Mathematics Books

Book SynopsisFour experienced teachers, who have written math curricular materials for the University of Chicago School Mathematics Project, present a comprehensive collection of innovative and fun activities easy enough for even the most math-phobic parents.Table of ContentsMath Around the House. Growing and Changing: Making a Personal Record Book. Calendar Math. Math on the Move. Animal Facts and Figures. Crafts that Use Math. Games and Math. Counting Rhymes and Stories. Index of Math Concepts.

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Book SynopsisContains 36 lectures solely on Fourier analysis and the FFT. Time and frequency domains, representation of waveforms in terms of complex exponentials and sinusoids, convolution, impulse response and the frequency transfer function, modulation and demodulation are among the topics covered. The text is linked to a complete FFT system on the accompanying disk where almost all of the exercises can be either carried out or verified. End-of-chapter exercises have been carefully constructed to serve as a development and consolidation of concepts discussed in the text.

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Book SynopsisIntroducing several important and useful methods for analyzing planar transmission line structures, this text discusses such topics as the theory and applications of Green's functions, the conformal mapping method, spectral domain methods, variational methods.Trade Review"...this book introduces the most commonly used techniques for analyzing microwave planar transmission live structures." (SciTech Book News, Vol. 25, No. 2, June 2001) "All important fundamental concepts and principles are covered as far as is possible with in a text of reasonable size...addresses student of electromagnetic theory...also...the engineer who is need of knowledge and practical, easy-to-apply formulas for the various line systems." (Measurement Science & Technology, Vol. 12, No. 10, October 2001) "...covers the analysis methods...from basics to advanced levels. All important fundamental concepts and principles are covered as far as is possible within a text of reasonable size." (Measurement Science & Technology, Vol. 12, No. 10, October 2001)Table of ContentsFundamentals of Electromagnetic Theory. Green's Function. Planar Transmission Lines. Conformal Mapping. Variational Methods. Spectral-Domain Method. Mode-Matching Method. Index.

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Book SynopsisIntroduces analysis, presenting analytical proofs backed by geometric intuition and placing minimum reliance on geometric argument. This edition separates continuity and differentiation and expands coverage of integration to include discontinuous functions. The discussion of differentiation of a vector function of a vector variable has been modernized by defining the derivative to be the Jacobian matrix; and, the general form of the chain rule is given, as is the general form of the implicit transformation theorem.Table of ContentsCALCULUS OF ONE VARIABLE. The Number System. Functions, Sequences, and Limits. Continuity and More Limits. Differentiation. Integration. The Elementary Transcendental Functions. VECTOR CALCULUS. Vectors and Curves. Functions of Several Variables. Limits and Continuity. Differential Functions. The Inversion Theorem. Multiple Integrals. Line and Surface Integrals. THEORY OF CONVERGENCE. Infinite Series. Sequence and Series of Functions. Uniform Convergence. The Taylor Series. Improper Integrals. Integral Representations of Functions. Gamma and Beta Functions. Laplace's Method and Stirling's Formula. Fourier Series. Elementary Differentiation and Integration Formulas. Answers, Hints, and Solutions. Index.

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Book SynopsisOutlines theory and techniques of calculus, emphasizing strong understanding of concepts, and the basic principles of analysis. Reviews elementary and intermediate calculus and features discussions of elementary-point set theory, and properties of continuous functions.Table of Contents1. Fundamentals of Elementary Calculus. 2. The Real Number System. 3. Continuous Functions. 4. Extensions of the Law of the Mean. 5. Functions of Several Variables. 6. The Elements of Partial Differentiation. 7. General Theorems of Partial Differentiation. 8. Implicit-Function Theorems. 9. The Inverse Function Theorem with Applications. 10. Vectors and Vector Fields. 11. Linear Transformations. 12. Differential Calculus of Functions from R¯nto R¯m. 13. Double and Triple Integrals. 14. Curves and Surfaces. 15. Line and Surface Integrals. 16. Point-Set Theory. 17. Fundamental Theorems on Continuous Functions. 18. The Theory of Integration. 19. Infinite Series. 20. Uniform Convergence. 21. Power Series. 22. Improper Integrals. Answers to Selected Exercises. Index.

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Book SynopsisContains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature.Table of ContentsPlanar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

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Book SynopsisThis book is devoted to the statistical theory of learning and generalization, that is, the problem of choosing the desired function on the basis of empirical data. The author will present the whole picture of learning and generalization theory. Learning theory has applications in many fields, such as psychology, education and computer science.Table of ContentsPreface xxi Introduction: The Problem of induction and Statistical inference 1 I Theory of learning and generation 1 Two Approches to the learnig problem 19 Appendix to chapter 1: Methods for solving III-posed problems 51 2 Estimation of the probability Measure and problem of learning 59 3 Conditions for Consistency of Empirical Risk Minimization Principal 79 4 Bounds on the Risk for indicator Loss Functions 121 Appendix to Chapter 4: Lower Bounds on the Risk of the ERM Principle 169 5 Bounds on the Risk for Real-valued loss functions 183 6 The structural Risk Minimization Principle 219 Appendix to chapter 6: Estimating Functions on the basis of indirect measurements 271 7 stochastic III-posed problems 293 8 Estimating the values of Function at given points 339 II Support Vector Estimation of Functions 9 Perceptions and their Generalizations 375 10 The Support Vector Method for Estimating Indicator functions 401 11 The Support Vector Method for Estimating Real-Valued functions 443 12 SV Machines for pattern Recognition 493 13 SV Machines for Function Approximations, Regression Estimation, and Signal Processing 521 III Statistical Foundation of Learning Theory 14 Necessary and Sufficient Conditions for Uniform Convergence of Frequencies to their Probabilities 571 15 Necessary and Sufficient Conditions for Uniform Convergence of Means to their Expectations 597 16 Necessary and Sufficient Conditions for Uniform One-sided Convergence of Means to their Expectations 629 Comments and Bibliographical Remarks 681 References 723 Index 733

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Book SynopsisThis book provides a modern and up-to-date treatment of the Hilberttransform of distributions and the space of periodic distributions.Taking a simple and effective approach to a complex subject, thisvolume is a first-rate textbook at the graduate level as well as anextremely useful reference for mathematicians, applied scientists,and engineers. The author, a leading authority in the field, shares with thereader many new results from his exhaustive research on the Hilberttransform of Schwartz distributions. He describes in detail how touse the Hilbert transform to solve theoretical and physicalproblems in a wide range of disciplines; these include aerofoilproblems, dispersion relations, high-energy physics, potentialtheory problems, and others. Innovative at every step, J. N. Pandey provides a new definitionfor the Hilbert transform of periodic functions, which isespecially useful for those working in the area of signalprocessing for computational purposes. This definiTable of ContentsThe Riemann-Hilbert Problem. The Hilbert Transform of Distributions in D'Lp, 1 p infinity. The Hilbert Transform of Schwartz Distributions. n-Dimensional Hilbert Transform. Further Applications of the Hilbert Transform, the HilbertProblem-- A Distributional Approach. Periodic Distributions, Their Hilbert Transform andApplications. Bibliography. Indexes.

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Book SynopsisThis text seeks to get students actively involved in problem-solving, especially of a geometric nature. The approach highlights the mathematical connections between concepts, and aims to enhance students' geometrical intuition.Table of ContentsGetting Started: Strategies for Solving Problems. Episodes in the Measurement of Length, Area, and Volume. Polyhedra. Shortest Path Problems. Kaleidoscopes. Symmetry. What Shapes Are Best? Beehives and Other Packing Problems. Where to Go From Here?: Project Ideas. Credits. Index.

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Book SynopsisDesigned to present the chief results of the Lebesgue theory of integration, this textbook provides students with detailed coverage of the main ideas of the Lebesgue measure. The approach is particularly well suited for students of analysis, probability and statistics.Table of ContentsTHE ELEMENTS OF INTEGRATION. Measurable Functions. Measures. The Integral. Integrable Functions. The Lebesgue Spaces Lp. Modes of Convergence. Decomposition of Measures. Generation of Measures. Product Measures. THE ELEMENTS OF LEBESGUE MEASURE. Volumes of Cells and Intervals. The Outer Measure. Measurable Sets. Examples of Measurable Sets. Approximation of Measurable Sets. Additivity and Nonadditivity. Nonmeasurable and Non-Borel Sets. References. Index.

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Book SynopsisThe Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T.W.Table of ContentsThe Use of Regression Analysis. Trends and Smoothing. Cyclical Trends. Linear Stochastic Models with Finite Numbers of Parameters. Serial Correlation. Stationary Stochastic Processes. The Sample Mean, Covariances, and Spectral Density. Estimation of the Spectral Density. Linear Trends with Stationary Random Terms. Appendices. Bibliography. Index.

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Book SynopsisPresents the basic theory of real analysis. The algebraic and order properties of the real number system are presented in a simpler fashion than in the previous edition.Table of ContentsA Glimpse at Set Theory. The Real Numbers. The Topology of Cartesian Spaces. Convergence. Continuous Functions. Functions of One Variable. Infinite Series. Differentiation in R?P Integration in R?P.

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Book SynopsisThis introduction to a wide range of theoretical studies in fluid dynamics, covers a great deal of material and offers updated information on topics such as stability and turbulence. It surveys nearly the entire field of classical fluid dynamics and discusses the various conceptual and analytical models of fluid flow.Trade Review"I know of no other modern book in theoretical fluid dynamics that covers so much material so well." (Physics Today, November 1998)Table of ContentsReview of Basic Concepts and Equations of Fluid Dynamics. Dynamics of Inviscid Incompressible Fluid Flows. Dynamics of Inviscid Compressible Fluid Flows. Dynamics of Viscous Fluid Flows. Hydrodynamic Stability. Dynamics of Turbulence. Bibliography. Index.

