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Advanced Color Image Processing and Analysis

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出版日:2004/05/06 作者:J. J. Duistermaat  出版社:Cambridge Univ Pr  裝訂:精裝
Two volume set of the authors' comprehensive and innovative work on multidimensional real analysis. These books are based on extensive teaching experience at Utrecht University and give a thorough account of analysis in multidimensional Euclidean space. They are an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects these books present an original treatment of the subject and they contain many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make these books ideal as either the text for a course, a source of problems for a seminar or for self study.
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Fourier Optics ─ An Introduction
滿額折
出版日:2004/05/05 作者:E. G. Steward  出版社:Dover Pubns  裝訂:平裝
Appropriate for engineering and physics students, this undergraduate textbook introduces Fourier series and transforms in the optical context, describes optical image formation and processing under co
優惠價: 9 853
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Analyzing Syntax:A Lexical-Functional Approach
90 折
出版日:2004/04/08 作者:Paul R. Kroeger  出版社:Cambridge Univ Pr  裝訂:平裝
Analyzing Syntax: A Lexical-Functional Approach is a comprehensive and accessible 2004 textbook on syntactic analysis, designed for students of linguistics at advanced undergraduate or graduate level. Working within the 'Lexical Functional Grammar' (LFG) approach, it provides students with a framework for analyzing and describing grammatical structure, using extensive examples from both European and non-European languages. Topics covered include: tests for constituency, passivization and other relation-changing processes, reflexive pronouns, the control relation, Topic and Focus, relative clauses and Wh-questions, causative constructions, serial verbs, 'quirky case', and ergativity. As well as building on what linguists have learned about language in general, particular attention is paid to the unique features of individual languages. While its primary focus is on syntactic structure, the book also deals with aspects of meaning, function and word-structure that are directly relevant to
優惠價: 9 2456
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出版日:2004/04/05 作者:Janet M. Box-Steffensmeier  出版社:Cambridge Univ Pr  裝訂:精裝
Event History Modeling, first published in 2004, provides an accessible guide to event history analysis for researchers and advanced students in the social sciences. The substantive focus of many social science research problems leads directly to the consideration of duration models, and many problems would be better analyzed by using these longitudinal methods to take into account not only whether the event happened, but when. The foundational principles of event history analysis are discussed and ample examples are estimated and interpreted using standard statistical packages, such as STATA and S-Plus. Critical innovations in diagnostics are discussed, including testing the proportional hazards assumption, identifying outliers, and assessing model fit. The treatment of complicated events includes coverage of unobserved heterogeneity, repeated events, and competing risks models. The authors point out common problems in the analysis of time-to-event data in the social sciences and make
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Event History Modeling
90 折
出版日:2004/04/01 作者:Janet M. Box-Steffensmeier  出版社:Cambridge Univ Pr  裝訂:平裝
Event History Modeling, first published in 2004, provides an accessible guide to event history analysis for researchers and advanced students in the social sciences. The substantive focus of many social science research problems leads directly to the consideration of duration models, and many problems would be better analyzed by using these longitudinal methods to take into account not only whether the event happened, but when. The foundational principles of event history analysis are discussed and ample examples are estimated and interpreted using standard statistical packages, such as STATA and S-Plus. Critical innovations in diagnostics are discussed, including testing the proportional hazards assumption, identifying outliers, and assessing model fit. The treatment of complicated events includes coverage of unobserved heterogeneity, repeated events, and competing risks models. The authors point out common problems in the analysis of time-to-event data in the social sciences and make
優惠價: 9 1813
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出版日:2004/03/18 作者:J. C. van den Berg  出版社:Cambridge Univ Pr  裝訂:平裝
This book surveys the application of the recently developed technique of the wavelet transform to a wide range of physical fields, including astrophysics, turbulence, meteorology, plasma physics, atomic and solid state physics, multifractals occurring in physics, biophysics (in medicine and physiology) and mathematical physics. The wavelet transform can analyze scale-dependent characteristics of a signal (or image) locally, unlike the Fourier transform, and more flexibly than the windowed Fourier transform developed by Gabor fifty years ago. The continuous wavelet transform is used mostly for analysis, but the discrete wavelet transform allows very fast compression and transmission of data and speeds up numerical calculation, and is applied, for example, in the solution of partial differential equations in physics. This book will be of interest to graduate students and researchers in many fields of physics, and to applied mathematicians and engineers interested in physical application.
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出版日:2004/03/04 作者:Joseph Rudnick  出版社:Cambridge Univ Pr  裝訂:精裝
Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.
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Cognitive Linguistics
90 折
出版日:2004/02/01 作者:William Croft  出版社:Cambridge Univ Pr  裝訂:平裝
Cognitive Linguistics argues that language is governed by general cognitive principles, rather than by a special-purpose language module. This introductory textbook surveys the field of cognitive linguistics as a distinct area of study, presenting its theoretical foundations and the arguments supporting it. Clearly organised and accessibly written, it provides a useful introduction to the relationship between language and cognitive processing in the human brain. It covers the main topics likely to be encountered in a course or seminar, and provides a synthesis of study and research in this fast-growing field of linguistics. The authors begin by explaining the conceptual structures and cognitive processes governing linguistic representation and behaviour, and go on to explore cognitive approaches to lexical semantics, as well as syntactic representation and analysis, focusing on the closely related frameworks of cognitive grammar and construction grammar. This much-needed introduction w
優惠價: 9 2164
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出版日:2004/01/15 作者:Michael F. Goodchild (EDT); Donald G. Janelle (EDT)  出版社:Oxford Univ Pr on Demand PBKUOXAR  裝訂:精裝
Spatial analysis assists theoretical understanding and empirical testing in the social sciences, and rapidly expanding applications of geographic information technologies have advanced the spatial dat
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出版日:2004/01/01 作者:Mario Paz; William E. Leigh  出版社:Kluwer Academic Pub  裝訂:精裝
The analysis and design of structures subjected to time-dependent dynamic loads are explained by Paz (U. of Louisville) and Leigh (U. of Central Florida) at a level suitable for advanced undergraduate
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出版日:2003/12/04 作者:Sajal Lahiri  出版社:Cambridge Univ Pr  裝訂:精裝
The existence of firms with different levels of efficiency within a country plays an important role in this in-depth analysis of industrial and trade policies in a multi-country trade-theoretic framework. Sajal Lahiri and Yoshiyasu Ono examine various industrial policies, R&D subsidies and trade policies under conditions of imperfect competition in a product market created by the presence of Cournot oligopolistic interdependence in production. Trade is defined broadly to include trade in commodity as well as trade in capital, specifically foreign direct investment. While the first part of the book focuses on commodity trade and assumes full employment, the latter considers foreign direct investment and assumes the presence of unemployment. Given the importance of industrial policies and the prevalence of imperfect competition, together with ongoing attention to theoretical issues concerning industrial economics, this research will excite interest amongst researchers, advanced students
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The Encyclopedia of Sewing Techniques: A Step-By-Step Visual Directory, With an Inspirational Gallery of Finished Works
滿額折
出版日:2003/12/03 作者:Wendy Gardiner  出版社:Running Pr Book Pub  裝訂:精裝
This complete, step-by-step guide to hand and machine sewing combines basic know-how for the beginner with advanced techniques for the more experienced. Beautifully illustrated with full-color photog
優惠價: 79 839
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The Limits of Symbolic Reform:The New Deal and Taxation, 19331939
90 折
出版日:2003/11/13 作者:Mark H. Leff  出版社:Cambridge Univ Pr  裝訂:平裝
In The Limits of Symbolic Reform, Mark Leff examines the gap between politics and economics, between symbol and substance in the New Deal. The New Deal never lacked for controversy, and tax policy reliably aroused the fiercest of emotions. Franklin Roosevelt's celebrated tax reform proposals - presented amidst verbal barrages against 'economic royalists' and the 'unjust concentration of wealth and economic power' - signified almost nothing in terms of revenue. Cosmetic higher rates on upper-income brackets generated far less revenue than lower-profile New Deal taxes on agricultural products, liquor, and payrolls (through social security) that burdened low incomes. But while 'soak the rich' tax initiatives were economically inconsequential, they were politically crucial to the image of compassion and action projected by the New Deal. Leff's analysis clarifies the reform priorities and the balance of political and economic that produced this paradoxical New Deal tax machinery.
優惠價: 9 1403
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出版日:2003/11/01 作者:Ron Kimmel  出版社:Springer Verlag  裝訂:精裝
Numerical Geometry of Images examines computational methods and algorithms in image processing. It explores applications like shape from shading, color-image enhancement and segmentation, edge integr
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出版日:2003/10/30 作者:A. C. Davison  出版社:Cambridge Univ Pr  裝訂:精裝
Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.
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出版日:2003/10/16 作者:Kanetada Nagamine  出版社:Cambridge Univ Pr  裝訂:精裝
Muons are unstable elementary particles that are found in space, which can also be produced in particle accelerators to an intensity a billion times greater than that occurring naturally. This book describes the various applications of muons across the spectrum of the sciences and engineering. Scientific research using muons relies both on their basic properties as well as the microscopic interaction between them and surrounding particles such as nuclei, electrons, atoms and molecules. Examples of research that can be carried out using muons include muon catalysis for nuclear fusion, the application of muon spin probes to study microscopic magnetic properties of advanced materials, electron labelling to help in the understanding of electron transfer in proteins, and non-destructive element analysis of the human body. Cosmic ray muons can also be used to study the inner structure of volcanoes.
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出版日:2003/09/25 作者:Edward Ziter  出版社:Cambridge Univ Pr  裝訂:精裝
The Orient on the Victorian Stage examines the representation of the Middle East in a variety of nineteenth-century entertainment forms, such as panoramas, melodrama, pantomime, ballet and opera. Ziter argues that changes in stage craft reflected the emerging idea that the significance of objects was evident in contextual relations, and relates the development of this stage craft to orientalist exhibitions and museum displays. Unlike other theatre histories and studies of orientalism, this book examines broader strategies of spatial representation and focuses on performance and popular culture. Ziter explores the plays and productions at a number of venues, including Drury Lane, Covent Garden, the Great Exhibition of 1851, the Crystal Palace at Sydenham, and the British Museum, among others. The book also includes an analysis of Byron's image in the theatre and an analysis of his play Sardanapalus.
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出版日:2003/09/16 作者:Dunis  出版社:John Wiley & Sons Inc  裝訂:精裝
This book provides a manual on quantitative financial analysis. Focusing on advanced methods for modelling financial markets in the context of practical financial applications, it will cover data, sof
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出版日:2003/08/28 作者:Helmut Kronmüller  出版社:Cambridge Univ Pr  裝訂:精裝
The main theme of this book is micromagnetism and microstructure as well as the analysis of the relations between characteristic properties of the hysteresis loop and microstructure. Also presented is an analysis of the role of microstructure in the fundamental magnetic properties (for example, magnetorestriction or critical behaviour) of crystalline and amorphous alloys. The authors apply the theory of micromagnetism to all aspects of advanced magnetic materials including domain patterns and magnetization processes under the influence of defect structures. Coverage includes modern developments in computational micromagnetism and its application to spin structures of small particles and platelets. It will be of interest to researchers and graduate students in condensed matter, physics, electrical engineering and materials science, as well as to industrial researchers working in the electrotechnical and recording industry.
