Mathematics Books

Book SynopsisCovering a growing area of research, Spatial Analysis highlights the latest advances in the field with an emphasis on applications. Written by world-renowned authors, this breakthrough text provides insight into the statistical investigation of the interdependence of random variables as a function of their proximity in space and time.Trade Review[Spatial Analysis] is a splendid text on spatial statistics written by two eminent scholars in the field who have beautifully presented a wide range of topics. The text begins with some very interesting examples of spatially oriented data and their features and is followed by some superbly compiled expository chapters. What is especially appealing, in my opinion, is the attention paid by the authors to the theoretical developments and exposition of seemingly abstruse topics. The book is compactly written while retaining mathematical rigor. Specifically, the chapters on different flavours of spatial random fields and that on conditional autoregression models stand out in terms of their clarity of presentation. Inference primarily focuses on likelihood based methods and kriging, while appearing somewhat late in the book (Chapter 7 out of eight chapters), receives a very detailed treatment that includes Bayesian prediction methods as well. In summary, this elegant text will serve students, researchers and scholars invested in spatial statistics very well as a source of reference as well as a text to build courses from. I congratulate the authors' on this wonderful accomplishment. — Sudipto Banerjee, PhD, Professor and Chair, Dept. of Biostatistics, UCLA Fielding School of Public Health This book, Spatial Analysis, by John Kent and Kanti Mardia is a must-read by all statisticians whose interests include spatial statistics, and it would make an excellent graduate-level text. The authors find the sweet spot at the juncture of intuition, methodology, and applications, and they show us in many ways how the validity of scientific inferences and its software has its genesis in the construction of valid statistical models. — Noel Cressie, Distinguished Professor and Director, Centre for Environmental Informatics, University of Wollongong, Australia The modern world of big data is often accompanied by little understanding. Often this data comes in a spatial form, and critically our understanding emerges from spatial analysis. It’s not possible to imagine two better guides to this domain than John Kent and Kanti Mardia. In Spatial Analysis Kent and Mardia provide a comprehensive guide to modern thinking that is classically grounded. This book is a must-read for those who are taking understanding seriously as part of handling modern spatial data sets across the domains of machine learning, statistics and data science. — Neil Lawrence, DeepMind Professor of Machine Learning, University of Cambridge [Spatial Analysis] is a delightful and authoritative book on the subject of spatial statistical analysis by two of the world’s most eminent researchers in the field of spatial statistics and shape analysis. The book eloquently discusses most of the topics in spatial analysis in a wonderfully organised manner. For example, there are two chapters on random fields, two chapters on estimation methods, one on modelling and another large chapter on kriging. With another chapter on additional topics such as Co-kriging, Bayesian hierarchical modeling, spatio-temporal modeling, and thin plate splines this book covers most of the concepts researchers need to know in this area. The main emphasis of the book is on theoretical aspects but it does not lose sight of applications. The chapter one itself motivates the theory with several example data sets which include fingerprint of the famous statistician Sir R A Fisher. The book does justice to the theory by presenting and explaining it in an accessible format for all – graduate students and researchers. The book also provides enjoyable to read personal historical notes and anecdotes regarding the course of development of the theory of spatial analysis. — Sujit Sahu, Professor of Mathematical Sciences, University of SouthamptonTable of ContentsList of Figures xiii List of Tables xvii Preface xix List of Notation and Terminology xxv 1 Introduction 1 1.1 Spatial Analysis 1 1.2 Presentation of the Data 2 1.3 Objectives 9 1.4 The Covariance Function and Semivariogram 11 1.4.1 General Properties 11 1.4.2 Regularly Spaced Data 13 1.4.3 Irregularly Spaced Data 14 1.5 Behavior of the Sample Semivariogram 16 1.6 Some Special Features of Spatial Analysis 22 Exercises 27 2 Stationary Random Fields 31 2.1 Introduction 31 2.2 Second Moment Properties 32 2.3 Positive Definiteness and the Spectral Representation 34 2.4 Isotropic Stationary Random Fields 36 2.5 Construction of Stationary Covariance Functions 41 2.6 Matérn Scheme 43 2.7 Other Examples of Isotropic Stationary Covariance Functions 45 2.8 Construction of Nonstationary Random Fields 48 2.8.1 Random Drift 48 2.8.2 Conditioning 49 2.9 Smoothness 49 2.10 Regularization 51 2.11 Lattice Random Fields 53 2.12 Torus Models 56 2.12.1 Models on the Continuous Torus 56 2.12.2 Models on the Lattice Torus 57 2.13 Long-range Correlation 58 2.14 Simulation 61 2.14.1 General Points 61 2.14.2 The Direct Approach 61 2.14.3 Spectral Methods 62 2.14.4 Circulant Methods 66 Exercises 67 3 Intrinsic and Generalized Random Fields 73 3.1 Introduction 73 3.2 Intrinsic Random Fields of Order k = 0 74 3.3 Characterizations of Semivariograms 80 3.4 Higher Order Intrinsic Random Fields 83 3.5 Registration of Higher Order Intrinsic Random Fields 86 3.6 Generalized Random Fields 87 3.7 Generalized Intrinsic Random Fields of Intrinsic Order k ≥ 0 91 3.8 Spectral Theory for Intrinsic and Generalized Processes 91 3.9 Regularization for Intrinsic and Generalized Processes 95 3.10 Self-Similarity 96 3.11 Simulation 100 3.11.1 General Points 100 3.11.2 The Direct Method 101 3.11.3 Spectral Methods 101 3.12 Dispersion Variance 102 Exercises 104 4 Autoregression and Related Models 115 4.1 Introduction 115 4.2 Background 118 4.3 Moving Averages 120 4.3.1 Lattice Case 120 4.3.2 Continuously Indexed Case 121 4.4 Finite Symmetric Neighborhoods of the Origin in Z d 122 4.5 Simultaneous Autoregressions (SARs) 124 4.5.1 Lattice Case 124 4.5.2 Continuously Indexed Random Fields 125 4.6 Conditional Autoregressions (CARs) 127 4.6.1 Stationary CARs 128 4.6.2 Iterated SARs and CARs 130 4.6.3 Intrinsic CARs 131 4.6.4 CARs on a Lattice Torus 132 4.6.5 Finite Regions 132 4.7 Limits of CAR Models Under Fine Lattice Spacing 134 4.8 Unilateral Autoregressions for Lattice Random Fields 135 4.8.1 Half-spaces in Z d 135 4.8.2 Unilateral Models 136 4.8.3 Quadrant Autoregressions 139 4.9 Markov Random Fields (MRFs) 140 4.9.1 The Spatial Markov Property 140 4.9.2 The Subset Expansion of the Negative Potential Function 143 4.9.3 Characterization of Markov Random Fields in Terms of Cliques 145 4.9.4 Auto-models 147 4.10 Markov Mesh Models 149 4.10.1 Validity 149 4.10.2 Marginalization 150 4.10.3 Markov Random Fields 150 4.10.4 Usefulness 151 Exercises 151 5 Estimation of Spatial Structure 159 5.1 Introduction 159 5.2 Patterns of Behavior 160 5.2.1 One-dimensional Case 160 5.2.2 Two-dimensional Case 161 5.2.3 Nugget Effect 162 5.3 Preliminaries 164 5.3.1 Domain of the Spatial Process 164 5.3.2 Model Specification 164 5.3.3 Spacing of Data 165 5.4 Exploratory and Graphical Methods 166 5.5 Maximum Likelihood for Stationary Models 168 5.5.1 Maximum Likelihood Estimates – Known Mean 169 5.5.2 Maximum Likelihood Estimates – Unknown Mean 171 5.5.3 Fisher Information Matrix and Outfill Asymptotics 172 5.6 Parameterization Issues for the Matérn Scheme 173 5.7 Maximum Likelihood Examples for Stationary Models 174 5.8 Restricted Maximum Likelihood (REML) 179 5.9 Vecchia’s Composite Likelihood 180 5.10 REML Revisited with Composite Likelihood 182 5.11 Spatial Linear Model 185 5.11.1 MLEs 186 5.11.2 Outfill Asymptotics for the Spatial Linear Model 188 5.12 REML for the Spatial Linear Model 188 5.13 Intrinsic Random Fields 189 5.14 Infill Asymptotics and Fractal Dimension 192 Exercises 195 6 Estimation for Lattice Models 201 6.1 Introduction 201 6.2 Sample Moments 203 6.3 The AR(1) Process on Z 205 6.4 Moment Methods for Lattice Data 208 6.4.1 Moment Methods for Unilateral Autoregressions (UARs) 209 6.4.2 Moment Estimators for Conditional Autoregression (CAR) Models 210 6.5 Approximate Likelihoods for Lattice Data 212 6.6 Accuracy of the Maximum Likelihood Estimator 215 6.7 The Moment Estimator for a CAR Model 218 Exercises 219 7 Kriging 231 7.1 Introduction 231 7.2 The Prediction Problem 233 7.3 Simple Kriging 236 7.4 Ordinary Kriging 238 7.5 Universal Kriging 240 7.6 Further Details for the Universal Kriging Predictor 241 7.6.1 Transfer Matrices 241 7.6.2 Projection Representation of the Transfer Matrices 242 7.6.3 Second Derivation of the Universal Kriging Predictor 244 7.6.4 A Bordered Matrix Equation for the Transfer Matrices 245 7.6.5 The Augmented Matrix Representation of the Universal Kriging Predictor 245 7.6.6 Summary 247 7.7 Stationary Examples 248 7.8 Intrinsic Random Fields 253 7.8.1 Formulas for the Kriging Predictor and Kriging Variance 253 7.8.2 Conditionally Positive Definite Matrices 254 7.9 Intrinsic Examples 256 7.10 Square Example 258 7.11 Kriging with Derivative Information 259 7.12 Bayesian Kriging 262 7.12.1 Overview 262 7.12.2 Details for Simple Bayesian Kriging 264 7.12.3 Details for Bayesian Kriging with Drift 264 7.13 Kriging and Machine Learning 266 7.14 The Link Between Kriging and Splines 269 7.14.1 Nonparametric Regression 269 7.14.2 Interpolating Splines 271 7.14.3 Comments on Interpolating Splines 273 7.14.4 Smoothing Splines 274 7.15 Reproducing Kernel Hilbert Spaces 274 7.16 Deformations 275 Exercises 277 8 Additional Topics 283 8.1 Introduction 283 8.2 Log-normal Random Fields 284 8.3 Generalized Linear Spatial Mixed Models (GLSMMs) 285 8.4 Bayesian Hierarchical Modeling and Inference 286 8.5 Co-kriging 287 8.6 Spatial–temporal Models 291 8.6.1 General Considerations 291 8.6.2 Examples 292 8.7 Clamped Plate Splines 294 8.8 Gaussian Markov Random Field Approximations 295 8.9 Designing a Monitoring Network 296 Exercises 298 Appendix A Mathematical Background 303 A. 1 Domains for Sequences and Functions 303 A. 2 Classes of Sequences and Functions 305 A.2. 1 Functions on the Domain Rd 305 A.2. 2 Sequences on the Domain Zd 305 A.2. 3 Classes of Functions on the Domain S d1 306 A.2 4 Classes of Sequences on the Domain ZNd, Where N = (n[1], .,n[d]) 306 A. 3 Matrix Algebra 306 A.3. 1 The Spectral Decomposition Theorem 306 A.3. 2 Moore–Penrose Generalized Inverse 307 A.3. 3 Orthogonal Projection Matrices 308 A.3. 4 Partitioned Matrices 308 A.3. 5 Schur Product 309 A.3. 6 Woodbury Formula for a Matrix Inverse 310 A.3. 7 Quadratic Forms 311 A.3. 8 Toeplitz and Circulant Matrices 311 A.3. 9 Tensor Product Matrices 312 A.3. 10 The Spectral Decomposition and Tensor Products 313 A.3. 11 Matrix Derivatives 313 A. 4 Fourier Transforms 313 A. 5 Properties of the Fourier Transform 315 A. 6 Generalizations of the Fourier Transform 318 A. 7 Discrete Fourier Transform and Matrix Algebra 318 A.7. 1 DFT in d = 1Dimension 318 A.7. 2 Properties of the Unitary Matrix G, d = 1 319 A.7. 3 Circulant Matrices and the DFT, d = 1 320 A.7. 4 The Case d > 1 321 A.7. 5 The Periodogram 322 A. 8 Discrete Cosine Transform (DCT) 322 A.8. 1 One-dimensional Case 322 A.8. 2 The Case d > 1 323 A.8. 3 Indexing for the Discrete Fourier and Cosine Transforms 323 A. 9 Periodic Approximations to Sequences 324 A. 10 Structured Matrices in d = 1Dimension 325 A. 11 Matrix Approximations for an Inverse Covariance Matrix 327 A.1. 1 The Inverse Covariance Function 328 A.11. 2 The Toeplitz Approximation to Σ − 1 330 A.11. 3 The Circulant Approximation to Σ − 1 330 A.11. 4 The Folded Circulant Approximation to Σ − 1 330 A.11. 5 Comments on the Approximations 331 A.11. 6 Sparsity 332 A. 12 Maximum Likelihood Estimation 332 A.2. 1 General Considerations 332 A.1. 2 The Multivariate Normal Distribution and the Spatial Linear Model 333 A.12. 3 Change of Variables 335 A.12. 4 Profile Log-likelihood 335 A.12. 5 Confidence Intervals 336 A.12. 6 Linked Parameterization 337 A.12. 7 Model Choice 338 A. 13 Bias in Maximum Likelihood Estimation 338 A.3. 1 A General Result 338 A.13. 2 The Spatial Linear Model 340 Appendix B A Brief History of the Spatial Linear Model and the Gaussian Process Approach 347 B.1 Introduction 347 B.2 Matheron and Watson 348 B.3 Geostatistics at Leeds 1977–1987 349 B.3.1 Courses, Publications, Early Dissemination 349 B.3.2 Numerical Problems with Maximum Likelihood 351 B.4 Frequentist vs. Bayesian Inference 352 References and Author Index 355 Index 367

