Customer Reviews (1)

difficult to read !
The book has some pages in "blank". I want to return it!
J.R. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
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. ... Read more

Product Description
A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods.
Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty.


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Customer Reviews (4)

Very good for struggling in Real Analysis
There is no problem solutions for Real Analysis texts available in U.S. since most of the teachers believe that Math students in grad level should be more creative. However, not all students in Real Analysis are potential mathmatician. If they lost in class and must study by theirselves, they may feel frustrated missing all the stuff contained in problems. The material in "Principles of Real Analysis" may not superior much than other famous text(like Royden, I think Royden is clear enough but too much mysterious things lie in problems.). But use it with this workbook, you will find much comfortable in self study. It helps a lot not only in my homework assignment, but also in my understanding.

A must have!!!
This book rocks! It covers practically all the major topics of an introductory course in graduate Real Analysis. Excellent solutions that aid in the understanding of the material. This book's worth is immeasurable, or should I say, non-measurable.

Must have one
Great guide, must have for anyone taking Real Analysis.

Must have for anyone taking Real Analysis
Before buying this book, I was failing Real Analysis.Now I have a prayer of passing.Thank goodness I found it in time.For it to be of use, you need to buy the companion book "Principles of Real Analysis",same authors.On the down side, it doesn't have an index, but overall,well worth the money.Besides, it is the only source I've found ofworked-out Real Analyis problems outside of borrowing from other studentswho have already taken the course. ... Read more

Product Description
The new edition of Function of Several Variables is an extensive revision. Like the first edition it presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. A new chapter on elementary topology makes the book more complete as an advanced calculus text; sections have been added introducing physical applications in thermodynamics, fluid dynamics, and classical rigid body mechanics.

Many mathematicians were first introduced to basic analysis by the first edition. The second edition makes this material available, in improved form, to a new generation of students. ... Read more

Customer Reviews (4)

A forerunner of what was to come, but not up to par now.
In 1965 it was about all that was, but today we have many more choices to choose from. Perhaps if you are a genius you may still think this the best thing under the sun , but I am not quite there.

The "advance calcuus" field has a ton of them now is what i am saying. And so does "smooth manifolds" theory. When I had "Calculus on Smooth Manifolds" by Spivak as the textbook from which I was learning, all this was obvious. That was a better middle ground between the two, even though it was inadequate in application examples.

A Note on Print Quality
I selected this text for a course I'm currently teaching in advanced multivariable calculus after examining a colleague's copy, which was printed back in 1977 when the second edition was published.When my desk copy arrived in the mail and the students' copies arrived in the campus bookstore, I learned that the quality of the recent printing of this book is very poor.The typesetting looks like an nth-generation photocopy of a printout from a defective, low-resolution inkjet printer.It's hard enough for math students to sit down and read their textbooks without making it harder for them by giving them a poorly printed book to read.This may be a deal-breaker as far as me selecting this text again in the future.

Very solid text
Fleming gives a very solid, rigorous presentation of advanced calculus of several real variables.The implicit function theorem and inverse function theorem play central roles in the development of the theory.Fleming uses vector notation throughout, treating single variable calculus as a special case of the vector theory.Differential forms, exterior algebra, and manifolds are treated, as well as Lebesgue integration.Examples tend to focus on special cases and counter-examples.The book is a little light on practical applications, with the exception of the final chapter.I have only two substantial complaints with the book.First, the book often fails to build intuition about certain concepts.Second, there are relatively few problems devoted to computation, as applied mathematicians might desire.Strong points include the clarity of notation, rigor of proofs of theorems, and the treatment of both manifold theory and Lebesque integration.I strongly recommend this book, but caution that it may be slightly too advanced for all but the most serious undergraduate students.Working through this book will, however, build a level of mathematical maturity to handle more advanced analytical texts, such as Rudin.

