Books in the Chapman & Hall/CRC Pure and Applied Mathematics series

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.

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 an introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M Sato and his colleagues. It also reviews hyperfunction-microfunction theory and the theory of D-modules.

Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. This book covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, and projective algebraic sets.

Explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and number theory. This work clarifies foundational concepts such as symmetric and limiting distributions of products. It describes models of interactive particles.

This book provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a new chapter that introduces the theory of separable algebras. It presents complete proofs of all the main results and incorporates many examples to enable a better understanding.

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.

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.

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.