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Book SynopsisThe Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A.C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Written by a physicist, Statistics is tailored to the needs of physical scientists, containing and explaining all they need to know. It concentrates on parameter estimation, especially the methods of Least Squares and Maximum Likelihood, but other techniques, such as hypothesis testing, Bayesian statistics and non-parametric methods are also included. Intended foTable of ContentsUsing Statistics. Describing the Data. Theoretical Distributions. Errors. Estimation. Least Squares. Probability and Confidence. Taking Decisions. Ranking Methods. Notes for Number Crunchers. Bibliography. Appendices. Index.

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Book SynopsisThis classic study probes the geometric interrelationships between art and life in discussions ranging from dissertations by Plato, Pythagoras, and Archimedes to examples of modern architecture and art. Other topics include the Golden Section, geometrical shapes on the plane, geometrical shapes in space, crystal lattices, and other fascinating subjects. 80 plates and 64 figures.

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Book SynopsisThis versatile undergraduate-level text contains enough material for a one-year course and serves as a support text and reference. It combines formal theory and related computational techniques. Solutions to selected exercises. 1978 edition.

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Book SynopsisThis general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.Trade Review'… It gives an excellent general introduction to epidemic modelling, starting with an interesting historical account and then describing the most important and useful models which can be used.' Robert MacMillan, Mathematical Gazette'The book will be accessible … and its study highly rewarding, to anyone with an interest in epidemic models…' V. S. Isham, Short Book Reviews'Daley and Gani's monograph is a concise and useful presentation of a variety of epidemiological models.' Daniel Haydon, Trends in Ecology and Evolution'… gives an excellent general introduction to epidemic modelling … should certainly be available to undergraduates.' Robert MacMillan, The Mathematical Gazette'This book had us hooked … [it] remains an important reference in our library and is frequently consulted for advice on how to think about modelling in related contexts.' Darfiana Nur and Kerrie L. Mengersen, The Australian and New Zealand Journal of Statistics'… the book is clear and well written … could serve as course literature for graduate, or possibly last year undergraduate, course in epidemic modelling.' Statistics in Medicine'I found the book very clear, concise and useful … I recommend the book very strongly as a teaching tool and as a research tool to academics and scientists who are interested in epidemic modeling. I also strongly recommend the book to applied mathematicians who are intetrested in stochastic models in general.' Mathematics TodayTable of ContentsPreface; 1. Some history; 2. Deterministic models; 3. Stochastic models in continuous time; 4. Stochastic models in discrete time; 5. Rumours: modelling spread and its cessation; 6. Fitting epidemic data; 7. The control of epidemics; References and author index; Subject index.

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Book SynopsisThis paperback, which comprises the first part of Introduction to Measure and Probability by J. F. C. Kingman and S. J. Taylor, gives a self-contained treatment of the theory of finite measures in general spaces at the undergraduate level. It sets the material out in a form which not only provides an introduction for intending specialists in measure theory but also meets the needs of students of probability. The theory of measure and integration is presented for general spaces, with Lebesgue measure and the Lebesgue integral considered as important examples whose special properties are obtained. The introduction to functional analysis which follows covers the material to probability theory and also the basic theory of L2-spaces, important in modern physics. A large number of examples is included; these form an essential part of the development.Table of ContentsPreface; 1. Theory of sets; 2. Point set topology; 3. Set functions; 4. Construction and properties of measure; 5. Definitions and properties of the integral; 6. Related Spaces and measures; 7. The space of measurable functions; 8. Linear functionals; 9. Structure of measures in special spaces; Index of notation; General index.