Well presented
This book revolves around three theorems: the inverse function theorem, the implicit function theorem, and Stokes' theorem. The prerequisites are a working knowledge of Linear algebra and undergraduate calculus. What distinguishes this text from other books on advanced calculus is that it focuses at the outset on R^N instead of on the real line. The advantage of starting out with R^N is that the reader becomes more quickly accustomed to the notation and can subsequently interpret the real line is a special case more easily. Later sections in the book cover exterior algebra and differential calculus and integration on manifolds. There is a discussion of the Lebesgue integral in R^N also. The notation is very clean and there are interesting exercises with corresponding numerical answers in the appendix. The writing is well paced, with a uniform level of difficulty throughout. I recommend this for an advanced undergraduate or beginning graduate student. ... Read more

Product Description
In the second edition of this MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, or as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier s introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy s attempts to establish a firm foundation for calculus, and considers his failures as well ashis successes. It culminates with Dirichlet s proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet s proof. ... Read more

Customer Reviews (3)

Excellent sequel
If you had calculus in high school or college then you learned about Newton, Leibnitz, and Riemann but probably did not encounter Lebesgue (pronounced le-bek). At the University of Alabama Huntsville learning about Lebesgue integration is key to advancing into graduate studies in mathematics. The natural follow-on course after Calculus I and II, etc. is Real Analysis. This book, using Lebesgue integration methods, is a good sequel to Lebesgue calculus.
I purchased this book, after reading about it in the Mathematical Association of America (MAA). For autodidacts like myself, it is a good first introduction to the topic.

A radically false account of history
This is not a bad book, but it does everyone a huge disservice by pretending to be historically informed when in fact it is propagating harmful and stupid myths that have no basis in historical fact whatever. An example should make this clear.

"Daniel Bernoulli suggested in 1753 that the vibrating string might be capable of infinitely many harmonics. The most general initial position should be an infinite sum of the form
(2.71) y(x) = a_1 sin(pi x / l) + a_2 sin(2 pi x / l) + a_3 sin(3 pi x / l) + ...
Euler rejected this possibility. The reason for his rejection is illuminating. The function in equation (2.71) is necessarily periodic with period 2l. Bernoulli's solution cannot handle an initial position that is not a periodic function of x. Euler seems particularly obtuse to the modern mathematician. We only need to describe the initial position between x=0 and x=l. We do not care whether or not the function repeats itself outside this interval. But this misses the point of a basic misunderstanding that was widely shared in the eighteenth century. For Euler and his contemporaries, a function was an expression: a polynomial, a trigonometric function, perhaps one of the more esoteric series arising as a solution of a differential equation. As a function of x, it existed as an organic whole for all values of x. ... To Euler, the shape of a function between 0 and l determined that function everywhere." (p. 53-54)

There is not a single line anywhere in any pre-19th century mathematical work that comes anywhere near making this sort of claim. Self-righteous "mathematicians" have invented these myths to justify their dogmatic and authoritative mode of "teaching" and their passionate hatred of intuition. In falsely lending these propaganda fabrications a veneer of historical truth, Bressoud is perhaps the worst lier of them all. It is not Euler who is "obtuse," but Bressoud. There was no "basic misunderstanding widely shared in the eighteenth century"; rather, the "basic misunderstanding" lies with Bressoud and his fellow poseur historians of today.

All of this is easily established by simply reading Euler. The relevant paper is E213, which is readily available online. Let me summarise what you will find if you read that paper.

