Product Description
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included.

This text is part of the Walter Rudin Student Series in Advanced Mathematics. ... Read more

Customer Reviews (102)

The so-called "baby Rudin", but where are....?
Good as a reference book and possibly good as a textbook for an introductory course in one-variable mathematical analysis by using its ealy chapters. However, as one reads toward its final chapters one finds serious omitions of basic topics. The multivariable Taylor's theorem is stated as an exercise, so that, if the undergraduate student does not realize this or can not prove it, he/she learns neither Taylor's theorem nor becomes aware of the theory of extrema and all... Is there any mention to constrained extrema and Lagrange's multiplier rule? Nowhere. Where is Fubini's theorem? Fubini's theorem is hidden (incorporated) in the definition 10.1.In fact, both Lagrange's and Fubini's names are not even mentioned in the book's index. The fame of the book is not proportional to its contents. Probably when it was first published (and used at MIT) it was among the few good available ones. To be sure, it contains many clever arguments and good (rather difficult) exercises, afterall, it was written by a well-knwon scholar for his many contribution in analysis. I have seen it in use as a textbook in advanced calculus courses, for sure, it does make the instructor lookmathematically sophisticatedin the eyes of his\her students..., at the same time it impresses students, however, very few learn from it and understand the subject... without having apriori knowledge of the subject, viz, having learned the subject from other sources...( a bit unclear and mistified story in the "baby Rudin" as some call it, isn' it?). The mature Rudin's "Functional Analysis" booktells a much better story much more clearly, with also clever proofs (with no tricks nor games) and with a cohesive strategy and developement (unlike the "baby" one!).

Excellent buy!
Excellent book with a modern presentation of the subject. Excellent packaging and delivery. Very satisfied.

A superb introduction to analysis
It is not really possible to add anything to the many positive reviews already here, so I will reaffirm the fact that Rudin's Principles of Mathematical Analysis is indeed the best book from which to learn basic analysis. While it is not an easy book to learn from, it forces you to really know the subject and be able to think for yourself.

It's a classic - should be in a museum, not the classroom.
From other reviewers:
"Imagine you are trying to learn the English language, but the only tool you have is an English dictionary. That is what it feels like using this book."
"... very few visualizations and examples."
"He goes out of his way to make his proofs terse and 'clever,' ..."
"The proofs are terse and Rudin makes them as short as possible, ..."

In an axiomatic system, one should be able to cite previous axioms, definitions, and theorems as justification for statements made. Some reviewers say the things left out in a Rudin proof are natural steps. However, some mathematical statements which seem obvious are actually the most difficult to prove. Rudin sometimes just states things without justification.

I think the way Rudin teaches analysis is akin to teaching someone to swim by throwing them into the deep end of the pool. If you don't make it, "Oh, well!"

Rudin is tradition. Just because we've always done it this way isn't a reason to keep doing it that way. I want to follow a path that illuminates.

Rudin is an obstacle. "Let's see how tricky we can be." In other words, let's see if we can trip up the students. I'm not into "baptism by fire."

What this book is REALLY like
Ok, so judging by all of the reviews here, each one of them will fall into two separate categories (1) This book is the divine word of God; as opposed to (2) this book sucks. It's a bit hard to really tell what this book is like with all the contradiction, so let me try to sort things up. Please note that my review is focused on only the first 8 chapters, for multivariable analysis I will be using Munkres' Analysis On Manifolds (Advanced Books Classics) (word on the street says that chapters 9, 10, and 11 of Baby Rudin are not that good).

What do I need to know to even consider reading this?
You should have solid proof-writing skills. I personally used Spivak's "Calculus" and this was more than enough preparation to comfortably go through Baby Rudin. I feel that a good meaty Calculus course like Spivak or Apostol will get you to the level you need to use this book. But what if you didn't have such a calculus course? I would then say two proof-orientated courses is good enough. In order to use this book and have an enjoyable experience doing so, you will need to be able to write proofs well.

How terse is it?
This book is not that terse. I feel that people mistake terseness for a lack of BS. Rudin "gives it to you straight" in the sense that every word and sentence is used effectively. There is no chit-chat and no wasted sentences.Despite what people on here will say, Rudin does not take giant leaps in his proofs. I found all of the small steps that he leaves out to be quite natural to fill in. Anytime he says something is obvious, all I had to do is do some scribbling on a couple lines and I normally found out that it was pretty easy to justify. It eventually got to a point where I started mentally filling in those small steps and there was no need for scribbling. I also like that he leaves small natural steps out because, in filling them in, you become actively engaged in the material that you are learning.