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Book SynopsisTable of ContentsSet Theory. Probability. Random Variables and Distribution Functions. Some Standard Probability Laws. Jointly Distributed Random Variables. Descriptive and Inferential Statistics. Estimation of Parameters. Tests of Hypotheses. Least Squares and Regression. Nonparametric Methods. Bayesian Methods. Appendices. Answers to Exercises. Index.

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Book SynopsisA thorough, accessible, and rigorous presentation of the central theorems of mathematical logic... ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems.Table of ContentsPartial table of contents: MATHEMATICAL STRUCTURES AND THEIR THEORIES. Relational Systems. Boolean Algebras. Terms and Formulas. Substitution of Terms. Theorems and Proofs. Generalization Rule and Elimination of Constants. Peano Arithmetic. Ultraproducts. Supplementary Questions. SELECTED TOPICS. Total Functions. Incompleteness of Arithmetic. Tarski's Theorem. Matiyasevich's Theorem. Guide to Further Reading. References. Index.

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Book SynopsisLomen/Lovelock present differential equations as a natural extension of calculus, and encourage students to see them as a natural tool for investigating many aspects of science and engineering. The book provides lively reading with compelling applications, projects and experiments that supply students with opportunities to explore the differential equation and the process it models. Lomen/Lovelock suggest throughout the text that students employ technology as an instrument to check, discover and interpret the behavior of solutions.Appropriate for Sophmore courses in Junior Colleges, State Schools and Universities.Table of ContentsBasic Concepts. Autonomous Differential Equations. First Order Differential Equations - Qualitative and Quantitative Aspects. Models and Applications Leading to New Techniques. First Order Linear Differential Equations and Models. Interplay Between First Order Systems and Second Order Equations. Second Order Linear Differential Equations with Forcing Functions. Second Order Linear Differential Equations - Qualitative and Quantitative Aspects. Linear Autonomous Systems. Nonlinear Autonomous Systems. Using Laplace Transforms. Using Power Series. Appendices. Answers. Index.

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Book SynopsisStructural Sensitivity in Econometric Models Edwin Kuh, John W. Neese and Peter Hollinger Provides a pathbreaking assessment of the worth of linear dynamic systems methods for probing the behavior of complex macroeconomic models. Representing a major improvement upon the standard black box approach to analyzing economic model structure, it introduces the powerful concept of parameter sensitivity analysis within a linear systems root/vector framework. The approach is illustrated with a good mediumsize econometric model (Michigan Quarterly Econometric Model of the United States). EISPACK, the Fortran code for computing characteristic roots and vectors has been upgraded and augmented by a model linearization code and a broader algorithmic framework. Also features an interface between the algorithmic code and the interactive modeling system (TROLL), making an unusually wide range of linear systems methods accessible to economists, operations researchers, engineers and physical scientists. Table of ContentsSelected Aspects of Multivariate Analysis. Principal Components Analysis. Factor Analysis. Multidimensional Scaling. Cluster Analysis. Multiple Regression. Some Practical Considerations: Data Analysis Problems. Cross-Classified Frequency Data. Canonical Correlation Analysis. Discriminant Analysis: The Two-Group Problem. Multiple Discriminant Analysis and Related Topics. Linear Structural Relations (LISREL). Latent Structure Analysis. Appendixes. References. Index.

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Book SynopsisA unique, heuristic approach to mathematical discovery and problem solving This combined edition of Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving is unique among mathematics texts. Espousing a heuristic approach to mathematical problem solving, the text may be followed sequentially or according to instructors'' individualized curricula. Beginning with a discussion of patterns and practical approaches to problem solving, the book then presents examples from various branches of math and science to help students discover how to solve problems on their own an invaluable skill for the classroom and beyond.Table of ContentsPATTERNS. The Pattern of Two Loci. The Cartesian Pattern. Recursion. Superposition. TOWARD A GENERAL METHOD. Problems. Widening the Scope. Solutions. Appendix. Bibliography. Index.

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Book SynopsisExplains the concepts and use of univariate Box-Jenkins/ARIMA analysis and forecasting through 15 case studies. Cases show how to build good ARIMA models in a step-by-step manner using real data. Also includes examples of model misspecification. Provides guidance to alternative models and discusses reasons for choosing one over another.Table of ContentsBASIC CONCEPTS. Overview. Introduction to Box-Jenkins Analysis of a Single Data Series. Underlying Statistical Principles. An Introduction to the Practice of ARIMA Modeling. Notation and the Interpretation of ARIMA Models. Identification: Stationary Models. Identification: Nonstationary Models. Estimation. Diagnostic Checking. Forecasting. Seasonal and Other Periodic Models. THE ART OF ARIMA MODELING. Practical Rules. References. Index.

