Mathematics Books

Book SynopsisThis book covers the analysis of pseudo-differential operators on manifolds with conical points and edges. The standard singular integral operators on the half-axis as well as boundary value problems on smooth manifolds are treated as particular cone and wedge theories. It features a self-contained presentation of the cone pseudo-differential calculus; a general method for pseudo-differential analysis on manifolds with edges for arbitrary model cones in spaces with discrete and continuous asymptotics; the presentation of the algebra of boundary value problems with the transmission property, obtained as a modification of the general wedge theory; and a new exposition of the pseudo-differential calculus with operator-valued symbols, based on twisted homogeneity as well as on parameter-dependent theories and reductions of orders.Table of ContentsPseudo-Differential Operators. Mellin Pseudo-Differential Operators on Manifolds with Conical Singularities. Pseudo-Differential Calculus on Manifolds with Edges. Boundary Value Problems. Bibliography. Index.

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Book SynopsisHájek was undoubtedly a statistician of enormous power who, in his relatively short life, contributed fundamental results over a wide range of topics... V. Barnett, University of Nottingham. Hájek''s writings in statistics are not only seminal but form a powerful unified body of theory. This is particularly the case with his studies of non-parametric statistics. His book The Theory of Rank Test, with ?idák, was described by W. Hoeffding as almost the last word on the subject. Hájek''s work still has great importance today, for example his research has proved highly relevant to recent investigations on bootstrap diagnostics. Much of Hájek''s work is scattered through the literature and some of it quite inaccessible, existing only in the original Czech version. This book provides a valuable unified text of the collective works of Hájek with additional essays by internationally renowned contributors. Undoubtedly this book will be essential reading to modern researchers in nonparametriTable of ContentsHISTORICAL OVERVIEW. Biography of Jaroslav Hájek. Hájek and the Superefficiency Breakthrough. Jaroslav Hájek and His Impact on the Theory of Rank Tests. Recollection of My Contacts with Jaroslav Hájek. On Some Early Papers of Jaroslav Hájek. Contributions of Jaroslav Hájek to Statistical Inference on Stochastic Processes. The Hájek Perspectives in Finite Population Sampling. Publications of Jaroslav Hájek. Hájek PhD Students. COLLECTED WORKS OF JAROSLAV HÁJEK Representative Cluster Sampling by a Method of Two Phases. Some Rank Distributions and Their Applications. Generalization of an Inequality of Kolmogorov. Asymptotic Efficiency of a Certain Sequence of Tests. Linear Estimation of the Mean Value of a Stationary Random Process with Convex Correlation Function. Inequalities for the Generalized Student's Distribution and their Applications. Predicting a Stationary Process when the Correlation Function is Convex. A Property of J-Divergence of Marginal Probability Distributions. On a Property of Normal Distributions of Any Stochastic Process. On the Distribution of Some Statistics in the Presence of Intraclass Correlation. On the Theory of Ratio Estimates. Some Contributions to the Theory of Probability Sampling. Optimum Strategy and Other Problems in Probability Sampling. On a Simple Linear Model in Gaussian Processes. Limiting Distributions in Simple Random Sampling from a Finite Population. On Plane Sample and Related Geometrical Problems. Some Extensions of the Wald-Wolfowitz-Noether Theorem. On Linear Estimation Theory for an Infinite Number of Observations. Concerning Relative Accuracy of Stratified and Systematic Sampling in a Plane. On Linear Statistical Problems in Stochastic Processes. An Inequality Concerning Random Linear Functionals on a Linear Space with a Random Norm and Its Statistical Application. Asymptotically Most Powerful Rank-Order Tests. Cost Minimization in Miltiparameter Estimation. Asymptotic Theory of Rejective Sampling with Varying Probabilities from a Finite Population. Extension of the Kolmogorov-Smirnov Test to Regression Alternatives. On Basic Concepts of Statistics. Locally Most Powerful Rank Tests of Independence. Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives. Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II. Miscellaneous Problems of Rank Test Theory. A Characterization of Limiting Distributions of Regular Estimates. Limiting Properties of Likelihoods and Inference. Local Asymptotic Minimax and Admissibility in Estimation. Asymptotic Sufficiency of the Vector of Ranks in the Bahadur Sense. Regression Designs in Autoregressive Stochastic Processes. Asymptotic Theories of Sampling with Varying Probabilities without Replacement.

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Book SynopsisStatistical inference is the process of drawing conclusions based upon the available data on the measurement of uncertainty of a defined event. It allows one to draw a conclusion or a generalization from the available data. , i.e. if there is smoke there is a good probability there is a fire.Table of ContentsIntroduction: Statistical Inference and Decision-making. An Illustration of the Different Approaches. Probability. Utility and Decision-making. Classical Inference. Bayesian Inference. Decision Theory. Other Approaches. Perspective. References. Index.

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Book SynopsisResearch in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.Trade Review"This excellent book provides an overall survey of the most important achievements in the field of extreme value theory." (Mathematical Reviews, 2005j) "...a useful reference for researchers wishing to learn more about the analysis of extreme data, including as it does a wealth of information about the topic..." (Technometrics, August 2005) "The book is well written and the authors make good use of graphical procedures to illustrate and illuminate their exposition." (International Statistical Institute, Vol 25 (2), August 2005) "...a very useful and readable text..." (Journal of the Royal Statistical Society, Vol 169 (1), January 2006) "…its strengths lie in the combination of the theory and applications." (Meteorologishe Zeitschrift, April 2007)Table of ContentsPreface. 1 WHY EXTREME VALUE THEORY? 1.1 A Simple Extreme Value Problem. 1.2 Graphical Tools for Data Analysis. 1.3 Domains of Applications. 1.4 Conclusion. 2 THE PROBABILISTIC SIDE OF EXTREME VALUE THEORY. 2.1 The Possible Limits. 2.2 An Example. 2.3 The Fr'echet-Pareto Case: ³ > 0. 2.4 The (Extremal) Weibull Case: ³ 0. 2.5 The Gumbel Case: ³ = 0. 2.6 Alternative Conditions for (C³ ). 2.7 Further on the Historical Approach. 2.8 Summary. 2.9 Background Information. 3 AWAY FROM THE MAXIMUM. 3.1 Introduction. 3.2 Order Statistics Close to the Maximum. 3.3 Second-order Theory. 3.4 Mathematical Derivations. 4 TAIL ESTIMATION UNDER PARETO-TYPE MODELS. 4.1 A Naive Approach. 4.2 The Hill Estimator. 4.3 Other Regression Estimators. 4.4 A Representation for Log-spacings and Asymptotic Results. 4.5 Reducing the Bias. 4.6 Extreme Quantiles and Small Exceedance Probabilities. 4.7 Adaptive Selection of the Tail Sample Fraction. 5 TAIL ESTIMATION FOR ALL DOMAINS OF ATTRACTION. 5.1 The Method of Block Maxima. 5.2 Quantile View--Methods Based on (C³). 5.3 Tail Probability View--Peaks-Over-Threshold Method. 5.4 Estimators Based on an Exponential Regression Model. 5.5 Extreme Tail Probability, Large Quantile and Endpoint Estimation Using Threshold Methods. 5.6 Asymptotic Results Under (C³ )-(C*³ ). 5.7 Reducing the Bias. 5.8 Adaptive Selection of the Tail Sample Fraction. 5.9 Appendices. 6 CASE STUDIES. 6.1 The Condroz Data. 6.2 The Secura Belgian Re Data. 6.3 Earthquake Data. 7 REGRESSION ANALYSIS. 7.1 Introduction. 7.2 The Method of Block Maxima. 7.3 The Quantile View--Methods Based on Exponential Regression Models. 7.4 The Tail Probability View--Peaks Over Threshold (POT) Method. 7.5 Non-parametric Estimation. 7.6 Case Study. 8 MULTIVARIATE EXTREME VALUE THEORY. 8.1 Introduction. 8.2 Multivariate Extreme Value Distributions. 8.3 The Domain of Attraction. 8.4 Additional Topics. 8.5 Summary. 8.6 Appendix. 9 STATISTICS OF MULTIVARIATE EXTREMES. 9.1 Introduction. 9.2 Parametric Models. 9.3 Component-wise Maxima. 9.4 Excesses over a Threshold. 9.5 Asymptotic Independence. 9.6 Additional Topics. 9.7 Summary. 10 EXTREMES OF STATIONARY TIME SERIES. 10.1 Introduction. 10.2 The Sample Maximum. 10.3 Point-Process Models. 10.4 Markov-Chain Models. 10.5 Multivariate Stationary Processes. 10.6 Additional Topics. 11 BAYESIAN METHODOLOGY IN EXTREME VALUE STATISTICS. 11.1 Introduction. 11.2 The Bayes Approach. 11.3 Prior Elicitation. 11.4 Bayesian Computation. 11.5 Univariate Inference. 11.6 An Environmental Application. Bibliography. Author Index. Subject Index.