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Book SynopsisThis book provides an extensive introduction to the numerical solution of a large class of integral equations. The initial chapters provide a general framework for the numerical analysis of Fredholm integral equations of the second kind, covering degenerate kernel, projection and Nystrom methods. Additional discussions of multivariable integral equations and iteration methods update the reader on the present state of the art in this area. The final chapters focus on the numerical solution of boundary integral equation (BIE) reformulations of Laplace's equation, in both two and three dimensions. Two chapters are devoted to planar BIE problems, which include both existing methods and remaining questions. Practical problems for BIE such as the set up and solution of the discretised BIE are also discussed. Each chapter concludes with a discussion of the literature and a large bibliography serves as an extended resource for students and researchers needing more information on solving particTrade Review' This outstanding monograph ... represents a major milestone in the list of books on the numerical solution of integral equations ... deserves to be on the shelf of any researcher and graduate student interested in the numerical solution of elliptic boundary-value problems.' H. Brunner, Mathematics Abstracts 'It will become the standard reference in the area.' Zietschrift fur Angwandte Mathematik und PhysikTable of ContentsPreface; 1. A brief discussion of integral equations; 2. Degenerate kernel methods; 3. Projection methods; 4. The Nystrom method; 5. Solving multivariable integral equations; 6. Iteration methods; 7. Boundary integral equations on a smooth planar boundary; 8. Boundary integral equations on a piecewise smooth planar boundary; 9. Boundary integral equations in three dimensions; Discussion of the literature; Appendix; Bibliography; Index.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisWritten by noted quantum computing theorist Scott Aaronson, this book takes readers on a tour through some of the deepest ideas of maths, computer science and physics. Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.Trade Review'Scott Aaronson has written a beautiful and highly original synthesis of what we know about some of the most fundamental questions in science: what is information? What does it mean to compute? What is the nature of mind and of free will? Highly recommended.' Michael Nielsen, author of Reinventing Discovery'I laughed, I cried, I fell off my chair - and that was just reading the chapter on computational complexity. Aaronson is a tornado of intellectual activity: he rips our brains from their intellectual foundations; twists them through a tour of physics, mathematics, computer science, and philosophy; stuffs them full of facts and theorems; tickles them until they cry 'Uncle'; and then drops them, quivering, back into our skulls. [He] raises deep questions of how the physical universe is put together and why it is put together the way it is. While we read his lucid explanations we can believe - at least while we hold the book in our hands - that we understand the answers, too.' Seth Lloyd, Massachusetts Institute of Technology and author of Programming the Universe'Not since Richard Feynman's Lectures on Physics has there been a set of lecture notes as brilliant and as entertaining. Aaronson leads the reader on a wild romp through the most important intellectual achievements in computing and physics, weaving these seemingly disparate fields into a captivating narrative for our modern age of information. [He] wildly runs through the fields of physics and computers, showing us how they are connected, how to understand our computational universe, and what questions exist on the borders of these fields that we still don't understand. This book is a poem disguised as a set of lecture notes. The lectures are on computing and physics, complexity theory and mathematical logic and quantum physics. The poem is made up of proofs, jokes, stories, and revelations, synthesizing the two towering fields of computer science and physics into a coherent tapestry of sheer intellectual awesomeness.' Dave Bacon, Google'… how can I adequately convey the scope, erudition, virtuosity, panache, hilarity, the unabashed nerdiness, pugnacity, the overwhelming exuberance, the relentless good humor, the biting sarcasm, the coolness and, yes, the intellectual depth of this book?' SIGACT News'It is the very definition of a Big Ideas Book … It's targeted to readers with a reasonably strong grounding in physics, so it's not exactly a light read, despite Aaronson's trademark breezy writing style. But for those with sufficient background, or the patience to stick with the discussion, the rewards will be great.' Sean Carroll and Jennifer Ouellette, Cocktail Party Physics, Scientific American blog'The range of subjects covered is immense: set theory, Turing machines, the P versus NP problem, randomness, quantum computing, the hidden variables theory, the anthropic principle, free will, and time travel and complexity. For every one of these diverse topics, the author has something insightful and thought provoking to say. Naturally, this is not a book that can be read quickly, and it is definitely worth repeated reading. The work will make readers think about a lot of subjects and enjoy thinking about them. It definitely belongs in all libraries, especially those serving general readers or students and practitioners of computer science or philosophy. Highly recommended.' R. Bharath, Choice'… lively, casual, and clearly informed by the author's own important work … stimulating … It should prove valuable to anyone interested in computational complexity, quantum mechanics, and the theory of quantum computing.' Francis Sullivan, Physics Today'Deep and important.' Times Higher Education'… a wonderful, personal exploration of topics in theory of computation, complexity theory, physics, and philosophy. His witty, informal writing style makes the material approachable as he weaves together threads of complexity theory, computing theory, mathematical logic, and the math and physics of quantum mechanics (QM) and quantum computing to show how these topics interrelate to each other, what that says about the universe, and something about us … this book is a treat.' G. R. Mayforth, Computing ReviewsTable of Contents1. Atoms and the void; 2. Sets; 3. Gödel, Turing, and friends; 4. Minds and machines; 5. Paleocomplexity; 6. P, NP, and friends; 7. Randomness; 8. Crypto; 9. Quantum; 10. Quantum computing; 11. Penrose; 12. Decoherence and hidden variables; 13. Proofs; 14. How big are quantum states?; 15. Skepticism of quantum computing; 16. Learning; 17. Interactive proofs and more; 18. Fun with the Anthropic Principle; 19. Free will; 20. Time travel; 21. Cosmology and complexity; 22. Ask me anything.

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Book SynopsisA crystal clear introduction to category theory that demystifies functors, natural transformations, limits and colimits, adjunctions and more. Any beginning postgraduate mathematician will find all they need in this excellent text to access the subject. Over 200 exercises are provided with solutions available online.Trade Review"This textbook presents a useful introduction to basic category theory, and would be suitable for a first course at the undergraduate level in computer science or mathematics." Steve Awodey, Mathematical ReviewsTable of ContentsPreface; 1. Categories; 2. Basic gadgetry; 3. Functors and natural transformations; 4. Limits and colimits in general; 5. Adjunctions; 6. Posets and monoid sets; Bibliography; Index.

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Book SynopsisThe concepts of a locally presentable category and an accessible category have turned out to be useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students. Firstly the properties of l-presentable objects, locally l-presentable categories, and l-accessible categories are discussed in detail, and the equivalence of accessible and sketchable categories is proved. The authors go on to study categories of algebras and prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapters they treat some topics in model theory and some set theoretical aspects. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.Trade Review"...the authors have taken the indicated material, organized it effectively, written a very lucid, readable development of it in 280 pages, and added helpful historical remarks to each chapter and a brief appendix on large cardinals. There are some novel results...most notably a significant improvement of the Gabriel-Ulmer theorem on "local generation" of locally presentable categories." J.R. Isbell, Mathematical ReviewsTable of ContentsPreliminaries; 1. Locally presentable categories; 2. Accessible categories; 3. Algebraic categories; 4. Injectivity classes; 5. Categories of models; 6. Vopenka's principle; Appendix: Large cardinals; Open problems.

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Book SynopsisThis text is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level.Trade Review' … the book is recommended to anyone seeking to get acquainted with the area.' American Scientist' … a certain amount of preliminary knowledge is assumed of the reader ... but anyone who has these prerequisites and who is interested in twistor theory could hardly do better than to start with this book.' Contemporary Physics'In all, the book provides a pleasant starting point for the study of this fascinating subject.' Dr F. E. Burstall, Contemporary PhysicsTable of Contents1. Introduction; 2. Review of tensor algebra; 3. Lorentzian spinors at a point; 4. Spinor fields; 5. Compactified Minkowski space; 6. The geometry of null congruences; 7. The geometry of twistor space; 8. Solving the zero rest mass equations I; 9. Sheaf cohomology; 10. Solving the zero rest mass equations II; 11. The twisted photon and Yang–Mills constructions; 12. The non-linear graviton; 13. Penrose's quasi-local momentum; 14. Cohomological functionals; 15. Further developments and conclusion; Appendix: The GHP equations.

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Book SynopsisThis book presents a new version of the local analysis section of the Feit–Thompson theorem. It includes a recent (1991) significant improvement by Feit and Thompson and a short revision by T. Peterfalvi of the separate final section of the second half of the proof.Trade Review'This book is written well … the authors have succeeded both in simplifying the proof of the Odd Order Theorem and in making it accessible to a wider audience.' Paul Flavell, Bulletin of the London Mathematical SocietyTable of ContentsPart I. Preliminary Results: 1. Notation and elementary properties of solvable groups; 2. General results on representations; 3. Actions of Frobenius groups and related results; 4. p-Groups of small rank; 5. Narrow p-groups; 6. Additional results; Part II. The Uniqueness Theorem: 7. The transitivity theorem; 8. The fitting subgroup of a maximal subgroup; 9. The uniqueness theorem; Part III. Maximal Subgroups: 10. The subgroups Ma and Me; 11. Exceptional maximal subgroups; 12. The subgroup E; 13. Prime action; Part IV. The Family of All Maximal Subgroups of G: 14. Maximal subgroups of type p and counting arguments; 15. The subgroup Mf; 16. The main results; Appendix; Prerequisites and p-stability.

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Book SynopsisIncluding many algorithms described in simple terms, this book stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter.Trade Review"Cameron covers an impressive amount of material in a relatively small space...an outstanding supplement to other texts..." M. Henle, Choice"...used as a text at the senior or graduate level and is an excellent reference....The range of topics is very good." The UMAP JournalTable of ContentsPreface; 1. What is combinatorics?; 2. On numbers and counting; 3. Subsets, partitions, permutations; 4. Recurrence relations and generating functions; 5. The principle of inclusion and exclusion; 6. Latin squares and SDRs; 7. Extremal set theory; 8. Steiner triple theory; 9. Finite geometry; 10. Ramsey's theorem; 11. Graphs; 12. Posets, lattices and matroids; 13. More on partitions and permutations; 14. Automorphism groups and permutation groups; 15. Enumeration under group action; 16. Designs; 17. Error-correcting codes; 18. Graph colourings; 19. The infinite; 20. Where to from here?; Answers to selected exercises; Bibliography; Index.

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Book SynopsisThis monograph is the first unified treatment of an indispensable technique for comparing statistical tests, especially in nonparametric statistics. It presents powerful new methods to evaluate explicitly different kinds of efficiencies. Many Russian results are published here for the first time in English.Trade Review'It is an excellent book. I believe that every mathematical statistician should have this book in his or her collection … I enjoyed reading this book. I am sure that others will also like it.' Ramalingam Shanmugam, SIAM ReviewsTable of ContentsIntroduction; 1. Asymptotic efficiency of statistical tests and mathematical means for its computation; 2. Asymptotic efficiency of nonparametric goodness-of-fit tests; 3. Asymptotic efficiency of nonparametric homogeneity tests; 4. Asymptotic efficiency of nonparametric symmetry tests; 5. Asymptotic efficiency of nonparametric independence tests; 6. Local asymptotic optimality of nonparametric tests and the characterisation of distributions.

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Book SynopsisThe thoroughly revised and updated second edition of this acclaimed text for a second course on linear algebra has more than 1,100 problems and exercises, along with new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices and much more.Trade ReviewReview of the first edition: 'The presentation is straightforward and extremely readable. The authors' enthusiasm pervades the book, and the printing is what we expect from this publisher. This will doubtless be the standard text for years to come.' American ScientistReview of the first edition: 'The reviewer strongly recommends that those working in either pure or applied linear algebra have this book on their desks.' SIAM ReviewReview of the first edition: 'There seems little doubt that the book will become a standard reference for research workers in numerical mathematics.' Computing ReviewsReview of the first edition: 'The authors have done an excellent job of supplying linear algebraists and applied mathematicians with a well-organized comprehensive survey, which can serve both as a text and as a reference.' Linear Algebra and its Applications'The book is well organized, completely readable, and very enlightening. For researchers in matrix analysis, matrix computations, applied linear algebra, or computational science, this second edition is a valuable book.' Jesse L. Barlow, Computing Reviews'With the additional material and exceedingly clear exposition, this book will remain the go-to book for graduate students and researchers alike in the area of linear algebra and matrix theory. I suspect there are few readers who will go through this book and not learn many new things. It is an invaluable reference for anyone working in this area.' Anne Greenbaum, SIAM Review'The new edition is clearly a must-have for anyone seriously interested in matrix analysis.' Nick Higham, Applied Mathematics, Software and Workflow blogTable of Contents1. Eigenvalues, eigenvectors, and similarity; 2. Unitary similarity and unitary equivalence; 3. Canonical forms for similarity, and triangular factorizations; 4. Hermitian matrices, symmetric matrices, and congruences; 5. Norms for vectors and matrices; 6. Location and perturbation of eigenvalues; 7. Positive definite and semi-definite matrices; 8. Positive and nonnegative matrices; Appendix A. Complex numbers; Appendix B. Convex sets and functions; Appendix C. The fundamental theorem of algebra; Appendix D. Continuous dependence of the zeroes of a polynomial on its coefficients; Appendix E. Continuity, compactness, and Weierstrass' theorem; Appendix F. Canonical pairs.

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Book SynopsisWritten for advanced undergraduates and graduate students in mathematics and related disciplines, this book explains the main approaches to statistical inference, with particular emphasis on the contrasts between them. It is the first textbook to synthesize material on computational topics with basic mathematical theory. Each chapter includes instructive problems.Trade Review'This is a delightful book! It gives a well-written exposure to inference issues in statistics, very suitable for a first-year graduate course … The authors present the material in a very good pedagogical manner. The examples are excellent, and the exercises are very instructive … very much up to date and includes recent developments in the field.' MAA Reviews'This is a solid book, ideal for advanced classes in the mathematical justification for statistical inference.' Journal of Recreational Mathematics'I wish that I had had such a textbook during my student days … this new book presents the core ideas of statistical inference in the unifying framework of decision theory and includes a fruitful discussion of the different foundational standpoints (Bayesian, Fisherian and frequentist) … [it is] sufficiently precise to satisfy a mathematician and yet omitting too much technical detail that could hide the core of the ideas. Carefully selected examples from a rainbow of application areas such as baseball, coal-mining disasters or gene expression data make it even more enjoyable to read … this book is a very nice graduate level textbook.' Journal of the Royal Statistical Society'[This] book gives a clear and comprehensive account of the basic elements of statistical theory. It should make a good text for an advanced course on statistical inference … Students will find it informative and challenging.' ISI Short Book Reviews'Essentials of Statistical Inference is a book worth having.' Jane L. Harvill, Journal of the American Statistical Association'The book is comprehensively written without dwelling in unnecessary details.' Iris Pigeot, Biometrics'… gives a clear and comprehensive account of the basic elements of statistical theory … a good text for an advanced course on statistical inference.' Publication of the International Statistical Institute'The text presents the main concepts and results underlying different frameworks of inference, with particular emphasis on the contrasts among frequentist, Fisherian, and Bayesian approaches. It provides a depiction of basic material on these main approaches to inference, as well as more advanced material on recent developments in statistical theory, including higher-order likelihood inference, bootstrap methods, conditional inference, and predictive inference.' Zentralblatt MATHTable of Contents1. Introduction; 2. Decision theory; 3. Bayesian methods; 4. Hypothesis testing; 5. Special models; 6. Sufficiency and completeness; 7. Two-sided tests and conditional inference; 8. Likelihood theory; 9. Higher-order theory; 10. Predictive inference; 11. Bootstrap methods.

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Book SynopsisAn integrated approach to the theory of nonnegative matrices, emphasising connections with game theory, optimisation, mathematical programming, mathematical economics and statistics. The minimal prerequisites make this accessible to new graduate students.Trade Review"It is a great work; great by its dimensions, written with extreme love and care, concentrating the knowledge of a generation which was supreme in the history of matrix theory. It is a very illuminating and highly readable exposition of interesting topics which are of great relevance both to theory and applications." Mathematical Reviews Clippings 98hTable of ContentsPreface; 1. Perron-Frobenius theory and matrix games; 2. Doubly stochastic matrices; 3. Inequalities; 4. Conditionally positive definite matrices; 5. Topics in combinatorial theory; 6. Scaling problems and their applications; 7. Special matrices in economic models; References; Index; Author index.

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Book SynopsisCombinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. This classic volume is the first to attempt to present a thorough treatment of this theory.Trade Review' … a thorough treatment of the theory of combinatorics.' Monatshefte für Mathematik'Since the first edition almost fifteen years ago, a new generation of young mathematicians has grown up on reading this book and solving the problems at the end of each chapter, thus deepening the understanding of the results read, analyzing special cases and proving additional results. Furthermore, this monograph is an excellent reference book for those working in this area of mathematics.' Acta Sci. Math.'This is an excellent book, essential for anybody working in the field. Although written by several authors, who constitute the collective author M. Lothaire, the book makes a surprisingly compact impression. As already mentioned, it has all prerequisites for an important reference tool.' EMSTable of Contents1. Words D. Perrin; 2. Square free words and idempotent semigroups J. Berstel and C. Reutenauer; 3. Van der Waerden's theorem J. E. Pin; 4. Repetitive mappings and morphisms G. Pirillo; 5. Factorizations of free monoids D. Perrin; 6. Subwords J. Sakarovitch and I. Simon; 7. Unavoidable irregularities in words M. P. Schützenberger; 8. The critical factorization theorem Choffrut; 9. Equations in words; 10. Rearrangements of words D. Foata; 11. Words and trees R. Cori.

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Book SynopsisIt has been realised for some time how game theory can model natural selection. Evolutionary game theory replaces the concept of rational players with the population dynamics of behavioural programmes and can be used to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions which punctuate evolution.Trade Review'… as a mathematical text on an important set of topics in theoretical biology, the book is superb. It is well organised and beautifully written. In choosing from the rich menu of mathematical topics broadly relevant to ecology, behaviour, evolution, and even theoretical immunology, it shows good taste.' The Times Higher Education Supplement'… [has] something for anyone interested in game models in organismal biology.' Marc Mangel, Nature'The book is a must for any mathematician economist, or biologist working in Evolutionary Game Theory.' C. Alos-Ferrer, International Mathematical News'This book can highly be recommended to mathematicians interested in applications in social sciences, biology, and population genetics.' Ethology'… an excellent publication that helps to bridge one of the gaps between biologists and mathematicians.' David Boukai, Folia GeobotanicaTable of ContentsIntroduction for game theorists; Introduction for biologists; Part I. Dynamical Systems And Lotka-Volterra Equations: 1. The logistic equation; 2. Lotka-Volterra for predator-prey systems; 3. Lotka-Volterra for two competitors; 4. Ecological equations for two species; 5. Lotka-Volterra for more than two populations; Part II. Game Dynamics And Replicator Equations: 6. Evolutionarily stable strategies; 7. Replicator equations; 8. Other game dynamics; 9. Adaptive dynamics; 10. Asymmetric conflicts; 11. More on bimatrix games; Part III. More On Lotka-Volterra And Replicator Dynamics: 12. Hypercircles and permanence; 13. Criteria for permanence; 14. Replicator networks; 15. Stability in n-species communities; 16. Some low-dimensional ecological systems; 17. Heteroclinic cycles and C-matrices; Part IV. Population Genetics: 18. Discrete dynamical systems in population genetics; 19. Continuous selection dynamics; 20. Mutation and recombination; 21. Fertility selection; 22. Game dynamics for Mendelian populations; Bibliography; Index.

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Book SynopsisA textbook for students with some background in probability that develops quickly a rigorous theory of Markov chains and shows how actually to apply it, e.g. to simulation, economics, optimal control, genetics, queues and many other topics, and exercises and examples drawn both from theory and practice.Trade Review'This is an admirable book, treating the topic with mathematical rigour and clarity, mixed with helpful informality; and emphasising numerous applications to a wide range of subjects.' D. V. Lindley, The Mathematical Gazette'My overall impression of this book is very positive … this is the best introduction to the subject that I have come across.' Contemporary Physics'An instructor looking for a suitable text, at the level of a Master of Mathematics degree, can use this book with confidence and enthusiasm.' John Haigh, University of Sussex'We recently based a seminar on this book … it is well suited for an elementary, technically modest, but still rigorous introduction into the heart of a lively and relevant area of stochastic processes.' M. Scheutzow, Zentralblatt MATHTable of ContentsIntroduction; 1. Discrete-time Markov chains; 2. Continuous-time Markov chains I; 3. Continuous-time Markov chains II; 4. Further theory; 5. Applications; Appendix; Probability and measure; Index.