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Book SynopsisA comprehensive, up-to-date text on linear programming. Covers all practical modeling, mathematical, geometrical, algorithmic, and computational aspects. Surveys recent developments in the field, including the Ellipsoid method. Includes extensive examples and exercises.Table of ContentsFormulation of Linear Programs. The Simplex Method. The Geometry of the Simplex Method. Duality in Linear Programming. Revised (Primal) Simplex Method. The Dual Simplex Method. Numerically Stable Forms of the Simplex Method. Parametric Linear Programs. Sensitivity Analysis. Degeneracy in Linear Programming. Bounded-Variable Linear Programs. The Decomposition Principle of Linear Programming. The Transportation Problem. Computational Complexity of the Simplex Algorithm. The Ellipsoid Method. Iterative Methods for Linear Inequalities and Linear Programs. Vector Minima. Index.

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Book SynopsisThe Fourth Edition of the best--selling text on the basic concepts, theory, methods, and applications of ordinary differential equations retains the clear, detailed style of the first three editions. Includes new material on matrix methods, numerical methods, the Laplace transform, and an appendix on polynomial equations.Table of ContentsDifferential Equations and Their Solutions. First-Order Equations for Which Exact Solutions AreObtainable. Applications of First-Order Equations. Explicit Methods of Solving Higher-Order Linear DifferentialEquations. Applications of Second-Order Linear Differential Equations withConstant Coefficients. Series Solutions of Linear Differential Equations. Systems of Linear Differential Equations. Approximate Methods of Solving First-Order Equations. The Laplace Transform. Appendices. Suggested Reading. Answers to Odd-Numbered Exercises. Index.

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Book SynopsisUpdates the original, comprehensive introduction to the areas of mathematical physics encountered in advanced courses in the physical sciences. Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.Table of ContentsInfinite Series, Power Series. Complex Numbers. Linear Equations: Vectors, Matrices, and Determinants. Partial Differentiation. Multiple Integrals: Applications of Integration. Vector Analysis. Fourier Series. Ordinary Differential Equations. Calculus of Variations. Coordinate Transformations: Tensor Analysis. Gamma, Beta, and Error Functions. Series Solutions of Differential Equations. Partial Differential Equations. Functions of a Complex Variable. Integral Transforms. Probability. Answers to Selected Problems. Index.

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Book SynopsisA concise, easy to understand introduction that emphasizes the relevance of statistics to real world problems. Describes traditional statistical methods, their uses and limitations, and explains how to reduce numerical data to statistical summaries, how to interpret the results, and how to present the data clearly.Table of ContentsSTATISTICAL VARIATION. Averages. Scatter. Structured Tables. FREQUENCY DISTRIBUTIONS. Observed Distributions. Theoretical Distributions. Probability Models. SAMPLING. Taking a Sample. How Sample Means Vary. Estimation. Tests of Significance. RELATIONSHIPS. Correlation. Regression. Many Sets of Data. Many Variables. COMMUNICATING DATA. Numbers. Tables. Graphs. Words. EMPIRICAL GENERALIZATIONS. Description. I Explanation. Observation and Explanation. Appendixes. Index.

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Book SynopsisModern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible.Table of ContentsREAL ANALYSIS. Fundamentals. Integration. Functional Analysis. More Measure Theory. COMPLEX ANALYSIS. Locally Holomorphic Functions. Harmonic Functions. Meromorphic and Entire Functions. Conformal Mapping. Defective Functions. Riemann Surfaces. Convexity and Complex Analysis. Several Complex Variables. Bibliography. Symbol List. Glossary/Index.

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Book SynopsisClearly explains the sampling methods associated with the inventory of forest resources. It avoids extensive coverage of theoretical statistics and mathematics in favor of thorough coverage of forest inventory topics for the practitioner.Table of ContentsA Review of Necessary Statistics and Notation. Elementary Sampling Methods: Selective, Simple Random, andSystematic Sampling. Horizontal Point Sampling. Stratified Random Sampling. Ratio and Regression Estimators. Double Sampling or Two-Phase Sampling. Multistage Sampling--Inventorying Large Acreages. Inventory Methods for Estimating Stand Growth. 3P and Line Intersect Sampling. Estimating Wildlife Population Sizes. Answers to Assorted Problems for Better Understanding. Index.

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Book SynopsisAn accessible book on sampling techniques with emphasis on and illustrations from surveys of human populations. Explains how to design and execute valid samples of moderate dimensions and difficulty, avoid selection biases and how to become more adept at evaluating sample results, judge their validity and limits of inference, applicability and precision. Contains numerous practical procedures, the domestic arts of sampling along with its science plus invaluable tricks that are usually learned only in apprenticeship.Table of ContentsFUNDAMENTALS OF SURVEY SAMPLING. Basic Concepts of Sampling. Stratified Sampling. Systematic Sampling; Stratification Techniques. Cluster Sampling and Subsampling. Unequal Clusters. Selection with Probabilities Proportional to Size Measures(PPS). The Economic Design of Surveys. SPECIAL PROBLEMS AND TECHNIQUES. Area Sampling. Multistage Sampling. Sampling from Imperfect Frames. Some Selection Techniques. RELATED CONCEPTS. Biases and Nonsampling Errors. Some Issues of Inference from Survey Data. Appendices. References. Answers to Selected Problems. Index.

