Action Principle and Partial Differential
Book SynopsisIntroduces methods in the theory of partial differential equations derivable from a Lagrangian. This book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E Noether.Table of ContentsGeneral Introduction 3 1 1.0 Introduction 7 1.1 The Lagrangian Picture 8 1.2 The Hamiltonian Picture 19 1.3 Examples 28 2 2.0 Introduction 51 2.1 The Canonlicd and Symplectic Forms 57 2.2 Symplectic Transformations 62 2.3 The Equations of Variation 79 2.4 The Circulation Theorem 84 2.5 The Euler System 87 2.6 Irrotational Solutions 96 2.7 The Equation of Continuity 99 3 3.0 Introduction 105 3.1 Compatible Currents 108 3.2 Null Currents and Null Lagragians 125 3.3 The Source Equations 128 3.4 The Generic Case n > 1 & m > 2 133 3.5 The Separable Case m > 2 141 3.6 The Case m = 2 144 3.7 Lie Flows and the Noether Current 146 4 4.1 Sections of Vector Bundles 159 5 5.0 Introduction 191 5.1 Relative Lagrangians 195 5.2 Ellipticity and Hyperbolicity 220 5.3 The Domain of Dependence 240 6 6.1 The Electromagnetic Field 263 6.2 Electromagnetic Symplectic Structure 272 6.3 Electromagnetic Compatible Currents 282 6.4 Causality in Electromagnetic etic Theory 299 Bibliography 315 Index 317
£78.20
Princeton University Press Homological Algebra
Book SynopsisThe invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology theory that embodies all three.Table of ContentsPreface v Chapter I. Rings and Modules 3 1. Preliminaries 3 2. Projective modules 6 3. Injective modules 8 4. Semi-simple rings 11 5. Hereditary rings 12 6. Semi-hereditary rings 14 7. Noetherian rings 15 Exercises 16 Chapter II. Additive Functors 18 1. Definitions 18 2. Examples 20 3. Operators 22 4. Preservation of exactness 23 5. Composite functors 27 6. Change of rings 28 Exercises 31 Chapter III. Satellites 33 1. Definition of satellites 33 2. Connecting homomorphisms 37 3. Half exact functors 39 4. Connected sequence of functors 43 5. Axiomatic description of satellites 45 6. Composite functors 48 7. Several variables 49 Exercises 51 Chapter IV. Homology 53 1. Modules with differentiation 53 2. The ring of dual numbers 56 3. Graded modules, complexes 58 4. Double gradings and complexes 60 5. Functors of complexes 62 6. The homomorphism x 64 7. The homomorphism x (continuation) 66 8. Kunneth relations 71 Exercises 72 Chapter V. Derived Functors 75 1.Complexes over modules; resolutions 75 2.Resolutions of sequences 78 3.Definition of derived functors 82 4.Connecting homomorphisms 84 5.The functors ROT and LOT 89 6.Comparison with satellites 90 7.Computational devices 91 8.Partial derived functors 94 9.Sums, products, limits 97 10.The sequence of a map 101 Exercises 104 Chapter VI. Derived Functors of 0 and Hom 106 1. The functors Tor and Ext 106 2. Dimension of modules and rings 109 3. Kunneth relations 112 4. Change of rings 116 5. Duality homomorphisms 119 Exercises 122 Chapter VII. Integral Domains 127 1. Generalities 127 2. The field of quotients 129 3. Inversible ideals 132 4. Prufer rings 133 5. Dedekind rings 134 6. Abelian groups 135 7. A description of Tor1, (A,C) 137 Exercises 139 Chapter VIII. Augmented Rings 143 1. Homology and cohomology of an augmented ring 143 2. Examples 146 3. Change of rings 149 4. Dimension 150 5. Faithful systems 154 6. Applications to graded and local rings 156 Exercises 158 Chapter IX. Associative Algebras 162 1. Algebras and their tensor products 162 2. Associativity formulae 165 3. The enveloping algebra Ae 167 4. Homology and cohomology of algebras 169 5. The Hochschild groups as functors of A 171 6. Standard complexes 174 7. Dimension 176 Exercises 180 Chapter X. Supplemented Algebras 182 1. Homology of supplemented algebras 182 2. Comparison with Hochschild groups 185 3. Augmented monoids 187 4. Groups 189 5. Examples of resolutions 192 6. The inverse process193 7. Subalgebras and subgroups 196 8. Weakly injective and projective modules 197 Exercises 201 Chapter XI. Products 202 1. External products 202 2. Formal properties of the products 206 3. Isomorphisms 209 4. Internal products 211 5. Computation of products 6. Products in the Hochschild theory 216 7. Products for supplemented algebras 219 8. Associativity formulae 222 9. Reduction theorems 225 Exercises 228 Chapter XII. Finite Groups 232 1. Norms 232 2. The complete derived sequence 235 3. Complete resolutions 237 4. Products for finite groups 242 5. The uniqueness theorem 244 6. Duality 247 7. Examples 250 8. Relations with subgroups 254 9. Double cosets 256 10 p-groups and Sylow groups 258 11. Periodicity 260 Exercises 263 Chapter XIII. Lie Algebras 266 1. Lie algebras and their enveloping algebras 266 2. Homology and cohomology of Lie algebras 270 3. The Poincare-Witt theorem 271 4. Subalgebras and ideals 274 5. The diagonal map and its applications 275 6. A relation in the standard complex 277 7. The complex V(g) 279 8. Applications of the complex V(g) 282 Exercises 284 Chapter XIV. Extensions 289 1. Extensions of modules 289 2. Extensions of associative algebras 293 3. Extensions of supplemented algebras 295 4. Extensions of groups 299 5. Extensions of Lie algebras 304 Exercises 308 Chapter XV. Spectral Sequences 315 1. Filtrations and spectral sequences 315 2. Convergence 319 3. Maps and homotopies 321 4. The graded case 323 5. Induced homomorphisms and exact sequences 325 6. Application to double complexes 330 7. A generalization 333 Exercises 336 Chapter XVI. Applications of Spectral Sequences 340 1. Partial derived functors 340 2. Functors of complexes 342 3. Composite functors 343 4. Associativity formulae 345 5. Applications to the change of rings 347 6. Normal subalgebras 349 7. Associativity formulae using diagonal maps 351 8. Complexes over algebras 352 9. Topological applications 355 10.The almost zero theory 358 Exercises 360 Chapter XVII. Hyperhomology 362 1. Resolutions of complexes 362 2. The invariants 366 3. Regularity conditions 368 4. Mapping theorems 371 5. Kunneth relations 372 6. Balanced functors 374 7. Composite functors 376 Appendix: Exact categories, by David A. Buchsbaum 379 List of Symbols 387 Index of Terminology 389
£85.00
Princeton University Press The Aspiring Adept Robert Boyle and His
Book SynopsisPresents a provocative view of Robert Boyle (1627-1691), one of the leading figures of the Scientific Revolution, by revealing his avid and lifelong pursuit of alchemy. This title shows that his alchemical quest positions him more accurately in the intellectual and cultural crossroads of the seventeenth century.Trade Review"Principe is to be congratulated on bringing [Boyle] into a new focus."--D. M. Knight, Nature "The Aspiring Adept is an audacious, enchanting, and deeply rewarding book, one that will be of equal interest to historians, chemists, and interested laypersons. It is a real treat."--A. J. Rocke, Chemistry in Britain "Lawrence Principe's book goes a long way toward recovering the complexity of Boyle's mind and work... [His] ability to reconstruct Boyle's laboratory practices, ascertain the relations between Boyle and a large community of like-minded practitioners, and retrieve, fully or partially, some of Boyle's alchemical writings is ... remarkable."--Mordechai Feingold, American Scientist "Principe has performed a great service by printing some of the choicer parts [of Boyle's unpublished works]... [He] avoids the easy temptation to interpret Boyle's alchemical operations in terms of modern chemistry."--Peter Dear, Physics WorldTable of ContentsAcknowledgmentsNote on Primary SourcesAbbreviationsIntroductionAlchemy and Chemistry: A Crucial Note on Terminology and CategoriesCh. IBoyle SpagyricizedCh. IISkeptical of the Sceptical ChymistCh. IIIThe Dialogue on Transmutation, Kinds of Transmutations, and Boyle's BeliefsCh. IVAdepti, Aspirants, and CheatsCh. VBoyle and Alchemical PracticeCh. VIMotivations: Truth, Medicine, and ReligionEpilogue: A New Boyle and a New AlchemyApp. 1Robert Boyle's Dialogue on the Transmutation and Melioration of MetalsApp. 2Interview Accounts of Transmutation and Prefaces to Boyle's Other Chrysopoetic WritingsApp. 3Dialogue on the Converse with Angels Aided by the Philosophers' StoneWorks CitedIndex
£42.50
Princeton University Press The Classical Groups
Book SynopsisDiscusses the symmetric, linear, orthogonal, and symplectic groups and determines their invariants and representations. This book covers topics such as matrix algebras, semigroups, commutators, and spinors, which help in understanding the group-theoretic structure of quantum mechanics.Table of Contents*Frontmatter, pg. i*Preface to the First Edition, pg. vii*Preface to the Second Edition, pg. ix*Table of Contents, pg. xi*Chapter I. Introduction, pg. 1*Chapter II. Vector Invariants, pg. 27*Chapter III. Matric Algebras and Group Rings, pg. 79*Chapter IV. The Symmetric Group and The Full Linear Group, pg. 115*Chapter V. The Orthogonal Group, pg. 137*Chapter VI. The Symplectic Group, pg. 165*Chapter VII. Characters, pg. 176*Chapter VIII. General Theory of Invariants, pg. 239*Chapter IX. Matric Algebras Resumed, pg. 280*Chapter X. Supplements, pg. 291*Errata and Addenda, pg. 307*Bibliography, pg. 308*Supplementary Bibliography, mainly for the years 1940-1945, pg. 314*Index, pg. 317
£999.99
Princeton University Press The Search for Mathematical Roots 18701940
Book SynopsisPresents the history of a critical period in mathematics that includes accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. This work provides surveys of many related topics and figures of the late nineteenth century.Trade Review"Grattan-Guiness's uniformly interesting and valuable account of the interwoven development of logic and related fields of mathematics ... between 1870 and 1940 presents a significantly revised analysis of the history of the period... [His] book is important because it supplies what has been lacking: a full account of the period from a primary mathematical perspective."--James W. Van Evra, IsisTable of ContentsCHAPTER 1 Explanations 1.1 Sallies 3 1.2 Scope and limits of the book 3 1.2.1 An outline history 3 1.2.2 Mathematical aspects 4 1.2.3 Historical presentation 6 1.2.4 Other logics, mathematics and philosophies 7 1.3 Citations, terminology and notations 1.3.1 References and the bibliography 9 1.3.2 Translations, quotations and notations 10 1.4 Permissions and acknowledgements 11 CHAPTER 2 Preludes: Algebraic Logic and Mathematical Analysis up to 1870 2.1 Plan of the chapter 14 2.2 'Logique' and algebras in French mathematics 14 2.2.1 The 'logique' and clarity of 'ideologie' 14 2.2.2 Lagrange's algebraic philosophy 15 2.2.3 The many senses of 'analysis' 17 2.2.4 Two Lagrangian algebras: functional equations and differential operators 17 2.2.5 Autonomy for the new algebras 19 2.3 Some English algebraists and logicians 20 2.3.1 A Cambridge revival: the 'Analytical Society, Lacroix, and the professing of algebras 20 2.3.2 The advocacy of algebras by Babbage, Herschel and Peacock 20 2.3.3 An Oxford movement: Whately and the professing of logic 22 2.4 A London pioneer: De Morgan on algebras and logic 25 2.4.1 Summary of his life 25 2.4.2 De Morgan's philosophies of algebra 25 2.4.3 De Morgan's logical career 26 2.4.4 De Morgan's contributions to the foundations of logic 27 2.4.5 Beyond the syllogism 29 2.4.6 Contretemps over 'the quantification of the predicate' 30 2.4.7 The logic of two place relations, 1860 32 2.4.8 Analogies between logic and mathematics 35 2.4.9 De Morgan's theory of collections 36 2.5 A Lincoln outsider: Boole on logic as applied mathematics 37 2.5.1 Summary of his career 37 2.5.2 Boole's 'general method in analysis' 1844 39 2.5.3 The mathematical analysis of logic, 1847. 'elective symbols' and laws 40 2.5.4 'Nothing' and the 'Universe' 42 2.5.5 Propositions, expansion theorems, and solutions 43 2.5.6 The laws of thought, 1854: modified principles and extended methods 46 2.5.7 Boole's new theory of propositions 49 2.5.8 The character of Boole's system 50 2.5.9 Boole's search for mathematical roots 53 2.6 The semi-followers of Boole 54 2.6.1 Some initial reactions to Boole's theory 54 2.6.2 The reformulation by Jevons 56 2.6.3 Jevons versus Boole 59 2.6.4 Followers of Boole and/or Jevons 60 2.7 Cauchy, Weierstrass and the rise of mathematical analysis 63 2.7.1 Different traditions in the calculus 63 2.7.2 Cauchy and the Ecole Polytechnique 64 2.7.3 The gradual adoption and adaptation of Cauchy's new tradition 67 2.7.4 The refinements of Weierstrass and his followers 68 2.8 Judgement and supplement 70 2.8.1 Mathematical analysis versus algebraic logic 70 2.8.2 The places of Kant and Bolzano 71 CHAPTER 3 Cantor: Mathematics as Mengenlehre 3.1 