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Book SynopsisThis book has its origins in the 1996 Durham Symposium on 'Galois representations in arithmetic algebraic geometry'. Included here are expositions of subjects on the interface between algebraic number theory and arithmetic algebraic geometry which have received substantial attention from many of the best known researchers in this field.Table of ContentsPreface; List of participants; Lecture programme; 1. The Eigencurve R. Coleman and B. Mazur; 2. Geometric trends in Galois module theory Boas Erez; 3. Mixed elliptic motives Alexander Goncharov; 4. On the Satake isomorphism Benedict H. Gross; 5. Open problems regarding rational points on curves and varieties B. Mazur; 6. Models of Shimura varieties in mixed characteristics Ben Moonen; 7. Euler systems and modular elliptic curves Karl Rubin; 8. Basic notions of rigid analytic geometry Peter Schneider; 9. An introduction to Kato's Euler systems A. J. Scholl; 10. La distribution d'Euler-Poincaré d'un groupe profini Jean-Pierre Serre.

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Book SynopsisNow revised and updated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of application in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include the geometry of finite-dimensional spaces, invariant subspaces, fixed-point theorems, and the Bishop-Phelps theorem. An outstanding feature is the large number of exercises, some straightforward, some challenging, none uninteresting.Trade Review' … a well-written concise introduction to functional analysis.' European Mathematical Society'Bollobás writes with clarity and has clearly thought about the needs of his readers. First-time students of functional analysis will thank him for his willingness to remind them about notation and to repeat definitions that he has not used for a while. Bollobás has written a fine book. it is an excellent introduction to functional analysis that will be invaluable to advanced undergraduate students (and their lectures). Steve Abbott, The Mathematical GazetteTable of ContentsPreface; 1. Basic inequalities; 2. Normed spaces and bounded linear operators; 3. Linear functional and the Hahn-Banach theorem; 4. Finite-dimensional normed spaces; 5. The Baire category theorem and the closed-graph theorem; 6. Continuous functions on compact spaces and the Stone-Weierstrass theorem; 7. The contraction-mapping theorem; 8. Weak topologies and duality; 9. Euclidean spaces and Hilbert spaces; 10. Orthonormal systems; 11. Adjoint operators; 12. The algebra of bounded linear operators; 13. Compact operators on Banach spaces; 14. Compact normal operators; 15. Fixed-point theorems; 16. Invariant subspaces; Index of notation; Index of terms.

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Book SynopsisFirst published in 1967, Professor Batchelor's classic text on fluid dynamics is still one of the foremost texts in the subject. The careful presentation of the underlying theories of fluids is still timely and applicable. This re-issue should ensure that a new generation of graduate students see the elegance of Professor Batchelor's presentation.Trade Review'This book gives an excellent introduction to fluid dynamics … many interesting and important photographs of fluid flows are included in order to help the students who do not have an opportunity of observing flow phenomena in a laboratory. The book also contains exercises at the end of each chapter. In comparison with many currently available books, I find this book by Batchelor especially stimulating and useful for students of applied mathematics and engineering.' L. Debnath, Zentralblatt MATH' … a must-read for a proper understanding of the subject …' ResonanceTable of ContentsPreface; Conventions and notation; 1. The physical properties of fluids; 2. Kinematics of the flow field; 3. Equations governing the motion of a fluid; 4. Flow of a uniform incompressible viscous fluid; 5. Flow at large Reynolds number: effects of viscosity; 6. Irrotational flow theory and its applications; 7. Flow of effectively inviscid liquid with vorticity; Appendices.

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Book SynopsisThe book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The motivation for these topics is the difficulty, both conceptually and in the technical execution, of combining elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains breakthrough solutions to meshing that fit into this category. This book emphasizes topics that are elementary, attractive, useful, interesting, and lend themselves to teaching, making it an ideal graduate text for courses on mesh generation.Trade Review'… a very readable exposition …'. Monatshefte für Mathematik'… well organised … We recommend the book to graduate students and researchers in computational geometry.' János Kincses, Acta Sci. Math.Table of Contents1. Delaunay triangulations; 2. Triangle meshes; 3. Combinatorial topology; 4. Surface simplification; 5. Delaunay tetrahedrizations; 6. Tetrahedron meshes; 7. Open problems.

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Book SynopsisHistorical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends.Trade Review"A fascinating in-depth study of the philosophical aspects of the concept of probability during its founding days." Andreas Karlsson, Uppsala University"[Hacking's] knowledge of the pertinent literature is considerable and the vigorous style of writing makes for enjoyable reading. Hacking states that his book was not written as history: be that as it may, but anyone who is interested in the history of probability and statistics, either as a philosopher or as a statistician, will find much here to think about." A.I. Dale, Mathematical ReviewsTable of ContentsIntroduction; 1. An absent family of ideas; 2. Duality; 3. Opinion; 4. Evidence; 5. Signs; 6. The first calculations; 7. The Roannez circle; 8. The great decision; 9. The art of thinking; 10. Probability and the law; 11. Expectation; 12. Political arithmetic; 13. Annuities; 14. Equipossibility; 15. Inductive logic; 16. The art of conjecturing; 17. The first limit theorem; 18. Design; 19. Induction.

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Book SynopsisThese two volumes provide a self-contained account of research on algebraic cycles and motives. Twenty-two contributions from leading figures survey the key research strands, including: Abel-Jacobi/regulator maps and normal functions; Voevodsky's triangulated category of mixed motives; conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups.Table of ContentsForeword; Part I. Survey Articles: 1. The motivic vanishing cycles and the conservation conjecture J. Ayoub; 2. On the theory of 1-motives L. Barbieri-Viale; 3. Motivic decomposition for resolutions of threefolds M. de Cataldo and L. Migliorini; 4. Correspondences and transfers F. D´eglise; 5. Algebraic cycles and singularities of normal functions M. Green and Ph. Griffiths; 6. Zero cycles on singular varieties A. Krishna and V. Srinivas; 7. Modular curves, modular surfaces and modular fourfolds D. Ramakrishnan.