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Book SynopsisDecision Theory An Introduction to Dynamic Programming and Sequential Decisions John Bather University of Sussex, UK Mathematical induction, and its use in solving optimization problems, is a topic of great interest with many applications. It enables us to study multistage decision problems by proceeding backwards in time, using a method called dynamic programming. All the techniques needed to solve the various problems are explained, and the author''s fluent style will leave the reader with an avid interest in the subject. * Tailored to the needs of students of optimization and decision theory * Written in a lucid style with numerous examples and applications * Coverage of deterministic models: maximizing utilities, directed networks, shortest paths, critical path analysis, scheduling and convexity * Coverage of stochastic models: stochastic dynamic programming, optimal stopping problems and other special topics * Coverage of advanced topics: Markov decision procesTable of ContentsIntroduction; PART I: Deterministic Models; Multi-Stage Decision Problems; Networks; Further Applications; Convexity; PART II: Stochastic Models; General Principles; Optimal Stopping; Special Problems; PART III: Markov Decision Processes; General Theory; Minimising Average Costs; Statistical Decision

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Book SynopsisReflecting the current high level of interest in the application of the principle of mathematical induction to the solution of optimization problems, this book offers a comprehensive introduction to the field.Trade Review"This textbook...draws on his many years of experience in teaching this topic as well as on his considerable professional expertise in the area. It is ideally suited to its stated purpose as a student text." (Short Book Reviews, Vol. 20. No. 3, December 2000) "...I was impressed with this book..." (The Statistician, Vol.51, No.2 2002) "...excellent for the audience to whom it is addressed, and it is to be hoped that the author will write a further textbook..." (Jnl of the Operational Research Society, Vol 54(10) 2003)Table of ContentsPreface xi 1 Introduction 1 1.1 Mathematical Induction 1 1.2 Historical Background 2 1.3 Dynamic Programming 5 1.4 The Executioner’s Tale 8 1.5 Summary 8 Exercises 10 I Deterministic Models 11 2 Multi-Stage Decision Problems 13 2.1 Maximizing Utilities 13 2.2 A General Model 17 2.3 Applications 19 Exercises 25 3 Networks 27 3.1 Shortest Paths 27 3.2 Directed Networks 29 3.3 Critical Path Analysis 30 Exercises 37 4 Further Applications 39 4.1 Discrete Actions 39 4.2 The Knapsack Problem 39 4.3 A Simple Replacement Model 42 4.4 Scheduling Problems 44 4.5 Johnson’s Algorithm 45 Exercises 49 5 Convexity 51 5.1 Convex and Concave Functions 51 5.2 Allocation Problems 56 5.3 Concave Utility Functions 60 Exercises 64 II Stochastic Models 67 6 Markov Systems 69 6.1 Introduction 69 6.2 Stochastic Dynamic Programming 70 6.3 Applications 72 Exercises 78 7 Optimal Stopping 79 7.1 Introduction 79 7.2 Stopping Times and Stopping Sets 82 7.3 Applications 90 Exercises 94 8 Special Problems 97 8.1 Introduction 97 8.2 Selling an Asset 97 8.3 The Marriage Problem 104 8.4 Prophet Inequalities 109 Exercises 116 III Markov Decision Processes 119 9 General Theory 121 9.1 Introduction 121 9.2 Minimizing Discounted Expectations 122 9.3 Policy Improvements 130 9.4 A Machine Replacement Model 137 10 Minimizing Average Costs 145 10.1 Introduction 145 10.2 Long-Term Average Costs 148 10.3 Extension to Infinitely Many States 153 10.4 Optimal Inventory Policies 158 11 Statistical Decisions 165 11.1 Introduction 165 11.2 Testing Statistical Hypotheses 166 11.3 The Sequential Probability Ratio Test 170 Notes On the Exercises 177 Chapter 1 177 Chapter 2 177 Chapter 3 178 Chapter 4 179 Chapter 5 179 Chapter 6 180 Chapter 7 181 Chapter 8 183 References 185 Index 187

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Book SynopsisThis revised edition concentrates on the techniques of risk measurement and their implementation in the management of risk. It is developed from the first edition, "Handbook of Risk Management and Analysis", with five new chapters.Trade Review"In what started as a second edition of the well received Handbook of Risk Management and Analysis, Carol Alexander has taken up the challenge of the increasing complexity of today's markets by selecting additional material to cover new aspects of risk modelling and new products, hence the present two volume edition. As before, the authors are well known not only for their expository skills. Sound theories and tried and tested methods are explained; new markets and products are clearly described. This is essential reading for the growing community of quantitatively-minded risk managers.", Dr Jacques Pezier, September 1998, , #Table of ContentsA Survey of Market Risk Measurment. Mathematical Models of Risk. Simulation 1. Simulation 2. Modelling Credit Risk. Credit Enhancement. Value at Risk. Enterprise Wide Risk. Risk Management Systems. Optimal Hedging Strategies. Volatility Trading.

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Book SynopsisTheory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis.Trade Review"...a comprehensive exposition of the theory of linear and integer programming...complementing the more practically oriented books." (Zentralblatt MATH, Vol. 970, 2001/20)Table of ContentsIntroduction and Preliminaries. Problems, Algorithms, and Complexity. LINEAR ALGEBRA. Linear Algebra and Complexity. LATTICES AND LINEAR DIOPHANTINE EQUATIONS. Theory of Lattices and Linear Diophantine Equations. Algorithms for Linear Diophantine Equations. Diophantine Approximation and Basis Reduction. POLYHEDRA, LINEAR INEQUALITIES, AND LINEAR PROGRAMMING. Fundamental Concepts and Results on Polyhedra, Linear Inequalities, and Linear Programming. The Structure of Polyhedra. Polarity, and Blocking and Anti-Blocking Polyhedra. Sizes and the Theoretical Complexity of Linear Inequalities and Linear Programming. The Simplex Method. Primal-Dual, Elimination, and Relaxation Methods. Khachiyan's Method for Linear Programming. The Ellipsoid Method for Polyhedra More Generally. Further Polynomiality Results in Linear Programming. INTEGER LINEAR PROGRAMMING. Introduction to Integer Linear Programming. Estimates in Integer Linear Programming. The Complexity of Integer Linear Programming. Totally Unimodular Matrices: Fundamental Properties and Examples. Recognizing Total Unimodularity. Further Theory Related to Total Unimodularity. Integral Polyhedra and Total Dual Integrality. Cutting Planes. Further Methods in Integer Linear Programming. References. Indexes.

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Book SynopsisProvides an excellent introductory text for students on the principles and methods of statistical analysis in the life sciences, helping them choose and analyse statistical tests for their own problems and present their findings.Table of ContentsMeasurement and Sampling Concepts. Processing Data. Presenting Data. Measuring the Average. Measuring Variability. Probability. Probability Distributions as Models of Dispersion. The Normal Distribution. Data Transformation. How Good are Our Estimates? The Basis of Statistical Testing. Analysing Frequencies. Measuring Correlations. Regression Analysis. Comparing Averages. Analysis of Variance - ANOVA. Multivariate Analysis. Appendices. Bibliography and Further Reading. Index.

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Book SynopsisThis superb text describes a novel and powerful method for allowing design engineers to firstly model a linear problem in heat conduction, then build a solution in an explicit form and finally obtain a numerical solution. It constitutes a modelling and calculation tool based on a very efficient and systemic methodological approach. Solving the heat equations through integral transforms does not constitute a new subject. However, finding a solution generally constitutes only one part of the problem. In design problems, an initial thermal design has to be tested through the calculation of the temperature or flux field, followed by an analysis of this field in terms of constraints. A modified design is then proposed, followed by a new thermal field calculation, and so on until the right design is found. The thermal quadrupole method allows this often painful iterative procedure to be removed by allowing only one calculation. The chapters in this book increase in complexiTrade Review"The book can be highly recommended to anyone who works in the area of integral transforms and heat transfer". (Zentralblatt MATH, Vol.964, No.14, 2001)Table of ContentsInterest in the Quadrupole Approach. Linear Conduction and Simple Geometries. One-Dimensional Quadrupoles. Multidimensional Transfers. Time-Dependent Periodic Regimes. Advanced Quadrupoles. Mass Transfer in a Porous Medium. The Quadrupole Approach Applied to Heat Transfer in Semi-Transparent Materials. Inverse Laplace Transform. Appendices. Index.

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Book SynopsisMeta--analysis is one of the main statistical methods used in clinical trials. Previous accounts of meta--analysis have given the impression that the topic is a series of separate techniques. This book provides a unified approach, developing the subject from mathematical theory through to practical discussions of implementation.Trade Review"…highly recommended as essential reading for medical statisticians…" (Short Book Reviews, April 2003) "...comprehensive and well illustrated contribution to the subject...useful for graduate students of medical statistics..." (Statistics in Medicine, Vol 23(3), 15 February 2004)Table of ContentsIntroduction Protocol development Estimating the treatment difference in an individual trial Combining estimates of a treatment difference across trials Meta-analysis using individual patient data Dealing with heterogeneity Presentation and interpretation of results Selection bias Dealing with non-standard datasets Inclusion of trials with different study designs A Bayesian approach to meta-analysis Sequential methods for meta-analysis Appendix Methods of estimation and hypothesis testing

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Book SynopsisIntroduced by Da Arcy Thompson in his classic work On Growth and Form, the area of spatio--temporal pattern formation is a research specialty within mathematical biology. It provides a mathematical model and analysis of the many variegated patterns in nature, such as the markings on a tiger or the growth of a shell.Trade Review"...a useful resource for mathematics students...recommend anyone interested in biomathematics to look at [it]..." (Mathematics Today, Dec 2003) "...scope of the book is broad...interesting for everyone regardless of expertise in this field..." (Simulation News Europe, Dec 2003)Table of ContentsProblems of Development: The Microcosm and the Macrocosm. Development of the Vertebrate Limb: A Model for Growth and Patterning. Pattern Formation on Butterfly Wings. Pattern Formation in Cancer. Turing Structures of the Second Kind. Pattern Formation Mechanisms in Skin and Hair: Some Experimental Tests. Some Mathematical Models for Biological Pattern Formation. On Pattern and Growth. Diversity in Pattern and Form of Biological Systems and Evolution: A Theoretical Approach. Developmental Morphologies Not Directly Specified by the Genome of the Individual. The Role of Chemotactic Cell Movement in Dictyostelium Morphogenesis. Angiogenesis: Experimental Data Relevant to Theoretical Analysis. Modelling the Growth and Form of Capillary Networks. On the Mechanochemical Theory of Biological Pattern Formation with Applications to Wound Healing and Angiogenesis. Statistics and Dynamics of Cellular Shape Changes. Shape Asymmetry and Developmental Stability. Invariance and Morphometrics: A Critical Appraisal of Statistical Techniques for Landmark Data. Statistical Shape Analysis and its Applications. Sphenoethmoidal Growth, Malgrowth, and Midfacial Profile Ontogeny and Phylogeny: Some Morphometric Approaches to the Skeletal Growth and Evolution. D'Arcy Thompson and the Problem of Biological Form. Index.

