Real Analysis: Modern Techniques and Their Applications

ISBN: 0471317160
ISBN 13: 9780471317166
By: Gerald B. Folland

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Genres

Analysis Currently Reading Currently Reading Maths Math Math Stats Math Textbooks Mathematics Nonfiction Reference To Read

About this book

This book covers the subject matter that is central to mathematical analysis: measure and integration theory, some point set topology, and rudiments of functional analysis. Also, a number of other topics are developed to illustrate the uses of this core material in important areas of mathematics and to introduce readers to more advanced techniques. Some of the material presented has never appeared outside of advanced monographs and research papers, or been readily available in comparative texts. About 460 exercises, at varying levels of difficulty, give readers practice in working with the ideas presented here.

Reader's Thoughts

Tim

Examples are lacking, that is nonexistent. On the other hand, the book is dense and clear.

Pietro

Read the measure/integration part. Not much motivation or intuition, but good job with the choice of axiomatic development (very abstract from the outset). Terrific exercises.

DJ

likely text for math 525a

Joecolelife

This book deserves at least 4 in my opinion. This is an advanced undergraduate or graduate level textbook. Lacking examples? Create yourself. This is one of the ways to know how maths objects behave. Definitions are not motivated? Good, motivate yourself. Too terse? It should not be that terse, after one has seen concrete treatment of Lebesgue integration, also having accquired the mathematical maturity from Weirstrass, Arzella Ascolli, Baire Category Theorems, and Fourier Analysis (Pugh's Real Mathematical Analysis, Carother's Real Analysis, Stein's Fourier Analysis are excellent) Being terse can be a good thing: intuitionise and geometrise the materials. Try to think of a way to present them in a manner so that people with (honours) 1st year calculus (Spivak, Apostol) can listen as stories. Regarding someone who reviewed the book, yes a picture is worth a thousand words. But eventually, seeing others' pictures is not sufficient; we need to learn to be mature enough to draw pictures ourselves. Folland provides the platform. I believe the negative reviews come from the fact that the readers have not yet had the sufficient preparation before coming to Folland (Poor organisation of courses exists everywhere, not students' fault). The book itself is actually a very good book to learn from.

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