Математика
Различные книги в жанре МатематикаThe Probabilistic Method
The leading reference on probabilistic methods in combinatorics-now expanded and updated When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications. The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or «probabilistic lenses,» are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes: * Several improved as well as new results * A continuous approach to discrete probabilistic problems * Talagrand's Inequality and other novel concentration results * A discussion of the connection between discrepancy and VC-dimension * Several combinatorial applications of the entropy function and its properties * A new section on the life and work of Paul Erdös-the developer of the probabilistic method
Physics of Plasmas
A short, self-sufficient introduction to the physics of plasma for beginners as well as researchers in a number of fields. The author looks at the dynamics and stability of magnetoplasma and discusses wave and transport in this medium. He also looks at such applications as fusion research using magnetic confinement of Deuterium plasma, solar physics with its plasma loops reaching high into the corona, sunspots and solar wind, engineering applications to metallurgy, MHD direct generation of electricity, and railguns, finally touching on the relatively new and difficult subject of dusty plasmas. The book includes mathematical notes and 99 exercises that supplement the theory presented and thus offers the beginner an easy introduction to this exciting field. It is an equally good textbook for final year undergraduates and first year research students.
Pricing Communication Networks
Traditionally engineers devised communication services without reference to how they should be priced. In today's environment pricing is a very complex subject and in practice depends on many parameters of the actual market – including amount of traffic, architecture of the network, technology, and cost. The challenge is to provide a generic service model which accurately captures aspects such as quality and performance, and can be used to derive optimal pricing strategies. Recent technology advances, combined with the deregulation of the telecommunication market and the proliferation of the internet, have created a highly competitive environment for communication service prividers. Pricing is no longer as simple as picking an appropriate model for a particular contract. There is a real need for a book that explains the provision of new services, the relation between pricing and resource allocation in networks; and the emergence of the internet and how to price it. Pricing Communication Networks provides a framework of mathematical models for pricing these multidimensional contracts, and includes background in network services and contracts, network techonology, basic economics, and pricing strategy. It can be used by economists to fill in the gaps in their knowledge of network services and technology, and for engineers and operational researchers to gain the background in economics required to price communication services effectively. * Provides a broad overview of network services and contracts * Includes a primer on modern network technology and the economic concepts relevant to pricing and competition * Includes discussion of mathematical models of traffic flow to help describe network capability and derive pricing strategies * Includes coverage of specialist topics, such as regulation, multicasting, and auctions * Illustrated throughout by detailed real examples * Suitable for anyone with an understanding of basic calculus and probability Primarily aimed at graduate students, researchers and practitioners from electrical engineering, computer science, economics and operations research Pricing Communication Networks will also appeal to telecomms engineers working in industry.
Thinking About Equations
An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension. Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.
Optimal Structural Analysis
This second edition of the highly acclaimed and successful first edition, deals primarily with the analysis of structural engineering systems, with applicable methods to other types of structures. The concepts presented in the book are not only relevant to skeletal structures but can equally be used for the analysis of other systems such as hydraulic and electrical networks. The book has been substantially revised to include recent developments and applications of the algebraic graph theory and matroids.
Positive Linear Systems
A complete study on an important class of linear dynamical systems-positive linear systems One of the most often-encountered systems in nearly all areas of science and technology, positive linear systems is a specific but remarkable and fascinating class. Renowned scientists Lorenzo Farina and Sergio Rinaldi introduce readers to the world of positive linear systems in their rigorous but highly accessible book, rich in applications, examples, and figures. This professional reference is divided into three main parts: The first part contains the definitions and basic properties of positive linear systems. The second part, following the theoretical exposition, reports the main conceptual results, considering applicable examples taken from a number of widely used models. The third part is devoted to the study of some classes of positive linear systems of particular relevance in applications (such as the Leontief model, the Leslie model, the Markov chains, the compartmental systems, and the queueing systems). Readers familiar with linear algebra and linear systems theory will appreciate the way arguments are treated and presented. Extraordinarily comprehensive, Positive Linear Systems features: * Applications from a variety of backgrounds including modeling, control engineering, computer science, demography, economics, bioengineering, chemistry, and ecology * References and annotated bibliographies throughout the book * Two appendices concerning linear algebra and linear systems theory for readers unfamiliar with the mathematics used Farina and Rinaldi make no effort to hide their enthusiasm for the topics presented, making Positive Linear Systems: Theory and Applications an indispensable resource for researchers and professionals in a broad range of fields.