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Book SynopsisOffers an in-depth report on advanced statistical tools for public health disease surveillance, which is the result of a prestigious World Health Organisation (WHO) and EU Biomed programme initiative. Traditionally, the role of public health disease surveillance has been to identify and evaluate morbidity and mortality but increasingly, more sophisticated methods are being applied as the authorities extend their studies to include control and prevention of disease. This book brings together leading experts to discuss complex methodologies for the statistical evaluation of disease mapping and risk assessment. It includes a broad variety of statistical techniques and where appropriate, examples are included on topical issues such as the analysis of putative health hazards. For easy reference the text is presented in five distinct sections, each with an introductory review: * Disease Mapping * Clustering of Disesase * Ecological Analysis * Risk AsseTrade Review"…full of rich ideas and methods that are useful..." (Journal of Statistical Computation and Simulation, April 2005) "...sure to be an essential reference for anyone working in this area" (ISCB Newsletter, December 2000)Table of ContentsPartial table of contents: DISEASE MAPPING. Disease Mapping and Its Uses. Disease Mapping with Hidden Structures Using Mixture Models. CLUSTERING OF DISEASE. Inference for Extremes in Disease Mapping. Edge Effects in Disease Mapping. Empirical Studies of Cluster DetectionDifferent Cluster Tests in Application to German Cancer Maps. ECOLOGICAL ANALYSIS. Introduction to Spatial Models in Ecological Analysis. Multilevel Modelling of Area-Based Health Data. RISK ASSESSMENT FOR PUTATIVE SOURCES OF HAZARD. A Review of Modelling Approaches in Health Risk Assessment around Putative Sources. Lung Cancer Near Point Emission Sources. PUBLIC HEALTH APPLICATIONS AND CASE STUDIES. Environmental Epidemiology, Public Health Advocacy and Policy. The Character and the Public Health Implications of Ecological Analyses. Estimating the Presence and the Degree of Heterogeneity of Disease Rates. Ecological Regression with Errors in Covariates: An Application. Lung Cancer Mortality in Women in Germany 1995: A Case Study in Disease Mapping. Appendix. Index.

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Book SynopsisSpatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization.Trade Review"While this edition maintains the overall structure of the first, there are substantial changes in the content..." (Mathematical Reviews, Issue 2001c) "...a must..." (Monatshefte fur Mathematik, Vol 131/2, 2000)Table of ContentsDefinitions and Basic Properties of Voronoi Diagrams. Generalizations of the Voronoi Diagram. Algorithms for Computing Voronoi Diagrams. Poisson Voronoi Diagrams. Spatial Interpolation. Models of Spatial Processes. Point Pattern Analysis. Locational Optimization Through Voronoi Diagrams. References. Index.

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Book SynopsisA good working knowledge of statistical principles is needed for both the design and analysis of biological experiments and the subsequent handling of the large amounts of data generated if worthwhile, reliable conclusions are to be reached. Practical Statistics for Experimental Biologists, Second Edition provides biologists with a user-friendly, non-technical introduction to the basics of statistics. The book has been thoroughly revised and updated to incorporate: * Worked examples and printouts from MINITAB * Relevant case studies and applications * Further Notes section for background explanations Written by a biologist with extensive experience of applying statistical procedures to experimental systems, this book will be invaluable to undergraduates, postgraduates and researchers in microbiology, immunology, biochemistry, botany, zoology, physiology, pharmacology and pharmacy. Review of the First Edition ...strongly recommended as the current first choicTrade Review"...a refreshing and useful book..." ---- Trends in Plant Science, September 2000Table of ContentsA Simple Experiment in Pipetting. How to Condense the Bulkiness of Data. Are Those Differences Significant? More About Measurement Differences. Awkward-Measurement Data. How to Deal with Count Data. How to Deal with Proportion Data. Correlation and Regression. Dose-Response Lines and Assays. References. Additional Reading. Appendices. Index.

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Book SynopsisFuzzy clustering, which combines fuzzy logic and cluster analysis techniques, has experienced a spur of interest in recent years owing to its important applications in image recognition. This revised, updated, and expanded translation of the German book deals with the ideas and algorithms of fuzzy clustering and their applications.Table of ContentsIntroduction. Basic Concepts. Classical Fuzzy Clustering Algorithms. Linear and Ellipsoidal Prototypes Shell Prototypes. Polygonal Object Boundaries. Cluster Estimation Models. Cluster Validity. Rule Generation with Clustering. Appendix. Bibliography.

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Book SynopsisMultilevel modelling facilitates the analysis of hierarchical data where observations may be nested within higher levels of classification. In health care research, for example, a study may be undertaken to determine the variability of patient outcomes where these also vary by hospital or health care region.Trade Review"...contains 13 well written chapters by experts...the references are recent and useful. It can be used as a textbook in graduate level modeling course." (Journal of Statistical Computation & Simulation, May 2004) "...exhibits a marvellous degree of coherence and clarity..." (Pharmaceutical Statistics, Vol 2, 2003) "...good introductions to multilevel models, and plenty of examples..." (Zentralblatt Math, 2003) "...I believe that the book all in all fulfils this promise..." (Statistics in Medicine, No.21, 2002) "...a very readable book whose audience does not seem to be limited to statisticians." (Technometrics, Vol. 44, No. 4, November 2002) "Highly recommended to biostatisticians, health care professionals and public health researchers in the application of multilevel model. It can also be used as a reference book for postgraduate students studying medical statistics." (ISCB News, December 2001)Table of ContentsPreface. Contributors. Introduction. Multilevel Data and Their Analysis (M. Healy). Modelling Repeated Measurements (H. Glodstein and G. Woodhouse). Binomial Regression (N. Rice). Poisson Regression (I. Langford and R. Day). Multivariate Multilevel Models (A. McLeod). Outliers, Robustness and the Detection of Discrepant Data (T. Lewis and I. Langford). Modelling Non-Hierarchical Structures (J. Rasbash and W. Browne). Multinomial Regression (M. Yang). Institutional Performance (E. Marshall and D. Spiegelhalter). Spatial Analysis (A. Leyland). Sampling (T. Snijders). Further Topics in Multilevel Modelling (H. Goldstein and A. Leyland). Software for Multilevel Analysis (J. de Leeuw and I. Kreft). References. Index.

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Book SynopsisThis work is a guide to the principles behind sensitivity analysis. It suggests suitable methods for particular types of problem, which allows a greater understanding of the entire causal assessment chain. This makes the impact of source uncertainties and framing assumptions more transparent.Trade Review"The book has a fair price...I think this is a book that everyone who does modeling should buy. It can readily be read piecemeal...so it is ideal for leisurely self-study..." (Technometrics Vol. 42, No. 4 May 2001) "...this book will prove helpful in the solution of many modeling problems." (La Doc Sti, September 2000) "...presents many different sensitivity analysis methodologies and demonstrates their usefulness in scientific research." (Zentralblatt MATH, Vol. 961, 2001/11)Table of ContentsWhat is Sensitivity Analysis. Hitchhiker's Guide to Sensitivity Analysis. METHODS. Designs of Experiments. Screening Methods. Local Methods. Sampling-Based Methods. Reliability Algorithms: FORM and SORM Methods. Variance-Based Methods. Managing the Tyranny of Parameters in Mathematical Modelling of Physical Systems. Bayesian Sensitivity Analysis. Graphical Methods. APPLICATIONS. Practical Experience in Applying Sensitivity and Uncertainty Analysis. Scenario and Parametric Sensitivity and Uncertainty Analysis in Nuclear Waste Disposal Risk Assessment: The Case of GESAMAC. Sensitivity Analysis for Signal Extraction in Economic Time Series. A Dataless Precalibration Analysis in Solid State Physics. Appplication of First-Order (FORM) and Second-Order (SORM) Reliability Methods: Analysis and Interpretation of Sensitivity Measures Related to Groundwater Pressure Decreases and Resulting Ground Subsidence. One-at-a-Time and Mini-Global Analyses for Characterizing Model Sensitivity in the Nonlinear Ozone Predictions from the US EPA Regional Acid Deposition Model (RADM). Comparing Different Sensitivity Analysis Methods on a Chemical Reactions Model. An Application of Sensitivity Analysis to Fish Population Dynamics. Global Sensitivity Analysis: A Quality Assurance Tool in Environmental Policy Modelling. CONCLUSIONS. Assuring the Quality of Models Designed for Predictive Tasks. Fortune and Future of Sensitivity Analysis. References. Appendix. Index.

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Book SynopsisCovers the period from the early Christian church to the 20th century, offering fresh appraisals of such encounters as the trial of Galileo, the formulation of the Newtonian worldview, and the controversies over 'scientific creationism'. This book explores not only the impact of religion on science, but also the influence of science and religion.