How difficult is it?
For the most part it has what I would say a "medium" difficulty. Here is what I mean. All of the problems are there for a reason, and each one teaches you something new. However, many of them have hints that guide you to the solution. However, there are a few problems each chapter that are mind stretching, and these are real gems for the problem solvers. Nothing that is used later on in the text is relegated to exercises (so it should be theoretically possible to just read the text alone.) However, the reader who persistently attacks the problems will start to make connections and witness changes in their mathematical reasoning after a couple chapters. There are also a couple of problems each chapter (increasingly more as you go further into the text) where he asks you to decide if something is true, and then prove your answer. These are great problems because they force you to develop a strong intuition in Analysis that other texts can not give you. I often times found that if I flipped ahead to see the problems I would be dealing with, they looked impossible. Yet, when I actually got there and started from exercise 1 and tackled most of them one-by-one, my skills had increased so much that I was able to come up with the solutions in a reasonable amount of time.

What about the lack of motivation and abstraction?
You already had calculus. You know what a derivative and integral are. He is not pulling these ideas out of thin air. While I might argue that motivation and paragraphs explaining where ideas came from are good in general, in this case they are not necessary. You already know the motivation from lower-division calculus, so what more do you want? (note that the lack-of-motivation problem is said to be serious in the last three chapters) The abstraction in this book is not bad if you already had a good single variable calc course. If not, then by taking two other proof-based courses you should be used to thinking abstractly and giving abstract arguments. If you can't handle Baby Rudin after this, then I would question the integrity of the mathematics department at your college/university.

Can I use this for self-study?
I am. I am going it alone right now, and I am having very little difficulty doing so. I had no prior topology before Rudin, and yet I was able to learn all of chapter 2 by myself using only this book. So once you get past the style that he wrote this book in, I feel that anyone with the right background can use this for self-study. But what about the lack of solutions? Well it happens to be a fact that most math texts do not contain solutions, and so we are all just going to have to deal with it. I often times went by a gut-feeling. That is, I knew when I got something right because I just did some many of the problems that I developed some sort of intuition for it. Yet, if I ever felt that something "just wasn't right" in a proof I gave, then I knew my proof was wrong. I would always be able to come up with a correct proof afterwards. If you have the right background, you will be able to develop this intuition as well. If you are still unsure, Baby Rudin is such a famous text that I am sure answers are on the internet somewhere.

Overall this is an absolutely first-rate textbook, and it is now one of my favorites. I am so glad that I gave it a try because I feel that I understand analysis at a much deeper level than what I previously did thanks to Rudin. In fact, I became such of fan of Walter Rudin that I bought Papa Rudin (Real and Complex Analysis (International Series in Pure and Applied Mathematics)) to go through as well! This is an incredibly well-written textbook, so DO NOT mistake poorly-written for a lack of BS (Walter Rudin won the Steele Prize for mathematical exposition for this and Papa Rudin, so don't bash it). There is a reason this has been the definitive undergrad analysis text for over four decades! I hope I was of help to you all. ... Read more

Product Description
This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts that are set in abstract settings. ... Read more

Customer Reviews (49)

A valuable reference for empirical modelers
My learning in statistics follows a funny order. Before receiving fundamental training in math stat, I took an introductory stochastic processes and graduate econometrics. I use Rice's book for a math stat course this summer and find this book a valuable reference!

This book helps me synthesize what I've learnt from stochastic processes and economoetrics. On top of that, it provides very useful techniques that will assitempirical modelers to perform estimation of probability models and dereviation of random variables. This book is not advanced enough for stat PhD students but definitely a must-read for non-stat majors who want to get a deep understanding of statistical sciences.

I personally obtain ideas from this book to solve problems confronted in model-development and data-manipulation.

The only thing I would complain about this book is its price.

Decent book but not for biological sciences
This book provides a decent review of basic statistical concepts with application examples.The strengths of the book are that it has a good background chapter on probability, provides some information on non-parametrics, and is firmly rooted in mathematics (ie proofs are offered to demonstrate how some formulas are obtained).Weaknesses of the book include an odd narrative (not typical for a textbook), poorly organized chapters, and inadequate coverage of some topics (ANOVA, MANOVA, ANCOVA, normality tests, K-S test, etc.).I do not recommend this book for anyone in the biological sciences because it does not adequately cover the most used "advanced" tests.

Bought out of compulsion
I had to buy this book just because my teacher used it as required text. The book is pretty mediocre, clearly not worth $135. You can get much better understanding of statistics using books by Schaums series. The book does have decent examples, but is very overpriced- I do not believe it should cost more than $20.