Post-Modern Algebra
Advanced algebra in the service of contemporary mathematical research– a unique introduction. This volume takes an altogether new approach to advanced algebra. Its intriguing title, inspired by the term postmodernism, denotes a departure from van der Waerden's Modern Algebra–a book that has dominated the field for nearly seventy years. Post-Modern Algebra offers a truly up-to-date alternative to the standard approach, explaining topics from an applications-based perspective rather than by abstract principles alone. The book broadens the field of study to include algebraic structures and methods used in current and emerging mathematical research, and describes the powerful yet subtle techniques of universal algebra and category theory. Classical algebraic areas of groups, rings, fields, and vector spaces are bolstered by such topics as ordered sets, monoids, monoid actions, quasigroups, loops, lattices, Boolean algebras, categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested in university courses. * A wealth of exercises illustrating concepts and their practical application. * Effective techniques for solving research problems in the real world. * Flexibility of presentation, making it easy to tailor material to specific needs. * Help with elementary proofs and algebraic notations for students of varying abilities. Post-Modern Algebra is an excellent primary or supplementary text for graduate-level algebra courses. It is also an extremely useful resource for professionals and researchers in many areas who must tackle abstract, linear, or universal algebra in the course of their work.
Theoretical Fluid Dynamics
Although there are many texts and monographs on fluid dynamics, I do not know of any which is as comprehensive as the present book. It surveys nearly the entire field of classical fluid dynamics in an advanced, compact, and clear manner, and discusses the various conceptual and analytical models of fluid flow. – Foundations of Physics on the first edition Theoretical Fluid Dynamics functions equally well as a graduate-level text and a professional reference. Steering a middle course between the empiricism of engineering and the abstractions of pure mathematics, the author focuses on those ideas and formulations that will be of greatest interest to students and researchers in applied mathematics and theoretical physics. Dr. Shivamoggi covers the main branches of fluid dynamics, with particular emphasis on flows of incompressible fluids. Readers well versed in the physical and mathematical prerequisites will find enlightening discussions of many lesser-known areas of study in fluid dynamics. This thoroughly revised, updated, and expanded Second Edition features coverage of recent developments in stability and turbulence, additional chapter-end exercises, relevant experimental information, and an abundance of new material on a wide range of topics, including: * Hamiltonian formulation * Nonlinear water waves and sound waves * Stability of a fluid layer heated from below * Equilibrium statistical mechanics of turbulence * Two-dimensional turbulence
Inside Your Calculator
Uncover the mysteries that lie within your calculator This remarkable book explores the simple internal calculator processes—algorithms and programs—that tell us, for example, that the cosine of 56? is 0.5591929035. Using carefully constructed diagrams and figures, the author effectively demonstrates how calculator keys compute powers, roots, logarithms, and trigonometry functions, while also providing insights into simple programming, the conversion between decimal and binary numeration, and perhaps most importantly, the structure of our numeration systems. Many people believe that the processes that drive calculators demand advanced mathematical concepts; however, this book proves that a minimal understanding of algebra and geometry is all that is needed to follow the step-by-step explanations of how scientific calculators work. Inside Your Calculator: From Simple Programs to Significant Insights is a complete and multifaceted exercise in critical thinking. This book features: A detailed explanation of how to use a graphics calculator and program basic functions A discussion of the history of mathematics when appropriate, which provides a foundation for further learning Fundamental mathematical lessons and interesting applications of pre-calculus mathematics A thorough review of the fundamentals of programming, algebra, and geometry needed to gain insight into why the algorithms work and how the results are meaningful in our lives While the simultaneous use of a calculator is not needed to gain insight into how the algorithms work, those who do have a programmable graphics calculator can experiment with the programs presented in the book. These programs may be used on TI-84 and TI-83 calculators, and additional information for other Texas Instruments calculators as well as the Casio FX series is available on the book's related web site. As a result of over fifty years of award-winning teaching experience in both high school and college classrooms, Dr. Rising anticipates and answers potential questions from readers, and he successfully brings this subject alive in an illuminating and entertaining way. This book is therefore not only ideal for undergraduate mathematics majors as either a primary or supplemental text, but it also appeals to anyone with an interest in mathematics and its ideas. View Dr. Rising's book presentation: http://www.youtube.com/watch?v=aqadHbc2YOA
Scaling, Fractals and Wavelets
Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling ? self-similarity, long-range dependence and multi-fractals ? are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.