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Book SynopsisThis book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given.Table of ContentsBernoulli, Euler and Stirling Numbers. Useful Methods and Techniques. The Gamma Function. Differential Equations. Hypergeometric Functions. Orthogonal Polynomials. Confluent Hypergeometric Functions. Legendre Functions. Bessel Functions. Separating the Wave Equation. Special Statistical Distribution Functions. Elliptic Integrals and Elliptic Functions. Numerical Aspects of Special Functions. Bibliography. Notations and Symbols. Index.

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Book SynopsisAn important new perspective on AFFINE AND PROJECTIVEGEOMETRY This innovative book treats math majors and math education studentsto a fresh look at affine and projective geometry from algebraic,synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninetyillustrations, and numerous examples and exercises, coveringmaterial for two semesters of upper-level undergraduatemathematics. The first part of the book deals with the correlationbetween synthetic geometry and linear algebra. In the second part,geometry is used to introduce lattice theory, and the bookculminates with the fundamental theorem of projectivegeometry. While emphasizing affine geometry and its basis in Euclideanconcepts, the book: * Builds an appreciation of the geometric nature of linear algebra * Expands students'' understanding of abstract algebra with itsnontraditional, geometry-driven approach * Demonstrates how one branch of mathematiTable of ContentsAffine Planes. Desarguesian Affine Planes. Introducing Coordinates. Coordinate Projective Planes. Affine Space. Projective Space. Lattices of Flats. Collineations. Appendices. Index.

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Book SynopsisStatistical inference is used to draw conclusions about the general from the particular. This book provides an introduction to the central ideas and methods of statistical inference by integrating conceptual development with the analysis of data.Trade Review"...provides an introduction to the central ideas and methods of statistical inference..." (Quarterly of Applied Mathematics, Vol. LIX, No. 2, June 2001)Table of ContentsStatistical Models. Bayesian, Fiducial and Likelihood Inference. Frequentist Inference. Large Sample Theory. Robust Inference. Randomization and Resampling. Principles of Inference. Appendix. References. Indexes.

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Book SynopsisPresents a step-by-step approach to do all kinds of business-math problems, including basic arithmetic, algebra, percentages, and conversions; specific, real-life applications such as figuring discounts, calculating simple and compound interest, reading balance sheets and income statements, and preparing graphs and charts; and, more.Table of ContentsBASIC MATH REVIEW. Basic Arithmetic. Simple Algebra. Percentages. RETAILING APPLICATIONS. Markup and Markdown. Trade and Cash Discounts. Taking Inventory. GENERAL BUSINESS APPLICATIONS. Simple Interest. Compound Interest and Present Value. Depreciation. The Balance Sheet. The Income Statement. STATISTICS AND GRAPHING TECHNIQUES. Basic Statistical Measures. Basic Graphing Techniques. Last Word. Glossary. Index.

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Book SynopsisThis book contains material on compound Poisson random variables including an identity which can be used to efficiently compute moments, Poisson approximations, and coverage of the mean time spent in transient states as well as examples relating to the Gibba s sampler, the Metropolis algorithm and mean cover time in star graphs.Table of ContentsPreliminaries. The Poisson Process. Renewal Theory. Markov Chains. Continuous-Time Markov Chains. Martingales. Random Walks. Brownian Motion and Other Markov Processes. Stochastic Order Relations. Poisson Approximations. Answers and Solutions to Selected Problems. Index.

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Book SynopsisA comprehensive, thoroughly modern approach to environmental quality assessment The only textbook to combine engineering transport fundamentals and equilibrium aquatic chemistry, Environmental Modeling brings a uniquely contemporary perspective to the assessment of environmental quality. Addressing key questions about fate, transport, and long-term effects of chemical pollutants in the environment, this inherently practical text gives readers the important tools they need to develop and solve their own mathematical models. Contains detailed examples from a wide range of crucial water quality areas-conventional pollutants in rivers, eutrophication of lakes, and toxic organic chemicals and heavy metals in both surface and groundwaters Examines current global issues, including atmospheric deposition, hazardous wastes, soil pollution, global change, and more Features over 200 high-quality illustrations, plus skill-building problems in every chapter <Table of ContentsTransport Phenomena. Chemical Reaction Kinetics. Equilibrium Chemical Modeling. Eutrophication of Lakes. Conventional Pollutants in Rivers. Toxic Organic Chemicals. Modeling Trace Metals. Groundwater Contamination. Atmospheric Deposition and Biogeochemistry. Global Change and Global Cycles. Appendices. Index.