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Book SynopsisA philosophical discussion of the concept of numberIn the book, The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, Gottlob Frege explains the central notions of his philosophy and analyzes the perspectives of predecessors and contemporaries. The book is the first philosophically relevant discussion of the concept of number in Western civilization. The work went on to significantly influence philosophy and mathematics. Frege was a German mathematician and philosopher who published the text in 1884, which seeks to define the concept of a number. It was later translated into English. This is the revised second edition.Table of Contents I. Views of certain writers on the nature of arithmetical propositions II. Views of certain writers on the concept of Number III. View on unity and one IV. The concept of number V. Conclusions

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Book SynopsisStatistics in Geography has established itself as the best introductory textbook on the subject: the author makes statistical concepts and techniques intellible and their applications in a wide variety of problems comprehensible, even exciting. The main feature of this much-awaited new edition is a set of 17 computer programs (with sample outputs) that cover nearly all the statistical techniques described. These have been carefully written to be user-friendly in an elementary subset of Basic to make them simple to implement on most micro computers. This means students can be more adventurous in their applications and interpretations of statistical techniques. The author has, at the same time, retained all the worked examples in the book so that the reader can gain insight into the logic of the methds by working through them by hand. These, together with problems of various levels of complexity plus comprehensive answers at the back of the book, provide the student with a clear aTrade Review Reviews of the first edition ‘… the book is one of the most successful among statistical geography texts in achieving its aim of a clear, painless, and well-illustrated introduction to difficult concepts.’ Geographical Analysis ‘Highly recommended for its clarity and exemplification … the author and publishers have certainly made the text clear, easily readable an interesting with many good figures and tables, worked examples and directly related exercises with 18 pages of answers and explanations to the latter.’ Royal Statistical Society ‘The features I particularly like are the number of examples and class exercises, the constant attempts to relate each method back to statistical theory, and the useful diagrams. The author succeeds at showing why statistical tests have sampling distributions, produces some outstanding diagrams to illustrate linear regression, and has a fine set of statistical tables.’ Journal of GeographyTable of ContentsPreface of the Second Edition. Preface of the First Edition. Statistical Concepts. Description. Samples and Sampling. Comparisons. Relationships. Trends. Spatial Statistics. References. Appendix A: Answers to Exercises. Appendix B: Probability Tables. Appendix C: Tables of Critical Values. Appendix D: Random Numbers. Appendix E: Data Matrix. Appendix F: Notes for Programmers. Index.

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Book Synopsisaeo This textbook is based on a course taught jointly by an economist and a mathematician making it a balanced and comprehensive introduction to mathematics in economics. aeo Mathematical techniques are always presented in the context of the economics problems they are used to solve.Trade Review"I wish Adam Ostaszewski good luck with this book. May it enjoy the success it deserves." Ken Binmore, University of Michigan "I believe Mathematics in Economics to be an excellent book, which is much needed in first year UK degree programmes. Its coverage of syllabus is better than its rivals and its treatment of the economics and the mathematics indicates that considerable rigour is needed to do things properly." Martin Cripps, University of Warwick "In this book the build-up in confidence is done gradually by means of carefully chosen examples." "Throughout the book the approach to mathematics is rigorous, and excellent use is made of graphs and other figures." "A valuable guide to the ways in which mathematics provides a basis for modern economics." Tony WhitfordTable of ContentsPart I:. 1. Sets and Numbers. 2. Matrices and Vectors. 3. Modelling Consumer Choice. 4. Discrete Variables. 5. Functions. 6. Equilibrium. 7. Eigenvalues and Eigenvectors. Part II:. 1. Limits and Their Uses. 2. Continuity and Its Uses. 3. Uses of the Derivative. 4. Continuous Compounding and Exponential Growth. 5. Partial Differentiation. 6. The Gradient. 7. Taylor's Theorem - An Approximation Tool. 8. Optimisation in Two Variables. 9. Economic Dynamics: Differential Equations.

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Book SynopsisAn introduction to quantitative methods delivering the knowledge and skills required to process, utilize and manipulate numerical information of the type and style found in the business environment. The practical application of quantitative methods is emphasized. An additional unit on basic mathematics is included which is suitable for students enrolling on business studies programs without formal mathematical qualifications. Contents include: foundation mathematics and business mathematics; data presentation; linear programming; regression and correlation analysis; probability and probability distribution.Table of Contents1. Basic Mathematics. 2. Business Mathematics. 3. Data Presentation. 4. Linear Programming. 5. Regression and Correlation. 6. Probability. 7. Probability Distributions. 8. Sampling. 9. Index Numbers and Time Series.

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Book SynopsisExplores the central problems and the most intriguing new directions in the philosophy of mathematics. The papers are organized thematically, rather than chronologically, to give the best overview of philosophical issues connected with mathematics and the development of mathematical knowledge.Trade Review"For breadth of coverage, Jacquette's anthology of recent work in philosophy of mathematics has few if any rivals. Many of Jacquette's selections are important for understanding current debates, and he provides helpful introductory discussions. This collection will very likely become a standard resource for students and teachers of this field." Sanford Shieh, Wesleyan University Table of ContentsPreface. Acknowledgments. Introduction: Mathematics and Philosophy of Mathematics: Dale Jacquette. Part I: The Realm of Mathematics:. 1. What is Mathematics About?: Michael Dummett. 2. Mathematical Explanation: Mark Steiner. 3. Frege versus Cantor and Dedekind: On the Concept of Number: William W. Tait. 4. The Present Situation in Philosophy of Mathematics: Henry Mehlberg. Part II: Ontology of Mathematics and the Nature and Knowledge of Mathematical Truth:. 5. What Numbers Are: N.P. White. 6. Mathematical Truth: Paul Benacerraf. 7. Ontology and Mathematical Truth: Michael Jubien. 8. An Anti-Realist Account of Mathematical Truth: Graham Priest. 9. What Mathematical Knowledge Could Be: Jerrold J. Katz. 10. The Philosophical Basis of our Knowledge of Number: William Demonpoulos. Part III: Models and Methods of Mathematical Proof:. 11. Mathematical Proof: G.H. Hardy. 12. What Does a Mathematical Proof Prove?: Imre Lakatos. 13. The Four-Color Problem: Kenneth Appel and Wolfgang Haken. 14. Knowledge of Proofs: Peter Pagin. 15. The Phenomenology of Mathematical Proof: Gian-Carlo Rota. 16. Mechanical Procedures and Mathematical Experience: Wilfried Sieg. Part IV: Intuitionism:. 17. Intuitionism and Formalism: L.E.J. Brouwer. 18. Mathematical Intuition: Charles Parsons. 19. Brouwerian Intuitionism: Michael Detlefsen. 20. A Problem for Intuitionism: The Apparent Possibility of Performing Infinitely Many Tasks in a Finite Time: A.W. Moore. 21. A Pragmatic Analysis of Mathematical Realism and Intuitionism: Michel J. Blais. Part V: Philosophical Foundations of Set Theory:. 22. Sets and Numbers: Penelope Maddy. 23. Sets, Aggregates, and Numbers: Palle Yourgrau. 24. The Approaches to Set Theory: John Lake. 25. Where Do Sets Come From? Harold T. Hodes. 26. Conceptual Schemes in Set Theory: Robert McNaughton. 27. What is Required of a Foundation for Mathematics? John Mayberry. Index.

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Book SynopsisQuantitative Methods for Finance and Investments ensures that readers come away from reading it with a reasonable degree of comfort and proficiency in applying elementary mathematics to several types of financial analysis.Trade Review"This excellent text patiently guides the reader through a wide array of mathematics, ranging from elementary matrix algebra to differential and integral calculus. The quantitative methods are illustrated with a rich and captivating assortment of applications to the analysis of portfolios, derivatives, exchange, fixed income instruments, and equities. Undergraduate and MBA-level students who have read this book will feel comfortable with the mathematics in their finance courses and their professors can focus on teaching finance as it should be taught." Kose John, Stern School of Business, New York University <1--end--> "This volume provides a comprehensive review of mathematics which will prove invaluable for students of finance. It is a reference book for the nonmathematician and a clear and concise text that will help fill the gaps in students' knowledge. Although the topic is quantitative methods, the organization, emphasis, applications, and numerous examples are all geared to the student of finance. Having Teall and Hasan on your bookshelf provides an essential safety net for students, teachers, and practitioners." Paul Wachtel, Stern School of Business, New York UniversityTable of ContentsPreface. Acknowledgments. 1. Introduction and Overview:. The Importance of Mathematics in Finance. Mathematical and Computer Modeling in Finance. Money, Securities, and Markets. Time Value, Risk, Arbitrage, and Pricing. The Organization of this Book. 2. Review of Elementary Mathematics: Functions and Operations:. Introduction. Variables, Equations, and Inequalities. Exponents. The Order of Arithmetic Operations and the Rules of Algebra. The Number e. Logarithms. Subscripts. Summations. Double Summations. Products. Factorial Products. Permutations and Combinations. Exercises. Appendix: An Introduction to the ExcelT Spreadsheet. 3. A Review of Elementary Mathematics: Algebra and Solving Equations:. Algebraic Manipulations. The Quadratic Formula. Solving Systems of Equations that Contain Multiple Variables. Geometric Expansions. Functions and Graphs. Exercises. Appendix: Solving Systems of Equations on a Spreadsheet. 4. The Time Value of Money:. Introduction and Future Value. Simple Interest. Compound Interest. Fractional Period Compounding of Interest. Continuous Compounding of Interest. Annuity Future Values. Discounting and Present Value. Present Value of a Series of Cash Flows. Annuity Present Values. Amortization. Perpetuity Models. Single-stage Growth Models. Multiple-stage Growth Models. Exercises. Appendix: Time Value Spreadsheet Applications. 5. Return, Risk, and Co-movement:. Return on Investment. Geometric Mean Return on Investment. Internal Rate of Return. Bond Yields. An Introduction to Risk. Expected Return. Variance and Standard Deviation. Historical Variance and Standard Deviation. Covariance. The Coefficient of Correlation and the Coefficient of Determination. Exercises. Appendix: Return and Risk Spreadsheet Applications. 6. Elementary Portfolio Mathematics:. An Introduction to Portfolio Analysis. Portfolio Return. Portfolio Variance. Diversification and Efficiency. The Market Portfolio and Beta. Deriving the Portfolio Variance Expression. Exercises. 7. Elements of Matrix Mathematics:. An Introduction to Matrices. Matrix Arithmetic. Inverting Matrices. Solving Systems of Equations. Spanning the State Space. Exercises. Appendix: Matrix mathematics on a Spreadsheet. 8. Differential Calculus:. Functions and Limits. Slopes, Derivatives, Maxima, and Minima. Derivatives of Polynomials. Partial and Total Derivatives. The Chain Rule, Product Rule, and Quotient Rule. Logarithmic and Exponential Functions. Taylor Series Expansions. The Method of LaGrange Multipliers. Exercises. Appendix: Derivatives of Polynomials. Appendix: A Table of Rules for Finding Derivatives. Appendix: Portfolio Risk Minimization on a Spreadsheet. 9. Integral Calculus:. Antidifferentiation and the Indefinite Integral. Riemann Sums. Definite Integrals and Areas. Differential Equations. Exercises. Appendix: Rules for Finding Integrals. Appendix: Riemann sums on a spreadsheet. 10. Elements of Options Mathematics:. An Introduction to Stock Options. Binomial Option Pricing: One Time Period. Binomial Option Pricing: Multiple Time Periods. The Black–Scholes Option Pricing Model. Puts and Valuation. Black–Scholes Model Sensitivities. Estimating Implied Volatilities. Exercises. References. Appendix A: Solutions to Exercises. Appendix B: The z-Table. Appendix C: Notation. Appendix D: Glossary. Index.

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Book SynopsisQuantitative Methods for Finance and Investments ensures that readers come away from reading it with a reasonable degree of comfort and proficiency in applying elementary mathematics to several types of financial analysis.Trade Review"This excellent text patiently guides the reader through a wide array of mathematics, ranging from elementary matrix algebra to differential and integral calculus. The quantitative methods are illustrated with a rich and captivating assortment of applications to the analysis of portfolios, derivatives, exchange, fixed income instruments, and equities. Undergraduate and MBA-level students who have read this book will feel comfortable with the mathematics in their finance courses and their professors can focus on teaching finance as it should be taught." Kose John, Stern School of Business, New York University <1--end--> "This volume provides a comprehensive review of mathematics which will prove invaluable for students of finance. It is a reference book for the nonmathematician and a clear and concise text that will help fill the gaps in students' knowledge. Although the topic is quantitative methods, the organization, emphasis, applications, and numerous examples are all geared to the student of finance. Having Teall and Hasan on your bookshelf provides an essential safety net for students, teachers, and practitioners." Paul Wachtel, Stern School of Business, New York UniversityTable of ContentsPreface Acknowledgments 1 Introduction and Overview 1 1.1 The importance of mathematics in finance 1 1.2 Mathematical and computer modeling in finance 2 1.3 Money, securities, and markets 3 1.4 Time value, risk, arbitrage, and pricing 5 1.5 The organization of this book 6 2 A Review of Elementary Mathematics: Functions and Operations 7 2.1 Introduction 7 2.2 Variables, equations, and inequalities 7 2.3 Exponents 8 Application 2.1: Interest and future value 9 2.4 The order of arithmetic operations and the rules of algebra 10 Application 2.2: Initial deposit amounts 11 2.5 The number e 11 2.6 Logarithms 12 Application 2.3: The time needed to double your money 13 2.7 Subscripts 14 2.8 Summations 14 Application 2.4: Mean values 15 2.9 Double summations 16 2.10 Products 17 Application 2.5: Geometric means 17 Application 2.6: The term structure of interest rates 18 2.11 Factorial products 19 Application 2.7: Deriving the number e 19 2.12 Permutations and combinations 20 Exercises 21 Appendix 2.A An introduction to the Excel™ spreadsheet 23 3 A Review of Elementary Mathematics: Algebra and Solving Equations 25 3.1 Algebraic manipulations 25 Application 3.1: Purchase power parity 27 Application 3.2: Finding break-even production levels 28 Application 3.3: Solving for spot and forward interest rates 29 3.2 The quadratic formula 29 Application 3.4: Finding break-even production levels 30 Application 3.5: Finding the perfectly hedged portfolio 31 3.3 Solving systems of equations that contain multiple variables 32 Application 3.6: Pricing factors 35 Application 3.7: External financing needs 35 3.4 Geometric expansions 38 Application 3.8: Money multipliers 40 3.5 Functions and graphs 41 Application 3.9: Utility of wealth 43 Exercises 44 Appendix 3.A Solving systems of equations on a spreadsheet 48 4 The Time Value of Money 51 4.1 Introduction and future value 51 4.2 Simple interest 51 4.3 Compound interest 52 4.4 Fractional period compounding of interest 53 Application 4.1: APY and bank account comparisons 55 4.5 Continuous compounding of interest 56 4.6 Annuity future values 57 Application 4.2: Planning for retirement 59 4.7 Discounting and present value 60 4.8 The present value of a series of cash flows 61 4.9 Annuity present values 62 Application 4.3: Planning for Retirement, Part Ii 64 Application 4.4: Valuing a bond 64 4.10 Amortization 65 Application 4.5: Determining the mortgage payment 66 4.11 Perpetuity models 67 4.12 Single-stage growth models 68 Application 4.6: Stock valuation models 70 4.13 Multiple-stage growth models 72 Exercises 73 Appendix 4.A Time value spreadsheet applications 77 5 Return, Risk, and Co-movement 79 5.1 Return on investment 79 Application 5.1: Fund performance 81 5.2 Geometric mean return on investment 82 Application 5.2: Fund Performance, Part Ii 83 5.3 Internal rate of return 84 5.4 Bond yields 87 5.5 An introduction to risk 88 5.6 Expected return 88 5.7 Variance and standard deviation 89 5.8 Historical variance and standard deviation 91 5.9 Covariance 93 5.10 The coefficient of correlation and the coefficient of determination 94 Exercises 95 Appendix 5.A Return and risk spreadsheet applications 99 6 Elementary Portfolio Mathematics 103 6.1 An introduction to portfolio analysis 103 6.2 Portfolio return 103 6.3 Portfolio variance 104 6.4 Diversification and efficiency 106 6.5 The market portfolio and beta 110 6.6 Deriving the portfolio variance expression 111 Exercises 113 7 Elements of Matrix Mathematics 115 7.1 An introduction to matrices 115 Application 7.1: Portfolio mathematics 116 7.2 Matrix arithmetic 117 Application 7.2: Portfolio Mathematics, Part Ii 120 Application 7.3: Put–call parity 121 7.3 Inverting matrices 123 7.4 Solving systems of equations 125 Application 7.4: External funding requirements 126 Application 7.5: Coupon bonds and deriving yield curves 127 Application 7.6: Arbitrage with riskless bonds 130 Application 7.7: Fixed income portfolio dedication 131 Application 7.8: Binomial option pricing 132 7.5 Spanning the state space 133 Application 7.9: Using options to span the state space 136 Exercises 137 Appendix 7.A Matrix mathematics on a spreadsheet 142 8 Differential Calculus 145 8.1 Functions and limits 145 Application 8.1: The natural log 146 8.2 Slopes, derivatives, maxima, and minima 147 8.3 Derivatives of polynomials 149 Application 8.2: Marginal utility 151 Application 8.3: Duration and immunization 153 Application 8.4: Portfolio risk and diversification 156 8.4 Partial and total derivatives 157 8.5 The chain rule, product rule, and quotient rule 158 Application 8.5: Plotting the Capital Market Line 159 8.6 Logarithmic and exponential functions 165 8.7 Taylor series expansions 166 Application 8.6: Convexity and immunization 167 Exercises 172 Appendix 8.A Derivatives of polynomials 176 Appendix 8.B A table of rules for finding derivatives 177 Appendix 8.C Portfolio risk minimization on a spreadsheet 178 9 Integral Calculus 180 9.1 Antidifferentiation and the indefinite integral 180 9.2 Riemann sums 181 9.3 Definite integrals and areas 185 Application 9.1: Cumulative densities 186 Application 9.2: Expected value and variance 188 Application 9.3: Valuing continuous dividend payments 189 Application 9.4: Expected option values 191 9.4 Differential equations 191 Application 9.5: Security returns in continuous time 193 Application 9.6: Annuities and growing annuities 194 Exercises 195 Appendix 9.A Rules for finding integrals 198 Appendix 9.B Riemann sums on a spreadsheet 199 10 Elements of Options Mathematics 203 10.1 An introduction to stock options 203 10.2 Binomial option pricing: one time period 205 10.3 Binomial option pricing: multiple time periods 207 10.4 The Black–Scholes option pricing model 210 10.5 Puts and valuation 212 10.6 Black–Scholes model sensitivities 213 10.7 Estimating implied volatilities 215 Exercises 219 References 222 Appendix A Solutions to Exercises 224 Appendix B The z-Table 266 Appendix C Notation 267 Appendix D Glossary 270 Index 274

