Product Description

By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs. Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises. A thorough reference for readers who need to increase or brush up on their advanced mathematics skills.

Customer Reviews (13)

ugh...
Steven Lay is every bad math teacher you've ever had rolled into one giant ball of smarm and uselessness.Let's go down the checklist:

- does he make every single concept more complicated than it needs to be, giving you page after page of gobbledygook when he could sum it up in one or two lines?CHECK!(For instance, for a function to be injective, any horizontal line can cross the function's graph only once.For it to be surjective, there must be exactly one horizontal line that intersects the graph at every point.There; that's everything that Section 7 needs to say, but instead it goes on and on uselessly for 12 pages).

- does he quiz you on concepts and terms that he didn't both to define and/or explain?CHECK!(Actually, the book's layout is so poor that important terms and definitions are buried in the middle of paragraphs; often it takes 2 or 3 passes to find the important stuff.A decent math book will be designed for easy reference, but apparently Lay assumed that we'd all memorize his text the first time through.)

- does he take every opportunity to prove that he's smarter than you, and that he doesn't really want you to learn anything?CHECK!(Insult to injury:instead of providing answers to the odd-numbered exercises, he seems to have randomly chosen the exercises which are answered in the back of the book.Or more likely, he only chose the easier ones.)

- does every example he does rely on some obscure trick or property that won't be utilized in the questions at the end of the section?CHECK!


This book is bad enough on its own; it's even printed on cheap paper that rips if you look at it wrong.God help you if you get this book in conjunction with a lousy Analysis teacher.I give it 2 stars only because, at the very least, it doesn't weigh much and doesn't take up too much space in my backpack.

Thumbs up!
Money saver! got this book for about 1/4 of the asking price at my local university.

Thanks a bunch
the item arrived on time and in the condition he said it would, thanks a bunch

Analysis With an Introduction to Proof
Lay's 4th edition of "Analysis" is one of the best elementary Real Analysis books in print. The prose and examples in this book prepare the reader to do ALL of the problems at the end of the sections. However, it requires a great deal of patience and a willingness to think outside the box.

It's probably not the best book for learning how to read and write proofs, but the techniques discussed in the first chapter are sufficient for an undergraduate RA course. My only complaint is that Lay mentions nothing about constructing truth tables or the order of precedence, which may not be familiar to reader's who've never taken high school geometry.

There are a lot of spelling errors in this book but they won't prevent you from understanding the material. For the most part, the book is very well written and contains a good number of graphs and pictures. This allows students to focus more on the most difficult aspect of Analysis(solving problems) rather than spending hours trying to decipher poorly written garble, a feature that seems all too common in abstract math books.

amazing condition. easy to follow text and apply concepts
amazing condition. easy to follow text and apply concepts. crystal clear directions, great for a student just starting off and with no previous knowledge of the subject. ... Read more

Product Description
Distributed real-time systems (DRTSs) are used in a wide range of applications, including command and control systems, flight control systems, robotics, patient monitoring systems, and many others. This volume provides an overview of various systematic approaches to the testing and debugging of DRTSs—tasks that typically consume 50% to 700f a new system's development costs.

Distributed Real-Time Systems covers both the theoretical and practical issues involved in monitoring, visualization, and analysis methodology for verifying and debugging DRTSs. It describes in detail how to overcome timing verification difficulties and improve system performance and reliability. Complete with many carefully worked-out examples, as well as dozens of illustrations, this timely and accessible work

Explains real-world debugging approaches—proposed or tested—using static analysis or dynamic analysis with or without monitoring

• Features step-by-step instructions for design implementation in hardware and software, detecting timing errors and their causes, graphical debugging methods, and more
• Covers numerous analytical techniques, including timed Petri nets, temporal logic, timed state transition systems, timed process algebra, and synchronous programming languages
• Makes distributed systems analysis accessible through examples such as a distributed telephone switching system and a fault-tolerant distributed system
• Reviews many relevant professional papers and current research work

The joint product of four leaders in the field, Distributed Real-Time Systems is an important text and reference for electrical and software engineers, graduate students, and anyone involved in computer and data processing technology. ... Read more

Customer Reviews (1)

review
i want to review this book before purchase ... Read more

Product Description
Fiduciary responsibilities and related court-imposed liabilities have forced investors to assess market conditions beyond gut level, resulting in the development of sophisticated decision-making tools. Roger Brown's use of historical real estate data enables him to develop tools for gauging the impact of circumstances on relative risk. His application of higher level statistical modeling to various aspects of real estate makes this book an essential partner in real estate research. Offering tools to enhance decision-making for consumers and researchers in market economies of any country interested in land use and real estate investment, his book will improve real estate market efficiency. With property the world's biggest asset class, timely data on housing prices just got easier to find and use.

*Excellent mixture of theory and application
*Data and database analysis techniques are the first of their kind
*CDROM contains pre-written code for data analysis tailored specifically to real estate settings ... Read more

Customer Reviews (1)

An Elegant Introduction to Real Estate
I work as an analyst at a small real estate development and finance firm, and I am always on the lookout for good texts. As a person with a mathematics background, I hate how most real estate books go to great lengths to avoid "hard math". In the end, many of these so-called "advanced" texts leave out important parts, or end up trying to reduce mathematical relationships to mere words. In so doing, they make what should be simple ideas into an impenetrable mess.

Roger Brown's booknicely sidesteps this problem, and immediately gets into non-trivial ideas that one would be hard-pressed to find in a standard textbook. Typical of this is his Chapter 3, "The Rules of Thumb". Instead of simply defining terms such as "cap rate," and maybe discussing some of the limitations of this tool, Brown brings up the real world: cap rates can easily be distorted, and it is your job as an analyst to determine if the cap rate you are using is an "honest one". Brown shows just how one can systematically do this using a corpus of transaction data, which can be found on sites such as costar.com.

There are numerous other innovative ideas in the book. My feeling is that if you have good access to data, and are smart and diligent, you could make a lot of money using some of these ideas . ... Read more

Product Description
Classic text delineates and explores intermediate steps between basics of calculus and ultimate stage of mathematics—abstraction and generalization. Examines sets and functions, rational numbers, the real line in terms of the real number system, sequences and functions of a real variable in terms of continuity, differentiability, more. Over 500 exercises.
... Read more

Product Description
Volume 2 provides a comprehensive review of integral analysis in multidimensional Euclidean space. ... Read more

Product Description
The theory of the Lebesgue integral is a main pillar in the foundation of modern analysis and its applications, including probability theory. This volume shows how and why the Lebesgue integral is such a universal and powerful concept.

The lines of development of the theory are made clear by the order in which the main theorems are presented. Frequent references to earlier theorems made in the proofs emphasize the interdependence of the theorems and help to show how the various definitions and theorems fit together. Counterexamples are included to show why a hypothesis in a theorem cannot be dropped.

The book is based upon a course on real analysis which the author has taught. It is particularly suitable for a one-year course at the graduate level. Precise statements and complete proofs are given for every theorem, with no obscurity left. For this reason the book is also suitable for self-study. ... Read more

Customer Reviews (2)

couldn't be better than this
This book is great for graduate students studying real analysis.
There are tons of problems and proofs helping you understand the details.

Excellent book!
It's a good book for 1st year grad students who try to learn the technique of proof! ... Read more

Product Description
Hogwood, Brian W.DESCRIP_ALLOWED ... Read more

Product Description
Students preparing for courses in real analysis often encounter either very exacting theoretical treatments or books without enough rigor to stimulate an in-depth understanding of the subject. Further complicating this, the field has not changed much over the past 150 years, prompting few authors to address the lackluster or overly complex dichotomy existing among the available texts.

The enormously popular first edition of Real Analysis and Foundations gave students the appropriate combination of authority, rigor, and readability that made the topic accessible while retaining the strict discourse necessary to advance their understanding. The second edition maintains this feature while further integrating new concepts built on Fourier analysis and ideas about wavelets to indicate their application to the theory of signal processing. The author also introduces relevance to the material and surpasses a purely theoretical treatment by emphasizing the applications of real analysis to concrete engineering problems in higher dimensions.

Expanded and updated, this text continues to build upon the foundations of real analysis to present novel applications to ordinary and partial differential equations, elliptic boundary value problems on the disc, and multivariable analysis. These qualities, along with more figures, streamlined proofs, and revamped exercises make this an even more lively and vital text than the popular first edition. ... Read more

Customer Reviews (3)

Not a bad choice.....
I have studied Real Analysis from both this book and Bartle and Sherbert. Personally, I like both for different reasons and could recommend both.

Krantz, in my opinion is very good at providing a means to developing a geometric intuition, as he introduces basic point set topology very early and uses it throughout the text (this is a strength of Baby Rudin as well). I feel that Krantz's proofs are not as complicated as those in Bartle and Sherbert, and thus are much easier to follow. I feel that this book is easy to understand and includes a helping or two of complex analysis as a bonus.

