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This graduate/advanced undergraduate textbook contains a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups.

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.

The tread of this book is formed by two fundamental principles of Harmonic Analysis: the Plancherel Formula and the Poisson S- mation Formula. The generalization of the Poisson Summation Formula to non-abelian groups is the S- berg Trace Formula, which we prove for arbitrary groups admitting uniform lattices.

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero.

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.

"Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry.

The book starts with preparatory and standard definitions and results, then moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Moris minimal model program of classification of algebraic varieties by proving the cone and contraction theorems.

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.

Geodesic and Horocyclic Trajectories provides an introduction to the topological dynamics of classical flows. The text highlights gateways between some mathematical fields in an elementary framework, and describes the advantages of using them.

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.

In this textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided for practice.

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.

The main purpose is on the one hand to train students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other hand to give them a solid theoretical background for numerical methods.

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.