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出版日:2003/07/03 作者:Graeme L. Cohen  出版社:Cambridge Univ Pr  裝訂:精裝
Designed for one-semester courses at the senior undergraduate level, this 2003 book will appeal to mathematics undergraduates, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance. Topics such as completeness and compactness are approached initially through convergence of sequences in metric space, and the emphasis remains on this approach. However, the alternative topological approach is described in a separate chapter. This gives the book more flexibility, making it especially useful as an introduction to more advanced areas such as functional analysis. Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for what further developments might look like. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, nu
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A Course in Modern Analysis and its Applications
90 折
出版日:2003/07/03 作者:Graeme L. Cohen  出版社:Cambridge Univ Pr  裝訂:平裝
Designed for one-semester courses at the senior undergraduate level, this 2003 book will appeal to mathematics undergraduates, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance. Topics such as completeness and compactness are approached initially through convergence of sequences in metric space, and the emphasis remains on this approach. However, the alternative topological approach is described in a separate chapter. This gives the book more flexibility, making it especially useful as an introduction to more advanced areas such as functional analysis. Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for what further developments might look like. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, nu
優惠價: 9 2866
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出版日:2003/06/30 作者:Brocklebank  出版社:John Wiley & Sons Inc  裝訂:平裝
Easy-to-read and comprehensive, this book shows how the SAS System performs multivariate time series analysis and features the advanced SAS procedures STATSPACE, ARIMA, and SPECTRA. The interrelations
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A Primer of Analytic Number Theory:From Pythagoras to Riemann
90 折
出版日:2003/06/23 作者:Jeffrey Stopple  出版社:Cambridge Univ Pr  裝訂:平裝
This 2003 undergraduate introduction to analytic number theory develops analytic skills in the course of studying ancient questions on polygonal numbers, perfect numbers and amicable pairs. The question of how the primes are distributed amongst all the integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeroes of his function, and the significance of the Riemann Hypothesis. Starting from a traditional calculus course and assuming no complex analysis, the author develops the basic ideas of elementary number theory. The text is supplemented by series of exercises to further develop the concepts, and includes brief sketches of more advanced ideas, to present contemporary research problems at a level suitable for undergraduates. In addition to proofs, both rigorous and heuristic, the book includes extensive graphics and tables to make analytic concepts as concrete as possible.
優惠價: 9 2515
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出版日:2003/06/23 作者:Jeffrey Stopple  出版社:Cambridge Univ Pr  裝訂:精裝
This 2003 undergraduate introduction to analytic number theory develops analytic skills in the course of studying ancient questions on polygonal numbers, perfect numbers and amicable pairs. The question of how the primes are distributed amongst all the integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeroes of his function, and the significance of the Riemann Hypothesis. Starting from a traditional calculus course and assuming no complex analysis, the author develops the basic ideas of elementary number theory. The text is supplemented by series of exercises to further develop the concepts, and includes brief sketches of more advanced ideas, to present contemporary research problems at a level suitable for undergraduates. In addition to proofs, both rigorous and heuristic, the book includes extensive graphics and tables to make analytic concepts as concrete as possible.
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出版日:2003/06/09 作者:E. T. Jaynes  出版社:Cambridge Univ Pr  裝訂:精裝
The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.
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出版日:2003/06/01 作者:Zbigniew Lubosny  出版社:Springer Verlag  裝訂:精裝
A comprehensive approach to Wind Turbine Generator Systems (WTGS) and their operation in dynamic electric power system analysis. The presented advanced models arose from the author's research. They de
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出版日:2003/05/29 作者:Stephen E. Derenzo  出版社:Cambridge Univ Pr  裝訂:精裝
This text describes in practical terms how to use a desk-top computer to monitor and control laboratory experiments. The author clearly explains how to design electronic circuits and write computer programs to sense, analyse and display real-world quantities, including displacement, temperature, force, sound, light, and biomedical potentials. The book includes numerous laboratory exercises and appendices that provide practical information on microcomputer architecture and interfacing, including complete circuit diagrams and component lists. Topics include analog amplification and signal processing, digital-to-analog and analog-to-digital conversion, electronic sensors and actuators, digital and analog interfacing circuits, and programming. Only a very basic knowledge of electronics is assumed, making it ideal for college-level laboratory courses and for practising engineers and scientists.
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Polyphenols contribute to the taste and color of tea and red wine and are increasingly recognized for their beneficial antioxidant effects in the body. Santos-Buelga (University of Salamanca, Spain) a
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Recycled Culture in Contemporary Art and Film
90 折
出版日:2003/05/01 作者:Vera Dika  出版社:Cambridge Univ Pr  裝訂:平裝
The reuse of images, plots and genres from film history has become prominent in contemporary culture. In this study, Vera Dika explores this phenomenon from a broad range of critical perspectives, examining works of art and film that resist the pull of the past. Dika provides an in-depth analysis of works in several media, including performance, photography, Punk film, and examples from mainstream American and European cinema. Proclaiming the renewed importance of the image and of genre, she investigates works as diverse as Cindy Sherman's Untitled Film Stills, Amos Poe's The Foreigner, Terence Malick's Badlands, and Francis Ford Coppola's One from the Heart. Her study positions avant-garde art work within the context of contemporary mainstream film practice, as well as in relationship to their historical moment.