Now, I would not be an honest person if I did not mention the mistakes in this book. Yeah, Krantz makes a few significant errors. They are sprinkled around so, just watch for them. I don't recall Bartle and Sherbert having as many.

Now, to contrast with Bartle and Sherbert. I feel that Krantz is lacking in its teaching of analysis techniques- Bartle and Sherbert achieve this well. Their proofs are much more complicated, but in that complication you learn a lot about how to DO analysis. Point set topology is mainly introduced in the last chapter so you lack that power through out the book (a poor choice of writing style in my opinion) but the machinery you develop in this book beats Krantz into the ground. Bartle and Sherbert is lacking a little on conceptual development in my opinion (but does have some strengths over Krantz even on this front).

Neither book is perfect, both are incomplete. As I said before, I could easily recommend both without reservation. I do recommend getting a copy of Rudin's Principles of Real Analysis as a supplementary text to either book. Rudin's book is very difficult for most undergraduates (It was very hard for me the first time I looked through it) but EXCELLENT. Given the choice, personally, I would have chosen Krantz because I felt that I understood analysis better after working through it. But having read Bartle and Sherbert first well prepared me for Krantz! Moral of the story: read both (if time permits).

To summarize:
1) Go with Krantz for concepts and to UNDERSTAND analysis
2) Go with Bartle and Sherbert for techniques and to DO analysis
3) Go with Walter Rudin to MASTER (undergraduate) real analysis after on of the other! (Unless you go to Berkeley or Harvard and are really smart- then just jump strait to Rudin)

Not Satisfied
The Krantz text- while it covers many of the topics of real analysis- its notation is not concise. I would look elsewhere.

Real Analysis and Foundations
This book is an excellent text for understanding the foundations of Analysis. I have used this book as a suplement for several math classes. It is a good refrence tool for math majors. ... Read more

Product Description

Real Analysis, 2/e is a carefully worded narrative that presents the ideas of elementary real analysis while keeping the perspective of a student in mind. The order and flow of topics has been preserved, but the sections have been reorganized somewhat so that related ideas are grouped together better. A few additional topics have been added; most notably, functions of bounded variation, convex function, numerical methods of integration, and metric spaces. The biggest change is the number of exercises; there are now more than 1600 exercises in the text.

... Read more

Customer Reviews (5)

Undergraduate Real Analysis
This book is great text for undergraduate real analysis. It may not be as rigorous as Rudin's but I would recommend it more because being more rigorous doesn't necessarily mean that students will learn more. The book contains both simple and challenging exercises. It is book that can be used as a first course in real analysis. It is both designed mainly for real-line analysis and not multivariate analysis. So, those wanting to see multivariate analysis need to buy another book. One book can't satisfy everyone and that's why there are other books out so that people can choose their flavour. This book is great in my eyes.

Real Analysis Book Review
It took a long time to get the book, something went wrong with the mail system (or so said the seller) but I finally recieved my item. It was 3 weeks late, but the book was in perfect condition.

Fantastic introduction to analysis
I am using another author's --Strichartz-- garbage text for an analysis course at Cornell.I saw this book at a local B&N near my home, and I immediately saw how superior it was to Strichartz's.This book keeps the beginner of analysis in mind, and the proofs of theorems are sharp and to the point.Plenty of exercises and problems to reinforce the material.The text includes a nice introduction to point-set topology and metric spaces.A++

A great 1-term-undergraduate text in Analysis
This book is a great introduction of the elements of real analysis.However the book chooses some awkward notation at times and skips pertinant depth where needed.My advice is to use as a supplement to a deeper text in analyis such as Maxwell Rosenlicht's, "An introduction to Analyis," Fitzpatrick's, "Advanced Calculus,"or the very terse Walter Rudin, "An Introduction to Mathematical Analyis."The book concludes before addressing multivariate analysis and leaves much needed topological aspect to the very end, this is why I recommend the book as a first-term undergraduate text in analyis in conjuction with my recommendation of Rosenlicht's text.Although, altogether very readable.

Real Analysis: A First Course in How to Think
Taking a course in Real Analysis from the author himself (Russell Gordon, Whitman College) is quite an experience, especially when the man's grading style is described as, "Take no prisoners."However, the book, like the author, is excellent and thoroughly challenges the intellect. Essentially a proof of calculus, the work details the majority of the theorems first-year calculus students are told just to accept and not question.After a grueling semester, one should feel confident about pursuing further studies in mathematics, as the text presents these (dare I say) "elementary" concepts in a clear, organized fashion.I only have one quibble: there should be a sticker on the cover that reads, "WARNING: Thinking Required," just in case the title itself didn't clue you in. ... Read more

Product Description
This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.

Closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, L(p)) classes, and various results about differentiation are examined in detail. Several applications of the theory to a specific branch of analysis--harmonic analysis--are also provided. Among these applications are basic facts about convolution operators and Fourier series, including results for the conjugate function and the Hardy-Littlewood maximal function.

Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis for student interested in mathematics, statistics, or probability. Requiring only a basic familiarity with advanced calculus, this volume is an excellent textbook for advanced undergraduate or first-year graduate student in these areas. ... Read more

Customer Reviews (6)

best book to learn measure theory from
this is a great, clearly written book that excels as a book to learn analysis from.the book takes a ground up approach, starting with only the positive real line and generalizing from there.being presented in the most simple context where all the abstraction is stripped away, the essence of the arguments is laid bare and thus the proofs are as understandable as possible.then, once the arguments are made and the intuition is in place, the book proceeds to generalize the results to more abstract circumstances. thus makingthe motivation for using more powerful tools clear.

this style can be compared to that of rudin's classic book, which is largely a disaster to learn out of.for instance, rudin's book oscillates between C and R for whatever gives the most slick, but often least insightful proof.this is fine, and even enjoyable once you understand the subject, but is terrible to learn from for most people.there isn't a better book to learn measure theory and integration out of than this book

One of the best real analysis books
For the past two semesters, our professor used this book as textbook. I didn't buy this book during that time. But when I was preparing for the final exam, I borrowed the book from library, and found it was really well-written. Basic materials are well organized and explained. Some profound and important topics are also covered, like Hardy-Littlewood max function; these materials are also explained in a clear and easy-to-follow way. Thus I decided to buy this book to prepare for my Real Analysis prelim and as future reference.

A (quasi) masterpiece
4 stars, which actually means 4.5. I don't rate it the maximum, because I think it lacks a couple of things to be perfect.

The pros:

1. the theory is built from the very ground up to the "ante-room", so to speak, of further and more advanced developments in abstract measure theory and functional analysis, in a deeply logical and clear way with the highest economy of words and of thought. From this viewpoint, for example, I don't see the fact of setting the theory in the R^n environment as a weakness: on the contrary, since it results from a deliberate choice of the authors, it actually ends up in an element of strength, because the reader/learner can take all the time he/she needs to become familiar with the "exact integration" approach of Lebesgue (which is *completely* different from Riemann's), and to visualize how things are going by using the familiar multivariable environment of R^n.

In other words: the reader can take all the time he/she needs to learn to swim, before he/she actually has to swim on the much longer and more difficult track of abstract measure theory (as a branch of functional analysis). I believe such a gradual approach to be better than a direct one, where from the very first page you are thrown into abstract measure theory, with the risk of being almost completely unable to understand what all that stuff is about.

2. The almost perfect way in which the authors build the theory and logically argument actually makes the book a fantastic school to learn the deep essence of the axiomatic method. This is its greatest strength, in my opinion: that is, the fact that in carefully going through the definitions, lemmas, theorems and corollaries (and in fact *working out* them) you can actually learn what the essence of correct mathematical thinking is. As long as I can remember, there are only a couple of other books, at the same level of this one, which are as good: i.e., Rudin 1 & 2 (the "Principles" and "R&C Analysis") and Einar Hille's "Lectures on Ordinary Differential Equations" (too bad it's definitely out of print. It would be such a great thing to have it reprinted in some economic edition).

The cons:

1. The Theorem of Integration by Substitution isn't demonstrated at all, with the possible exception of a particular case in the problems. Since it is a fundamental result and since its demonstration can be very enlightening from a geometric point of view, I think this is a weakness.

2. The part about Indefinite Integral and Differentiation (Vitali's Covering Lemma, and all the results deriving from it) isn't on the same level of the preceding chapters, and isn't as clear and well built as it is on Royden's "Real Analysis" (another great book): maybe because in the latter it fits naturally into the rest of the book (which is, in the first chapters where the theory is built from the foundations, intrinsically one-dimensional) as a necessary development of what comes before, while in Wheeden-Zygmund it seems to be forced in a book which, until that point, had been developing in an intrinsically multi-dimensional way: and this cannot happen at no cost.

Everything considered, it's worth its price (which, btw, is a little too high for a book of less than 300 pages ;) )

A good textbook for new learners
This book uses both classical and abstract approaches to introduce Lebesgue measure and integral. It starts with the classical approach and bases its presentation on Euclidean space. This makes it easier for new learners like me since it is more intuitive. In later chapters an abstract approach is also used. I find this repetition natural and helpful. This book has almost no typo. Its exercises are reasonably challenging.

It could be improved in page layout if the end of each proof is clearly indicated.

An excellent choice
This is the book we used when I was a grad student. This is indeed quite a nicely written book: logical progression of concepts, a large number of exercises of varying difficulty (hard ones have hints) and no typos (always a big plus with me). All the classical results are included. My only suggestions to make this book better would be to have some longer discussions of the concepts introduced to break the litany of definition-theorem-proofs and to include historical notes. This would make this book a little bit less dry and an even more enjoyable read. Nevertheless, this is one of the best books on the subjects, better than the book by Royden which is also used by some professors. ... Read more

Product Description

This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level. It provides a rigorous and comprehensive treatment of the theoretical concepts of analysis. The book contains most of the topics covered in a text of this nature, but it also includes many topics not normally encountered in comparable texts. These include the Riemann-Stieltjes integral, the Lebesgue integral, Fourier series, the Weiestrass approximation theorem, and an introduction to normal linear spaces.

The Real Number System; Sequence Of Real Numbers; Structure Of Point Sets; Limits And Continuity; Differentiation; The Riemann And Riemann-Stieltjes Integral; Series of Real Numbers; Sequences And Series Of Functions; Orthogonal Functions And Fourier Series; Lebesgue Measure And Integration; Logic and Proofs; Propositions and Connectives

For all readers interested in real analysis.

Customer Reviews (3)

Real Analysis purchase
Super fast shipping!Was exactly what was described.Would luv to buy from this seller again

Professors Should Choose Another Book
This was my undergraduate textbook for Advanced Calculus I and II (as they were called at my school).I am returning to school to start my master's degree this next term and am going through the book to refresh my memory.

Wow, it is just the way I remember it.Frankly, I can't believe the other reviewers ratings.So, I thought I'd balance the average rating a bit with a review of my own.

When I was in college, this was my most dreaded reading material.It is a difficult subject to master, sure, but the author does not help matters by using failing to use a clear structure with emphasis on key points.Instead, there is barely any structure at all.Headings consist of unenlightening phrases such as "Theorem."Pragraphs are downplayed by the typesetting style as well, making each section almost an undifferentiated block of information.(The author has not even used an end-of-proof symbol!)

And not only is this book unfriendly, it is dry.The author tends to use strictly symbolic language when explaining in words would be so much clearer.In fact, he frequently skips the explanatory material altogether and moves straight to the examples.What is the context or object for these examples?The reader is mystified.

If you are a professor, please do not choose this book for your analysis class.I have a feeling it is only comprehensible to those who already thouroughly understand the material.

If you are a student who has come here to buy this book, you have my sympathy.

Another excellent Real Analysis Text
The style of this book is a bit like Robert Bartle's Introduction to Real Analysis. It is detailed and rigorous. It is an excellent book for those who want to learn Real Analysis. ... Read more

Product Description
Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals. ... Read more

Customer Reviews (24)

A good intro book, but
My school's advanced calculus class uses this book, so I bought it from amazon. It is pretty good for beginners who goes into advanced calculus. However, sometimes the proof is hard to follow. I remember getting lost once or twice when I was reading it.

A good purchase
Thank you for speedy shipping. I am working on it and it is hard to analyze. HA!

The perfect transition to life after calculus
I certainly wasn't ready for Rudin after my freshman calculus series, and Ross's book was the perfect stepping stone. Almost nothing is assumed of the reader, the book starts out gently holding your hand through all the proofs, skipping not even trivial calculations. Don't worry the proofs get more concise as the book moves on to more complicated topics, but still maintains a high degree of readability. The examples are very insightful and there are many figures to speak to and help develop the readers intuition. This also makes it a great book for self study. In addition the sketch of the proofs to many of the exercises are provided in the back of the book!

From a pedagogical standpoint many colleges do not require their "mathematics education" majors to take analysis, perhaps because they don't have a course at the level of this book. A high school math teacher doesn't necessarily need to master Real Analysis at the level of Rudin, but they certainly need to know the basic theory of one dimensional calculus (especially if they are going to teach AP calc).