First of all, Bernoulli never claimed that (2.71) can express any initial position of the string. He merely argued for a general series solution of the vibrating string equation which *implies* that the initial position is of the form (2.71). Hence Euler's main objection, which is this: I can bring the string into any position whatever, let go, and it will move according to the vibrating string differential equation. Thus Bernoulli's solution is not completely general insofar as (2.71) does not express any possible initial position of the string. And since Bernoulli has provided no argument that (2.71) can in fact express any initial position, nor in fact any method for calculating the coefficients a_i, we have no reason to believe that his solution is completely general. At this point Euler preempts a hypothetical counterargument: perhaps, says Euler, some might argue that "owing to the infinite number of undetermined coefficients," equation (2.71) "is so general as to include all possible curves." This, however, is plainly false, Euler points out by noting the periodicity properties of (2.71). Now, at this point it would be possible for a Bernoullian to retreat still further and say that (2.71) can express any function, not on the real line, but on the interval [0,l]. This is a perfectly valid argument, but it is an argument which Bernoulli never raised and which Euler never claimed to have refuted. So much for the periodicity argument, which Bressoud has obviously distorted most unfairly. But worse still is Bressoud's generalisation from this case to the alleged "basic misunderstanding." This is sheer stupidity and fabrication, as is plain to anyone capable of reading at a fourth grade level. In fact, every last word of it is plainly and unambiguously rejected by Euler in the very article in question when he points out that the initial position of the string can be any curve, which "often cannot be expressed by any equation, be it algebraic or transcendental, and is not even included in any law of continuity."

Getting there naturally
I am a topologist by training who was Shanghaied into being an analyst when I was hired as a teacher.As a consequence of this, the Advanced Calculus course I taught was rather heavy on topology.

Over the course of time--having been transformed into more of an analyst that I would have ever dreamed--I've come to the conclusion that analysis is best learned before topology.

This is a text that accomplishes that by using the historical approach.

One learns how Newton approached problems, how Euler did, how Cauchy did.Not only is it interesting, it is enlightening.I've taught this course for 15 years now, and of all of the approaches I've taken, this has been the most fruitful.

My students have come from calculational courses, and the historical approach of this book provides a bridge over which they may come into the land of proof.They also see the issues that caused the need for modern rigor face to face

I do supplement the course with material that is more modern (Hardy's book A Course of Pure Mathematics) and material on the Riemann integral, but I've been spoiled for any other approach.

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Customer Reviews (2)

Excellent Introductory Text for Real Analysis
The best thing about this book is its clarity and simplicity in defining real analysis concepts. The author conveys his point in a convincing and understandable way without loosing the details involved. I think its a very good text specially for those who are newer to this field.

comprehension look at this book.
This book is an excellent look at real analysis using the philosophical basis around the application of Topology.This book is also one of the easier readers that one will experience when it comes to mathematics. ... Read more

Product Description
In recent years, mathematics has become valuable in many areas, including economics and management science as well as the physical sciences, engineering and computer science. Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral. ... Read more

Customer Reviews (29)

Real Analysis
This book came in great condition. It looks brand new, no marks, and half the price as anywhere else I could find.

If i wanted a book with bent corners, i could have bought used
I had many options at the time that i purchased this book. I could have ordered a used book in excellent condition for far less than a new one..one in good condition with only bent corners for even less.. But on the other hand,if i bought a new one i could sell it when my class was over and recover most of my money. I chose to go new. When i recieved the book the corners were all bent because there was nothing in the box to protect it. I guess just beware..if your buying a very expensive text book and plan to resale it when your done..look for the best deal on used because the high price of new will not get you a much better book!!

A relatively difficult but extremely rewarding book
I used this book all through my freshman and sophomore years. I struggled with it and really tried hard to solve the problems. I mulled over every word and every proof of the first few chapters for days. However at the end of this rather trying exercise, I had a real sense of satisfaction and thought I had a firm grasp of the basics of real analysis. This is not one of those volumes that will instantly get you hooked but it's a volume that rewards patience like few other math books do. If you master the first few chapters of the book including those on series and sequences, you should have as good as grasp of elementary real analysis as anyone else. The book is for the serious student of mathematics and it provides a rigorous and comprehensive introduction to real analysis. To master it you will have to read and understand the proofs as carefully as possible; don't be discouraged and become impatient if you cannot do this easily, since the time spent on doing it is worth it. However, having a good instructor to help out will be enormously useful.

Way better than Pugh
What a breath of fresh air after dealing with Pugh's book!The language is clear.The proofs are concise and easy to follow.The illustrations are good without being overwhelming.I cannot say enough good things about this book.Poor math teachers are obsessed with the most general case and introduce it first.A good teacher starts with a specific case, relates it to what the student already knows, and then begins to generalize it slowly, layer by layer until the most general case is achieved.This is how the mind works, this is how mathematics really developed over time, and this is how math should always be taught!Bartle and Sherbert do a outstanding job of this!

One word of caution.Don't let real analysis be your first proofing class.Take a proofing class first and if your university doesn't have one, demand one!.Real analysis is not the place to learn propositional logic, quantifiers, truth tables and the like!.Learn that stuff first and do your first proofs in elementary number theory or geometry, then when you have a repertoire of proofing tools and some skill in proofing, then take real analysis.You cannot learn proofing and real analysis at the same time.First learn to proof, then take real analysis! If not you will be miserable and you will take it out on your teacher and text!

Really hard, but Really good
Like some others, I really disliked Real Analysis at first b/c the proofs were so much more complex than anything else I had seen. I struggled, ordered other analysis books to help me, only to find that this one really is good! You do need a great instructor to go with this book or you may be lost. That said, the appendices are fantastic and the authors give "hints" (and some answers) to selected problems. The proofs themselves are terse, so without an instructor who understands the gaps, you may not connect the steps solo. Good text which is now part of my math library. ... Read more

Product Description

Real Analysis, Fourth Edition, covers the basic material that every reader should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in mathematics and familiarity with the fundamental concepts of analysis.

Customer Reviews (4)

Great Text with Great Proofs
In some presentations rigor is sacrificed for an intuitive overview of the material. This is a mistake in my view, particularly for an undergraduate course in analysis, which is the perfect environment for rigorous proof-writing skills to be developed.

Goldberg makes no such sacrifice. His proofs are great. His exposition is very clear. If I have a complaint, it's that it's not colorful enough, there aren't enough different kinds of pictures and graphs. The text DOES contain pictures and diagrams, and they are good, but they are not great. On the other hand, this might be seen as a feature, for it forces the student to work on coming up with her own, which is a very important skill to develop.

Great introduction to Real Analysis
This book reads like an instructor would teach in class. It derives all the important theorems quite rigorously and throws in a few lines of intuition which is very helpful when you are trying to self-study something as intense as real analysis. He also has two or three examples following every major result and shows clearly how to "use" the result just derived to solve an actual math problem.
I went through lots of great analysis books (Rudin, Shilov, Kolmogorov, Aliprantis, Johnsonbaugh, Rosenlicht and Protter among others) until finally learning from this. After getting my foundations and intuitions right, I now feel like I am better equipped to read and understand the results from the above books which, in general, treat proofs more tersely and cover a lot more material in the process.
This book does not cover the origin of real numbers and it's axioms. It covers standard results from elementary set theory, sequences, limits, metric spaces, open and closed sets, completeness, compactness and connectedness, the derivative, Taylor Series, exps and logs, the Lebesgue integral and Fourier Series.

Well worth it.
I come to real analysis from a non-mathematics background.I began with Steven Lay's "Analysis with an Introduction to Proof" which was great for an absolute beginner. Goldberg's text is the next step up.Andwell worth the money!

Clear and to the point
This is an excellent textbook for an introductory course in Real Analysis.The text is rigorous, but contains enough examples to be readily understood.If you honestly want to learn the subject matter, this book isworth the money.However, if you would rather struggle with it, there areplenty of those books floating around . . . ... Read more

Product Description
This self-contained reference/text presents a thorough account of the theory of real function algebras. Employing the intrinsic approach, avoiding the complexification technique, and generalizing the theory of complex function algebras, this single-source volume includes: an introduction to real Banach algebras; various generalizations of the Stone-Weierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and a detailed bibliography.;Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f(2), Re f(3), and Re f(4); and the positivity of the real part of a linear functional on a subspace of C(X).;With over 600 display equations, this reference is for mathematical analysts; pure, applied, and industrial mathematicians; and theoretical physicists; and a text for courses in Banach algebras and function algebras. ... Read more

Customer Reviews (1)

Algebra pure applied
Super algebra bookit does not get too complex to loose the useability, but is up-to-date account of the theory and real function algebras. Is a convenient highly useful reference for mathematical analysts. ... Read more

Product Description
Clear, accessible text for a first course in abstract analysis, suitable for undergraduates with a good background in the calculus of functions of one and several variables. Sets and relations, real number system and linear spaces, normed spaces, normed linear spaces, Lebesque integral, approximation theory, Banach fixed-point theorem, Stieltjes integrals, more. Problems.
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Customer Reviews (9)

Occasionally enlightening, usually obnoxious
This is the first real analysis text I've studied, and so I should begin by saying that, for all I know, every real analysis book suffers from the flaws I'm about to describe. With that said, I'll point out a few things that make this volume totally inappropriate for self study.

1) In three hundred pages, there are two illustrations, and they're both on the same page. Not only is there a terrific absence of pictures and graphs, but even tables, charts and lists are nowhere to be found. It might be argued that the authors did not wish for students to rely too heavily on visual intuition, given that enlightening visual interpretations simply do not exist for some of the concepts presented. But there are very clearly arguments in this book that are drenched in geometric terminology. Connectedness, compactness, the development of the Lebesgue measure, metric spaces, ... these issues would be made infinitely clearer by a couple of well placed pictures.

2) The concepts are totally unmotivated. No attention is paid to explaining why some theorem might be of importance (with the notable exception of the fixed point theorem). More than once, a hierarchy of definitions and theorems will be laboriously developed, only to unexpectedly disappear and never resurface, leaving the reader wondering what the point was.

3) No solutions to any of the exercises are provided. This is partially admissible given that many of the problems consist of "prove that X is true", and a solution would occupy half a page of work. But there are certainly more computational problems for which answers should be given.

4) There is no narration whatsoever. Outside the preface, the reader is never addressed directly, and rarely acknowledged to exist. It is fully possible to understand the proof of a theorem without having any intuitive, satisfying understanding of the theorem. When presenting unexpected and paradoxical results, the authors take no time to explain things, apparently considering the proof to be sufficient explanation. The reader has no idea, ahead of time, which ideas are critical and which are secondary. The reader has no sense of where the discussion is going, nor is the reader given any historical context of the mathematics. These are issues that actual human beings care about. The authors have written something closer to a reference text, appropriate for robots. Enthusiasm and excitement are absent; the text is dry, uniform, unmotivated and boring.

With that said, the text is very rigorous and thorough, although I have read that there are errors in some of the proofs. It's a cheap purchase and, despite the authors' intentions, you will learn some Real Analysis by going through it.

Can I get a refund??
That Shane Guy is "DEAD ON".No examples, No pictures, there is a reason this is the cheapest Real Analysis book around. ...Where is the list of errors for this book, because for every Y pages there are X many errors, s.t. X = alot.

worst book ever
contains almost no illustrations or examples.No answer key either.Worst math book ever.

so sad it is dover (2)...a cry forbetter editions...
Hi, I am the previous reviewer of the "so sad it is dover" review. I feel deep respect for the review of Daniel R Greenfield. And I fully agree that this book is excellent! And of course, Dover books are cheap, so this book is definitely worth its money. Though I want to clarify my Dover critics a little bit more. To all those guys who admire Dover books , I wonder whether they use these books as a reference or as a text to study from. I can swear you : it is not so much fun to study high level mathematics in such a dense text! Too my opinion it is essential that you need enough space between the different statements of a complex proof. I believe that the great authors of this book deserve better then a cheap Dover edition. But since Dover owns the rights of these authors, nobody can create this text in a better edition.

User friendly editions however seems to be a common problem for all abstract math books. Why is it that we, students of pure mathematics,have to learn from such user-unfriendly editions.
For instance look at the size : I think user friendly books should have have a size of at least 9.8 x 7.1 inch. Forphysics,chemistry or calculus you find enough books of this size, with with enough spacing and nice motivating pictures, just to alleviate the learning process...But apparently if you want tot study higher level math, no such books exist, as far as I know ...

This review is a call (even a cry) to editors of advanced math books just to make their editions more user-friendly. If some readers agree that there is a need for this, just vote by clicking the "review was helpfull - yes" button. I hope some editors will then see that there is a market place for user friendly books on advanced math. Even if you have to pay a little more for a book of bigger size, please realize how it will make your life so much easier. Your learning productivity would increase a lot, so better editions are definitely woth its money!!!! Compare it with a professional worker who wants the best and most productive tools.
Unfortunately these critics do not apply to Dover books only, even a lot of more expensive editors just bring their texts in the same user-unfriendly format. On the exiting subject of abstract math, up until now, I even did not find the ideally formatted book.

If some readers agree with my, please vote by telling this review was helpfull (click "yes" button). Hopefully this will inspire editors for future editions. If you really like to study from Dover Editions, please vote by using the review was helpfull-No button. If most people vote "No", I am probably the exceptional guy and will stop complaining about Dover editions.

So Sad It's Dover?
Yes this book is an excellent introduction to real analysisand assumes minimal preparation beyond linear algebra and two semesters of calculus. I have been looking everywhere for a clear and lucid treatment of the Banach Fixed Point Theorem, and here it is. At a time when most math textbooks (even paperback) cannot be had for less than $50, Dover has been a godsend for those of us who want to collect a decent mathematics library. If it were not for Dover Publications, Iwould not have this text in my library, nor would I be able to afford it. Please visit Dover Publications website to view all the other fine mathematics texts which they offer at bargain prices. Incidentally, all these fine Dover mathematics books that can be had for chump change are reprints of original texts that have long been out of print and hard to find. To a previous reviewer who critized Dover Publications, I would simply say: Don't bite the hand that feeds you. ... Read more

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This is the classic introductory graduate text. Heart of the book is measure theory and Lebesque integration.

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Customer Reviews (24)

Good candidate for the worst math book ever
This book is absolutely horrific .Royden proves (mostly handwaves) a few theorems , and then expects the student to be able to solve the exercises easily given this background.Can we even call this a Math Book?? As it is unfortunately the case with most graduate level textbooks in the U.S , the exercises are minimally related to what the author develops (or tries to develop).Books like this do not take much effort to write , while the students trying to learn this hard subject are the real victims.I agree with another reviewer that this book was written by Royden just to impress his peers.The important theorems are just given with the most minimal explanations possible ,and no effort whatsoever is made to get to the intuitive roots of the subject.Important examples are also close to nonexistent.Can anything be worse??

Classic text, but a poor reference.
Halsey Royden's Real Analysis has become the de facto standard for teaching a graduate course on real analysis and integration.It has, however, become a bit dated.First off, the method of developing the Lebesgue integral before general measure theory is out of style.It is now generally accepted that learning the (relatively easy concept of) general measure theory first, and then the Lebesgue measure as an example, is a superior pedagogical approach.

That said, Royden is very good at explaining things in more detail; it is both a complement and a criticism that the book manages to cover a good deal less than Folland's text in almost twice the length.Complementary in the sense that the book motivates the material and gives explanations without leaving the reader to any important developments, critical in that the book is more or less useless as a reference.What's more is the fact that in the book's 444 pages it only manages to cover about half of what Gerald Folland goes through in his shorter book; this makes the ridiculous price of the book even less justifiable.

All of this said, I would still recommend this book for study.It explains well and would be a good read for self study.As for the criticisms that label the book as either "too difficult" or "too dense," disregard them.Those who make these claims are probably just not very good with Analysis.For a book that is truly awful, see M.A. Armstrong's Basic Topology.

Really Great for Certain Topics
Great for the bookshelf but really pretty hard - you need a good proof course and a year suffering through baby Rudin - and believe me, you will suffer - but will be a better person (and mathematician) for it.

Maybe good as a supplement, or a first time looking at the material
There are three books that are usually used for a first graduate course in analysis, including measure theory, namely Rudin's Real and Complex Analysis, Folland's Real Analysis, and Royden's book. Of the three, I would say Royden's book is the easiest, both in terms of the exposition, material, and exercises. Of the three, Royden is the only one to fully develop the Lebesgue measure and the associated integral before developing a more general theory of measure and integration. Furthermore, he does not develop Hilbert and Banach space theory, the very basics of functional analysis, to anywhere near the extent that Folland and Rudin do.

There is some debate as to whether it is better to start with the Lebesgue integral, and then talk about abstract integration, or the other way around. Personally, I found the development of the Lebesgue integral a bit tedious; the whole thing works a bit better when you first talk about abstract integration, which really isn't a terribly difficult concept, prove the basic integration theorems, then show how to construct an outer measure, and suddenly, the Lebesgue measure and integral just falls into place. I'm not sure anything is lost in the process.

The biggest shortcoming in this book would have to be the exercises: for the most part, they are not very difficult, particularly when you compare them to say, Rudin's text. For the most part, the exercises are fairly trivial, and if they are difficult, or require a bit of creativity, Roydenoften gives you lots and lots of hand-holding, sometimes even in the form of sketching out the proof for you. In spite of the relatively low difficulty level, most of the exercises are fairly instructive, in so far as they highlight, elucidate, and expand upon the material.

For the most part, this book is not bad. It makes a good supplement to a book like Rudin or Folland, as it is less abstract, and does a better job motivating the material. The exercises here can work well if you want some extra practice that won't take up too much time. If you're a student of econ, or physics, or you just feel like learning graduate-level real analysis, then this book is probably adequate (although I should qualify that statement by saying that I know nothing of econ and little of physics). But if you are a serious student of mathematics, particularly the pure variety, this is really not the book you should be using. It is just too easy.

Classic text on measure & integration theory
Many people criticize this book as unclear and unnecessarily abstract, but I think these comments are more appropriately directed at the subject than at this book and its particular presentation.I find this classic to be one of the best books on measure theory and Lebesgue integration, a difficult and very abstract topic.Royden provides strong motivatation for the material, and he helps the reader to develop good intuition.I find the proofs and equations exceptionally easy to follow; they are concise but they do not omit as many details as some authors (i.e. Rudin).Royden makes excellent use of notation, choosing to use it when it clarifies and no more--leaving explanations in words when they are clearer.The index and table of notation are excellent and contribute to this book's usefulness as a reference.

The construction of Lebesgue measure and development of Lebesgue integration is very clear.Exercises are integrated into the text and are rather straightforward and not particularly difficult.It is necessary to work the problems, however, to get a full understanding of the material.There are not many exercises but they often contain crucial concepts and results.

This book contains a lot of background material that most readers will either know already or find in other books, but often the material is presented with an eye towards measure and integration theory.The first two chapters are concise review of set theory and the structure of the real line, but they emphasize different sorts of points from what one would encounter in a basic advanced calculus book.Similarly, the material on abstract spaces leads naturally into the abstract development of measure and integration theory.