優惠價: 9 1696
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Political Parties and Elections: Legislating for Representative Democracy
滿額折
出版日:2003/04/24 作者:Anika Gauja  出版社:Ashgate Pub UK  裝訂:精裝
Political Parties and Elections presents a comparative analysis of the ways in which advanced industrial democracies seek to regulate the activities of political parties in electoral contests. Actual
定價:7875 元
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出版日:2003/04/21 作者:G. J. O. Jameson  出版社:Cambridge Univ Pr  裝訂:精裝
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
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The Prime Number Theorem
90 折
出版日:2003/04/21 作者:G. J. O. Jameson  出版社:Cambridge Univ Pr  裝訂:平裝
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
優惠價: 9 1871
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出版日:2003/04/14 作者:Elhanan Helpman  出版社:Cambridge Univ Pr  裝訂:精裝
This book contains fifteen major essays on international economics. The authors investigate five principal themes: theory, and empirics, of financial issues in open economies; economic growth; public economies; and political economy. Written to honor Professor Assaf Razin of Tel Aviv and Cornell Universities on the occasion of his sixtieth birthday, the essays pay close attention to policy issues as well as formal analysis. The contributors include renowned specialists in international economics based in North America, Europe, Israel, and China. This volume of advanced research will be of interest to scholars, policy makers, and advanced students alike.
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出版日:2003/03/17 作者:Ákos Seress  出版社:Cambridge Univ Pr  裝訂:精裝
Permutation group algorithms are one of the workhorses of symbolic algebra systems computing with groups. They played an indispensable role in the proof of many deep results, including the construction and study of sporadic finite simple groups. This book describes the theory behind permutation group algorithms, including developments based on the classification of finite simple groups. Rigorous complexity estimates, implementation hints, and advanced exercises are included throughout. The central theme is the description of nearly linear time algorithms, which are extremely fast both in terms of asymptotic analysis and of practical running time. A significant part of the permutation group library of the computational group algebra system GAP is based on nearly linear time algorithms. The book fills a significant gap in the symbolic computation literature. It is recommended for everyone interested in using computers in group theory, and is suitable for advanced graduate courses.
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出版日:2003/03/01 作者:Mangatiana A. Robdera  出版社:Springer Verlag  裝訂:平裝
This text introduces to undergraduates the more abstract concepts of advanced calculus, smoothing the transition from standard calculus to the more rigorous approach of proof writing and a deeper unde
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Goethe contra Newton:Polemics and the Project for a New Science of Color
90 折
出版日:2003/02/13 作者:Dennis L. Sepper  出版社:Cambridge Univ Pr  裝訂:平裝
This book explains the background and rationale of the German poet Johann Wolfgang von Goethe's notorious attack on Isaac Newton's classic theory of white light and colors. Though the merits of Goethe's color science, as advanced in his massive Zur Farbenlehre, have often been acknowledged, it has been almost unanimously proclaimed invalid as physics. How could Goethe have been so mistaken? In his book, Dennis Sepper shows that the condemnation of Goethe's attacks on Newton has been based on erroneous assumptions about the history of Newton's theory and the methods and goals of Goethe's color science. By illuminating the historical background and the experimental, methodological, and philosophical aspects of Goethe's work, the author shows that his color theory is in an important sense genuinely physical and that, as simultaneously poet, scientist, historian, and philosopher, Goethe managed to anticipate important twentieth-century research not only in the history and philosophy of sci
優惠價: 9 2398
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出版日:2003/02/01 作者:Chris Haywood; Mairtin Mac an Ghaill  出版社:Open Univ Pr  裝訂:平裝
“a sharp and impressive book, providing an excellent advanced introductory text to the field. The book combines an impressive range of contextual and theoretical analysis, suggests new directio
定價:3150 元
無庫存
Sets for Mathematics
90 折
出版日:2003/01/27 作者:F. William Lawvere  出版社:Cambridge Univ Pr  裝訂:平裝
Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure
優惠價: 9 2515
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出版日:2003/01/20 作者:F. William Lawvere  出版社:Cambridge Univ Pr  裝訂:精裝
Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure
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出版日:2003/01/13 作者:George Tourlakis  出版社:Cambridge Univ Pr  裝訂:精裝
This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.
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