A good introduction, good reference
This is one of the most readable mathematical statistics textbooks. The level of math used is just right for this course. You need to use is mostly univariate calculus, but partial derivatives may pop up in a few places. You also need to know matrix algebra to read most of the chapter on linear models. All derivations and explanations are clear. The statistics portion of the text starts with sampling theory. In fact, it has more on sampling than I personally wanted to learn, such as sampling from finite populations and stratified sampling. Then it continues with estimation methods and hypothesis testing. There is a very good chapter on descriptive statistics. The later chapters focus on specific models, such as comparing the means of two samples, analysis of variance, categorical analysis,and finally the linear regression. The first chapters summarize probability theory, so the text is very much self-contained even for those with no probability background. There is also a chapter on Bayesian methods, which I haven't read.

The two features that I personally like in this text is that for some models the author presents such modern and sophisticated topics like non-parametric statistical techniques and bootstrap methods for obtaining standard errors. Overall, this is a fine textbook. It gives a solid introduction to statistics for people who need to do statistical analysis on their own and for whom this is their first and last statistics course. This text also gives a nice introduction for students of statistics who plan to move onto more advanced texts. There are one or two places where the derivation is simple but gets a little daunting (I think one of them is one of Wilcoxon's tests). But in the end, you must accept one fact. This is a serious university level applied math text for sophomores/juniors. This book can't be read like a novel, though it is a very readable text as far as mathematical stats goes.

Ignore most of those negative comments from readers many of whom clearly have not mastered their calculus and probability skills before taking a stats course. Undergraduate mathematical statistics is a kind of a course that attracts lots of people from many different majors and math backgrounds. Some take stats only because they have to, not because they want to. In the end, (this may sound arrogant), but the quality and motivation of students in an undergraduate mathematical statistics courses may be very variable. Some probably do not belong in a serious stats course. Hence, the flood of negative reviews for this text.

Dont waste your money and this book is really confusing
if you have choice, dont buy this book, it just waste your money and it will totally confuse you. you wont understand the concept through this book. unclear definition, useless example, if you have to use this textbook, you have better have time to search statistic information online by yourself. i am currently suffering from this book, since it is written by a professor in our school. i dont think he knows students well, the book is so unclear and confusing :( ... Read more

Product Description
The Student Solutions Manual provides completely worked-out solutions to all odd-numbered problems in the text. ... Read more

Customer Reviews (5)

Quite Good Condition
The book is in quite good condition, but I have to say the delivery sucks.

Shipping issue
The book came and great condition. But was poorly packaged, the book was hanging out of the packaging, luckily it was not lost in the mail. Other then this it was a great buy.

The book is fine
the only thing i was very not happy with was the shipping because it took so long so I felt behind in my material

Nice book!
This book is really easy to understand. Its language is so simple. Anyone can read and understand it so well, even if your first language is not English. It gives nice examples with details to explain the solutions of the problems. It's about 19 chapters and they are: 0. Algebra Refresher. 1. Equations. 2. Applications of Equations and Inequalities. 3. Functions and Graphs. 4. Line, Parbolas, and Systems. 5. Exponential and Logarthimic Functions. 6. Matrix Algebra. 7. Linear Programming. 8. Mathematics of Finance. 9. Introduction of Probability and Statistics. 10. Additional Topics in Probablity. 11. Limits and Continuity. 12. Differentiation. 13. Additional Differentiation Topics 14. Curve Sketching. 15. Applications of Differentiation 16. Integration. 17. Methods of Applications of Integration. 18. Continuous Random Variables. 19. Multivariable Calculus. I recommend this book for students or readers for business because it teaches the basics of the topics (above)

You've got to have this!
The authors of this book seems to be a mathematician if you take a good look at all his other books. Great for intermediate mathematicians! ... Read more

Product Description

Customer Reviews (4)

great for self-teaching
I am currently reading this book so I can learn calculus the "right" way. My undergrad courses in advance calculus and complex variables (notice I say variables and not analysis) were written for engineers and science majors that needed to know math, but not at this level. I find the sequence of topics (sets and functions, real numbers, sequences, ...) extremely helpful for understanding the material. One topic leads to another in a very logical and progressive manner. The problems range from the very easy "one liners" to more complex problems. The book contains hints to solving them at the end of the book. Very nice for self-teaching.

my advice : buy this as a reference
The pro's : Very good, everything is explained in a clear way, starting from the beginning, no gaps left in the proofs, and the material is abstract enough to motivate math lovers...In fact every math undergraduate and graduate should have this book as a reference, this cannot be a problem when you see the price.

The con's : Dover always has cheap price editions. While there is definitely a market for this, let' s face it : these editions have some disadvantages :While the contents of this book are very well suited not only as a reference but also to learn the material, the dense layout is not so comfortable to learn from. In that sense, the authors deserve a better edition... Maybe a question to the Dover guys : is it possible to bring your excellent science books in two editions : the existing cheap editions, and another more comfortable edition : bigger size, more whitespace on each page, ....

One of the better math textbooks
A very good introduction to real analysis, with all the appropriate theorems and proofs presented in a well ordered and understandable fashion. I use it regularly in my own teaching and research.