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Book SynopsisOffers a presentation of classical first-order logic. This book presents a truth tree system based on the work of Jeffrey, as well as a natural deduction system inspired by that of Kalish and Montague.Trade Review“Deduction is the best logic textbook on the market. It is modern, clean, elegant, sharp and direct. It is a perfect accompaniment to the most recent developments in philosophy and logic; in every sense the logic textbook for the twenty-first century.” Rick Benitez, University of SydneyTable of ContentsPreface to the Second Edition viii Acknowledgments x 1 Basic Concepts of Logic 1 1.1 Arguments 1 1.2 Validity 16 1.3 Implication and Equivalence 23 1.4 Logical Properties of Sentences 27 1.5 Satisfiability 31 2 Sentences 36 2.1 The Language of Sentential Logic 36 2.2 Truth Functions 40 2.3 A Sentential Language 46 2.4 Symbolization 49 2.5 Validity 56 2.6 Truth Tables 60 2.7 Truth Tables for Formulas 63 2.8 Truth Tables for Argument Forms 68 2.9 Implication, Equivalence, and Satisfiability 71 3 Truth Trees 76 3.1 Thinking Backwards 76 3.2 Constructing Truth Trees 80 3.3 Negation, Conjunction, and Disjunction 84 3.4 The Conditional and Biconditional 93 3.5 Other Applications 101 4 Natural Deduction 107 4.1 Natural Deduction Systems 107 4.2 Rules for Negation and Conjunction 110 4.3 Rules for the Conditional and Biconditional 118 4.4 Rules for Disjunction 122 4.5 Derivable Rules 125 5 Quantifiers 137 5.1 Constants and Quantifiers 138 5.2 Categorical Sentence Forms 144 5.3 Polyadic Predicates 148 5.4 The Language Q 153 5.5 Symbolization 156 6 Quantified Truth Trees 173 6.1 Rules for Quantifiers 174 6.2 Strategies 178 6.3 Interpretations 189 6.4 Constructing Interpretations from Trees 199 7 Quantified Natural Deduction 206 7.1 Deduction Rules for Quantifiers 206 7.2 Universal Proof 214 7.3 Derived Rules for Quantifiers 220 8 Identity and Function Symbols 225 8.1 Identity 225 8.2 Truth Tree Rules for Identity 231 8.3 Deduction Rules for Identity 235 8.4 Function Symbols 238 9 Necessity 249 9.1 If 249 9.2 Modal Connectives 251 9.3 Symbolization 256 9.4 Modal Truth Trees 261 9.5 Other Tree Rules 265 9.6 World Travelling 268 9.7 Modal Deduction 278 9.8 Other Modal Systems 289 10 Between Truth and Falsehood 295 10.1 Vagueness and Presupposition 295 10.2 Many-Valued Truth Tables 300 10.3 Many-Valued Trees 314 10.4 Many-Valued Deduction 325 10.5 Fuzzy Logic 332 10.6 Intuitionistic Logic 344 11 Obligation 361 11.1 Deontic Connectives 362 11.2 Deontic Truth Trees 370 11.3 Deontic Deduction 381 11.4 Moral and Practical Reasoning 387 12 Counterfactuals 395 12.1 The Meaning of Counterfactuals 399 12.2 Truth Tree Rules for Counterfactuals 402 12.3 Deduction Rules for Counterfactuals 409 12.4 Stalnaker’s Semantics: System CS 418 12.5 Lewis’s Semantics: System CL 423 13 Common-Sense Reasoning 434 13.1 When Good Arguments Go Bad 435 13.2 Truth Trees 439 13.3 Defeasible Deduction 454 13.4 Defeasible Deontic Logic 466 14 Quantifiers and Modality 475 14.1 Quantified S5 475 14.2 Free Logic 487 Bibliography 504 Index 507

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Book SynopsisEcologists are increasingly tackling difficult issues like global change, loss of biodiversity and sustainability of ecosystem services. These and related questions are enormously challenging, requiring unprecedented multidisciplinary collaboration and rapid synthesis of large amounts of diverse data into information and ultimately knowledge.Table of Contents1. Research Design: Translating Ideas to Data. 2. Data Management Principles, Implementation. 3. Scientific Databases. 4. Data Quality Assurance. 5. Metadata. 6. Archiving Ecological Data and Information. 7. Transforming Data into Information and Knowledge. 8. Ecological Knowledge and Future Data Challenges

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Book SynopsisInsect Sampling in Forest Ecosystems highlights the problems faced by entomologists working in forest ecosystems. Insects play a major part in all aspects of ecology Brings together the methodology needed to investigate insects through the various strata of the forest canopy Covers techniques associated with various specialised groups of forest insects Each chapter is backed up by a sound approach to experimental design and data analysis Essential reading for advanced students and researchers as well as teachers Trade Review"This book was a great read. I enjoyed all of the chapters and it should be part of anyone's library who is interested in issues of sampling in theory and practice." Ecology "The chapters are concise but well illustrated and the index of methods is a real bonus. Coverage is excellent and there's enough material to plan sampling or to discuss it in a wider context. With a lot of coverage in a compact form this text would be a good addition to a field work library." Teaching Ecology Group Newsletter, January 2005 "This is a book to delve into, when you need some inspiration on how to sample insects, since a novel method might prove to be significantly superior to the one you have been using - all those rare beetles are really quite numerous. I recommend acquiring a copy for your bookshelf." The British Journal of Entomology and Natural History, March 2006 “Addressing the needs of ecologists…this text brings together ten papers dealing with specific sampling challenges. Each paper includes extensive references.” Northeastern NaturalistTable of ContentsContributors. Methods in Ecology series. Preface. 1 Sampling theory and practice: Simon R. Leather & Allan D. Watt. 2 Sampling insects from roots: Alan C. Gange. 3 Pitfall trapping in ecological studies: B.A. Woodcock. 4 Sampling methods for forest understorey vegetation: Claire M.P. Ozanne. 5 Sampling insects from trees: shoots, stems, and trunks: Martin R. Speight. 6 Insects in flight: Mark Young. 7 Techniques and methods for sampling canopy insects: Claire M.P. Ozanne. 8 Sampling methods for water-filled tree holes and their artificial analogues: S.P. Yanoviak & O.M. Fincke. 9 Sampling devices and sampling design for aquatic insects: Leon Blaustein & Matthew Spencer. 10 Methods for sampling termites: David T. Jones, Robert H.J. Verkerk & Paul Eggleton. 11 Parasitoids and predators: Nick Mills. Index

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Book Synopsisaeo provides all the specialist knowledge, understanding and confidence needed to use models aeo focuses on life--cycle modelling, from the commissioning of a building through to demolition aeo offers practitioners an insight through detailed case studies to use of models.Table of ContentsPreface. Chapter 1 Heat Transfer in Building Elements. 1.1 Heat and mass transfer processes in buildings. 1.2 Heat transfer through external walls and roofs. 1.3 Analytical methods for solving the one-dimensional transient heat conduction equation. 1.4 Lumped capacitance methods. 1.5 Heat transfer through glazing. Chapter 2 Modelling Heat Transfer in Building Envelopes. 2.1 Finite Difference Method – A Numerical Method for Solving the Heat Conduction Equation. 2.2 Heat Transfer in Building Spaces. 2.3 Synthesis of Heat Transfer Methods. 2.4 Latent Loads and Room Moisture Content Balance. Chapter 3 Mass Transfer, Air Movement and Ventilation. Chapter 4 Steady-State Plant Modelling. 4.1 Model Formulations for Plant. 4.2 Mathematical Models of Air-conditioning Equipment using Equation-fitting. 4.3 A Detailed Steady-state Cooling and Dehumidifying Coil Model. 4.4 Modelling Distribution Networks. 4.5 Modelling Air-conditioning Systems. Chapter 5 Modelling Control Systems. 5.1 Distributed System Modelling. 5.2 Modelling Control Elements. 5.3 Modelling Control Algorithms. 5.4 Solution Schemes. Chapter 6 Modeling in Practice I. 6.1 Developments in General. 6.2 Internal Ventilation Problems6.3 Wind Flow Around Buildings. 6.4 Applications to Plant. 6.5 Applications to Control and Fault Detection. Chapter 7 Modeling in Practice II. 7.1 Interrelationships Between Methodologies. 7.2 Tools and Their Integration. 7.3 Validation and Verification. References. Appendix A. Appendix B. Index

