Introduction to Abstract Analysis: 1st Edition (Paperback) book cover

Introduction to Abstract Analysis

1st Edition

By W. Light

Chapman and Hall/CRC

208 pages

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Paperback: 9780412310904
pub: 1990-07-01
$115.00
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Description

Abstract analysis, and particularly the language of normed linear spaces, now lies at the heart of a major portion of modern mathematics. Unfortunately, it is also a subject which students seem to find quite challenging and difficult. This book presumes that the student has had a first course in mathematical analysis or advanced calculus, but it does not presume the student has achieved mastery of such a course. Accordingly, a gentle introduction to the basic notions of convergence of sequences, continuity of functions, open and closed set, compactness, completeness and separability is given.

The pace in the early chapters does not presume in any way that the readers have at their fingertips the techniques provided by an introductory course. Instead, considerable care is taken to introduce and use the basic methods of proof in a slow and explicit fashion. As the chapters progress, the pace does quicken and later chapters on differentiation, linear mappings, integration and the implicit function theorem delve quite deeply into interesting mathematical areas.

There are many exercises and many examples of applications of the theory to diverse areas of mathematics. Some of these applications take considerable space and time to develop, and make interesting reading in their own right.

The treatment of the subject is deliberately not a comprehensive one. The aim is to convince the undergraduate reader that analysis is a stimulating, useful, powerful and comprehensible tool in modern mathematics. This book will whet the readers' appetite, not overwhelm them with material.

Reviews

"Gently introduces the reader to abstract analysis with an eye toward setting the stage for further readings in functional analysis."

-American Mathematics Monthly

About the Series

Chapman Hall/CRC Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT037000
MATHEMATICS / Functional Analysis