Prefaces 75 3.1.1 Plan of the chapter 75 3.1.2 Cantor's career 75 3.2 The launching of the Mengenlehre, 1870-1883 79 3.2.1 Riemann's thesis: the realm of discontinuous functions 79 3.2.2 Heine on trigonometric series and the real line, 1870-1872 81 3.2.3 Cantor's extension of Heine's findings, 1870-1872 83 3.2.4 Dedekind on irrational numbers, 1872 85 3.2.5 Cantor on line and plane, 1874-1877 88 3.2.6 Infinite numbers and the topology of linear sets, 1878-1883 89 3.2.7 The Grundlagen, 1883: the construction of number-classes 92 3.2.8 The Grundlagen: the definition of continuity 95 3.2.9 The successor to the Grundlagen, 1884 96 3.3 Cantor's Acta mathematica phase, 1883-1885 97 3.3.1 Mittag-Lefler and the French translations, 1883 97 3.3.2 Unpublished and published 'communications' 1884-1885 98 3.3.3 Order-types and partial derivatives in the 'communications' 100 3.3.4 Commentators on Cantor, 1883-1885 102 3.4 The extension of the Mengenlehre, 1886-1897 103 3.4.1 Dedekind's developing set theory, 1888 103 3.4.2 Dedekind's chains of integers 105 3.4.3 Dedekind's philosophy of arithmetic 107 3.4.4 Cantor's philosophy of the infinite, 1886-1888 109 3.4.5 Cantor's new definitions of numbers 110 3.4.6 Cardinal exponentiation: Cantor's diagonal argument, 1891 110 3.4.7 Transfinite cardinal arithmetic and simply ordered sets, 1895 112 3.4.8 Transfinite ordinal arithmetic and well-ordered sets, 1897 114 3.5 Open and hidden questions in Cantor's Mengenlehre 114 3.5.1 Well-ordering and the axioms of choice 114 3.5.2 What was Cantor's 'Cantor's continuum problem'? 116 3.5.3 "Paradoxes" and the absolute infinite 117 3.6 Cantor's philosophy of mathematics 119 3.6.1 A mixed position 119 3.6.2 (No) logic and metamathematics 120 3.6.3 The supposed impossibility of infinitesimals 121 3.6.4 A contrast with Kronecker 122 3.7 Concluding comments: the character of Cantor's achievements 124 CHAPTER 4 Parallel Processes in Set Theory, Logics and Axiomatics, 1870s-1900s 4.1 Plans for the chapter 126 4.2 The splitting and selling of Cantor's Mengenlehre 126 4.2.1 National and international support 126 4.2.2 French initiatives, especially from Borel 127 4.2.3 Couturat outlining the infinite, 1896 129 4.2.4 German initiatives from Mein 130 4.2.5 German proofs of the Schroder-Bernstein theorem 132 4.2.6 Publicity from Hilbert, 1900 134 4.2.7 Integral equations and functional analysis 135 4.2.8 Kempe on 'mathematical form' 137 4.2.9 Kempe-who? 139 4.3 American algebraic logic: Peirce and his followers 140 4.3.1 Peirce, published and unpublished 141 4.3.2 Influences on Peirre's logic: father's algebras 142 4.3.3 Peirce's first phase: Boolean logic and the categories, 1867-1868 144 4.3.4 Peirce's virtuoso theory of relatives, 1870 145 4.3.5 Peirce's second phase, 1880: the propositional calculus 147 4.3.6 Peirre's second phase, 1881: finite and infinite 149 4.3.7 Peirce's students, 1883: duality, and 'Quantifying' a proposition 150 4.3.8 Peirre on 'icons' and the order of 'quantifiers; 1885 153 ~~~ 4.3.9 The Peirceans in the 1890s 154 4.4 German algebraic logic: from the Grassmanns to Schr6der 156 4.4.1 The Grassmanns on duality 156 4.4.2 Schroder's Grassmannian phase 159 4.4.3 Schroder's Peirrean 'lectures' on logic 161 4.4.4 Schrrider's first volume, 1890 161 4.4.5 Part of the second volume, 1891 167 4.4.6 Schroder's third volume, 1895: the 'logic of relatives' 170 4.4.7 Peirce on and against Schroder in The monist, 1896-1897 172 4.4.8 Schroder on Cantorian themes, 1898 174 4.4.9 The reception and publication of Schroder in the 1900s 175 4.5 Frege: arithmetic as logic 177 4.5.1 Frege and Frege' 177 4.5.2 The 'concept-script' calculus of Frege's 'pure thought; 1879 179 4.5.3 Frege's arguments for logicising arithmetic, 1884 183 4.5.4 Keny's conception of Fregean concepts in the mid 1880s 187 4.5.5 Important new distinctions in the early 1890s 187 4.5.6 The 'fundamental laws' of logicised arithmetic, 1893 191 4.5.7 Frege's reactions to others in the later 1890s 194 4.5.8 More 'fundamental laws' of arithmetic, 1903 195 4.5.9 Frege, Korselt and Thomae on the foundations of arithmetic 197 4.6 Husserl: logic as phenomenology 199 4.6.1 A follower of Weierstrass and Cantor 199 4.6.2 The phenomenological 'philosophy of arithmetic; 1891 201 4.6.3 Reviews by Frege and others 203 4.6.4 Husserl's 'logical investigations; 1900-1901 204 4.6.5 Husserl's early talks in Gottingen, 1901 206 4.7 Hilbert: early proof and model theory, 1899-1905 207 4.7.1 Hilbert's growing concern with axiomatics 207 4.7.2 Hilbert's diferent axiom systems for Euclidean geometry, 1899-1902 208 4.7.3 From German completeness to American model theory 209 4.7.4 Frege, Hilbert and Korselt on the foundations of geometries 212 4.7.5 Hilbert's logic and proof theory, 1904-1905 213 4.7.6 Zermelo's logic and set theory, 1904-1909 216 CHAPTER 5 Peano: the Formulary of Mathematics 5.1 Prefaces 219 5.1.1 Plan of the chapter 219 5.1.2 Peano's career 219 5.2 Formalising mathematical analysis 221 5.2.1 Improving Genocchi, 1884 221 5.2.2 Developing Grassmann's 'geometrical calculus; 1888 223 5.2.3 The logistic of arithmetic, 1889 225 5.2.4 The logistic of geometry, 1889 229 5.2.5 The logistic of analysis, 1890 230 5.2.6 Bettazzi on magnitudes, 1890 232 5.3 The Rivista: Peano and his school, 1890-1895 232 5.3.1 The 'society of mathematicians' 232 5.3.2 'Mathematical logic, 1891 234 5.3.3 Developing arithmetic, 1891 235 5.3.4 Infinitesimals and limits, 1892-1895 236 5.3.5 Notations and their range, 1894 237 5.3.6 Peano on definition by equivalence classes 239 5.3.7 Burali-Forti's textbook, 1894 240 5.3.8 Burali-Forti's research, 1896-1897 241 5.4 The Formulaire and the Rivista, 1895-1900 242 5.4.1 The first edition of the Formulaire, 1895 242 5.4.2 Towards the second edition of the Formulaire, 1897 244 5.4.3 Peano on the eliminability of 'the' 246 5.4.4 Frege versus Peano on logic and definitions 247 5.4.5 Schroder's steamships versus Peano's sailing boats 249 5.4.6 New presentations of arithmetic, 1898 251 5.4.7 - Padoa on classhoody 1899 253 5.4.8 Peano's new logical summary, 1900 254 5.5 Peanists in Paris, August 1900 255 5.5.1 An Italian Friday morning 255 5.5.2 Peano on definitions 256 5.5.3 Burali-Forti on definitions of numbers 257 5.5.4 Padoa on definability and independence 259 5.5.5 Pieri on the logic of geometry 261 5.6 