Bücher der Reihe Universitext

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.

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.

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 volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner.

As well as offering the reader a complete theory of Sobolev spaces, this volume explains how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems.

This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook.

Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational classification of higher dimensional algebraic varieties. This is the first book in this extremely important and active field of research and will become a key resource for graduate students wanting to get into the area.

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing.

The first of two volumes that comprehensively treat partial differential equations, this revised second edition focuses on geometric and complex variable methods involving integral representations. Topics such as Brouwer's mapping degree are treated in detail.

In two comprehensive volumes, updated and revised in a second edition, this textbook spans elliptic, parabolic, and hyperbolic types, and several variables. This second part emphasizes functional analytic methods and applications to differential geometry.

This book is based on notes for a master's course given at Queen Mary, University of London, in the 1998/9 session. Two particular places that are heavy going are the proof at the end of Chapter 1 that a language recognised by a Turing machine is type 0, and the proof in Chapter 2 that a Turing machine computable function is partial recursive.

Translated from the German, with some additional material, by Schulz, William C.

however, classical logic is a good introduction to logic because of its simplicity, and a good basis for applications because it is the foundation of classical mathematics, and thus of the exact sciences which are based on it.

Plotkin divides a logic of discovery into a logic of induction: studying the notion of justification of a hypothesis, and a logic of suggestion: studying methods of suggesting reasonable hypotheses. The rest falls into two parts: Part A - a logic of induction, and Part B - a logic of suggestion.

The text of this book is derived from courses taught by the author in the Department of Applied Mathematics and Statistics at the State University of New York at Stony Brook. The audience for these courses was composed almost entirely of fourth year undergraduate students majoring in the mathematical sciences.

According to this intention, the second edition of the book has been enlarged by further biological examples for network analysis, not by more network theory. Recent results for excitable systems represented by feedback networks have also been included in the second edition, especially for limit cycle networks.

VECTOR FIELDS ON MANIFOLDS 1. Integration of vector fields. Direction fields. Vector fields and isotopies. THE LOCAL BEHAVIOUR OF VECTOR FIELDS 39 1. Linear differential equations with periodic coefficients. Variation field of a vector field. PLANAR VECTOR FIELDS 75 1.

This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol.

The constantly growing demand for energy, as well as the realization during the past decade that fossil energy reserves to satisfy ever increasing energy consumption are limited, have helped, as part of the search for alternative energy sources, to bring the subject of geothermics to its present level of significance.

Methods of optimal decision rules illustrated he re are applicable in three broad areas: (a) applied economic models in resource allocation and economic planning, (b) operations research models involving portfolio analysis and stochastic linear programming and (c) systems science models in stochastic control and adaptive behavior.

The homotopy or Conley index, which provides an algebraic-topologi cal measure of an isolated invariant set, is defined to be the ho motopy type of the quotient space N /N , where is a certain 1 2 1 2 compact pair, called an index pair.

Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings.

This book provides a mathematical introduction into algorithmic geometry with applications to robotics and computer graphics, from classical problems to Grobner bases. Illustrated by applications in computer graphics, curve reconstruction and robotics.

Synthesizing two key texts from Frederic Pham's groundbreaking research in algebraic geometry, this essential introduction to the singularities of integrals focuses on topological and geometrical aspects before moving on to explain the analytical approach.

By focusing on quadratic numbers, this advanced undergraduate or master's level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory.