NOTE: This International Student Edition is not available in the USA or Canada.
Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.
The first edition became a widely used text in universities worldwide as well as the standard reference for professionals. The second edition featured new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming. The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, and substantial additions to the chapter on recurrences (now called "Divide-and-Conquer"). It features improved treatment of dynamic programming and greedy algorithms and a new notion of edge-based flow in the material on flow networks. Many new exercises and problems have been added for this edition.
Thomas H. Cormen is Professor of Computer Science and former Director of the Institute for Writing and Rhetoric at Dartmouth College.
Charles E. Leiserson is Professor of Computer Science and Engineering at the Massachusetts Institute of Technology.
Ronald L. Rivest is Andrew and Erna Viterbi Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology.
Clifford Stein is Professor of Industrial Engineering and Operations Research at Columbia University.
978-0-262-53305-8 Softcover
978-0-262-03384-8 Hardcover
Oxford Mathematical Monographs
432 pages | 26 illustrations | 234x156mm
978-0-19-954164-5 | Hardback | September 2009 (estimated)
Generalized dynamic thermoelasticity is a vital area of research in continuum mechanics, free of the classical paradox of infinite propagation speeds of thermal signals in Fourier-type heat conduction. Besides that paradox, the classical dynamic thermoelasticity theory offers either unsatisfactory or poor descriptions of a solid's response at low temperatures or to a fast transient loading (say, due to short laser pulses). Several models have been developed and intensively studied over the past four decades, yet this book, which aims to provide a point of reference in the field, is the first monograph on the subject since the 1970s.
Thermoelasticity with Finite Wave Speeds focuses on dynamic thermoelasticity governed by hyperbolic equations, and, in particular, on the two leading theories: that of Lord-Shulman (with one relaxation time), and that of Green-Lindsay (with two relaxation times). While the resulting field equations are linear partial differential ones, the complexity of the theories is due to the coupling of mechanical with thermal fields. The mathematical aspects of both theories - existence and uniqueness theorems, domain of influence theorems, convolutional variational principles - as well as with the methods for various initial/boundary value problems are explained and illustrated in detail and several applications of generalized thermoelasticity are reviewed.
Preface
Introduction
1: Fundamentals of linear thermoelasticity with finite wave speeds
2: Formulations of initial-boundary value problems
3: Existence and uniqueness theorems
4: Domain of influence theorems
5: Convolutional variational principles
6: Central equation of thermoelasticity with finite wave speeds
7: Exact aperiodic-in-time solutions of Green-Lindsay theory
8: Kirchhoff type formulas and integral equations in Green- Lindsay theory
9: Thermoelastic polynomials
10: Moving discontinuity surfaces
11: Time-periodic solutions
12: Physical aspects and applications of hyperbolic thermoelasticity
13: Nonlinear hyperbolic rigid heat conductor of the Coleman type
References
Index
288 pages | 234x156mm
978-0-19-957511-4 | Hardback | October 2009 (estimated)
Clear and engaging writing
A thought provoking approach to metaphysics
Provides an original treatment of both historical and contemporary issues
No knowledge of physics assumed
Time, Space, and Metaphysics engages with major philosophical questions concerning time and space, a framework for the investigation being provided by the debate between the absolutists and the relationists, so between Newton and Leibniz, and their followers. The investigation brings to the fore questions of the nature and reality of time and space, and leads on to more recent debates, such as those relating to anti-realism, time travel, temporal parts, geometry, convention, and the infinitude of time and space. These in turn raise more general issues, issues involving such concepts as those of identity, objectivity, causation, facts, and verifiability. Their examination falls within metaphysics, thought of as the investigation and analysis of fundamental philosophical concepts, but there is also metaphysics of a more contentious character, where the subject-matter is provided by propositions which transcend what can be known either through experience or by pure reasoning. In this connection, a central aim is to show how, without dismissing them as nonsensical, we may arrive at a fruitful interpretation of such propositions.
Readership: Advanced students and scholars of philosophy.
1: Conceptions of Time and Space
2: Time, Order, and Direction
3: Time and Tense
4: Observer-Dependence
5: The Past
6: The Future
7: Grammar and Ontology
8: Equality of time intervals
9: Temporal asymmetries
10: Space
11: Time and Change
References
Cloth | November 2009
248 pp. | 6 x 9
This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available.
Harald Niederreiter is professor of mathematics and computer science at the National University of Singapore. Chaoping Xing is professor of mathematics at the Nanyang Technological University in Singapore. They are the authors of Rational Points on Curves over Finite Fields: Theory and Applications.
Preface ix
Chapter 1: Finite Fields and Function Fields 1
1.1 Structure of Finite Fields 1
1.2 Algebraic Closure of Finite Fields 4
1.3 Irreducible Polynomials 7
1.4 Trace and Norm 9
1.5 Function Fields of One Variable 12
1.6 Extensions of Valuations 25
1.7 Constant Field Extensions 27
Chapter 2: Algebraic Varieties 30
2.1 Affine and Projective Spaces 30
2.2 Algebraic Sets 37
2.3 Varieties 44
2.4 Function Fields of Varieties 50
2.5 Morphisms and Rational Maps 56
Chapter 3: Algebraic Curves 68
3.1 Nonsingular Curves 68
3.2 Maps Between Curves 76
3.3 Divisors 80
3.4 Riemann-Roch Spaces 84
3.5 Riemann's Theorem and Genus 87
3.6 The Riemann-Roch Theorem 89
3.7 Elliptic Curves 95
3.8 Summary: Curves and Function Fields 104
Chapter 4: Rational Places 105
4.1 Zeta Functions 105
4.2 The Hasse-Weil Theorem 115
4.3 Further Bounds and Asymptotic Results 122
4.4 Character Sums 127
Chapter 5: Applications to Coding Theory 147
5.1 Background on Codes 147
5.2 Algebraic-Geometry Codes 151
5.3 Asymptotic Results 155
5.4 NXL and XNL Codes 174
5.5 Function-Field Codes 181
5.6 Applications of Character Sums 187
5.7 Digital Nets 192
Chapter 6: Applications to Cryptography 206
6.1 Background on Cryptography 206
6.2 Elliptic-Curve Cryptosystems 210
6.3 Hyperelliptic-Curve Cryptography 214
6.4 Code-Based Public-Key Cryptosystems 218
6.5 Frameproof Codes 223
6.6 Fast Arithmetic in Finite Fields 233
A Appendix 241
A.1 Topological Spaces 241
A.2 Krull Dimension 244
A.3 Discrete Valuation Rings 245
Bibliography 249
Index 257
Cloth | February 2010
376 pp. | 6 x 9 | 88 line illus. 135 tables.
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part.
Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization.
This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
Gene H. Golub (1932-2007) was the Fletcher Jones Professor of Computer Science at Stanford University and the coauthor of Matrix Computations. Gerard Meurant, the author of three books on numerical linear algebra, has worked in scientific computing for almost four decades. He is retired from France's Commissariat a l'Energie Atomique.