# Search Results for "introduction-to-the-analysis-of-metric-spaces-australian-mathematical-society-lecture-series"

## Introduction to the Analysis of Metric Spaces

**Author**: John R. Giles**Publisher:**Cambridge University Press**ISBN:**9780521359283**Category:**Mathematics**Page:**257**View:**4908

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.

## Introduction to the Analysis of Normed Linear Spaces

**Author**: J. R. Giles**Publisher:**Cambridge University Press**ISBN:**9780521653756**Category:**Mathematics**Page:**280**View:**2022

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.

## Lectures on Real Analysis

**Author**: Finnur Lárusson**Publisher:**Cambridge University Press**ISBN:**1139511041**Category:**Mathematics**Page:**N.A**View:**4567

This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The author's exposition is concise and to the point, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced students who need a foundation in real analysis.

## Introduction to the Analysis of Normed Linear Spaces

**Author**: J. R. Giles**Publisher:**Cambridge University Press**ISBN:**9780521653756**Category:**Mathematics**Page:**280**View:**6881

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.

## Wavelets

*A Student Guide*

**Author**: Peter Nickolas**Publisher:**Cambridge University Press**ISBN:**1107612519**Category:**Mathematics**Page:**280**View:**3433

Makes the intrinsically advanced theory of wavelets accessible to senior undergraduate students with a mathematical background.

## Notices of the American Mathematical Society

**Author**: American Mathematical Society**Publisher:**N.A**ISBN:**N.A**Category:**Mathematics**Page:**N.A**View:**5177

## Notes on Counting: An Introduction to Enumerative Combinatorics

**Author**: Peter J. Cameron**Publisher:**Cambridge University Press**ISBN:**1108279325**Category:**Mathematics**Page:**N.A**View:**9953

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.

## Publicationes mathematicae

**Author**: Kossuth Lajos Tudományegyetem. Matematikai Intézet**Publisher:**N.A**ISBN:**N.A**Category:**Mathematics**Page:**N.A**View:**6740

## Gazette - Australian Mathematical Society

**Author**: Australian Mathematical Society**Publisher:**N.A**ISBN:**N.A**Category:**Mathematics**Page:**N.A**View:**679

## 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:**1678

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:**2837

Presents an introduction to chaos theory.

## AI 2002: Advances in Artificial Intelligence

*15th Australian Joint Conference on Artificial Intelligence, Canberra, Australia, December 2-6, 2002, Proceedings*

**Author**: Bob McKay,John Slaney**Publisher:**Springer**ISBN:**N.A**Category:**Artificial intelligence**Page:**730**View:**1942

This book constitutes the refereed proceedings of the 15th Australian Joint Conference on Artificial Intelligence, AI 2002, held in Canberra, Australia in December 2002. The 62 revised full papers and 12 posters presented were carefully reviewed and selected from 117 submissions. The papers are organized in topical sections on natural language and information retrieval, knowledge representation and reasoning, deduction, learning theory, agents, intelligent systems. Bayesian reasoning and classification, evolutionary algorithms, neural networks, reinforcement learning, constraints and scheduling, neural network applications, satisfiability reasoning, machine learning applications, fuzzy reasoning, and case-based reasoning.

## An Introduction to Banach Space Theory

**Author**: Robert E. Megginson**Publisher:**Springer Science & Business Media**ISBN:**1461206030**Category:**Mathematics**Page:**599**View:**8810

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.

## Introduction to Operator Space Theory

**Author**: Gilles Pisier**Publisher:**Cambridge University Press**ISBN:**9780521811651**Category:**Mathematics**Page:**478**View:**4159

An introduction to the theory of operator spaces, emphasising applications to C*-algebras.

## Report

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Computer engineering**Page:**N.A**View:**4653

## CPU Performance Evaluation and Execution Time Prediction Using Narrow Spectrum Benchmarking

**Author**: Rafael H. Saavedra-Barrera**Publisher:**N.A**ISBN:**N.A**Category:**Bench-marks**Page:**264**View:**8665

We have developed tools to measure the performance of a variety of machines, from workstations to supercomputers. We have also characterized the execution of many large applications, including the SPEC and Perfect benchmark suites. By merging these machine and program characterizations, we can estimate execution times quite accurately for arbitrary machine-program combinations. Another aspect of the research has consisted in characterizing the effectiveness of optimizing compilers. Another contribution of this dissertation is to propose and investigate new metrics for machine and program similarity and the information that can be derived from them.

## Set Theory and Metric Spaces

**Author**: Irving Kaplansky**Publisher:**American Mathematical Soc.**ISBN:**0821826948**Category:**Mathematics**Page:**140**View:**5265

This is a book that could profitably be read by many graduate students or by seniors in strong major programs ... has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. ... There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem ... The presentation of metric spaces before topological spaces ... should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar. --Canadian Mathematical Bulletin Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent. -- Lance Small, UC San Diego This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.

## Operator Theory in Function Spaces

**Author**: Kehe Zhu**Publisher:**American Mathematical Soc.**ISBN:**0821839659**Category:**Mathematics**Page:**348**View:**6015

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.

## A Course in Modern Analysis and Its Applications

**Author**: Graeme Laurence Cohen**Publisher:**Cambridge University Press**ISBN:**9780521526272**Category:**Mathematics**Page:**333**View:**1418

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

## Real Analysis

*An Introduction to the Theory of Real Functions and Integration*

**Author**: Jewgeni H. Dshalalow**Publisher:**CRC Press**ISBN:**1420036890**Category:**Mathematics**Page:**584**View:**6557

Designed for use in a two-semester course on abstract analysis, REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration illuminates the principle topics that constitute real analysis. Self-contained, with coverage of topology, measure theory, and integration, it offers a thorough elaboration of major theorems, notions, and constructions needed not only by mathematics students but also by students of statistics and probability, operations research, physics, and engineering. Structured logically and flexibly through the author's many years of teaching experience, the material is presented in three main sections: Part 1, chapters 1through 3, covers the preliminaries of set theory and the fundamentals of metric spaces and topology. This section can also serves as a text for first courses in topology. Part II, chapter 4 through 7, details the basics of measure and integration and stands independently for use in a separate measure theory course. Part III addresses more advanced topics, including elaborated and abstract versions of measure and integration along with their applications to functional analysis, probability theory, and conventional analysis on the real line. Analysis lies at the core of all mathematical disciplines, and as such, students need and deserve a careful, rigorous presentation of the material. REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration offers the perfect vehicle for building the foundation students need for more advanced studies.