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Problem-Solving Strategies (Problem Books in Mathematics)
by Arthur EngelA unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.
One-Parameter Semigroups for Linear Evolution Equations (Graduate Texts in Mathematics #194)
by Klaus-Jochen Engel Rainer NagelThis book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background.
Practical Analysis in One Variable (Undergraduate Texts in Mathematics)
by Donald EstepThis text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer.
Foundations of Differential Calculus
by EulerThe positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.
Inside Calculus (Undergraduate Texts in Mathematics)
by George R. ExnerThe approach here relies on two beliefs. The first is that almost nobody fully understands calculus the first time around. The second is that graphing calculators can be used to simplify the theory of limits for students. This book presents the theoretical pieces of introductory calculus, using appropriate technology, in a style suitable to accompany almost any first calculus text. It offers a large range of increasingly sophisticated examples and problems to build an understanding of the notion of limit and other theoretical concepts. Aimed at students who will study fields in which the understanding of calculus as a tool is not sufficient, the text uses the "spiral approach" of teaching, returning again and again to difficult topics, anticipating such returns across the calculus courses in preparation for the first analysis course. Suitable as the "content" text for a transition to upper level mathematics course.
Statistical Design and Analysis for Intercropping Experiments: Volume II: Three or More Crops (Springer Series in Statistics)
by Walter T. FedererIntercropping is an area of research for which there is a desperate need, both in developing countries where people are rapidly depleting scarce resources and still starving, and in developed countries, where more ecologically and economically sound ways of feeding ourselves must be developed. The only published guidelines for conducting such research and analyzing the data have been scattered about in various journal articles, many of which are hard to find. This book condenses these methods and will be immensely valuable to agricultural researchers and to the statisticians who help them design their experiments and interpret their results.
Feedforward Neural Network Methodology (Information Science and Statistics)
by Terrence L. FineThis decade has seen an explosive growth in computational speed and memory and a rapid enrichment in our understanding of artificial neural networks. These two factors provide systems engineers and statisticians with the ability to build models of physical, economic, and information-based time series and signals. This book provides a thorough and coherent introduction to the mathematical properties of feedforward neural networks and to the intensive methodology which has enabled their highly successful application to complex problems.
An Introduction to Wavelets Through Linear Algebra (Undergraduate Texts in Mathematics)
by Michael W. FrazierWavelet theory is on the boundary between mathematics and engineering, making it ideal for demonstrating to students that mathematics research is thriving in the modern day. Students can see non-trivial mathematics ideas leading to natural and important applications, such as video compression and the numerical solution of differential equations. The only prerequisites assumed are a basic linear algebra background and a bit of analysis background. Intended to be as elementary an introduction to wavelet theory as possible, the text does not claim to be a thorough or authoritative reference on wavelet theory.
Bayesian Nonparametrics (Springer Series in Statistics)
by J.K. Ghosh R.V. RamamoorthiThis book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.
Stochastic Dynamics
by Hans Crauel Matthias GundlachFocusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.
Configurational Forces as Basic Concepts of Continuum Physics (Applied Mathematical Sciences #137)
by Morton E. GurtinIncluded is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture.
Relative Distribution Methods in the Social Sciences (Statistics for Social and Behavioral Sciences)
by Mark S. Handcock Martina MorrisThis monograph presents methods for full comparative distributional analysis based on the relative distribution. This provides a general integrated framework for analysis, a graphical component that simplifies exploratory data analysis and display, a statistically valid basis for the development of hypothesis-driven summary measures, and the potential for decomposition - enabling the examination of complex hypotheses regarding the origins of distributional changes within and between groups. Written for data analysts and those interested in measurement, the text can also serve as a textbook for a course on distributional methods.
Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)
by Robin HartshorneThis book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Matrix Algebra From a Statistician's Perspective
by David A. HarvilleA knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions."
Quasi-Likelihood And Its Application: A General Approach to Optimal Parameter Estimation (Springer Series in Statistics)
by Christopher C. HeydeThe first account in book form of all the essential features of the quasi-likelihood methodology, stressing its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential principles rather than detailed proofs, and readers are assumed to have a firm grounding in probability and statistics at the graduate level. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided.