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Book SynopsisChemometrics encompasses a variety of statistical tools used to effectively design, analyze and interpret experimental data. The field has evolved rapidly over the last several years due to the widespread availability of powerful, inexpensive computers and available software packages.Trade Review"...probably the best introductory text that I have read on the subject...I would recommend this book for an introductory course...whithout the slightest hesitation." (Microchemical Journal, Vol. 69, 2001)Table of ContentsThe Six Habits of an Effective Chemometrician. Defining the Problem. Preprocessing. Pattern Recognition. Multivariate Calibration and Prediction. References. Index.

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Book SynopsisDevised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today's sciences. This book offers readers a solid grounding on the origin of these abstract, general theories.Table of ContentsGauss Sums. Jacobi Sums and Cyclotomic Numbers. Evaluation of Jacobi Sums Over Fp. Determination of Gauss Sums Over Fp. Difference Sets. Jacobsthal Sums Over Fp. Residuacity. Reciprocity Laws. Congruences for Binomial Coefficients. Diagonal Equations over Finite Fields. Gauss Sums over Fq. Eisenstein Sums. Brewer Sums. A General Eisenstein Reciprocity Law. Research Problems. Bibliography. Notation. Indexes.

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Book SynopsisThis book is an expanded and updated version of Chapter 11 of Distributions in Statistics: Discrete Distributions, written by Norman L. Johnson and Samuel Kotz in 1969. It provides detailed explanations of discrete multivariate distributions, including their properties and usefulness.Table of ContentsGeneral Remarks. Multinominal Distributions. Negative Multinominal and Other Multinominal-RelatedDistributions. Multivariate Poisson Distributions. Multivariate Power Series Distributions. Multivariate Hypergeometric and Related Distributions. Multivariate Polya-Eggenberger Distributions. Multivariate Ewens Distribution. Multivariate Distributions of Order s. Miscellaneous Distributions. Abbreviations. Indexes.

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Book SynopsisContains 36 lectures solely on Fourier analysis and the FFT. Time and frequency domains, representation of waveforms in terms of complex exponentials and sinusoids, convolution, impulse response and the frequency transfer function, modulation and demodulation are among the topics covered. The text is linked to a complete FFT system on the accompanying disk where almost all of the exercises can be either carried out or verified. End-of-chapter exercises have been carefully constructed to serve as a development and consolidation of concepts discussed in the text.Table of ContentsCONTINUOUS FOURIER ANALYSIS. Background. Fourier Series for Periodic Functions. The Fourier Integral. Fourier Transforms of Some Important Functions. The Method of Successive Differentiation. Frequency-Domain Analysis. Time-Domain Analysis. The Properties. The Sampling Theorems. DISCRETE FOURIER ANALYSIS. The Discrete Fourier Transform. Inside the Fast Fourier Transform. The Discrete Fourier Transform as an Estimator. The Errors in Fast Fourier Transform Estimation. The Four Kinds of Convolution. Emulating Dirac Deltas and Differentiation on the Fast FourierTransform. THE USER'S MANUAL FOR THE ACCOMPANYING DISKS. Appendices. Answers to the Exercises. Index.

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Book SynopsisIn this text on statistical decision-making, the authors use examples such as computing values for the stock market, conducting market research reports or using an options pricing model to illuminate the subject matter.Table of ContentsIntroduction to Quantitative Decision Making. Discrete Probability and Decision Analysis. Decision Making with Binomial and Normal Probabilities. Decisions Based on Sample Statistics. Sample Design and Estimation. Decisions Based on Linear Relationships. Hypothesis Testing. Quality Control. Forecasting. Analysis of Variance. Simulation. Linear Programming. Appendices. Data Disk Files. Selected References. Answers to Even-Numbered Problems. Index.

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Book SynopsisPATTERN CLASSIFICATION a unified view of statistical and neural approaches The product of years of research and practical experience in pattern classification, this book offers a theory-based engineering perspective on neural networks and statistical pattern classification. Pattern Classification sheds new light on the relationship between seemingly unrelated approaches to pattern recognition, including statistical methods, polynomial regression, multilayer perceptron, and radial basis functions. Important topics such as feature selection, reject criteria, classifier performance measurement, and classifier combinations are fully covered, as well as material on techniques that, until now, would have required an extensive literature search to locate. A full program of illustrations, graphs, and examples helps make the operations and general properties of different classification approaches intuitively understandable. Offering a lucid presentation of complex appTable of ContentsStatistical Decision Theory. Need for Approximations: Fundamental Approaches. Classification Based on Statistical Models Determined by First-and-Second Order Statistical Moments. Classification Based on Mean-Square Functional Approximations. Polynomial Regression. Multilayer Perceptron Regression. Radial Basis Functions. Measurements, Features, and Feature Section. Reject Criteria and Classifier Performance. Combining Classifiers. Conclusion. STATMOD Program: Description of ftp Package. References. Index.

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Book SynopsisThis applied statistics book examines sampling methods from a biomedical standpoint. The authors draw on their work at the National Cancer Institute, helping practitioners analyze real-world health data even with no prior experience in survey methods.Trade ReviewThe book fulfills the authors' purpose of providing neededexpertise for statisticians who are limited in their knowledge ofsurvey research. There are excellent questions at the end of eachchapter so it would make a good textbook for a course in surveyanalysis. (Journal of Official Statistics, Vol. 16, 2000) A strength of this book is the exercises at the ends of eachchapter [...]. This makes the book ideal either for independentstudy or for a survey methods course at final year undergraduate orpostgraduate level. Since the book is based on the two authors'many years of experience working in this field, it shows highlevels of sound judgement and good advice. (Biometrics, 2000) The analytic components of books about survey sampling oftenrestrict their discussion to the analysis of relatively simpleparameters of interest, such as population means and linearregression slopes. On the other hand, texts not devoted to surveysampling rarely discuss in detail the effect of complex sampledesigns on data analysis. This book provides a great service to thehealth research community by tying together the tools of modernstatistical analysis and survey research in one package. Korn andGraubard write clearly and concisely, using well-chosen examples toilluminate potentially confusing concepts. (JASA, March 2001) If you are involved in analyzing data from very large surveys, thenyou will want to buy this book. Statisticians who enjoy expandingtheir horizons in statistics by reading practical and usefulstatistics books should also get a copy of the book. More and moreof this health-survey data becomes available all the time, soperhaps data analysis no longer needed in industry can find a newhome somewhere analyzing health-survey data. (Technometrics, May2001, Vol. 42, No. 4) "...provides a great service to the health research community bytying together...tools of modern statistical analysis and surveyresearch...." (Journal of the American Statistical Association)Table of ContentsBasic Survey Methodology. Statistical Analysis with Survey Data. Sample Weights and Imputation. Additional Issues in Variance Estimation. Cross-Sectional Analyses. Analysis of Longitudinal Surveys. Analyses Using Multiple Surveys. Population-Based Case-Control Studies. Appendices. References. Indexes.

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Book SynopsisMethods of subjective statistical analysis have seen a resurgence of activity in the last decade. This book treats the theory of probability and the logic of uncertainty in a systematic way. It features a technical presentation of the mathematical impact of personal beliefs and values on statistical analysis.Trade Review"...has a merit for everyone who wonders about the foundations ofinference..." (Australian & New Zealand J Statistics, 2000)Table of ContentsPhilosophical and Historical Introduction. Quantities, Prevision, and Coherency. Coherent Statistical Inference. Related Forms for Asserting Uncertain Knowledge. Distribution Functions. Proper Scoring Rules. The Multivariate Normal Distribution and Its Mixtures. Sequential Forecasting Based on Linear Conditional PrevisionStructures: Theory and Practice of Linear Regression. The Direction of Statistical Research. References. Index.

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Book SynopsisComprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry. Conformal Differential Geometry and Its Generalizations systematically presents the foundations and manifestations of conformal differential geometry.Table of ContentsConformal and Pseudoconformal Spaces. Hypersurfaces in Conformal Spaces. Submanifolds in Conformal and Pseudoconformal Spaces. Conformal Structures on a Differentiable Manifold. The Four-Dimensional Conformal Structures. Geometry of the Grassmann Manifold. Manifolds Endowed with Almost Grassmann Structures. Bibliography. Symbols Frequently Used. Indexes.

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Book SynopsisBasic mathematics has never been so easy to learn! This user-friendly book presents clear and concise explanations of basic mathematics in a way that will help readers break through their anxiety about these concepts. By using contextual problems, the author also shows readers the relevance of the material in the real world.Trade Review"This is an excellent reference book for statisticians who try to comprehend the basic ideas of mathematical statistics or probability concepts." (Journal of Statistical Computation and Simulation, February 2006) "…careful attention to detail…" (The Mathematical Gazette, July 2004) "...explanation…are easy to read and…are as thorough as possible...a solid and useful reference work..." (Journal of Recreation Mathematics, (currently posted on Amazon)) "...excellent reference...recommended..." (Choice, Vol. 40, No. 5 January 2003) "...a useful reference..." (The American Statistician, Vol. 57, No. 3, August 2003)Table of ContentsPreface. Acknowledgments. A - Z.

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Book SynopsisUnlike other books on variance components, Statistical Tests for Mixed Linear Models continues beyond point estimation to cover hypothesis and data testing. By addressing these areas, the author presents practical applications of variance component models through testing of fixed effects and variance components.Trade Review"...compiles the available results in this area into a single volume." (Quarterly of Applied Mathematics, Vol. LIX, No. 3, September 2001) "...the authors are to be congratulated for this important and useful book...the authors state...'it will contribute to the development of the area, and enhance its exposure and usefulness.' The reviewers agree." (Mathematical Geology)Table of ContentsNature of Exact and Optimum Tests in Mixed Linear Models. Balanced Random and Mixed Models. Measures of Data Imbalance. Unbalanced One-Way and Two-Way Random Models. Random Models with Unequal Cell Frequencies in the Last Stage. Tests in Unbalanced Mixed Models. Recovery of Inter-Block Information. Split-Plot Designs Under Mixed and Random Models. Tests Using Generalized P-Values. Multivariate Mixed and Random Models. Appendix. General Bibliography. Indexes.