Very good
Everybody seems to think that Rudin's Principles of Mathematical Analysis is the best for whatever reason, & I agree that it's good for reference after being exposed to the material. Pfaffenberger doesn't construct the real numbers using Dedekind cuts, he makes a list of 13 axioms that basically say that the reals is the only complete ordered field. I think I liked this approach better than Rudin's (or Hardy's) more abstract approach. He also spends much more time developing metric spaces (including the Baire Category Theorem & nowhere dense sets, etc, which Rudin omits except for a couple exercises) and the Riemann-Stieltjes Integral. Then there's a short chapter where transcendental functions exp, sin & cos are defined which I think Rudin skips, and then introduction to inner-product spaces. Fourier series is introduced in the chapter on general inner-iroduct spaces (with a first look at Banach Spaces as an aside) rather than the chapter on sequences & series of functions. I also liked this better than Rudin's text or other calculus texts. Rudin includes a whole chapter on functions of several variables, but Pfaffenberger doesn't have anything on them. Instead, there's a chapter on normed linear spaces and the Riesz Representation Theorem, and then similar to Rudin, a chapter on the Lesbesgue Integral. This book has many more problems than Rudin's or Apostol's, and in general they are a bit easier. Of course every section has its difficult ones but the first ones are almost always just "verify that blah blah is true". The last ones are about on the same level as the ones in Rudin's book. ... Read more

Product Description
Mathematical Reasoning helps your child devise strategies to solvea wide variety of math problems. These books emphasize problem solvingand computation to build the math reasoning skills necessary for success inhigher level math and math assessments. This book written to the standardsof the National Council of Teachers of Mathematics. Book 2 is supplemental at the higher grade levels. These highly effective activities take students far beyond drill-and-practiceby using step-by-step, discussion-based problem solving to developa conceptual bridge between computation and the reasoning required forupper-level math. Activities and units spiral slowly, allowing students tobecome comfortable with concepts but also challenging them to continuebuilding their math skills. Publisher: The Critical Thinking Company Format: 296 pages, paperback ISBN: 978-0-89455-402-5 ... Read more

Customer Reviews (1)

Critical Thinking: Math
This is a good book that needs some teaching assistance to get the most of the subjects. Parents can also use this too. Its not your ordinary math book. Some of the material requires thinking and critical but I would recommend this book for parents or teachers who want to enhance the student thinking skills in math.Also, this book is excellent for students who enjoy math a lot. There no pictures for entertainment at all.There isn't any answer keys in the back.You have to purchase the answer book which adds more to the cost. ... Read more

Product Description
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises. ... Read more

Customer Reviews (12)

One of the Best Books in Analysis, or even Maths
I dont know how to say how good this book is: it not only teaches us the technical aspects of mathematics, it also teaches us intuitions, ideas behind the proofs, styles, and philosophy.

I would like to also start with a comparison of the classic baby Rudin:

While Rudin's little book is also a real gem, I would say Pugh's belongs to a slightly higher level (due to its problems mainly and topic selection and coverage). Rudin's book could either be used in 1st year one semester as a strong first course in basic analysis (1st 7 chapters) for extremely motivated and hardworking students (such as those at MIT, Harvard, Princeton, and many other good institutions), or ought to be supplemented in an honour's undergrad real analysis (in 2nd year or 3rd year). Its presentation of Lebesgue theory is rather incomplete and no one virtually uses it for lebesgue theory. On the other hand, pugh has a full chapter on it, covering almost all the standard undergrad lebesgue materials.

Pugh's book on the other hand can be the last reading before attempting Folland and Big Rudin. Knowing pugh well and having solved its problems would make Folland and big Rudin not hard, whereas little rudin may not surve this purpose that well. Many Rudin's problems are hard but standard (Prove, Show this. Very few is it true? what about?), whereas Pugh's is more thought provoking (Is it true? What about? What do you think? which mimics a key part in maths research).

Moreover. mathematics is not just about formalism and logic, especially in analysis ang geometry. The ideas and our feeling about how the objects behave are at least equally important. (Anyone can write proofs well with sufficient training; yet not everyone feels that a measurable function is no more complicated than continuous ones in a sense; why lebesgue's definition of length and integral are powerful; weirstrass approximation is as simple as "taking expectations of functionals", etc.) Amazingly Pugh's book trains people to this direction very well.