Concluding comments: the character of Peano's achievements 262 5.6.1 Peano's little dictionary, 1901 262 5.6.2 Partly grasped opportunities 264 5.6.3 Logic without relations 266 CHAPTER 6 Russell's Way In: From Certainty to Paradoxes, 1895-1903 6.1 Prefaces 268 6.1.1 Plans for two chapters 268 6.1.2 Principal sources 269 6.1.3 Russell as a Cambridge undergraduate, 1891-1894 271 6.1.4 Cambridge philosophy in the 1890s 273 6.2 Three philosophical phases in the foundation of mathematics, 1895-1899 274 6.2.1 Russell's idealist axiomatic geometries 275 6.2.2 The importance of axioms and relations 276 6.2.3 A pair of pas de deux with Paris: Couturat and Poincare on geometries 278 6.2.4 The emergence of "itehead, 1898 280 6.2.5 The impact of G. E. Moore, 1899 282 6.2.6 Three attempted books, 1898-1899 283 6.2.7 Russell's progress with Cantor's Mengenlehre, 1896-1899 285 6.3 From neo-Hegelianism towards 'Principles', 1899-1901 286 6.3.1 Changing relations 286 6.3.2 Space and time, absolutely 288 6.3.3 'Principles of Mathematics, 1899-1900 288 6.4 The first impact of Peano 290 6.4.1 The Paris Congress of Philosophy, August 1900: Schroder versus Peano on 'the' 290 6.4.2 Annotating and popularising in the autumn 291 6.4.3 Dating the origins of Russell's logicism 292 6.4.4 Drafting the logic of relations, October 1900 296 6.4.5 Part 3 of The principles, November 1900: quantity and magnitude 298 6.4.6 Part 4, November 1900: order and ordinals 299 6.4.7 Part 5, November 1900: the transfinite and the continuous 300 6.4.8 Part 6, December 1900: geometries in space 301 6.4.9 Whitehead on 'the algebra of symbolic logic, 1900 302 6.5 Convoluting towards logicism, 1900-1901 303 6.5.1 Logicism as generalised metageometry, January 1901 303 6.5.2 The first paper for Peano, February 1901: relations and numbers 305 6.5.3 Cardinal arithmetic with "itehead and Russell, June 1901 307 6.5.4 The second paper for Peano, March August 1901: set theory with series 308 6.6 From 'fallacy' to 'contradiction', 1900-1901 310 6.6.1 Russell on Cantor's 'fallacy; November 1900 310 6.6.2 Russell's switch to a 'contradiction' 311 6.6.3 Other paradoxes: three too large numbers 312 6.6.4 Three passions and three calamities, 1901-1902 314 6.7 Refining logicism, 1901-1902 315 6.7.1 Attempting Part 1 of The principles, May 1901 315 6.7.2 Part 2, June 1901: cardinals and classes 316 6.7.3 Part 1 again, April-May 1902: the implicational logicism 316 6.7.4 Part 1: discussing the indefinables 318 6.7.5 Part 7, June 1902: dynamics without statics; and within logic? 322 6.7.6 Sort-of finishing the book 323 6.7.7 The first impact of Frege, 1902 323 6.7.8 AppendixA on Frege 326 6.7.9 Appendix B: Russell's first attempt to solve the paradoxes 327 6.8 The roots of pure mathematics? Publishing The principles at last, 1903 328 6.8.1 Appearance and appraisal 328 6.8.2 A gradual collaboration with Whitehead 331 CHAPTER 7 Russell and Whitehead Seek the Principia Mathematica, 1903-1913 7.1 Plan of the chapter 333 7.2 Paradoxes and axioms in set theory, 1903-1906 333 7.2.1 Uniting the paradoxes of sets and numbers 333 7.2.2 New paradoxes, mostly of naming 334 7.2.3 The paradox that got away: heterology 336 7.2.4 Russell as cataloguer of the paradoxes 337 7.2.5 Controversies over axioms of choice, 1904 339 7.2.6 Uncovering Russell's 'multiplicative axiom, 1904 340 7.2.7 Keyser versus Russell over infinite classes, 1903-1905 342 7.3 The perplexities of denoting, 1903-1906 342 7.3.1 First attempts at a general system, 1903-1905 342 7.3.2 Propositional functions, reducible and identical 344 7.3.3 The mathematical importance of definite denoting functions 346 7.3.4 'On denoting' and the complex, 1905 348 7.3.5 Denoting, quantification and the mysteries of existence 350 7.3.6 Russell versus MacColl on the possible, 1904-1908 351 7.4 From mathematical induction to logical substitution, 1905-1907 354 7.4.1 Couturat's Russellian principles 354 7.4.2 A second pas de deux with Paris: Boutroux and Poincare on logicism 355 7.4.3 Poincare on the status of mathematical induction 356 7.4.4 Russell's position paper, 1905 357 7.4.5 Poincare and Russell on the vicious circle principle, 1906 358 7.4.6 The rise of the substitutional theory, 1905-1906 360 7.4.7 The fall of the substitutional theory, 1906-1907 362 7.4.8 Russell's substitutional propositional calculus 364 7.5 Reactions to mathematical logic and logicism, 1904-1907 366 7.5.1 The International Congress of Philosophy, 1904 366 7.5.2 German philosophers and mathematicians, especially Schonflies 368 7.5.3 Activities among the Peanists 370 7.5.4 American philosophers: Royce and Dewey 371 7.5.5 American mathematicians on classes 373 7.5.6 Huntington on logic and orders 375 7.5.7 Judgements fiom Shearman 376 7.6 Whitehead's role and activities, 1905-1907 377 7.6.1 Whitehead's construal of the 'material world' 377 7.6.2 The axioms of geometries 379 7.6.3 Whitehead's lecture course, 1906-1907 379 7.7 The sad compromise: logic in tiers 380 7.7.1 Rehabilitating propositional functions, 1906-1907 380 7.7.2 Two reflective pieces in 1907 382 7.7.3 Russell's outline of 'mathematical logic, 1908 383 7.8 The forming of Principia mathematica 384 7.8.1 Completing and funding Principia mathematica 384 7.8.2 The Organisation of Principia mathematica 386 7.8.3 The propositional calculus, and logicism 388 7.8.4 The predicate calculus, and descriptions 391 7.8.5 Classes and relations, relative to propositional functions 392 7.8.6 The multiplicative axiom: some uses and avoidance 395 7.9 Types and the treatment of mathematics in Principia mathematica 396 7.9.1 7~pes in orders 396 7.9.2 Reducing the edifice 397 7.9.3 Individuals, their nature and number 399 7.9.4 Cardinals and their finite arithmetic 401 7.9.5 The generalised ordinals 403 7.9.6 The ordinals and the alephs 404 7.9.7 The odd small ordinals 406 7.9.8 Series and continuity 406 7.9.9 Quantity with ratios 408 CHAPTER 8 The Influence and Place of Logicism, 1910-1930 8.1 Plans for two chapters 411 8.2 Whitehead's and Russell's transitions from logic to philosophy, 1910-1916 412 8.2.1 The educational concerns of "itehead, 1910-1916 412 8.2.2 Whitehead on the principles of geometry in the 1910s 413 8.2.3 British reviews of Principia mathematica 415 8.2.4 Russell and Peano on logic, 1911-1913 416 8.2.5 Russell's initial problems with epistemology, 1911-1912 417 8.2.6 Russell's first interactions with Wittgenstein, 1911-1913 418 8.2.7 Russell's confrontation with Wiener, 1913 419 8.3 Logicism and epistemology in America and with Russell, 1914-1921 421 8.3.1 Russell on logic and epistemology at Harvard, 1914 421 8.3.2 Two long American reviews 424 8.3.3 Reactions from Royce students: Sheffer and Lewis 424 8.3.4 Reactions to logicism in New York 428 8.3.5 OtherAmerican estimations 429 8.3.6 Russell's 'logical atomism' and psychology, 1917-1921 430 8.3.7 Russell's 'introduction'to logicism, 1918-1919 432 8.4 Revising logic and logicism at Cambridge, 1917-1925 434 8.4.1 New Cambridge authors, 1917-1921 434 8.4.2 Wittgenstein's 'Abhandlung' and Tractatus, 1921-1922 436 8.4.3 The limitations of Wittgenstein's logic 437 8.4.4 Towards extensional logicism: Russell's revision of Principia mathematica, 1923-1924 440 8.4.5 Ramsey's entry into logic and philosophy, 1920-1923 443 8.4.6 Ramsey's recasting of the theory of types, 1926 444 8.4.7 Ramsey on identity and comprehensive extensionality 446 8.5 Logicism and epistemology in Britain and America, 1921-1930 448 8.5.1 Johnson on logic, 1921-1924 448 8.5.2 Other Cambridge authors, 1923-1929 450 8.5.3 American reactions to logicism in mid decade 452 8.5.4 Groping towards metalogic 454 8.5.5 Reactions in and around Columbia 456 8.6 Peripherals: Italy and France 458 8.6.1 The occasional Italian survey 458 8.6.2 New French attitudes in the Revue 459 8.6.3 Commentaries in French, 1918-1930 461 8.7 German-speaking reactions to logicism, 1910-1928 463 8.7.1 (Neo-)Kantians in the 1910s 463 8.7.2 Phenomenologists in the 1910s 467 8.7.3 Frege's positive and then negative thoughts 468 8.7.4 Hilbert's definitive 'metamathematics; 1917-1930 470 8.7.5 Orders of logic and models of set theory: Lowenheim and Skolem, 1915-1923 475 8.7.6 Set theory and Mengenlehre in various forms 476 8.7.7 Intuitionistic set theory and logic: Brouwer and Weyl, 1910-1928 480 8.7.8 (Neo-)Kantians in the 1920s 484 8.7.9 Phenomenologists in the 1920s 487 8.8 The rise of Poland in the 1920s: the Lvnv-Warsaw school 489 8.8.1 From Lv6v to Warsaw: students of Twardowski 489 8.8.2 Logics with Lukasiewicz and Tarski 490 8.8.3 Russell's paradox and Lesniewski's three systems 492 8.8.4 Pole apart: Chwistek's 'semantic' logicism at Cracov 495 8.9 The rise of Austria in the 1920s: the Schlick circle 497 8.9.1 Formation and influence 497 8.9.2 The impact of Russell, especially upon Camap 499 8.9.3 'Logicism ' in Camap's Abriss, 1929 500 8.9.4 Epistemology in Camap's Aufbau, 1928 502 8.9.5 Intuitionism and proof theory: Brouwer and Godel, 1928-1930 504 CHAPTER 9 Postludes: Mathematical Logic and Logicism in the 1930s 9.1 Plan of the chapter 506 9.2 Godel's incompletability theorem and its immediate reception 507 9.2.1 The consolidation of Schlick's 'Vienna' Circle 507 9.2.2 News from G6del: the Konigsberg lectures, September 1930 508 9.2.3 G6del's incompletability theorem, 1931 509 9.2.4 Effects and reviews of G6del's theorem 511 9.2.5 Zermelo against Godeb the Bad Elster lectures, September 1931 512 9.3 Logic(ism) and epistemology in and around Vienna 513 9.3.1 Carnap for 'metalogic' and against metaphysics 513 9.3.2 Carnap's transformed metalogic: the 'logical syntax of language; 1934 515 9.3.3 Carnap on incompleteness and truth in mathematical theories, 1934-1935 517 9.3.4 Dubislav on definitions and the competing philosophies of mathematics 519 9.3.5 Behmann's new diagnosis of the paradoxes 520 9.3.6 Kaufmann and Waismann on the philosophy of mathematics 521 9.4 Logic(ism) in the U.S.A. 523 9.4.1 Mainly Eaton and Lewis 523 9.4.2 Mainly Weiss and Langer 525 9.4.3 Whitehead's new attempt to ground logicism, 1934 527 9.4.4 The debut of Quine 529 9.4.5 Two journals and an encyclopaedia, 1934-1938 531 9.4.6 Carnap's acceptance of the autonomy of semantics 533 9.5 The battle of Britain 535 9.5.1 The campaign of Stebbing for Russell and Carnap 535 9.5.2 Commentary from Black and Ayer 538 9.5.3 Mathematicians-and biologists 539 9.5.4 Retiring into philosophy: Russell's return, 1936-1937 542 9.6 European, mostly northern 543 9.6.1 Dingler and Burkamp again 543 9.6.2 German proof theory after Godel 544 9.6.3 Scholz's little circle at Munster 546 9.6.4 Historical studies, especially by Jorgensen 547 9.6.5 History philosophy, especially Cavailles 548 9.6.6 Other Francophone figures, especially Herbrand 549 9.6.7 Polish logicians, especially Tarski 551 9.6.8 Southern Europe and its former colonies 553 CHAPTER 10 The Fate of the Search 10.1 Influences on Russell, negative and positive 556 10.1.1 Symbolic logics: living together and living apart 556 10.1.2 The timing and origins of Russell's logicism 557 10.1.3 (Why) was Frege (so) little read in his lifetime? 558 10.2 The content and impact of logicism 559 10.2.1 Russell's obsession with reductionist logic and epistemology 560 10.2.2 The logic and its metalogic 562 10.2.3 The fate of logicism 563 10.2.4 Educational aspects, especially Piaget 566 10.2.5 The role of the U.S.A.: judgements in the Schi1pp series 567 10.3 The panoply of foundations 569 10.4 Sallies 573 CHAPTER 11 Transcription of Manuscripts 11.1 Couturat to Russell, 18 December 1904 574 11.2 Veblen to Russell, 13 May 1906 577 11.3 Russell to Hawtrey, 22 January 1907 (or 1909?) 579 11.4 Jourdain's notes on Wittgenstein's first views on Russell's paradox, April 1909 580 11.5 The application of Whitehead and Russell to the Royal Society, late 1909 581 11.6 Whitehead to Russell, 19 January 1911 584 11.7 Oliver Strachey to Russell, 4 January 1912 585 11.8 Quine and Russell, June-July 1935 586 11.8.1 Russell to Quine, 6 June 1935 587 11.8.2 Quine to Russell, 4 July 1935 588 11.9 Russell to Henkin, 1 April 1963 592 BIBLIOGRAPHY 594 INDEX 671
£103.70
Princeton University Press Continuous Geometry
Book SynopsisBased on von Neumann's lecture notes, this book begins with the development of the axioms of continuous geometry, dimension theory, and - for the irreducible case - the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries.Trade Review"This historic book should be in the hands of everyone interested in rings and projective geometry."--R. J. Smith, The Australian Journal of Science "Much in this book is still of great value, partly because it cannot be found elsewhere ... partly because of the very clear and comprehensible presentation. This makes the book valuable for a first study of continuous geometry as well as for research in this field."--F. D. Veldkamp, Nieuw Archief voor WiskundeTable of ContentsForewordFoundations and Elementary Properties1Independence8Perspectivity and Projectivity. Fundamental Properties16Perspectivity by Decomposition24Distributivity. Equivalence of Perspectivity and Projectivity32Properties of the Equivalence Classes42Dimensionality54Theory of Ideals and Coordinates in Projective Geometry63Theory of Regular Rings69Appendix 182Appendix 284Appendix 390Order of a Lattice and of a Regular Ring93Isomorphism Theorems103Projective Isomorphisms in a Complemented Modular Lattice117Definition of L-Numbers; Multiplication130Appendix133Addition of L-Numbers136Appendix148The Distributive Laws, Subtraction; and Proof that the L-Numbers form a Ring151Appendix158Relations Between the Lattice and its Auxiliary Ring160Further Properties of the Auxiliary Ring of the Lattice168Special Considerations. Statement of the Induction to be Proved177Treatment of Case I191Preliminary Lemmas for the Treatment of Case II197Completion of Treatment of Case II. The Fundamental Theorem199Perspectivities and Projectivities209Inner Automorphisms217Properties of Continuous Rings222Rank-Rings and Characterization of Continuous Rings231Center of a Continuous Geometry240Appendix 1245Appendix 2259Transitivity of Perspectivity and Properties of Equivalence Classes264Minimal Elements277List of Changes from the 1935-37 Edition and comments on the text by Israel Halperin283Index297
£85.00
Princeton University Press Algebraic Theory of Numbers
Book SynopsisExplores fundamental concepts in arithmetic. This book begins with the definitions and properties of algebraic fields. It then discusses the theory of divisibility from an axiomatic viewpoint, rather than by the use of ideals. It also gives an introduction to p-adic numbers and their uses, which are important in modern number theory.Table of ContentsCh. I Algebraic Fields 1 Ch. II Theory of Divisibility (Kronecker, Dedekind) 33 Ch. III Local Primadic Analysis (Kummer, Hensel) 71 Ch. IV Algebraic Number Fields 141 Amendments 223
£63.75
Princeton University Press PCT Spin and Statistics and All That
Book SynopsisAxiomatic Quantum Field Theory gives precise mathematical responses to questions like: What is a quantized field? And what are the physically indispensable attributes of a quantized field? This title offers a summary of and introduction to the achievements of Axiomatic Quantum Field Theory.Table of Contents*Frontmatter, pg. i*Contents, pg. v*Preface, pg. vii*Introduction, pg. 1*1. Relativistic Transformation Laws, pg. 4*2. Some Mathematical Tools, pg. 31*3. Fields and Vacuum Expectation Values, pg. 96*4. Some General Theorems of Relativistic Quantum Field Theory, pg. 134*Appendix, pg. 179*Index, pg. 205
£46.75
Princeton University Press The Evolution of Animal Communication
Book SynopsisGull chicks beg for food from their parents. Peacocks spread their tails to attract potential mates. Meerkats alert family members of the approach of predators. But are these sometimes dishonest? This book probes such question by reviewing the empirical data and game theory models available, and by asking how well theory matches data.Trade Review"William Searcy and Stephen Nowicki provide a fascinating perspective on the honesty of signals in animal communication systems... [A] comprehensive yet concise review of what we currently know concerning signal reliability in animals, enriched with many in-depth examples."--Katherine E. LeVan and Noah Wilson-Rich, Science "The book is well written and informative... Searcy and Nowicki are well-known experts in the field of animal communication and sexual selection, and they provide a thorough and careful overview of this important, but often under-discussed, topic."--R. Andrew Hayes, Austral Ecology "The book is a fascinating evaluation of the present state of reliability and deception in animal signaling systems. It would make a perfect, albeit somewhat controversial, focus for an honors biology or graduate seminar course on animal communication."--H.Jane Brockmann, BioScienceTable of ContentsFigures, Boxes, and Table ix Acknowledgments xiii Introduction 1 Chapter 1: Definitions 2 Some History 6 Categories of Signal Costs 13 Alternative Explanations for Reliability 16 Deception Redux 17 Evolutionary Interests of Signalers and Receivers 20 Chapter 2: Signaling When Interests Overlap 24 Signaling Between Relatives: Theory 24 Begging 36 Alarms 53 Food Calls 68 Individually Directed Skepticism 73 Conclusions 77 Chapter 3: Signaling When Interests Diverge 78 Mating Signals: Theory 78 Carotenoid Pigmentation 86 Songs in Oscine Birds 97 Tail Length in Birds 123 Conclusions 131 Chapter 4: Signaling When Interests Oppose 134 Signaling in Aggressive Contexts: Theory 134 Postural Displays of Aggression in Birds 141 Badges of Status 147 Weapon Displays in Crustaceans 160 Dominant Frequency in Calls of Frogs and Toads 169 Conclusions 178 Chapter 5: Honesty and Deception in Communication Networks 181 Third-Party Receivers 182 "Eavesdropping" versus "Interception" 183 Eavesdropping in Signaling Interactions 185 Third-Party Receivers and Reliability 203 Conclusions 206 Chapter 6: Conclusions 207 Reliability 208 Alternatives to the Handicap Mechanism 214 Deceit 218 The Balance of Reliability and Deceit 223 References 225 Author Index 257 Subject Index 263
£999.99
Princeton University Press Statistics in Theory and Practice
Book SynopsisAimed at a diverse scientific audience, this book explains the theory underlying the classical statistical methods. It covers topics that include common probability distributions; sampling and the distribution of sampling statistics; confidence intervals, hypothesis testing, and the theory of tests; estimation; and more.Trade Review"Aimed at a diverse scientific audience, including physicists, astronomers, chemists, geologists, and economists, this book explains the theory underlying the classical statistical methods ...There are nearly one hundred problems (with answers) designed to bring out points in the text and to cover topics lightly outside the main line of development."--Zentralblatt fur Mathematik
£78.20
