Universitext - Böcker

Algebraic Geometry is a fascinating branch of Mathematics that combines methods from both Algebra and Geometry. It transcends the limited scope of pure Algebra by means of geometric construction principles. Putting forward this idea, Grothendieck ...

Läs mer »

There are numbers of all kinds: rational, real, complex, p-adic, and more. The p-adic numbers are not as well known as the others, but they play a fundamental role in number theory and in other parts of mathematics, capturing information related t...

Läs mer »

This is an introductory textbook of linear programming, written mainly for students of computer science and mathematics. Our guiding phrase is, "what every theoretical computer scientist should know about linear programming".¿The book is relativel...

Läs mer »

The first two chapters of this book have been thoroughly revised and sig nificantly expanded. Sections have been added on elementary methods of in tegration (on homogeneous and inhomogeneous first-order linear equations and on homogeneous and quas...

Läs mer »

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativi...

Läs mer »

The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics cov...

Läs mer »

The following lecture notes correspond to a course taught for several years, first at the University of Paris-Nord (France) and then at the University of Bologna (Italy). They are mainly addressed to nonspecialists in the subject, and their purpos...

Läs mer »

This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotop...

Läs mer »

This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background ma...

Läs mer »

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book prese...

Läs mer »

Complex dynamics is today very much a focus of interest. Though several fine expository articles were available, by P. Blanchard and by M. Yu. Lyubich in particular, until recently there was no single source where students could find the material ...

Läs mer »

This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields. Arithmetic topology is now becoming a powerful gu...

Läs mer »

This textbook presents the spectral theory of self-adjoint operators on Hilbert space and its applications in quantum mechanics. Based on a course taught by the author in Paris, the book not only covers the mathematical theory but also provides it...

Läs mer »

Discrete dynamical systems are essentially iterated functions. Given the ease with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamica...

Läs mer »

The abstract branch of theoretical computer science known as Computation Theory typically appears in undergraduate academic curricula in a form that obscures both the mathematical concepts that are central to the various components of the theory a...

Läs mer »

The second part of the book concludes with Plancherel's theorem in Chapter 8. This theorem is a generalization of the completeness of the Fourier series, as well as of Plancherel's theorem for the real line. The third part of the book is intended ...

Läs mer »

Homological Algebra has grown in the nearly three decades since the rst e- tion of this book appeared in 1979. Two books discussing more recent results are Weibel, An Introduction to Homological Algebra, 1994, and Gelfand- Manin, Methods of Homolo...

Läs mer »

If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of li...

Läs mer »

Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical g...

Läs mer »

In the Leibniz-Newton calculus, one learns the di?erentiation and integration of deterministic functions. A basic theorem in di?erentiation is the chain rule, which gives the derivative of a composite of two di?erentiable functions. The chain rule...

Läs mer »

From Math Reviews: "This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in...

Läs mer »

Sequential Dynamical Systems (SDS) are a class of discrete dynamical systems which significantly generalize many aspects of systems such as cellular automata, and provide a framework for studying dynamical processes over graphs. This text is the f...

Läs mer »

ThetheoryofstronglycontinuoussemigroupsoflinearoperatorsonBanach spaces, operator semigroups for short, has become an indispensable tool in a great number of areas of modern mathematical analysis. In our Springer Graduate Text [EN00] we presented ...

Läs mer »

This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on locatedness in normed spaces ...

Läs mer »

Applied Stochastic Processes uses a distinctly applied framework to present the most important topics in the field of stochastic processes. Key features: -Presents carefully chosen topics¿such as Gaussian and Markovian processes, Markov chains, Po...

Läs mer »

The calculus of variations has a long history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications...

Läs mer »

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 ...

Läs mer »

Ordinary di?erential equations serve as mathematical models for many exciting "real-world" problems, not only in science and technology, but also in such diverse ?elds as economics, psychology, defense, and demography. Rapid growth in the theory o...

Läs mer »

From Math Reviews: This is Volume II of a two-volume introductory text in classical algebra. The text moves carefully with many details so that readers with some basic knowledge of algebra can read it without difficulty. The book can be recommende...

Läs mer »

Class field theory, the study of abelian extensions of algebraic number fields, is one of the largest branches of algebraic number theory. It brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly gene...

Läs mer »