In summary this book is excellent for (1) freshman and sophomores taking calculus who want a bit more theory, (2) an analysis course for math education majors, (3) a transition course to a more advanced class, (4) current high school and community college math teachers who want a light brush up on the theory behind what they teach, (5) a reference for when you get lost in a more advanced text.

Good Intro Text
If you had a rigorous, proof-heavy calculus course, you could probably skip this book and go straight to something more advanced, like Apostol or Rudin. On the other hand, if your calculus class skimped on proofs, preferred a cookbook approach, or if the word "limit" doesn't automatically conjure up images of deltas and epsilons, then this is the analysis book for you.

While Ross assumes a working knowledge of calculus and basic proof-writing skills, he does NOT assume the reader has encountered too many of the results before. Thus, he includes numerous examples and exercises to familiarize the reader the definitions. The theorems aren't proven in the simplest way possible, but rather in a more intuitive way with few gaps. Sure, the proofs would be a lot shorter if he used some basic results from topology, but that would be a bit distracting for someone who wasn't very familiar with the material or with proof-writing in general.

In summary, this is an excellent introductory book for newcomers to analysis. If you learned calculus from Stewart, go here first. If you learned calculus from Apostol or Courant, this is a good companion to Rudin.

Excellent book
I went through a lot of math books that made me wonder if the author was purposely making it hard or if they were just bad at explaining things.
I didn't have that experience with this book. This book is well written and easy to understand (given its subject). Highly recommended for anyone learning Advanced Calculus 1 for the first time.



... Read more

Product Description

Basic Real Analysis and Advanced Real Analysis systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.

Key topics and features:

* The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them

* Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds

* The texts include many examples and hundreds of problems, and each provides a lengthy separate section giving hints or complete solutions for most of the problems

Because they focus on what every young mathematician needs to know about real analysis, the books are ideal both as course texts and for self-study, especially for graduate students preparing for qualifying examinations. Their scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, their clarity and breadth make them a welcome addition to the personal library of every mathematician.

Customer Reviews (3)

Kindle edition is unreadable
The kindle edition has many unreadable equations in it.
I don't know the root cause (translation to kindle format, etc.)
The bottom line is some of the equations are worthless.
Don't buy this book in this format.

Basic Real Analysis and Advanced Real Analysis Set
I have only scanned the book very quickly but the book appears to be well written which is why i purchased the books.They appear very clear and easy to follow for self study.I like the fact that everything is explained including "standard" notation.Unfortunately, I have only scratched the surface in each book; however, they seem perfectly suited for a non mathematician interested in becoming one.

Great book for real analysis
This is a fabulous book for learning real analysis. I've never taken a course in the subject (High school doesn't have one) but I have used the book for an independent study. After a fair study of point-set topology, this book can take you in and out of real analysis with ease. It's comprehensive and provides interesting insight into fields you thought you knew. It first tackles the problem of axiomatizing basic calculus, thenit gives some background on metric spaces before hitting calculus of several variables and ordinary differential equations. The chapter on metric spaces was far more comprehensive than any I've read, and I've never seen a book that develops the theory of differential equations from an abstract perspective (none to this degree at least).

After this, it hits the meat of real analysis: Measure theory (and Lebesgue integration). Again, the author does an excellent job explaining and elaborating on this powerful theory. Euclidean spaces, topological spaces, L^p spaces, and Hilbert/Banach spaces take up the rest of this book. It even includes a very interesting chapter on Fourier transforms for Euclidean spaces. Overall, it's definitely worth the buy.
... Read more

Product Description

This new approach to real analysis stresses the use of the subject in applications, by showing how the principles and theory of real analysis can be applied in a variety of settings in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization. Users will be prepared for more intensive work in each topic through these applications and their accompanying exercises. Chapter topics under the abstract analysis heading include: the real numbers, series, the topology of R^n, functions, normed vector spaces, differentiation and integration, and limits of functions. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. This book is appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra.

Review of the first edition, Real Analysis with Real Applications:

"A well balanced book! The first solid analysis course, with proofs, is central in the offerings of any math.-dept.;-- and yet, the new books that hit the market don't always hit the mark: The balance between theory and applications, --between technical proofs and intuitive ideas,--between classical and modern subjects, and between real life exercises vs. the ones that drill a new concept. The Davidson-Donsig book is outstanding, and it does hit the mark. The writing is both systematic and engaged.- Refreshing! Novel: includes wavelets, approximation theory, discrete dynamics, differential equations, Fourier analysis, and wave mechanics." (Palle E. T. Jorgenson, Review from Amazon.com)

Product Description

Product Description
A Course in Real Analysis provides a firm foundation in real analysis concepts and principles while presenting a broad range of topics in a clear and concise manner. This student-oriented text balances theory and applications, and contains a wealth of examples and exercises. Throughout the text, the authors adhere to the idea that most students learn more efficiently by progressing from the concrete to the abstract. McDonald and Weiss have also created real application chapters on probability theory, harmonic analysis, and dynamical systems theory. The text offers considerable flexibility in the choice of material to cover.

* Motivation of Key Concepts: The importance of and rationale behind key ideas are made transparent
* Illustrative Examples: Roughly 200 examples are presented to illustrate definitions and results
* Abundant and Varied Exercises: Over 1200 exercises are provided to promote understanding
* Biographies: Each chapter begins with a brief biography of a famous mathematician ... Read more

Customer Reviews (1)

One of the better books on real analysis
I have several books in real analysis including those by rudin, kolmogorov, reisz, etc.Of all the book I have on real analysis, this is by far the most lucid.It is thicker than all of them but only because the authors (McDonald and Weiss) spend time in explaining and motiviating the material.I have learned more in a shorter amount of time from this book than any other advanced math book I own (and I own at least 50 on everything from topology to stochastic processes to algebra).The proofs are clear and the steps are explained in layman's terms (at the level of something like Scientific American's typical readership).The material covers the Lebesgue theory of integration, abstract measure theory, mesure theoretic probability, hilbert spaces, etc.My goal is to learn stochastic calculus beyond the mere manipulation of Ito's lemma and I must say this book, more than any other, is getting me to that level of mathematical maturity quickly.Now I feel pretty confident I can understand that proof in HJM (for you finance buffs out there) involving the stochastic version of Fubini's theorem that always bugged me! ... Read more

Product Description
Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible.The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces.For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts. ... Read more

Customer Reviews (3)

traditional text on real analysis
Professor Trench has made the online version of this text that is absolutely free.I think this is a very traditional real analysis book appropriate for advanced undergraduate mathematics students.My experience with real analysis is the old classics by Walter Rudin,Thomas Apostol and Halsey Royden.Unlike those tests which can be used for advanced undergraduate or graduate level texts, this book has two chapters covering introductory calculus which can serve as a refresher for undergraduates who have not seen this material for three years.The material is well-established and with Professor Trench's long experience as a teacher it is inconceivable that the text would be filled with errors.The online version was made available in late 2009 and is essentially the same as the hard cover 2002 text except that it has corrected some errors and misprints from the 2002 version which is now out of print.So new copies of the 2002 hard cover issue may be hard to come by.The online issue looks just as professional as the hardcover version.

The content is typical for a first course in real analysis and is certainly worth considering for a class text.Each chapter contains an ample number of problems to give as homework problemns to reinforce what is covered in lecture.

I would also like to add that the review by "A customer" is written by a student who would not necessarily have a good insight into what constitutes a good text on real analysis. Also there is no content to support his remarks which are purely sarcastic.I am skeptical about the remark that his professor did not like the book and only used it becuase he is a friend of French.Being that there are so many texts that could be used for this type of course in real analysis it is inconceivable to me that a professor who seriously wants his students to learn the subject would pick a text that he thought was not the most helpful for his students and that he would feel comfortable teaching from.If this were really the case then I wouldn't be surprised to know that the instructor was a poor teacher who didn't care much about teaching the subject.In that case the student could easily be disguntled because he did poorly in the course and chose to blame the text rather than the instructor.But students rarely depend on the text to learn the course and the instructor plays a crucial role in courses that are taught in a traditional manner.

I took my courses in real analysis many years ago and so I am not sure exactly what constitutes an indergraduate course in real analysis in 2010.However, from my experience much of what is covered in the book was covered in first and second year calculus when I was an undergraduate and chapters 1 and 8 are most like the material in texts like Rudin's.

It's not as bad as the other guys says.
I've been reading the online version of this book and I am unsure why the original reviewer is so unhappy with it. I'm only on Chapter 3 so far, so I cannot fully judge its contents, but from what I've read it's been very readable and I have learned from it. Is it my favorite book ever? No, but it has not once struck me to be categorized as one of the worst.

Read it for yourself:
[...]

Horrible, useless rife with errors
While there may be books covering the subject of real analysis worth even less than this book, I am not aware of their existence.My professor even admits Trench's book is not very good and only used it because the two of them are friends.The bonds of fraternity are not so strong; however that he will ever use it again.