Princeton University Press Automata Studies
Book SynopsisThe description for this book, Automata Studies. (AM-34), will be forthcoming.Table of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. ix*Representation of Events in Nerve Nets and Finite Automata, pg. 3*Probabilistic Logics and the Synthesis of Reliable Organisms From Unreliable Components, pg. 43*Some Uneconomical Robots, pg. 99*Some Universal Elements for Finite Automata, pg. 117*Gedanken-Experiments on Sequential Machines, pg. 129*A Universal Turing Machine with Two Internal States, pg. 157*A Note on Universal Turing Machines, pg. 167*The Inversion of Functions Defined by Turing Machines, pg. 177*Computability by Probabilistic Machines, pg. 183*Design for an Intelligence-Amplifier, pg. 215*The Epistemological Problem for Automata, pg. 235*Conditional Probability Machines and Conditioned Reflexes, pg. 253*Temporal and Spatial Patterns in a Conditional Probability Machine, pg. 277
£999.99
Princeton University Press Consistency of the Continuum Hypothesis
Book SynopsisThe 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. In this book, Kurt Godel sets forth his proof for this problem.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. vii*INTRODUCTION, pg. 1*CHAPTER I. THE AXIOMS OF ABSTRACT SET THEORY, pg. 3*CHAPTER II. EXISTENCE OF CLASSES AND SETS, pg. 8*CHAPTER III. ORDINAL NUMBERS, pg. 21*CHAPTER IV. CARDINAL NUMBERS, pg. 30*CHAPTER V. THE MODEL DELTA, pg. 35*CHAPTER VI. PROOF OF THE AXIOMS OF GROUPS A-D FOR THE MODEL DELTA, pg. 45*CHAPTER VII. PROOF THAT V = L HOLDS IN THE MODEL DELTA, pg. 47*CHAPTER VIII. PROOF THAT V = L IMPLIES THE AXIOM OF CHOICE AND THE GENERALISED CONTINTUUM-HYPOTHESIS, pg. 53*APPENDIX, pg. 62*INDEX, pg. 63*Notes Added to the Second Printing, pg. 67*BIBLIOGRAPHY, pg. 72
£40.50
Princeton University Press Contributions to Fourier Analysis
Book SynopsisIn the theory of convergence and summability whether for ordinary Fourier series or other expansions emphasis is placed on the phenomenon of localization whenever such occurs, and in the present paper a certain aspect of this phenomenon will be studied for the problem of best approximation as well.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. v*I. LOCALIZATION OF BEST APPROXIMATION, pg. 1*II. DIRICHLET PROBLEM FOR DOMAINS BOUNDED BY SPHERES, pg. 24*III. THE FRECHET VARIATION AND PRINGSHEIM CONVERGENCE OF DOUBLE FOURIER SERIES, pg. 46*IV. NORMS OF DISTRIBUTION FUNCTIONS ASSOCIATED WITH BILINEAR FUNCTIONALS, pg. 104*V. NOTE ON THE BOUNDARY VALUES OF FUNCTIONS OF SEVERAL COMPLEX VARIABLES, pg. 145*VI. ON THE THEOREM OF HAUSDORFF-YOUNG AND ITS EXTENSIONS, pg. 166
£66.30
Princeton University Press Contributions to the Theory of Nonlinear
Book SynopsisAnnals of Mathematics Studies: Number 41The present volume of the Contributions, fourth in the series, covers, like its predecessors, a great variety of topics in non-linear differential equations.Table of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*I. On the Non-Linear Difference-Differential Equation y1(t) = [A - By(t-r) ly (t), pg. 1*II. On the Critical Points of a Class of Differential Equations, pg. 19*III. Optimal Discontinuous Forcing Terms, pg. 29*IV. On the Structure of Symmetric Periodic Solutions of Conservative Systems, with Applications, pg. 53*V. Asymptotic Behavior of Solutions of Canonical Systems Near a Closed, Unstable Orbit, pg. 85*VI. Small Periodic Perturbations of an Autonomous System of Vector Equations, pg. 111*VII. Rotated Vector Fields and an Equation for Relaxation Oscillations, pg. 125*VIII. A Survey of Lyapunov's Second Method, pg. 141*IX. On Phase Portraits of Critical Points in n-Space, pg. 167*X. On Non-Linear Repulsive Forces, pg. 201*Backmatter, pg. 214
£72.25
Princeton University Press Introduction to NonLinear Mechanics
Book SynopsisThe description for this book, Introduction to Non-Linear Mechanics. (AM-11), will be forthcoming.Table of Contents*Frontmatter, pg. i*INTRODUCTION, pg. v*TABLE OF CONTENTS, pg. vii*I. SOME NON-LINEAR OSCILLATORY SYSTEMS, pg. 1*II. ELEMENTARY THEORY OF THE FIRST APPROXIMATION, pg. 8*III. REFINEMENT OF THE FIRST APPROXIMATION, pg. 28*IV. CONSTRUCTION OF THE HIGHER APPROXIMATIONS, pg. 40*V. LINEARIZATION, pg. 55*VI. APPLICATION OF SYMBOLIC METHODS TO LINEARIZATION, pg. 63*VII. MULTIPLY PERIODIC SYSTEMS, pg. 73*VIII. INFLUENCE OF PERIODIC DISTURBANCES, pg. 79*IX. COMPLEMENTS, pg. 87*BIBLIOGRAPHY, pg. 100*ERRATA, pg. 106
£999.99
Princeton University Press Isoperimetric Inequalities in Mathematical
Book SynopsisThe description for this book, Isoperimetric Inequalities in Mathematical Physics. (AM-27), will be forthcoming.Table of Contents*Frontmatter, pg. i*PREFACE, pg. v*TABLE OF CONTENTS, pg. xi*CHAPTER I. DEFINITIONS, METHODS AND RESULTS, pg. 1*CHAPTER II. THE PRINCIPLES OP DIRICHLET AND THOMSON, pg. 42*CHAPTER III. APPLICATIONS OP THE PRINCIPLES OP DIRICHLET AND THOMSON TO ESTIMATION OP THE CAPACITY, pg. 63*CHAPTER IV. CIRCULAR PLATE CONDENSER, pg. 79*CHAPTER V. TORSIONAL RIGIDITY AND PRINCIPAL FREQUENCY, pg. 87*CHAPTER VI. NEARLY CIRCULAR AND NEARLY SPHERICAL DOMAINS, pg. 127*CHAPTER VIII. ON ELLIPSOID AND LENS, pg. 171*NOTE A. SURFACE-AREA AND DIRICHLET'S INTEGRAL, pg. 182*NOTE B. ON CONTINUOUS SYMMETRIZATION, pg. 200*NOTE C. ON SPHERICAL SYMMETRIZATION, pg. 205*NOTE D. ON A GENERALIZATION OF DIRICHLET'S INTEGRAL, pg. 211*NOTE E. HEAT-CONDUCTION ON A SURFACE, pg. 217*NOTE F. ON MEMBRANES AND PLATES, pg. 230*NOTE G. VIRTUAL MASS AND POLARIZATION, pg. 239*TABLES FOR SOME SET-FUNCTIONS OF PLANE DOMAINS, pg. 247*BIBLIOGRAPHY, pg. 275*LIST OF SYMBOLS, pg. 278
£69.70
Princeton University Press Knot Groups
Book SynopsisThe description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), will be forthcoming.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. v*CHAPTER I. INTRODUCTION, pg. 1*CHAPTER II. NOTATION AND CONVENTIONS, pg. 5*CHAPTER III. COMBINATORIAL COVERING SPACE THEORY FOR 3-MANIFOLDS, pg. 9*CHAPTER IV. THE COMMUTATOR SUBGROUP AND THE ALEXANDER MATRIX, pg. 25*CHAPTER V. SUBGROUPS, pg. 49*CHAPTER VI. REPRESENTATIONS, pg. 61*CHAPTER VII. AUTOMORPHISMS, pg. 67*CHAPTER VIII. A GROUP OF GROUPS, pg. 75*CHAPTER IX. THE CHARACTERIZATION PROBLEM, pg. 87*CHAPTER X. THE STRENGTH OP THE GROUP, pg. 93*CHAPTER XI. PROBLEMS, pg. 99*APPENDIX BY S. Eileriberg, pg. 103*REFERENCES, pg. 107*INDEX, pg. 113