This book would be an excellent textbook for a course, and I think it would be suitable for self-study as well.Reading and understanding this book, and working most of the problems is not an unreachable goal as it is with many books at this level.This book does require a strong background, however.Due to the difficult nature of the material I think it would be unwise to try to learn this stuff without a strong background in analysis or advanced calculus.A student finding all this book too difficult, or wanting a slower approach, might want to examine the book "An Introduction to Measure and Integration" by Inder K. Rana, but be warned: read my review of that book before getting it. ... Read more

Product Description
Assuming minimal background on the part of students, this text gradually develops the principles of basic real analysis and presents the background necessary to understand applications used in such disciplines as statistics, operations research, and engineering. The text presents the first elementary exposition of the gauge integral and offers a clear and thorough introduction to real numbers, developing topics in n-dimensions, and functions of several variables. Detailed treatments of Lagrange multipliers and the Kuhn-Tucker Theorem are also presented. The text concludes with coverage of important topics in abstract analysis, including the Stone-Weierstrass Theorem and the Banach Contraction Principle. ... Read more

Customer Reviews (2)

Correcting a mistake in my review...
In the place where it says that the Feynman-Kac formula is proven using gauge integration, please ignore it, because it's not true.

A unique introductory book on real analysis
So, we have another book on introductory real analysis. Yes, But this one has its own shine, keeping it apart from the classics (Rudin, Apostol, Bartle): It contains the first (and maybe the only) elementary expositionof the marvellous gauge integral. It's a clever and surprising extension ofthe definition of the Riemann integral, made by Kurzweil and Henstock inthe fifties, with the purpose of constructing a Riemann-type integral withall the properties of the Lebesgue integral, and recovering the originalspirit of Newton and Leibiniz (as far as primitives are concerned). McShanelater showed that this kind of integral totally supersedes the concept ofLebesgue integral and measure. The gauge integral also supersedes theimproper and Stieljes integrals, with the big pedagogical advantages of theRiemann integral.

However, the book form presentations of this integral(given mainly by its creators) are incomprehensible, period. On the otherhand, Depree/Swartz achieves the previously unfulfilled purpose of giving ahuman-readable presentation of the gauge integral. It uses it as the maintool for teaching integration, and this is great, because all the book isvery readable and down-to-earth. This book has other pearls, like his greatpresentation of differentiation in several variables (done with Frechet andGateaux derivatives in a very smooth and clear way, better than Lang), andgood topological stuff concerned with analysis as needed. It develops adifferent way of thinking about analysis, and all you need is a littlebasic calculus.

All things concerned, it's a first-class book thatdeserves to be read more and more. Gauge integration is a unfairlyforgotten tool, that can enlighten many unsolved problems in mathematics(constructive mathematical analysis) and physics (path integration, as seenfor example in the Feynman-Kac formula, proven using gauge integration), orsimply make people think about advanced integration and analysis in asimpler way. ... Read more

Product Description
Intense competition makes intelligent state of the art real estate office management the key not only to success but to survival. The Real Estate Brokerage Council produced the first edition of Real Estate Office Management for brokers' classes taught by the Realtor's National Marketing Institute where it is still required reading.

Highlights of this book include:

* Leadership, planning, organizing and communicating.

* Recruiting, agency types, and training.

* Retaining, motivating, and terminating employees.

* Record keeping and financial systems.

* Marketing and utilizing statistical records.

* Analyzing Real Estate growth patterns.

* Mergers and acquisitions. ... Read more

Customer Reviews (5)

Ready Set GO!!
This is a good book to read and underling and then make a to do list from. If you are thinking about opening a real estate brokerage, read this it will ease your mind and help you prepare.

Real Estate Office Management
The book is everything as advertised, it could have been sent a little faster, but it got here just fine.

very helpful for my business
This book gave me a lot of ideas of running my business and is complementary to the general managerial studies I've made. Unfortunately,
Greek universities do not offer studies in "Real Estate", and this book provided me the basic knowledge for my office.

Exactly What I was looking for....
This mangement guide is exactly what I was looking for.A Realtor for 6 years I was looking for a mangement perspective to help me navigate and negotiate my future.I found it to be comprehensive and an easy read.

Is an index really that difficult?
While this book contains some useful information, it is choppy and disorganized, perhaps a result of being 30 years old and being re-issued 4 times.And to add to the confusion, the index is terrible.Since this is primarily a reference book, lack of a thorough index is inexcusable.Needs to be revamped and brought up to date. ... Read more