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Book SynopsisThis book is aimed at the trouble with trying to learn about probability. A story of the misconceptions and difficulties civilization overcame in progressing toward probabilistic thinking, Randomness is also a skillful account of what makes the science of probability so daunting in our own day.Trade ReviewClearly, the computation of probabilities is not just an arid game… As Deborah Bennett shows in her excellent little book on the mathematics of chance, the concept has been controversial for thousands of years… [Her] cultured and accessible book goes a long way towards demystifying the science of probability and thereby offers the reader a useful variety of conceptual tools with which to probe the future and illuminate the present. -- Steven Poole * The Guardian *[Randomness] can most easily be described as a brief history of chance… I can cheerfully recommend it to anyone who is a total beginner when it comes to probability, what it means, why it is desperately puzzling, and what it can do for us despite that… It is fascinating to read about the pioneers of probability, such as Pierre Simon de Laplace with his ‘normal distribution’—now more familiar as the notorious bell curve—and Adolphe Quetelet, perhaps the first to realise that there are statistical patterns in human behaviour. And I applaud the blunt reminder that when it comes to the real world the ‘normal’ distribution is actually highly abnormal… My main criticism: it left me wanting more. A sequel, please. -- Ian Stewart * Times Higher Education Supplement *Chances are high that reading this book will clear up your misconceptions about randomness and probabilities. In this very entertaining little book, simply written but intended for careful readers, some of the most common mistakes people make about chance are carefully analyzed. While describing interesting aspects of the mathematics of probability, the author takes frequent detours into the history of humanity’s understanding (and misunderstanding) of the laws of chance, touching on subjects as diverse as chance in decision-making and the fairness of those decisions, gambling and our intuitive understanding of chance, the likelihood of the extremely rare, the existence of true randomness and how computers have helped shape modern thinking about probabilities… An insightful chapter is ‘Chance or Necessity?’ The question is very, very old (determinism versus chaos), and the answer is not clear even today. The author describes the problem beautifully: ‘Is random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors?’ Einstein grappled with this conundrum until his death and never ceased to combat the idea that God could conceivably throw dice… Whether well-educated in mathematics or not, people have always been fascinated by randomness and intrigued by the fundamental question of the real nature of randomness, of how you can tell randomness from something that is not. -- J. A. Rial * American Scientist *The great strength of this book is the way it uses history and even prehistory of probability to chart its present territory and cast light on its core point of contention: does true randomness exist in nature, or is it only a psychological artefact?… Bennett’s text…is like a café conversation between likable cognoscenti…nothing could more provoke and excite the reader. -- Simon Ings * New Scientist *In this book, Bennett seeks to account for the centuries-long lapse between early uses of chance in decision making and the more technical studies of probability first undertaken in the seventeenth century. At the same time, she explores the confusions and misunderstandings about probability that persist today. She argues that the notion of randomness played a crucial role in inhibiting conceptual progress in probability and that it also accounts for present-day struggles to come to terms with the subject… Bennett’s book is written in a lucid, engaging style and provides an entertaining introduction to some questions in probability. -- Patti Wilger Hunter * Isis *[A] sharp analysis of the way we assess probability in everyday life. -- Robert Winder * New Statesman & Society *Randomness, by mathematician Deborah J. Bennett, was obviously a labor of love. The result is an interesting book that combines a well-researched, anecdotally presented survey of the history of chance, probability and randomness along with some elementary instruction in probability… It includes a wide-ranging and rich bibliography that reflects the passion of the author for the subject. Anybody interested in gaming, random numbers, the Monte Carlo method and so on will find nice anecdotal descriptions of these topics, together with detailed notes and references to the bibliography for more detailed study. It is a good book to have. -- Stephen Gasiorowicz * Physics Today *In 1996 Charles Hailey and David Helfand reported their calculations of the odds of a commercial airliner being struck by a meteor, in response to speculation about TWA flight 800… They conclude that, in over 30 years of air travel, the probability that a commercial flight would have been hit by a meteor big enough to crash it is 1 in 10. This bit of probability trivia is an indication of human beings continuous struggle to understand probability and chance through the ages, and Deborah Bennett captures the fascination with numbers in this pocket-sized volume. The book is filled with…gems. * Skeptic *This volume is exceptionally readable. It takes away much of the mystery of probability while adding to our sense of wonder. * Wordtrade *The fact that randomness, agency, and holiness can readily displace each other in phenomenological explanations of human action is the central concern that might draw students of consciousness to Bennett’s book. Bennett does an excellent job, explaining and drawing out the major questions that swirl around the randomness–agency–holiness issue. -- T. W. Draper * Journal of Consciousness Studies *[This book] examines randomness and several other notions that were critical to the historical development of probabilistic thinking and that also play an important role in any individual’s understanding of the laws of chance. [It] addresses why, from ancient times to today, people have resorted to chance in making decisions; whether a decision made by random choice is a fair decision; how to figure the odds; what role gambling has played in understanding chance; whether extremely rare events are likely in the long run; why some societies and individuals reject randomness; whether true randomness exists; the view of randomness as uncertainty; why even experts disagree about the many meanings of randomness; and why probability is so counterintuitive. * Journal of Economic Literature *Mathematics is its own language, and sometimes it doesn’t translate readily into other human tongues. But Bennett is brilliantly bilingual, well able to put mathematical concepts into clear, expressive English. Her topic is intrinsically fascinating, for who has not felt buffeted by random events, and who has not sought to see when the wheel of fortune may turn up good luck?… More than an intriguing exploration of a peculiarly fascinating part of mathematics, its coverage, ranging from ancient games of chance to modern probability mind-games, makes it comprehensive as well as compulsively readable. -- Patricia Monaghan * Booklist *A clear and detailed examination of the role of pure chance, with fascinating historical asides. * Kirkus Reviews *A careful and well-written treatment of an intriguing subject. -- Donald Goldsmith, author of The Ultimate EinsteinRandomness tells us about chance by recalling the real history of probability and solving many of its engaging puzzles. Beginners will find themselves welcomed and well led. -- Frederick Mosteller, Harvard UniversityRandomness explains probability and odds in an accessible way. This book puts risk and chance into perspective for the airline passenger and the lottery player alike. -- Henry Petroski, author of Invention by Design: How Engineers Get from Thought to ThingTable of Contents* Chance Encounters * Why Resort to Chance? * When the Gods Played Dice * Figuring the Odds * Thought Games for Gamblers * Chance or Necessity? * Order in Apparent Chaos * Wanted: Random Numbers * Randomness as Uncertainty * Paradoxes in Probability * Notes * Bibliography * Index

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Book SynopsisIn these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.Trade ReviewParsons is a much admired and highly respected philosopher of mathematics and logic, well-known for his thoughtful and careful reflections on both the great historical figures and on work of the previous century. He is also an astute commentator on the current literature, engaging the contemporary debates and offering illuminating insights about its content and direction. This volume offers a unique opportunity for those not fortunate enough to have attended classes of Parsons’s to form some idea of what such an experience would be like. -- William Demopoulos, University of Western OntarioThis is a truly superb book. Parsons is quite possibly the most distinguished writer on philosophy of mathematics now working and certainly the most careful and probing. These essays examine a rather wide range of historical opinion on mathematical matters, both with an eye to demanding more careful interpretations and formulations from important writers such as Kant or Gödel while remaining sympathetic to their overall philosophical ambitions. Parsons’s treatments are unsurpassed. -- Mark Wilson, University of Pittsburgh

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Book SynopsisAndreu Mas-Colell revolutionized our understanding of competitive markets, price formation, and the behavior of market participants. This volume presents the papers that solidified his standing as one of the preeminent economic theorists of our time. It also is invaluable for anyone wishing to study the craft of a master of economic modeling.

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Book SynopsisSelected Logic Papers, long out of print and now reissued with eight additional essays, includes much of the author's important work on mathematical logic and the philosophy of mathematics from the past sixty years.Trade Review[Quine] is at once the most elegant expounder of systematic logic in the older, pre-Gödelian style of Frege and Russell, the most distinguished American recruit to logical empiricism, probably the contemporary American philosopher most admired in the profession, and an original philosophical thinker of the first rank… This is an amazing feat of condensation with something solid to say in its brief scope about every major topic of interest in modern formal logic. * New York Review of Books *What [Quine] is expert in is, of course, logic… What [this book offers] is a view of the expert at work. Selected Logic Papers shows him actually doing logic… Logic is not a guide to life, but then Quine has never maintained that it was. It is a powerful adjunct to empirical inquiry, whose proper use requires prior discipline; its virtue lies in the fact that if we supply it with truth, it will never yield falsehood. Few have shown the manner of its use with more authority. * Partisan Review *This book is of continuing, not just historical interest. Quine is the greatest American philosopher of the twentieth century. His work in logic is inseparable from his work in other parts of philosophy. -- George Boolos, Massachusetts Institute of TechnologyTable of ContentsWhitehead and the Rise of Modern Logic (1941); Logic, Symbolic (1954); A Method of Generating Part of Arithmetic Without Use of Intuitive Logic (1934); Definition of Substitution (1936); Concatenation as a Basis for Arithmetic (1946); Set-theoretic Foundations for Logic (1936); Logic Based on Inclusion and Abstraction (1937); On Ordered Pairs and Relations (1945-46); On w-Inconsistency and a So-called Axiom of Infinity (1952); Element and Number (1941); On an Application of Tarski's Theory of Truth (1952); On Frege's Way Out (1954); Completeness of the Propositional Calculus (1937); On Cores and Prime Implicants of Truth Functions (1958); Two Theorems about Truth Functions (1951); On Boolean Functions (1949); On the Logic of Quantification (1945); A Proof Procedure for Quantification Theory (1954); Interpretations of Sets of Conditions (1953); Church's Theorem on the Decision Problem (1954); Quantification and the Empty Domain (1953); Reduction to a Dyadic Predicate (1953); Variables Explained Away (1960); Truth, Paradox, and Godel's Theorem (1992); Immanence and Validity (1991); MacHale on Boole (1985); Peirce's Logic (1989); Peano as Logician (1982); Free Logic, Description, and Virtual Classes (1994); The Inception of "New Foundations" (1987); Pythagorean Triples and Fermat's Last Theorem (1992).

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Book SynopsisThe interplay between analysis on Lie groups and the theory of special functions is well known. This book deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. It develops Littlewood-Paley-Stein theory for the expansions and uses the theory to prove multiplier theorems.

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Book SynopsisDeals with the characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. This book compares monodromy groups corresponding to different parameters and proves commensurability modulo inner automorphisms of PU(1,n).Table of Contents*Frontmatter, pg. i*CONTENTS, pg. v*ACKNOWLEDGMENTS, pg. vii* 1. INTRODUCTION, pg. 1* 2. PICARD GROUP AND COHOMOLOGY, pg. 10* 3. COMPUTATIONS FOR Q AND Q+, pg. 17* 4. LAURICELLA'S HYPERGEOMETRIC FUNCTIONS, pg. 27* 5. GELFAND'S DESCRIPTION OF HYPERGEOMETRIC FUNCTIONS, pg. 35* 6. STRICT EXPONENTS, pg. 43* 7. CHARACTERIZATION OF HYPERGEOMETRIC-LIKE LOCAL SYSTEMS, pg. 55* 8. PRELIMINARIES ON MONODROMY GROUPS, pg. 71* 9. BACKGROUND HEURISTICS, pg. 80* 10. SOME COMMENSURABILITY THEOREMS, pg. 84* 11. ANOTHER ISOGENY, pg. 102* 12. COMMENSURABILITY AND DISCRETENESS, pg. 119* 13. AN EXAMPLE, pg. 124* 14. ORBIFOLD, pg. 135* 15. ELLIPTIC AND EUCLIDEAN mu'S, REVISITED, pg. 142* 16. LIVNE'S CONSTRUCTION OF LATTICES IN PU(1,2), pg. 161* 17. LIN E ARRANGEMENTS: QUESTIONS, pg. 169*Bibliography, pg. 182

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Book SynopsisSimple games are mathematical structures inspired by voting systems in which a single alternative. The mathematical study of the subject as a coherent subfield of finite combinatorics, this book includes introductory material, with an emphasis on Boolean subgames and the Rudin-Keisler order as unifying concepts.Trade Review"The authors do a nice job of bringing material from game theory, voting theory, graph theory, and threshold logic together with new results of the authors and presenting it coherently in the context of simple games. As such, it is a useful text for anyone looking for an introduction to simple games that gives not only several perspectives from which to view them, but also some of the latest results in the field and still-open questions."—Deanna B. Haunsperger, Carleton College"The authors provide a deep analysis of simple games, particularly with respect to their central concerns of trading, weightedness, and coalitional ordering. They bring a fresh perspective to the field by approaching it from a voting-theoretic angle and utilizing the tools of threshold logic."—Duncan J. Melville, St. Lawrence UniversityTable of ContentsPreface ix Acknowledgments xv Chapter 1 - Fundamentals 3 1.1 Introduction 3 1.2 Examples 8 1.3 The Dual Game 14 1.4 The Algebra of Simple Games 19 1.5 The Two-Point Constant-Sum Extension of a Game 26 1.6 Pregames and Weighted Graphs 29 1.7 Vector-Weighted Simple Games and Dimension Theory 34 1.8 The Voting Bloc and Bicameral Meet Characterization 39 1.9 The Game behind a Simple Game 40 Chapter 2 General Trading: Weighted Games 43 2.1 Introduction 43 2.2 Trading Transforms and Trading Matrices 45 2.3 Sequential Transfers 54 2.4 The Trading Characterization of Weighted Games 56 2.5 Pregraphs and Graphs 63 2.6 The Traditional Approaches: Systems of Linear Inequalities and Separating Hyperplanes 68 2.7 The Gabelman Examples 74 2.8 A General Framework 79 Chapter 3 Pairwise Trading: Linear Games and Winder Games 86 3.1 Introduction 86 3.2 The Desirability Relation on Individuals and Swap Robustness 87 3.3 Shift Minimal Winning Coalitions and the Ordinal Power Structure of a Simple Game 92 3.4 A Classification Theorem for Linear Games 97 3.5 Chvatal's Conjecture 103 3.6 The PSA Pseudoweighting Characterization of Linear Games 110 3.7 The Local Weighting Characterization of Linear Games 115 3.8 Two-Trade Robustness and Winder Games 120 3.9 A Weighting Characterization of Winder Games 122 3.10 The Hereditarily Dual-Comparable Characterization of Winder Games 123 Chapter 4 - Cycle Trading: Weakly Acyclic Games and Strongly Acyclic Games 125 4.1 Introduction 125 4.2 An Impossibility Result for Coalitional Desirability Relations 125 4.3 Possibilities, and More Impossibilities, from the Weight-Induced Order 134 4.4 Lapidot's Desirability Relation on Coalitions and Weakly Acyclic Games 139 4.5 The SSA Pseudoweighting Characterization of Weakly Acyclic Games, and a Generalization 142 4.6 An Inductive Construction of SSA Pseudoweightings for Weakly Acyclic Games 145 4.7 Winder's Desirability Relation on Coalition and Strongly Acyclic Games 150 4.8 A Pseudoweighting Characterization of Strongly Acyclic Games 156 4.9 Sequential Transfer Trading for L and W 157 4.10 Peleg's Question on the Weightedness of Constant-Sum Acyclic Games 165 Chapter 5 - Almost General Trading: Chow Games, Completely Acyclic Games, and Weighted Games 178 5.1 Introduction 178 5.2 Chow Games and Chow-Lapidot Parameters 179 5.3 A Gabelman-Style, Nonweighted Chow Game 183 5.4 The Trading Version of Lapidot's Desirability Relation 190 5.5 The Trading Version of Winder's Desirability Relation 196 5.6 Multiweightings 201 5.7 Weighted Games and the Weight-Induced Order 205 Appendix I: Systems of Linear Inequalities 215 Appendix II: Separating Hyperplanes 220 Appendix III: Duality and Transitivity for Binary Relations 223 References 229 Index 235

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Book SynopsisPresents many of the main developments in the study of real submanifolds in complex space, providing background material for researchers and advanced graduate students. This work addresses topics such as the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds.Table of ContentsPrefaceCh. IHypersurfaces and Generic Submanifolds in C[superscript N]3Ch. IIAbstract and Embedded CR Structures35Ch. IIIVector Fields: Commutators, Orbits, and Homogeneity62Ch. IVCoordinates for Generic Submanifolds94Ch. VRings of Power Series and Polynomial Equations119Ch. VIGeometry of Analytic Discs156Ch. VIIBoundary Values of Holomorphic Functions in Wedges184Ch. VIIIHolomorphic Extension of CR Functions205Ch. IXHolomorphic Extension of Mappings of Hypersurfaces241Ch. XSegre Sets281Ch. XINondegeneracy Conditions for Manifolds315Ch. XIIHolomorphic Mappings of Submanifolds349Ch. XIIIMappings of Real-algebraic Subvarieties379References390Index401

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Book SynopsisPresenting the story of Poincare's work, this book traces the history of attempts to solve the problems of celestial mechanics posed in Isaac Newton's "Principia" in 1686. It introduces the people whose ideas led to the field called nonlinear dynamics.Trade ReviewOne of Choice's Outstanding Academic Titles for 1997 "[S]tories about the history of celestial mechanics are the subject of this delightful book. The authors interweave numerous anecdotes about the personalities involved in the discoveries with technical details of the mathematical ideas themselves... a pleasant mix of things technical and things historical... written in a lively and informative way."--Robert L. Devaney, Science "This book, which should be required reading for every nonspecialist astronomer, may well be headed toward becoming a classic."--Choice "A particular strength of Celestial Encounters is the impression, conveyed with a deft touch, that mathematics is an international and collective effort made by real people for real reasons in the real world. All the players in the drama, alive or dead, come over as human beings who happen to have a passion for mathematics and an ability to fulfill that passion. This feature alone justifies buying the book."--Ian Stewart, New Scientist "A lively introduction to the fascinating story of celestial mechanics."--Jacques Laskar, Nature "Throughout the book one finds a vital quality that derives from the authors' real success in presenting mathematics as a human endeavor... A valuable and accessible contribution to the chaos literature."--June Barrow-Green, Isis "A pleasant mix of things technical and things historical... Written in a lively and informative way."--Robert Devaney, ScienceTable of ContentsPreface and Acknowledgments A Note to the Reader 1. A Great Discovery - And a Mistake 2. Symbolic Dynamics 3. Collisions and Other Singularities 4. Stability 5. KAM Theory Notes Bibliography Index

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Book SynopsisHarald Cramér’s classic synthesis of statistical mathematical theory—an invaluable resource for students and practitioners alikeIn the 1930s, as British and American statisticians were developing the science of statistical inference, French and Russian probabilitists transformed the classical calculus of probability into a rigorous and pure mathematical theory. In this incisive and authoritative book, Harald Cramér unites these two major lines of development, providing a masterly exposition of the mathematical methods of modern statistics that set the standard in the field still followed today.Requiring only a working knowledge of undergraduate mathematics, this self-contained book begins with an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. It goes on to discuss the general theory of random variables and probability distributions, the theory of sampling, statistical estimation, and tesTable of ContentsPt. 1Mathematical IntroductionSets of Points3Theory of Measure and Integration in R[subscript 1]19Theory of Measure and Integration in R[subscript n]76Various Questions89Pt. 2Random Variables and Probability DistributionsFoundations137Variables and Distributions in R[subscript 1]166Variables and Distributions in R[subscript n]260Pt. 3Statistical InferenceGeneralities323Sampling Distributions341Tests of Significance, I416Theory of Estimation473Tests of Significance, II525Table 1The Normal Distribution557Table 2The Normal Distribution557Table 3The x[superscript 2]-Distribution559Table 4The t-Distribution560List of References561Index571

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Book SynopsisFibre bundles are an integral part of differential geometry. This book begins with an introduction to bundles, including such topics as differentiable manifolds and covering spaces. It then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles.Table of ContentsPart I. THE GENERAL THEORY OF BUNDLES 1. Introduction 3 2. Coordinate bundles and fibre bundles 6 3. Construction of a bundle from coordinate transformations 14 4. The product bundle 16 5. The Ehresmann-Feldbau definition of bundle 18 6. Differentiable manifolds and tensor bundles 20 7. Factor spaces of groups 28 8. The principal bundle and the principal map 35 9. Associated bundles and relative bundles 43 10. The induced bundle 47 11. Homotopies of maps of bundles 49 12. Construction of cross-sections 54 13. Bundles having a totally disconnected group 59 14. Covering spaces 67 Part II. THE HOMOTOPY THEORY OF BUNDLES 15. Homotopy groups 72 16. The operations of Pi1 on Pi n 83 17. The homotopy sequence of a bundle 90 18. The classification of bundles over the n-sphere 96 19. Universal bundles and the classification theorem 100 20. The fibering of spheres by spheres 105 21. The homotopy groups of spheres 110 22. Homotopy groups of the orthogonal groups 114 23. A characteristic map for the bundle Rn+1 over S n 118 24. A characteristic map for the bundle Un over S 2n - 1 124 25. The homotopy groups of miscellaneous manifolds 131 26. Sphere bundles over spheres 134 27. The tangent bundle of S n 140 28. On the non-existence of fiberings of spheres by spheres 144 Part III. THE COHOMOLOGY THEORY OF BUNDLES 29. The stepwise extension of a cross-section 148 30. Bundles of coefficients 151 31. Cohomology groups based on a bundle of coefficients 155 32. The obstruction cocycle 166 33. The difference cochain 169 34. Extension and deformation theorems 174 35. The primary obstruction and the characteristic cohomology class 177 36. The primary difference of two cross-sections 181 37. Extensions of functions, and the homotopy classification of maps 184 38. The Whitney characteristic classes of a sphere bundle 190 39. The Stiefel characteristic classes of differentiable manifolds 199 40. Quadratic forms on manifolds 204 41. Complex analytic manifolds and exterior forms of degree 2 209 Appendix 218 Bibliography 223 Index 228

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