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

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.

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.

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.

Suitable for the second-semester course in linear algebra, this work creates a bridge from linear algebra concepts to more advanced abstract algebra and matrix theory. It focuses on the development of the Moore-Penrose inverse. It provides MATLAB[registered] examples and exercises as well as homework problems and suggestions for further reading.

The ingratiating title notwithstanding, this is in no standard sense a text but a monograph, based largely upon the authors' research over a period of years, and intended to be read by sophisticated students of theoretical statistics. No exercises attach to the nine chapters, nor are they interrup

A rather pretty little book, written in the form of a text but more likely to be read simply for pleasure, in which the author (Professor Emeritus of Mathematics at the U. of Kansas) explores the analog of the theory of functions of a complex variable which comes into being when the complexes are re

"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."

Realizing the specific needs of first-year graduate students, this reference allows readers to grasp and master fundamental concepts in abstract algebra. Prepares students for further studies in the mathematical sciences. Includes self-test exercises.

This book presents a systematic, self-contained treatment of a new, more precise classification of Lipschitz mappings and its application in many topics of metric fixed point theory. The mean Lipschitz condition introduced by Goebel, Japón Pineda, and Sims is relatively easy to check and turns out to satisfy several principles: regulating the possible growth of the sequence of Lipschitz constants k(Tn), ensuring good estimates for k0(T) and k¿(T), and providing some new results in metric fixed point theory.

Intended for specialists in functional analysis and stability theory, this work presents a systematic exposition of estimations for norms of operator-valued functions, and applies the estimates to spectrum perturbations of linear operators and stability theory. The author demonstrates his own approach to spectrum perturbations.

Offers theoretical, algorithmic and computational guidelines for solving the frequently encountered linear-quadratic optimization problems. This textbook provides an overview of advances in control and systems theory, numerical line algebra, numerical optimization, scientific computations and software engineering.

This book provides a systematic treatment of properties common to the classifications of point sets. It unifies analogies between Baire category and Lebesgue measure by carrying general topological concepts to a higher level of abstraction. The book is intended for graduate mathematics students.

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.

Offers an introduction to differential geometry with applications to mechanics and physics. This title covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; and, tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms.

Presents a theory of difference and functional equations with argument based on a generalization of the Riemann integral introduced by N E Norlund. This title discusses linear transformations that state conditions for convergence of Newton series and Norlund sums.

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.

This book presents a systematic, self-contained treatment of a new, more precise classification of Lipschitz mappings and its application in many topics of metric fixed point theory. The mean Lipschitz condition introduced by Goebel, Japón Pineda, and Sims is relatively easy to check and turns out to satisfy several principles: regulating the possible growth of the sequence of Lipschitz constants k(Tn), ensuring good estimates for k0(T) and k¿(T), and providing some new results in metric fixed point theory.

Discusses the orderability of a group. This book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. It offers a fresh presentation of the theory of varieties of lattice-ordered groups.

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.

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.

This book gives an account of two celebrated theorems of Gelfand and Naimark for commutative C*-algebras, their tangled history, generalizations and applications, in a form accessible to mathematicians working in various applied fields, and also to students of pure and applied mathematics.

This book serves as an introductory text in mathematical programming and optimization for students having a mathematical background that includes one semester of linear algebra and a complete calculus sequence. It includes computational examples to aid students develop computational skills.

This book presents a systematic introduction to the theory of holomorphic mappings in normed spaces which has been scattered throughout the literature. It gives the necessary, elementary background for all branches of modern mathematics involving differential calculus in higher dimensional spaces.

Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for various principal types of partial differential equations. It covers methods of linear and nonlinear analysis, and the theory of differential equations in Banach spaces.

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.

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.

Discusses graph domination. This book covers various developments in domination in graphs and digraphs, dominating functions, and combinatorial problems on chessboards.