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Book SynopsisOne of two volumes which lay the foundations for understanding differential geometry. This work familiarizes readers with various techniques of computation.Table of ContentsSubmanifolds. Variations of the Length Integral. Complex Manifolds. Homogeneous Spaces. Symmetric Spaces. Characteristic Classes. Appendices. Notes. Bibliography. Summary of Basic Notations. Index.

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Book SynopsisOne of two volumes which lay the foundations for understanding differential geometry. This work familiarizes readers with various techniques of computation.Table of ContentsDifferentiable Manifolds. Theory of Connections. Linear and Affine Connections. Riemannian Connections. Curvature and Space Forms. Transformations. Appendices. Notes. Summary of Basic Notations. Bibliography. Index.

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Book SynopsisThe standard topics for a one-term undergraduate real analysis course are covered in this book. In addition, examples are given that show the ways in which real analysis is used in ordinary and partial differential equations, probability theory, numerical analysis, and number theory.Table of ContentsPreface Chapter 1 Preliminaries 1 The Real Numbers 1 Sets and Functions 6 Cardinality 15 Methods of Proof 20 Chapter 2 Sequences 27 Convergence 27 Limit Theorems 35 Two-state Markov Chains 40 Cauchy Sequences 44 Supremum and Infimum 52 The Bolzano-Weierstrass Theorem 55 The Quadratic Map 60 Projects 68 Chapter 3 The Riemann Integral 73 Continuity 73 Continuous Functions on Closed Intervals 80 The Riemann Integral 87 Numerical Methods 95 Discontinuities 103 Improper Integrals 113 Projects 119 Chapter 4 Differentiation 121 Differentiable Functions 121 The Fundamental Theorem of Calculus 129 Taylor’s Theorem 134 Newton’s Method 140 Inverse Functions 147 Functions of Two Variables 151 Projects 159 Chapter 5 Sequences of Functions 163 Pointwise and Uniform Convergence 163 Limit Theorems 169 The Supremum Norm 175 Integral Equations 183 The Calculus of Variations 188 Metric Spaces 196 The Contraction Mapping Principle 203 Normed Linear Spaces 210 Projects 219 Chapter 6 Series of Functions 223 Lim sup and Lim inf 223 Series of Real Constants 228 The Weierstrass M-test 238 Power Series 245 Complex Numbers 252 Infinite Products and Prime Numbers 260 Projects 270 Chapter 7 Differential Equations 273 Local Existence 273 Global Existence 283 The Error Estimate for Euler’s Method 289 Projects 296 Chapter 8 Complex Analysis 299 Analytic Functions 299 Integration on Paths 305 Cauchy's Theorem 312 Projects 320 Chapter 9 Fourier Series 323 The Heat Equation 323 Definitions and Examples 331 Pointwise Convergence 337 Mean-square Convergence 345 Projects 355 Chapter 10 Probability Theory 359 Discrete Random Variables 359 Coding Theory 368 Continuous Random Variables 376 The Variation Metric 386 Projects 398 Bibliography 403 Symbol Index 406 Index 409

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Book SynopsisClearly demonstrates a wide range of sampling methods now in use by governments, in business, market and operations research, social science, medicine, public health, agriculture, and accounting. Gives proofs of all the theoretical results used in modern sampling practice.Table of Contents1 Chapter Introduction 1 2 Chapter Simple Random Sampling 18 3 Chapter Sampling Proportions and Percentages 50 4 Chapter The Estimation of sample Size 72 5 Chapter Further Aspects of Stratified Sampling 115 6 Chapter Ratio Estimators 150 7 Chapter Regression Estimators 189 8 Chapter Systematic Sampling 205 9 Chapter Single-Stage Cluster Sampling: Clusters of Equal Sizes 233 9. A Chapter Single-Stage Cluster Sampling: Clusters of Unequal Sizes 249 10 Subsampling With Units of Equal Size 274 11 Chapter Subsampling With Units of Unequal Sizes 292 12 Chapter Double sampling 327 13 Chapter Sources of Error in Surveys 359 References 400 Answers to Exercises 412 Author Index 419 Subject Index 422

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Book SynopsisAn authoritative, full-year course on both group theory and ordinary character theory--essential tools for mathematics and the physical sciences One of the few treatments available combining both group theory and character theory, Groups and Characters is an effective general textbook on these two fundamentally connected subjects.Table of ContentsPreliminaries. Some Groups. Counting with Groups. Transfer and Splitting. Representations and Characters. Induction and Restriction. Computing Character Tables. Characters of Sn and An. Frobenius Groups. Splitting Fields. Bibliography. Index.

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