Fosters an in-depth understanding of the concepts covered Offers a concise discussion of the main pillars of Shannon’s information theory Is ideal for a one-semester foundational course on information theory This book presents a succinct and mathematically rigorous treatment of the main pillars of Shannon’s information theory, discussing the fundamental concepts and indispensable results of Shannon’s mathematical theory of communications. It includes five meticulously written core chapters (with accompanying problems), emphasizing the key topics of information measures; lossless and lossy data compression; channel coding; and joint source-channel coding for single-user (point-to-point) communications systems. It also features two appendices covering necessary background material in real analysis and in probability theory and stochastic processes. The book is ideal for a one-semester foundational course on information theory for senior undergraduate and entry-level graduate students in mathematics, statistics, engineering, and computing and information sciences. A comprehensive instructor’s solutions manual is available.
Due 2018-05-21 1st ed. 2018, XIV, 358 p. 30 illus.
Hardcover ISBN 978-981-10-8000-5
Provides an essential overview of computational conformal geometry applied to engineering fields Explores fundamental problems in specific fields of application Developed from courses given by the authors at the University of Louisiana at Lafayette, the State University of New York at Stony Brook, and Tsinghua University This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields. It introduces readers to conformal geometry theory and discusses implementation issues from an engineering perspective. The respective chapters explore fundamental problems in specific fields of application, and detail how computational conformal geometric methods can be used to solve them in a theoretically elegant and computationally efficient way. The fields covered include computer graphics, computer vision, geometric modeling, medical imaging, and wireless sensor networks. Each chapter concludes with a summary of the material covered and suggestions for further reading, and numerous illustrations and computational algorithms complement the text. The book draws on courses given by the authors at the University of Louisiana at Lafayette, the State University of New York at Stony Brook, and Tsinghua University, and will be of interest to senior undergraduates, graduates and researchers in computer science applied Mathematics and engineering.
Due 2018-06-02 1st ed. 2018, XII, 304 p. With online files/update.
Hardcover ISBN 978-3-319-75330-0
Provides a gentle, yet thorough, introduction to abstract algebra Includes careful proofs of theorems and numerous worked examples Written in an informal, readable style This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.
Due 2018-05-22 1st ed. 2018, X, 281 p. 7 illus.
Softcover ISBN 978-3-319-77648-4
Contains applications in mathematics, engineering, economics, and optimization theory Can be used as a research monograph or a graduate textbook Thorough update of reference list This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some of the most advanced topics. The new edition includes considerably more material emphasizing the rich applicability of convex analysis to concrete examples. Chapters 4, 5, and 6 are entirely new, covering important topics such as the Hardy-Littlewood-Polya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory. This book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering, and it can also be used as a reference text for graduate courses on convex functions and applications.
Due 2018-06-03 2nd ed. 2018, XVI, 414 p.
Hardcover ISBN 978-3-319-78336-9
A Functional Approach Collects recent results on transfer operators, anisotropic Banach spaces, and dynamical determinants of hyperbolic systems Gives a self-contained account of proofs (some of them new) starting with the basic case of expanding maps for easier readability Each chapter ends with a list of open research problems The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley?Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.
Due 2018-06-08 1st ed. 2018, XIV, 291 p. 1 illus.
Hardcover ISBN 978-3-319-77660-6
Presents the basic theory of quasivarieties in an accessible manner Provides examples throughout, showing how the algorithms are applied in practice Includes appendix with recent developments and references to the literature This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The book starts with a clear and comprehensive presentation of the basic structure theory of quasivariety lattices, and then develops new methods and algorithms for their analysis. Particular attention is paid to the role of quasicritical algebras. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures. An appendix gives an overview of the theory of quasivarieties. Extensive references to the literature are provided throughout.
Due 2018-06-13 1st ed. 2018, X, 179 p.
Hardcover ISBN 978-3-319-78234-8
Presents several strands of the most recent research on the calculus of variations Builds on powerful analytical techniques such as Young measures to provide the reader with an effective toolkit for the analysis of variational problems in the vectorial setting Includes 120 exercises to consolidate understanding This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the EulerLagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and -convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.
Due 2018-05-22 1st ed. 2018, XI, 409 p. 36 illus., 2 illus. in color.
Softcover ISBN 978-3-319-77636-1