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Book SynopsisThis lively and engaging book explains the basic ideas of association and regression, and tells you the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own.Trade Review'At last, a second course in statistics that is serious, correct, and interesting. The book teaches regression, causal modeling, maximum likelihood, and the bootstrap. Everyone who analyzes real data should read this book.' Persi Diaconis, Stanford University'This book is outstanding for the clarity of its thought and writing. It prepares readers for a critical assessment of the technical literature in the social and health sciences, and provides a welcome antidote to the standard formulaic approach to statistics.' Erich L. Lehmann, University of California, Berkeley'In Statistical Models, David Freedman explains the main statistical techniques used in causal modeling - and where the skeletons are buried. Complex statistical ideas are clearly presented and vividly illustrated with interesting examples. Both newcomers and practitioners will benefit from reading this book.' Alan Krueger, Princeton University'Regression techniques are often applied to observational data with the intent of drawing causal conclusions. In what circumstances is this justified? What are the assumptions underlying the analysis? Statistical Models answers these questions. The book is essential reading for anybody who uses regression to do more than summarize data. The treatment is original, and extremely well written. Critical discussions of research papers from the social sciences are most insightful. I highly recommend this book to anybody who engages in statistical modeling, or teaches regression, and most certainly to all of my students.' Aad van der Vaart, Vrije Universiteit Amsterdam'A pleasure to read, Statistical Models shows the field's most elegant writer at the height of his powers. While most textbooks hurry past core assumptions in order to explicate technique, this book places the spotlight on the core assumptions, challenging readers to think critically about how they are invoked in practice.' Donald Green, Yale University'Statistical Models, a modern introduction to the subject, discusses graphical models and simultaneous equations among other topics. There are plenty of instructive exercises and computer labs. Especially valuable is the critical assessment of the main 'philosophers's stones' in applied statistics. This is an inspiring book and a very good read, for teachers as well as students.' Gesine Reinert, Oxford University'Statistical models: theory and practice is lucid, helpful, insightful and a joy to read. It focuses on the most common tools of applied statistics with a clear and simple presentation.' Mathematical ReviewsTable of Contents1. Observational studies and experiments; 2. The regression line; 3. Matrix algebra; 4. Multiple regression; 5. Multiple regression: special topics; 6. Path models; 7. Maximum likelihood; 8. The bootstrap; 9. Simultaneous equations; 10. Issues in statistical modeling.

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Book SynopsisThe is an introduction to simple type theory, exploring the relationship between proof and calculation. Each of its 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject. An appendix contains complete solutions to them.Trade Review'A well-written introduction to proof theory and its connections with computability.' Leon Harkleroad, Zentralblatt für Mathematik'… recommended for the student or researcher who's been exposed to bits and pieces of the Curry-Howard correspondence, but wants a sharper idea of the big picture and is willing to work through the exercises to see how the details fit together. Simmons has succeeded in pulling together the main fruits of the correspondence for simple types in a single text. … It can't be emphasized enough that the great thing about this book is its many well-chosen completely solved exercises. This alone makes it a valuable text, especially for self-study.' ACM SIGACT NewsTable of ContentsIntroduction; Preview; Part I. Development and Exercises: 1. Derivation systems; 2. Computation mechanisms; 3. The typed combinator calculus; 4. The typed l-calculus; 5. Substitution algorithms; 6. Applied l-calculi; 7. Multi-recursive arithmetic; 8. Ordinals and ordinal notation; 9. Higher order recursion; Part II. Solutions: A. Derivation systems; B. Computation mechanisms; C. The typed combinator calculus; D. The typed l-calculus; E. Substitution algorithms; F. Applied l-calculi; G. Multi-recursive arithmetic; H. Ordinals and ordinal notation; I. Higher order recursion; Postview; Bibliography; Commonly used symbols; Index.

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Book SynopsisThis introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selTrade Review'This is a fine book. Any computer scientist with some logical background will benefit from studying it. It is written by two of the experts in the field and comes up to their usual standards of precision and care.' Ray Turner, Computer JournalTable of Contents1. Introduction; 2. N-systems and H-systems; 3. Gentzen systems; 4. Cut elimination with applications; 5. Bounds and permutations; 6. Normalization for natural deduction; 7. Resolution; 8. Categorical logic; 9. Modal and linear logic; 10. Proof theory of arithmetic; 11. Second-order logic; Solutions to selected exercises. Bibliography; Symbols and notation; Index.

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Book SynopsisThis new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.Trade Review'Recommended for every academic mathematics collection.' Choice'… an excellent introductory textbook on ordered sets and lattices and it is intended for undergraduate and beginning graduate students in mathematics.' Vaclav Slavic, Zentralblatt für Mathematik'I used Introduction to Lattices and Order as the sole textbook in a one semester course. The students enrolled were a heterogeneous group including modestly prepared undergraduates, well trained graduate students, and a few applications-oriented computer science students … In short, the textbook was a success.' Joel Berman, Australian Mathematical Society Gazette'… a well-written, satisfying, informative, and stimulating account of applications that are of great interest, particularly in computer science and social science … it will surely become a classic.' Mathematical Reviews'Altogether, this is a great book. It would be interesting (and educational) to give a course based on it - almost makes me wish I hadn't retired!' Australian Mathematical Society Gazette'… a valuable source to anyone who needs to use ordered structures in any context.' EMS Newsletter'It can be recommended as a valuable source to anyone who needs to use ordered structures in any context.' European Mathematical Society'The book is written in a very engaging and fluid style. The understanding of the content is aided tremendously by the very large number of beautiful lattice diagrams … The book provides a wonderful and accessible introduction to lattice theory, of equal interest to both computer scientists and mathematicians.' Jonathan Cohen, SIGACT NewsTable of ContentsPreface; Preface to the first edition; 1. Ordered sets; 2. Lattices and complete lattices; 3. Formal concept analysis; 4. Modular, distributive and Boolean lattices; 5. Representation theory: the finite case; 6. Congruences; 7. Complete lattices and Galois connections; 8. CPOs and fixpoint theorems; 9. Domains and information systems; 10. Maximality principles; 11. Representation: the general case; Appendix A. A topological toolkit; Appendix B. Further reading; Notation index; Index.

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Book SynopsisThe problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages. In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed in this book, first published in 2004, are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting, rather than the shortest, path to the results. Along the way, they illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.Trade Review'I recommend this book highly as a source of rewarding projects for undergraduates (and others) to home their analytic skills and gain an appreciation for this area of mathematics. The authors clearly had great love for the material and their enthusiasm comes through in an infectious manner.' SIAM Review'The authors have managed to write a very readable account about integrals, accessible even to advanced undergraduates. Some of the topics of the book could be used for undergraduate reading and research projects. This way the book could serve as a 'springboard to many unexpected investigations and discoveries in mathematics.' Zentralblatt MATHTable of Contents1. Introduction; 2. Factorials and binomial coefficients; 3. The method of partial fractions; 4. A simple rational function; 5. A review of power series; 6. The exponential and logarithm functions; 7. The trigonometric functions and pi; 8. A quartic integral; 9. The normal integral; 10. Euler's constant; 11. Eulerian integrals: the Gamma and Beta functions; 12. The Riemann zeta function; 13. Logarithmic integrals; 14. A master formula; 15. Appendix: the revolutionary WZ method.

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