Bøger i Universitext serien

Easily accessible Includes recent developmentsAssumes very little knowledge of differentiable manifolds and functional analysisParticular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

They coined the term symbolic dynamics and began to study sequence spaces with the shift transformation as dynamical systems. Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics.

This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry.

Translated from the French, this book is an introduction to first-order model theory. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.

With an Appendix by P.A. Meyer

Based on courses taught at the University of Dublin, Carnegie Mellon University, and mostly at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view.

Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena.

Linear Programming Duality is one of the cornerstones in combinatorial optimization. Giving an elementary introduction to the theory of oriented matroids, this book presents an approach which clarifies the theoretical basis of linear programming and also simplifies the proofs of standard results.

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem.

A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It also includes the theory of stationary random processes, martingales, generalized random processes, and Brownian motion.

This introductory text is the first book about quantum principal bundles and their quantum connections which are natural generalizations to non-commutative geometry of principal bundles and their connections in differential geometry.

Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus. From the reviews:"Introduction to Stochastic Integration is exactly what the title says.

Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way.

A set of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics.

This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics.

From the reviews: "Do you know M.Padberg's Linear Optimization and Extensions? [...] Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. [...] For those who strive for good exercises and case studies for LP this is an excellent volume."

A compilation of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics.

This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.

Here is a rigorous introduction to solution methods of stochastic control problems for jump diffusions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Levy processes, and a section on optimal stopping with delayed information.

A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces.

Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations.

This book uses a distinctly applied framework to present the most important topics in stochastic processes, including Gaussian and Markovian processes, Markov Chains, Poisson processes, Brownian motion and queueing theory.

This book is the result of reworking part of a rather lengthy course of lectures of which we delivered several versions at the Leningrad and Moscow Universities. In these lectures we presented an introduction to the fundamental topics of topology: homology theory, homotopy theory, theory of bundles, and topology of manifolds.

This book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas.

This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space.

This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.

From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions."

The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces.