Bøger i Chapman & Hall/CRC Pure and Applied Mathematics serien

Containing data on number theory, encryption schemes, and cyclic codes, this textbook presents coding theory, construction, encoding, and decoding of specific code families. Introducing the mathematics as it is needed and providing exercises with solutions, it includes a section on cryptography, designed for an introductory course on the subject.

This book represents the current (1985) state of knowledge about Zariski surfaces and related topics in differential equations in characteristic p > 0. It is aimed at research mathematicians and graduate and advanced undergraduate students of mathematics and computer science.

This book presents to the reader a modern axiomatic construction of three-dimensional Euclidean geometry in a rigorous and accessible form. It is helpful for high school teachers who are interested in the modernization of the teaching of geometry.

This book includes information on elementary general topology, the Cauchy Integral Theorem and concepts of homology and homotopy in their application to the Cauchy theory. It is intended for an introductory course in complex analysis at the first-year graduate and advanced undergraduate level.

Covers comodules, rational modules and bicomodules; cosemisimple, semiperfect and co-Frobenius algebras; bialgebras and Hopf algebras; actions and coactions of Hopf algebras on algebras; and, finite dimensional Hopf algebras, with the Nicholas-Zoeller and Taft-Wilson theorems and character theory.

This book explores the use of the concept of biorthogonality and discusses the various recurrence relations for the generalizations of the method of moments, the method of Lanczos, and the biconjugate gradient method. It is helpful for researchers in numerical analysis and approximation theory.

Covers important aspects of symmetric structures in function of a single real variable. This book provides a historical perspective, proofs and useful methods for addressing problems. It provides assistance for real analysis problems involving symmetric derivatives, symmetric continuity and local symmetric structure of sets or functions.

This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.

Intends to bridge the gap between modern differential geometry and the mathematical physics of general relativity. This text includes material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, and the generic condition.

A textbook for either a semester or year course for graduate students of mathematics who have had at least one course in topology. Introduces continuum theory through a combination of classical and modern techniques. Annotation copyright Book News, Inc. Portland, Or.

A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu

This book introduces both the theory and applications of elementary analysis, with emphasis on the genesis and resolution of a variety of applied problems. It is helpful for the motivated student whose mathematical background consists of only a two-or three-semester calculus sequence.

Describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types. This work provides a review of the various aspects of measure and integration theory using examples, exercises and applications. It is suitable for pure and applied mathematicians and mathematical analysts.

This book deals with solutions of second order, linear, parabolic partial differential equations on an infinite strip emphasizing their integral representation, their initial values in several senses, and the relations between these. It is useful for graduate students, analysts and specialists.

Presents the fundamental axioms of the real number system. This book also features the core of real analysis. It presents the essentials needed for analysis, including the concepts of sets, relations, and functions. It covers the theory of calculus on the real line, exploring limits, convergence tests.

Cover the structure theory of semigroups. This title examines constructions and descriptions of semigroups and emphasizes finite, commutative, regular and inverse semigroups. It introduces various structure theorems on regular and commutative semigroups.

Exploring the qualitative aspects of periodic solutions of ODEs, this title presents the treatment of two-dimensional systems as well as periodic solutions in small parameter problems. It illustrates theorems with various examples, and provides an account of the Bendixson theory of solutions of two-dimensional autonomous systems.

This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems.

Suitable for a one-semester course in linear algebra for graduate or upper-level undergraduate students of mathematics and engineering, this title employs a matrix perspective, and emphasizes training in definitions, theorems, and proofs.

Covers the results of the theory of non-commutative semigroup rings.

This outstanding reference presents current, state-of-the-art research on importantproblems of finite-dimensional nonlinear optimal control and controllability theory

This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.

Suitable for specialists in functional analysis and stability theory, this work presents an exposition of estimations for norms of operator-valued functions, and applies the estimates to spectrum perturbations of linear operators and stability theory. It demonstrates the author's own approach to spectrum perturbations.

Addresses linear algebra from the basics to the spectral theorem and examines a range of topics in multivariable calculus. This title introduces the derivative as a linear transformation, presents linear algebra in a concrete context based on complementary ideas in calculus, and explains differential forms on Euclidean space.

Features a theoretical framework to model phenomena with discontinuous changes. This book presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations. It also applies this method to derive suitable fixed point theorems in ordered abstract spaces.

Offers an overview of the basic theories and techniques of functional analysis and its applications. This work explores three fundamental results on Banach spaces, together with Grothendieck's structure theorem for compact sets in Banach spaces and Helley's selection theorem. It also examines vector topologies and vector bornologies.

This book offers vital background information on methods for solving hard classification problems of algebraic structures. It explains how algebraists deal with the problem of the structure of modules over rings and how they make use of these structures to classify rings.

This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.

Presents an introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. This work contains information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.