£51.00
Princeton University Press Lectures on Curves on an Algebraic Surface
Book SynopsisTable of Contents*Frontmatter, pg. i*INTRODUCTION, pg. vii*CONTENTS, pg. xi*LECTURE 1. RAW MATERIAL ON CURVES ON SURFACES, AND THE PROBLEMS SUGGESTED, pg. 1*LECTURE 2. THE FUNDAMENTAL EXISTENCE PROBLEM AND TWO ANALYTIC PROOFS, pg. 7*LECTURE 3. PRE-SCHEMES AND THEIR ASSOCIATED "FUNCTOR OF POINTS", pg. 11*LECTURE 4. USES OF THE FUNCTOR OF POINTS, pg. 17*APPENDIX TO LECTURE 4. RE REPRESENTABLE FUNCTORS AND ZARISKI TANGENT SPACES, pg. 25*LECTURE 5. Pro j AND INVERTIBLE SHEAVES, pg. 27*APPENDIX TO LECTURE 5, pg. 35*LECTURE 6. PROPERTIES OP MORPHISMS AND SHEAVES, pg. 37*LECTURE 7. RESUME OF THE COHOMOLOGY OF COHERENT SHEAVES ON Pn, pg. 47*LECTURE 8. FLATTENING STRATIFICATIONS, pg. 55*LECTURE 9. CARTIER DIVISORS, pg. 61*LECTURE 10. FUNCTORIAL PROPERTIES OF EFFECTIVE CARTIER DIVISORS, pg. 69*LECTURE 11. BACK TO THE CLASSICAL CASE, pg. 75*LECTURE 12. THE OVER-ALL CLASSIFICATION OF CURVES ON SURFACES, pg. 83*LECTURE 13. LINEAR SYSTEMS AND EXAMPLES, pg. 91*LECTURE 14. SOME VANISHING THEOREMS, pg. 99*LECTURE 15. UNIVERSAL FAMILIES OF CURVES, pg. 105*LECTURE 16. THE METHOD OF CHOW SCHEMES, pg. 111*LECTURE 17. GOOD CURVES, pg. 119*LECTURE 18. THE INDEX THEOREM, pg. 127*LECTURE 19. THE PICARD SCHEME : OUTLINE, pg. 133*LECTURE 20. INDEPENDENT 0-CYCLES ON A SURFACE, pg. 139*LECTURE 21. THE PICARD SCHEME: CONCLUSION, pg. 145*LECTURE 22. THE CHARACTERISTIC MAP OP A FAMILY OP CURVES, pg. 151*LECTURE 23. THE FUNDAMENTAL THEOREM VIA KODAIRA-SPENCER, pg. 157*LECTURE 24. THE STRUCTURE OF PHI, pg. 161*LECTURE 25. THE FUNDAMENTAL THEOREM VIA GROTHENDIECK-CARTIER, pg. 167*LECTURE 26. RING SCHEMES; THE WITT SCHEME, pg. 171*APPENDICES TO LECTURE 26 APPENDICES TO LECTURE 26, pg. 189*LECTURE 27. THE FUNDAMENTAL THEOREM IN CHARACTERISTIC p, pg. 193*WORKS REFERRED TO, pg. 199*Backmatter, pg. 204
£63.75
Princeton University Press Lectures on Fourier Integrals
Book SynopsisThe description for this book, Lectures on Fourier Integrals. (AM-42), will be forthcoming.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. vii*CHAPTER I. BASIC PROPERTIES OF TRIGONOMETRIC INTEGRALS, pg. 1*CHAPTER II. REPRESENTATION - AND SUM FORMULAS, pg. 23*CHAPTER III. THE FOURIER INTEGRAL THEOREM, pg. 46*CHAPTER IV. STIELTJES INTEGRALS, pg. 78*CHAPTER V. OPERATIONS WITH FUNCTIONS OF THE CLASS FO, pg. 104*CHAPTER VI. GENERALIZED TRIGONOMETRIC INTEGRALS, pg. 138*CHAPTER VII. ANALYTIC AND HARMONIC FUNCTIONS, pg. 182*CHAPTER VIII. QUADRATIC INTEGRABILITV, pg. 214*CHAPTER IX. FUNCTIONS OF SEVERAL VARIABLES, pg. 231*APPENDIX, pg. 264*REMARKS - QUOTATIONS, pg. 281*MONOTONIC FUNCTIONS, STIELTJES INTEGRALS AND HARMONIC ANALYSIS, pg. 292*SYMBOLS, pg. 332
£78.20
Princeton University Press Seminar on the AtiyahSinger Index Theorem
Book SynopsisThe description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), will be forthcoming.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. v*PREFACE, pg. ix*CHAPTER I. STATEMENT OF THE THEOREM OUTLINE OF THE PROOF, pg. 1*CHAPTER II. REVIEW OF K-THEORY, pg. 13*CHAPTER III. THE TOPOLOGICAL INDEX OF AN OPERATOR ASSOCIATED TO A G-STRUCTURE, pg. 27*CHAPTER IV. DIFFERENTIAL OPERATORS ON VECTOR BUNDLES, pg. 51*CHAPTER V. ANALYTICAL INDICES OF SOME CONCRETE OPERATORS, pg. 95*CHAPTER VI. REVIEW OF FUNCTIONAL ANALYSIS, pg. 107*CHAPTER VII. FREDHDIM OPERATORS, pg. 119*CHAPTER VIII. CHAINS OP HILBERTIAN SPACES, pg. 125*CHAPTER IX. THE DISCRETE SOBOLEV CHAIN OF A VECTOR BUNDLE, pg. 147*CHAPTER X. THE CONTINUOUS SOBOLEV CHAIN OF A VECTOR BUNDLE, pg. 155*CHAPTER XI. THE SEELEY ALGEBRA, pg. 175*CHAPTER XII. HOMOTOPY INVARIANCE OF THE INDEX, pg. 185*CHAPTER XIII. WHITNEY SUMS, pg. 191*CHAPTER XIV. TENSOR PRODUCTS, pg. 197*CHAPTER XV. DEFINITION OF ia AND it ON K(M), pg. 215*CHAPTER XVI. CONSTRUCTION OF Intk, pg. 235*CHAPTER XVII. COBORDISM INVARIANCE OP THE ANALYTICAL INDEX, pg. 285*CHAPTER XVIII. BORDISM GROUPS OF BUNDLES, pg. 303*CHAPTER XIX. THE INDEX THEOREM: APPLICATIONS, pg. 313*APPENDIX I. THE INDEX THEOREM FOR MANIFOLDS WITH BOUNDARY, pg. 337*APPENDIX II. NON-STABLE CHARACTERISTIC CLASSES AND THE TOPOLOGICAL INDEX OP CLASSICAL ELLIPTIC OPERATORS, pg. 353*Backmatter, pg. 368
£92.65
Princeton University Press Topology Seminar Wisconsin 1965
Book SynopsisDuring the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing. Twenty-five of these lectures are included in this study, among them Professor Bing's lecture describing the recent attacks of Haken and Poincare on the Poincare conjectures, and sketching a proof of Haken's main result.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. vii*PREFACE, pg. ix*MONOTONE DECOMPOSITIONS OF E3, pg. 1*EQUIVALENT DECOMPOSITIONS OF E3, pg. 27*ANOTHER DECOMPOSITION OP E3 INTO POINTS AND INTERVALS, pg. 33*CRUMPLED CUBES, pg. 53*SEWINGS OF CRUMPLED CUBES WHICH DO NOT YIELD S3, pg. 57*CANONICAL NEIGHBORHOODS IN THREE-MANIFOLDS, pg. 61*BOUNDARY LINKS, pg. 69*SURFACES IN E3, pg. 73*ADDITIONAL QUESTIONS ON 3-MANIFOLDS, pg. 81*HOW NOT TO PROVE THE POINCARE CONJECTURE, pg. 83*MAPPING A 3 -SPHERE ONTO A HOMOTOPY 3 -SPHERE, pg. 89*CONCERNING FAKE CUBES, pg. 101*ON CERTAIN FIRST COUNTABLE SPACES, pg. 103*REMARKS ON THE NORMAL MOORE SPACE METRIZATION PROBLEM, pg. 115*TWO CONJECTURES IN POINT SET THEORY, pg. 121*ALMOST CONTINUOUS FUNCTIONS AND FUNCTIONS OF BAIRE CLASS 1, pg. 125*CHAINABLE CONTINUA, pg. 129*THE EXISTENCE OP A COMPLETE METRIC FOR A SPECIAL MAPPING SPACE AND SOME CONSEQUENCES, pg. 135*FINITE DIMENSIONAL SUBSETS OF INFINITE DIMENSIONAL SPACES, pg. 141*TYPES OF ULTRAFILTERS, pg. 147*ADDITIONAL QUESTIONS ON ABSTRACT SPACES, pg. 152*TAMING POLYHEDRA IN THE TRIVIAL RANGE, pg. 153*SOME NICE EMBEDDINGS IN THE TRIVIAL RANGE, pg. 159*APPROXIMATIONS AND ISOTOPIES IN THE TRIVIAL RANGE, pg. 171*ON A SPHERICAL EMBEDDINGS OF 2 -SPHERES IN THE 4-SPHERE, pg. 189*GEOMETRIC CHARACTERIZATION OP DIFFERENTIABLE MANIFOLDS IN EUCLIDEAN SPACE, pg. 197*WHITEHEAD TORSION AND h-COBORDISM, pg. 211*ADDITIONAL QUESTIONS ON N-MANIFOLDS, pg. 217*COMPLETELY REGULAR MAPPINGS, FIBER SPACES, THE WEAK BUNDLE PROPERTIES, AND THE GENERALIZED SLICING STRUCTURE PROPERTIES, pg. 219*FIBER SPACES AND n-REGULARITY, pg. 229*FIBER SPACES WIT H TOTALLY PATHWISE DISCONNECTED FIBERS, pg. 235*SOME QUESTIONS IN THE THEORY OP NORMAL FIBER SPACES FOR TOPOLOGICAL MANIFOLDS, pg. 241
£69.70
