Introduction to the Analysis of Normed Linear Spaces

Author: J. R. Giles

Publisher: Cambridge University Press

ISBN: 9780521653756

Category: Mathematics

Page: 280

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This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory with a great variety of example spaces.

Introduction to the Analysis of Metric Spaces

Author: John R. Giles

Publisher: Cambridge University Press

ISBN: 9780521359283

Category: Mathematics

Page: 257

View: 4583

Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fundamental analysis structures underlying a variety of applications. Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier. It is intended that metric spaces be studied in some detail before general topology is begun. This follows the teaching principle of proceeding from the concrete to the more abstract. Graded exercises are provided at the end of each section and in each set the earlier exercises are designed to assist in the detection of the abstract structural properties in concrete examples while the latter are more conceptually sophisticated.

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

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Notes on Counting: An Introduction to Enumerative Combinatorics

Author: Peter J. Cameron

Publisher: Cambridge University Press

ISBN: 1108279325

Category: Mathematics

Page: N.A

View: 5754

Enumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the Redfield–Pólya theory of cycle indices, Möbius inversion, the Tutte polynomial, and species.

Lectures on Real Analysis

Author: Finnur Lárusson

Publisher: Cambridge University Press

ISBN: 1107026784

Category: Mathematics

Page: 117

View: 3481

A rigorous introduction to real analysis for undergraduates. Concise yet comprehensive, it includes a gentle introduction to metric spaces.

Neverending Fractions

An Introduction to Continued Fractions

Author: Jonathan Borwein,Alf van der Poorten,Jeffrey Shallit,Wadim Zudilin

Publisher: Cambridge University Press

ISBN: 0521186498

Category: Mathematics

Page: 224

View: 9492

This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.

Chaos: A Mathematical Introduction

Author: John Banks,Valentina Dragan,Arthur Jones

Publisher: Cambridge University Press

ISBN: 9780521531047

Category: Mathematics

Page: 294

View: 3327

Presents an introduction to chaos theory.

An Introduction to Banach Space Theory

Author: Robert E. Megginson

Publisher: Springer Science & Business Media

ISBN: 1461206030

Category: Mathematics

Page: 599

View: 3927

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Choice

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Publicationes mathematicae

Author: Kossuth Lajos Tudományegyetem. Matematikai Intézet

Publisher: N.A

ISBN: N.A

Category: Mathematics

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Operator Theory in Function Spaces

Author: Kehe Zhu

Publisher: American Mathematical Soc.

ISBN: 0821839659

Category: Mathematics

Page: 348

View: 4933

This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.

Foundations of Convex Geometry

Author: W. A. Coppel

Publisher: Cambridge University Press

ISBN: 9780521639705

Category: Mathematics

Page: 222

View: 4181

This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here real affine space is characterised by a small number of axioms involving points and line segments making the treatment self-contained and thorough, many results being established under weaker hypotheses than usual. The treatment should be totally accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.

Wavelets

A Concise Guide

Author: Amir-Homayoon Najmi

Publisher: JHU Press

ISBN: 1421405598

Category: Mathematics

Page: 304

View: 8865

Najmi’s primer will be an indispensable resource for those in computer science, the physical sciences, applied mathematics, and engineering who wish to obtain an in-depth understanding and working knowledge of this fascinating and evolving field.

A Course in Modern Analysis and Its Applications

Author: Graeme Laurence Cohen

Publisher: Cambridge University Press

ISBN: 9780521526272

Category: Mathematics

Page: 333

View: 6692

An advanced 2003 undergraduate text on mathematical analysis designed for pure or applied mathematicians, covering theory as well as applications.

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

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ISBN: N.A

Category: American literature

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Books in Print

Author: R.R. Bowker Company

Publisher: N.A

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Category: American literature

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

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