I prefer Bartle and Sherbert
I used this book in my first Real Analysis course and thoroughly disliked it.I seems that everyone else who reviews this book mentions Rudin.I haven't had a chance to read Rudin yet but I prefer Intro to Real Analysis by Robert G. Bartle and Donald R. Sherbert over this book.Many people like Pugh for it's conversational tone but I found it annoying.This might be a good secondary book but I wouldn't recommend this as your first book in real analysis.Pugh makes the cardinal mistake of mathematicians in introducing the most general case first.The most important thing in mathematics is not the most general case but the process of generalization itself.This is like saying the journey is as important as the destination.To generalize one must start with a specific case and then work, layer by layer, to the most general case.That's one reason I prefer Bartle and Sherbert.It starts with functionsfrom R to R and generalizes from there.It takes up where undergraduate calculus leaves off.I also prefer the exercises in Bartle and Sherbert better. They are challenging without being infuriating. They are still general proofing exercises but are specific enough to deal with specific functions, series, sequences, and so forth.I was also annoyed by the way Pugh qualifies his proofs like Chapter 1 Theorem 2: "Proof Easy" ,or theorem 9: "Proof Tricky!", or Chapter 2 Theorem 10:"Proof, Totally natural!".I feel his language is imprecise and sloppy. I feel the section on cuts is superfluous. It seems that cuts are a lot of work and headaches just to prove that everything I learned in elementary school is correct. I was worried that x+0 didn't really equal x but now with cuts, I can rest assured that it does! Whew, what a relief!The only plus to Pugh is the thorough chapter on metric spaces helps put things into a broader context.All and all I dislike Pugh's book and highly recommend Bartle and Sherbert. as the best introduction to Real Analysis.

Excellent problems and diagrams -- great book
This is an excellent introductory text on real analysis. It is very approachable, and he does a very good job at supplementing the traditional "definition-theorem-proof" style with intuitive explanations and wonderfully descriptive diagrams (the diagrams are one of the strongest points of this book -- and are something that are sadly left out of many otherwise good books on analysis).

My only (minor) complaint is with the layout/formatting of the book -- it is very jumbled together, the typesetting is poor, and it looks like it was printed on a low-resolution $10 printer.

Other than that, it is an excellent companion to a more in-depth/advanced treatment. As far as more "advanced" books go, I would recommend -- Apostol's "Mathematical Analysis" and/or Shilov's "Real and Complex Analysis" -- both of which are incredibly well written and informative.

Pugh is wonderful. Rudin is good too, but both texts working together is the best.
I wish that I had discovered Pugh in my first semester of undergraduate analysis. The assigned text was Rudin and it was a great choice. The exposition there is excellent. The exercises are incredibly well done. Pugh covers just about the same material as Rudin, and in the same rigor, but is more likely to give you paragraphs before and after important theorems/definitions that help to clarify things. I must admit I am not too familiar with the first half of Pugh's text as I didn't discover it until I was well in chapter 10 of Rudin ~~ chapter 5 of Pugh. But, if the first chapters are as good as the fourth and fifth, you can get just as much from Pugh as from Rudin, if not more.

Sometimes, you get a picture (this would have been really helpful back when I was learning what an open cover was). Other times, Pugh actually gives a better presentation. For instance, when discussion the rank theorem, Rudin's statement of it is hard to follow. The proof is about as difficult. Pugh, however, introduces C' equivalence and then gives an alternate statement of the theorem which is much more intuitive. AND some pictures after the proof. Some think having pictures in analysis books is bad--Pugh gives evidence otherwise.

It is difficult to say which text has better exercises as I have not attempted them all. But Pugh definitely has more of them. I think the best thing for any undergraduate to do is to just own both books. Rudin is the standard for a good reason. Pugh's or someone else's exposition may become the standard in the future, but Rudin will always be an excellent reference. Doing Rudin's exercises will help prepare you for your qualifying exams if you ever take them. Pugh has some UC Berkeley good prelim exam questions in his book which prepare you for future math endeavors as well. So I say just buy both. But if you can only buy one.... probably get Pugh because he's cheaper. Or you can get International Edition Rudin for cheaper still.

Brilliant
The style is friendly and fun, and the presentation is really intuitive! My personal favorite! ... Read more

Product Description
Gian-Carlo Rota was one of those rare mathematicians who made major contributions to several areas of mathematics. Presented in the first part of this volume are reprints of his papers in analysis, which were written at the beginning of his career. These papers on differential equations, operator theory, ergodic theory, and other subjects have a continuing and pervasive influence. Reprints of his papers on convexity and probability theory are presented in the second part of the work. These were written towards the end of his career and contain many ideas that have yet to be fully developed. Comprehensive commentaries are included in every chapter. These survey articles detail work inspired by Rota's papers and also include discussions of many unsolved problems.

As is customary with Rota's writings, the papers included in the volume---some published here for the first time---contain many fresh and unexpected ideas for further research. Thus, this volume will be of interest to both experts and beginners in the above-mentioned fields.

Contributors: J. Dhombres, P.L. Duren, W.N. Everitt, D.A. Klain, J.P.S. Kung, A. Ramsay, M.M. Rao, J. Rovnyak, H.H. Schaefer, B. Schultze, J.T. Schwartz, N. Starr, G. Strang, D.C. Torney, R. Zaharopol, A. Zettl, X.-D. Zhang ... Read more

Product Description

It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

... Read more

Customer Reviews (19)

Excellent Text on Analysis
This is an excellent text on analysis-- much superior to Rudin's Analysis.Rudin is too spare;Apostol has plentiful examples and material.Covers more ground too.

Classic introduction to analysis.
Apostol's Mathematical Analysis is a classic introduction to analysis.The book truely is an advanced calculus book, which makes it a great place to start developing the fundamental concepts of analysis.The material covered will look familiar to the calculus student, and it is covered in a clear and concise enough manner to be easily accessible.

Excellent Intermediate Real Analysis Text
"Mathematical Analysis (2nd Ed.)," by Tom Apostol, does an excellent job of bridging the gap between standard introductory calculus texts and full-fledged treatments of topics in analysis.Apostol's book covers significantly more material than the gold standard of such texts, "Principles of Mathematical Analysis" by Rudin, and does so in a very different style.Where Rudin is brief and elegant, Apostol is thorough, detailed and friendly.Both Apostol's and Rudin's books have been around a long time, for very good reasons.

Unlike some intermediate texts, Apostol's book spends little time restating the particular results of elementary calculus (e.g., the derivative of sin x or x^n) in the new language of a more theoretical approach.Unlike Rudin and similar texts, Apostol *does* give detailed proofs, with thorough explanations.As a result of this approach, Apostol's book is not particularly well-suited to serve as a reference work for use by more advanced students or by professionals -- it is strictly a vehicle, and a very good vehicle indeed, for moving from elementary calculus to an introductory careful theoretical treatment of the material.Apostol does a particularly good job of presenting the "backbone ideas" of limits and continuity in a brief but very clear chapter (Chapter 4).

Apostol's problems are excellent and should be considered an important part of his presentation of the material.(This is one area in which Apostol perhaps surpasses Rudin, although MIT's online materials contain answers to so many of Rudin's problems that they now must be viewed as "worked-out examples!")Students find Apostol's tone, and the hints given in connection with the problems, to be helpful and engaging.

I suspect that the final few chapters of Apostol's book are used only rarely, due to the typical two-semester structure of real analysis courses (with a third semester being devoted to complex analysis).If true, this is a shame, because Apostol does a nice job of moving from a fairly standard treatment of the Lebesgue integral to Fourier integrals, multiple Riemann integrals and multiple Lebesgue integrals.

I should mention, as a minor point, that students can become confused, at least momentarily and episodically, by Apostol's parallel system of numbering (i) subsections and (ii) theorems and definitions.For example, the first line of page 166 reads "7.23RIEMANN-STIELTJES INTEGRALS DEPENDING ON A PARAMETER" and the very next line reads (in italics) "Theorem 7.38Let f be continuous at each point (x,y) of a rectangle . . . "Although the fonts differentiate these two parallel numbering systems, confusion can occur.

Great "second" book in introductory analysis...
This is an outstanding textbook that is also one of the more comprehensive books as advanced calculus and introductory analysis texts go.It makes an excellent reference because it is quite comprehensive, covering a number of topics that don't make it into most introductory analysis books.

Other reviewers have said enough about the quality of this book; I just want to add a few comments.The second edition of this book is very different from the first--it cuts out much of the material on vector calculus, but it adds material on Lebesgue integration, which it presents without the use of measure theory.

Anyone who finds this text a little too difficult might want to look at the book "Advanced Calculus" by Taylor & Mann.It moves a little bit slower than this book, is a little bit less abstract, and covers less material.This book is in some ways a logical "next step" after that book.I strongly prefer this book to the "baby" Rudin, both as a learning text and a reference.This book is more detailed, and the dependency of the material is less strict--it's easier to open this book to a specific topic and understand it without having to cross-reference earlier theorems.

One of the best I own...
I own books on mathematical analysis by Browder (0387946144), Douglas S Bridges (0387982396
), Haaser Sullivan (0486665097), Pfaffenberger(0486421740), Dudley (0521007542),Abbot(0387950605) and Apostol.

All books cover abstract multivariable spaces, except Abbott who limits himself to the real line.
None of these books are perfect, but of all these books Apostol is the one I prefer for the following reasons :

1. The contents :I think a beginning analysis course should serve two aims :
a. teach basic techniques that can be used in other theoretical oriented courses like physics,economics,...
b. at the same time let the students discover the beauty of abstract and rigorous math.

In this context Apostol has reached the ideal mix between abstraction and usability. He covers practical topics , used as a basis in a lot of other courses, but he does this by making the needed level of abstraction in order to proof everything in a rigorous way.