Analysis and Simulation of Chaotic Systems (Applied Mathematical Sciences #94)
by Frank C. HoppensteadtBeginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable models for further mathematical analysis or computer simulations. For the most part, derivations are based on perturbation methods, and the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro-differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.
Finite Element Analysis of Acoustic Scattering (Applied Mathematical Sciences #132)
by Frank IhlenburgA cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations, while the main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. In the final chapter, three dimensional computational simulations are presented and compared with experimental data. The author also includes broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditions, infinite elements and the perfectly matched layer. A self-contained and easily readable work.
Interfacial Instability
by Lewis E. Johns Ranga NarayananEssays are written to fulfill the needs of both teachers and graduate students; Problems have been selected so that they can be solved by hand; Discussion notes are at the end of many of the essays to serve as a basis for discussion; Endnotes provide background information which the reader may need in order to enjo the essay
Ordinal Data Modeling (Statistics for Social and Behavioral Sciences)
by Valen E. Johnson James H. AlbertOrdinal Data Modeling is a comprehensive treatment of ordinal data models from both likelihood and Bayesian perspectives. A unique feature of this text is its emphasis on applications. All models developed in the book are motivated by real datasets, and considerable attention is devoted to the description of diagnostic plots and residual analyses. Software and datasets used for all analyses described in the text are available on websites listed in the preface.
Foundations of Modern Probability (Probability and Its Applications)
by Olav KallenbergUnique for its broad and yet comprehensive coverage of modern probability theory, ranging from first principles and standard textbook material to more advanced topics. In spite of the economical exposition, careful proofs are provided for all main results. After a detailed discussion of classical limit theorems, martingales, Markov chains, random walks, and stationary processes, the author moves on to a modern treatment of Brownian motion, L=82vy processes, weak convergence, It=93 calculus, Feller processes, and SDEs. The more advanced parts include material on local time, excursions, and additive functionals, diffusion processes, PDEs and potential theory, predictable processes, and general semimartingales.Though primarily intended as a general reference for researchers and graduate students in probability theory and related areas of analysis, the book is also suitable as a text for graduate and seminar courses on all levels, from elementary to advanced. Numerous easy to more challenging exercises are provided, especially for the early chapters.From the author of "Random Measures".
Methods of Mathematical Finance (Stochastic Modelling And Applied Probability Ser. #39)
by Ioannis Karatzas Steven ShreveThis sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.
Mathematical Physiology (Interdisciplinary Applied Mathematics #8)
by James Keener James SneydDivided into two parts, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing.
Single-Facility Location Problems with Barriers (Springer Series in Operations Research and Financial Engineering)
by Kathrin KlamrothThis text develops the mathematical implications of barriers to the geometrical and analytical characteristics of continuous location problems. The book will appeal to those working in operations research and management science, and mathematicians interested in optimization theory and its applications.
The Basics of S-PLUS (Statistics and Computing)
by Andreas Krause Melvin OlsonIn a clear style the most important ideas of S-PLUS are introduced through the use of many examples. Each chapter includes a collection of exercises, fully worked-out solutions and detailed comments.
The Basics of S and S-PLUS (Statistics and Computing)
by Andreas Krause Melvin OlsonA lucid explanation of the basics of S-PLUS at a level suitable for users with little computing or statistical knowledge. Unlike the S-PLUS manuals, the book does not strive to be comprehensive, but instead introduces the most important ideas of S-PLUS through the use of many examples. Each chapter includes a collection of exercises that are accompanied by fully worked-out solutions and detailed comments, and the whole is rounded off with practical hints on how to work efficiently in S-PLUS, making it well-suited for both self-study and as a textbook. This second edition has been updated to incorporate the completely revised S Language and its implementation in S-PLUS, while new chapters have been added to explain the Windows GUI, how to explore relationships in data using the powerful Trellis graphics system, and how to understand and use object-oriented programming. In addition, the programming chapter has been extended to cover some of the more technical but important aspects of S-PLUS.