Of particular disinterest are chapters 5 and 6. Both are so full of mathematical errors that I suggest any student, unfortunate enough to use this book, supplement his or her reading by finding a text that manages to actually define what a gradient is. ... Read more

Product Description

Customer Reviews (12)

Back on BP Meds

I have been free&clear of blood pressure meds for 3 years know and after reviewing this book for a few newbies in my department, I'm back on meds again. I normally read reviews by others with a grain of salt. I echo BEJTLICH's review at this ill fated attempt to explain packet analysis using Wireshark. This book needs to be pulled and is in dire need of a thorough technical review. Newbies would be better off reading Jeanna Matthews - Computer Networking: Internet Protocols in action. After reading and spending sometime with MATTHEWS's book, you would be better prepared to analyze packet information from Wireshark or Nmap and the like on your own, better than PPA ever could. Cheers.

The title states the obvious
While this book will give you a passable introduction to the technical aspects of packet analysis and WireShark, the goal is to introduce the reader to some practical uses of WireShark. It answers questions that the accidental, occasional or beginning user asks themselves. I do not fault the author for a few inaccuracies as almost every technical/boring tome has them if you stay awake long enough to come across them. Since this book is so short, it made an easy target for the trained professional reviewer to rip it to shreds. Oh well.

If you want serious, practical training in the use of WireShark, find out about the consummate expert in teaching this subject. Her name is Laura Chappell. Search the web for more info. She goes light years beyond any publication in print with on demand and live video seminars and training for the serious student. Chappell has numerous titles (10 or more) specific to this subject listed on Amazon.com.

Foot Wetter
This book would be great for a beginner or computer tech that is becoming a network tech. This book gets the idea of Wireshark and its possible uses across very well and is an easy two-day read. Some stuff left out but not bad considering that the book is under 170 pages. This book will introduce you to Wireshark, and inspire you to dig deeper to read more about packet analysis and TCP/IP.

worth a look
As there aren't too many books out there on use of wireshark I found this book to be quite useful for people wanting to get their hands onto trying. I was looking for some books that would be good as a learning tool that I can throw to new members on my team and this book was roundly accepted, particularily the real world examples. By no means should this book be the only one on your shelf as there are many concepts that need to be delved into to really get a firm understanding. The book begins with a basic intro to general router concepts and hardware, it then goes into the functions of Wireshark. I found that this information could of been found on the Wireshark userguide or help file. It was basically a re-hash here so that space could of been better used providing more info about routers in general instead as a lot of the real world problems come from misconfigured routers or machines.

Overall after reading the book the reader should get a fair understanding of TCP/IP concepts and communication on a network and is a good jump off point onto more advanced books.

A must for Wireshark users
Lately I have been reading reviews after I buy books just to see how they stack up, and this is no exception.I bought the book after checking it out at the book store and saw that there was good stuff in it. If you use Wireshark, or if you are learning it, you should have this book on your shelf period.
Chris Sanders not only does a great job of introducing you to the mindset of packet analysis, he shows a side of it that most of the people I interact with don't consider...the day to day administrator's needs for a way to diagnose network problems.

If you live the world of network monitoring and information security then this books works for you as well. The concepts are what is important and they are presented very well.

As to those who say there are too many things like the mis-representation of the three-way handshake I say Thanks for pointing it out to the novice among us. For the novice, now you know, so...buy the book anyway.If I put a technical book back every time I saw a mistake that the proofer missed, I'd have empty shelves.

Thanks Chris for taking a tough subject and making it much easier to digest. ... Read more

Product Description
From the Foreword by R.N. Bracewell, Stanford University:

"...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied."

A sweeping exploration of essential concepts and applications in modern mathematics and science through the unifying framework of Fourier analysis! This unique, extensively illustrated book describes the evolution of harmonic analysis, integrating theory and applications in a way that requires only some general mathematical sophistication and knowledge of calculus in certain sections.

Key features:

* Historical sections interwoven with key scientific developments showing how, when, where, and why harmonic analysis evolved* Exposition driven by more than 150 illustrations and numerous examples* Concrete applications of harmonic analysis to signal processing, computerized music, Fourier optics, radio astronomy, crystallography, CT scanning, nuclear magnetic resonance imaging and spectroscopy* Includes a great deal of material not found elsewhere in harmonic analysis books* Accessible to specialists and non-specialists

"The Evolution of Applied Harmonic Analysis" will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, applied mathematics. ... Read more