Bücher der Reihe CMS Books in Mathematics

A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations.

From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

The book is self-contained, with appendices covering results that are required, but not necessarily in the pre-requisite background of a student ready to choose an area for research in harmonic analysis.

The book is intended for those who love mathematics, including undergraduate students of mathematics, more experienced students and the vast unseen host of amateur mathematicians.

We shall consider convex functions from the most modern point of view: a function is de?ned to be convex whenever its epigraph, the set of the points lying above the graph, is a convex set. Except for trivial cases, the minimum value must be taken at a point where the function is not +?, hence at a point in the constraint set.

He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.

In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks.

This monograph leads the reader to the frontiers of the very latest research developments in what is regarded as the central zone of discrete geometry. It is constructed around four classic problems in the subject, including the Kneser-Poulsen Conjecture.

This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory.

This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis.

This book is devoted exclusively to Lebesgue spaces and their direct derived spaces. Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions and nonincreasing rearrangement.

Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research

This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.

Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This new edition adds material on semismooth optimization, as well as several new proofs.

The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.

Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysisProvides a good introduction to the topic

The authors provide a friendly introduction to the delights of algebraic number theory via Pell's Equation. The only prerequisites are knowledge of elementary number theory and abstract algebra. There are references for those following up on various topics.

An overview of the dramatic reorganization in reaction to N. Karmakar's seminal 1984 paper on algorithmic linear programming in the area of algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. Aimed at readers familiar with advanced calculus and numerical analysis.

The Kenneth May Lectures have never before been published in book form Important contributions to the history of mathematics by well-known historians of scienceShould appeal to a wide audience due to its subject area and accessibility

This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry.

Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research

This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures.

The objective of this book is to provide tools for solving problems which involve cubic number fields. Many such problems can be considered geometrically; both in terms of the geometry of numbers and geometry of the associated cubic Diophantine equations that are similar in many ways to the Pell equation. With over 50 geometric diagrams, this book includes illustrations of many of these topics. The book may be thought of as a companion reference for those students of algebraic number theory who wish to find more examples, a collection of recent research results on cubic fields, an easy-to-understand source for learning about Voronoi¿s unit algorithm and several classical results which are still relevant to the field, and a book which helps bridge a gap in understanding connections between algebraic geometry and number theory.The exposition includes numerous discussions on calculating with cubic fields including simple continued fractions of cubic irrational numbers, arithmetic using integer matrices, ideal class group computations, lattices over cubic fields, construction of cubic fields with a given discriminant, the search for elements of norm 1 of a cubic field with rational parametrization, and Voronoi's algorithm for finding a system of fundamental units. Throughout, the discussions are framed in terms of a binary cubic form that may be used to describe a given cubic field. This unifies the chapters of this book despite the diversity of their number theoretic topics.

This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures.

This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Coverage includes Radon-Nikodym property, finite-dimensional spaces and local theory on tensor products, and more.

This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible.