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 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.

Presents the concepts of type dimension, a natural class, and a type submodule, by exploring how they enter into much of ring and module theory. This book develops the foundations of the subject and the advanced theorems. It is suitable for those with some background in basic ring and module theory.

Presents important results in classical analysis, wavelets, and interpolation theory. This book contains topics such as Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, and various measures of the smoothness of functions.

With many examples and historical notes, this book provides a treatment of the Hahn-Banach theorem. It explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes a chapter on vector-valued Hahn-Banach theorems.

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.

Offers a self-contained account of integro-differential equations of the Barbashin type and partial integral operators. This title presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results.

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.

Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. This book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.

This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.

"Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."

Covers design methods for optimal (or quasioptimal) control algorithms in the form of synthesis for deterministic and stochastic dynamical systems - with applications in aerospace, robotic, and servomechanical technologies. This title provides fresh results on exact and approximate solutions of optimal control problems.

Presents a study of linear abstract degenerate differential equations, using the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. This title describes the results on PDEs and algebraic-differential equations.

Utilizes linear algebra and operator techniques to develop classical and modern results in linear systems analysis and control design. This title presents stability and performance results for linear systems, provides a geometric perspective on controllability and observability, and develops state space realizations of transfer functions.

Focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry.

A text for mathematics courses that covers the basics such as relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It includes material on normal forms and Goodstein sequences. It provides important ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.

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

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.

Serves as an introduction for solving differential equations using Lie's theory and related results. This book covers Loewy's theory, Janet bases, the theory of continuous groups of a 2-D manifold, Lie's symmetry analysis, and equivalence problems.

A comprehensive presentation of abstract algebra and a treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

Presents an account of the theory of real function algebras. This volume includes: an introduction to real Banach algebras; various generalizations of the Stone-Weierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and, a bibliography.

Offers a treatise on finite difference inequalities that have important applications to theories of various classes of finite difference and sum-difference equations. This title includes several linear and nonlinear finite difference inequalities.

This classic text provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then introducing a more general treatment based on abstract notions characterized by axioms and with less geometric content. Packed with new exercises and material, the long-awaited second edition of this highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students, instructors, and mathematicians.

Contains the contributions of 45 internationally distinguished mathematicians. This work covers various areas of approximation theory - written in honor of the pioneering work of Arun K Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions.

Addresses various topics in Fourier series, emphasizing the concept of approximate identities and presenting applications, particularly in time series analysis. This title stresses in the idea of homogenous Banach spaces and provides results. It utilizes techniques from functional analysis and measure theory.

Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. This title covers fractality and Fredholmness. It explains the phenomena of the asymptotic splitting of the singular values, and more.

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.

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.

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.