Each book is self contained, though none of these books give a good introduction into basic mathematical logic. However an introduction to set theory is explained well in all books.
Dudley 's beautifull book is the most abstract but requires the highest level of mathematical maturity.

2 Layout : The books of Haaser Sullivan , Pfaffenberger cover excellent material in a very clear way but they are cheap Dover editions, putting as much text as possible on one page. Browder 's contents I like most (and contains really excellent explanations), but his layout is also very dense and not always comfortable to read. The layout of Apostol is the best of all these books, its pages are well filled, but the difficult proofs contain enough whitspace for a confortable read.

3.Completeness and rigor : Apostol and all these books, except Abbott and Douglas S Bridges, proof everything they mention (exceptionally, they leaf a proof as an exercise, but then the proof is relatively easy enough if you understand the material). This is an approach I like : present the complete theory and then (like all of them do) create challenging exercises seperate from the basic theory.
In contrast, the book of Douglas S Bridges represents all material as one big exercise.This is nice if you have anough time, but most of us do not have that much time,I am afraid. Also Abbott has a lot of difficult proofs left as an exercise to the reader. But at the same time, Abbott is the best in motivating the reader. Abbott often provides excellent background in order to motivate the reader and sharpen the readers mathematical intuition.

While Apostol is not best on all the criteria mentioned above, Apostol scores good on all off them and as a consequence he has the best total average. This being said, I must omit that reading Apostol requires patience. Yes his explanations are clear, but can be very terse (especially his examples). Though, in principle everything is explained without gaps. This book requires reading every word carefully and take the time to reflect, but maybe that is the only way to learn advanced math.

Finally a remark about the price, I bought this book in Europe where it is much cheaper (check amazon.co.uk)

So compared with the others this a very good book. ... Read more

Product Description

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

Product Description
Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, series, the derivative, higher derivatives, the integral and more. Each chapter contains a problem set (hints and answers at the end), while a wealth of examples and applications are found throughout the text. Over 340 theorems fully proved. 1973 edition.
... Read more

Customer Reviews (9)

The price is right...
Can't beat the price, and the material is well-presented and organized, but it's stripped down to the bare essentials - theorem, proof, lemma, corollary, etc. It's not a book on proof methodology, for sure. I graduated with a degree in computer science, but I haven't done a proof for a while and never took a class beyond linear algebra, and I wanted to teach myself analysis. While I don't find the material too difficult to follow, I really don't find it all that great for self-study. The book yields conclusion after conclusion, but among all the results, I find the text doesn't do a great job of conveying its methodology. In other words, the book spends the vast majority of the time developing new results (the "what" of analysis), but it does little to prepare the reader to understand the "how" of analysis. I feel as though the book is giving me a fish, rather than teaching me to fish.

And there are some idiosyncracies. You need to be wary of an occasionally swapped subscript, for instance. And in chapter 1 problem 5: Which is larger, Sqrt(3) + Sqrt(5) or Sqrt(2) + Sqrt(6)? The answer in the back of the book is plain wrong. And the book proves something as fundamental as the uniqueness of 1; and yet it invokes the binomial theorem out of the blue?

Anyway, the price is right, but beware that it might make a better reference or a collection of examples than a primary self-study guide.It's not that it's "too easy" as one reader put it; rather, it doesn't integrate the material with exercises and explanations well enough for my liking.

It is one very interesting book
To me, the best chapters of this book are that about series and integrals. The text is plenty of interesting notions, like that of direction that is related with the notion of limit. I appreciated very much the study that Shilov does about parameter-dependent proper and improper integrals. The topologicalnotions are placed in one intuitive manner. Without doubt, this is one very good and clear exposition about the subject. However, I think that the problems are not easy. Also sometimes Shilov states the theorems with additional conditions that are not useful. For example, this happens usually in the chapter about derivatives because the definition of derivative given by Shilov imposes that any function with derivative in the interval of the domain has continuous derivative in the interior points of its domain. However, Shilov charges some theorems with the extra condition of continuous derivative.
When the Taylor's formula is presented in page 252 - Theorem 8.22, it is stated that the error of the approximation is computed in some interior point of the interval, what is not completely correct. For example, take the second degree Taylor's approximation around x = 0 of the function x raised to the third power, and you will see that in this case the error is computed on one extreme point of the interval.
Also the proof of the theorem 10.49b (page 415) has logical problems of the kind that may arise during the translation.
However, these remarks are small questions without consequences for the course of the exposition.

An excellent pure maths text.
I purchased this book to study some complex analysis.Being a physicist I would like to brush up on this.The book was completely different to what I expected.

Some applications would have been nice, but this text is pure maths.The book is well written, easy to follow and concise.I ended up reading it and gained and appreciation for the thorough consideration of elementary real and complex numbers.

Shilov is thorough and avoids making leaps and assertions.This would make the book readable to lower undergraduates.However the significance of some things is not explained, or explained in a very dry manner so people might miss this.

I highly recommend this book if you are interested in real and complex analysis from a pure mathematics perspective.

Getting started in math analysis
This book by Shilov covers the fundamentals in beginning analysis(both real and complex). It has in common with Walter Rudin's book (entitled 'Real and Complex Analysis') that it covers both real functions (integration theory and more), as well as Cauchy's theorems for analytic functions. Shilov's book is at an undergraduate level, and it can easily be used for self-study. The Dover edition is affordable. Rudin's book is for the beginning graduate level, and it is widely used in math departments around the world. Both books have stood the test of time.
Comparison of Shilov with Rudin: Rudin's 'Real and Complex' has become an institution, and I have to admit I have loved it since I was a student myself, but conventional wisdom will have it that Shilov is a lot gentler on students, and much easier to get started with: It stresses motivation a bit more, the exercises are easier (some of Rudin's exercises are notorious, but I find the challenge charming--not all of my students do though!), and finally Shilov gets to touch upon a few applications; fashionable these days. But that part easily gets dated. I will expect that beginning students will enjoy Shilov's book.
Personally, I find that with perseverance, students who keep at it with Rudin's book, will end up with a lot stronger foundation. They are more likely to have proofs in their blood. I guess Shilov can always serve as a leisurely supplementary reading to Rudin.
There will never be another book like Rudin's 'Real and Complex', just like there will never be another van Gogh. But the fact that we love van Gogh doesn't prevent us from enjoying other paintings.

Possibly too simple
As Shilov write in the introduction "I have tried to accomodate the interests of larger population of those concerned with mathematics" and at that he seems to do. However, the book does require some mathematical background as he appears to omit defining a few things. I believe the book would be ideal for those who want a handy reference, or an easier book when struggling with an analysis course.

However, for the more mathematically inclined readers, the problems are often too easy, and many things are proved that could be better left as exercises. For a more difficult Analysis book, I would reccomend Rudin. ... Read more

Product Description
Unusually clear, accessible coverage of set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals and more. Written for junior and senior undergraduates. Problems at end of each chapter cover a wide range of difficulty. Assumes a year of calculus.
... Read more

Customer Reviews (15)

Excellent
As someone who has taken courses in analysis and topology, this book helped me very much. I somehow managed to make it through with excellent grades without ever truly understanding what was going on. Out of my own curiosity to truly learn and understand I picked up a copy of this book. I know feel as though I really understand the importance of things like compactness, completeness, and so on. This book also helped me understand the connection between analysis and topology. It is an excellent book for someone with passing familiarity of concepts. The only problem I found was that there were no solutions in the back of the book. So, this may not be good for self-study. However, it is still an interesting read.

good book
I highly suggest this book for those new to analysis. Use it as a supplemental text. Introduction to Analysis approaches topics a bit differently from its counterparts. When I was learning analysis, one book was enough to do the proofs and the Rudin problems, but to really understand the theory and the groundwork, I needed to look to more than one source. This was one of them, and was my favorite. It's also a very readable refresher on some concepts after you've been away from analysis for a while.

It is important to understand, though, that this book is not a single tell it all guide to analysis. There are books more comprehensive, more advanced, covering deep into the theory. In fact, the book, from my experience, was not very useful as a supplemental guide for introductory topics beginning with integration and furthering into special functions and such.

For the purpose of a fresh text with a unique treatment of the basics for newcomers, and those wanting a quick refresher on some of the beginning concepts, this book was nearly perfect and I highly recommend it.

really good for understand some concepts of analysis
Buen libro para comenzar en el mundo del analisis real. Ideal para personas no acostumbradas al lenguaje matematico puro.

cynthia
This book was brand new and shipped really quickly with the standard shipping. I am very pleased.

What can you say about a math book?
This is a good book in that it synopsizes the things that you would need for some type of Economics study (the point of my reading this book was to learn enough math to be able to intelligently read some economic articles that I had seen before). It was not quite enough math, but it did show you what you should know by the time you get to the level of needing analysis.

There are no problems/ solutions in this book, and so if you wanted to test your skills/ knowledge, then this is not the book for you.
Take it for what it is: A reference, but not a proper math book. ... Read more

Product Description
This is a textbook suitable for a year-long course in analysis at the advanced undergraduate or beginning graduate level. It is intended for students with a strong background in calculus and linear algebra. The first semester of this course is the basic introductory course in analysis, introducing the words "compact", "complete" " connected", "continuous", "convergent", etc. Among traditional purposes of such a course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. The topics covered in the second semester, and the second half of this book, are differentiation (of vector-valued functions of several variables), integration, and the connection between these concepts which is displayed in the theorem of Stokes, in its general form.Also included are some beautiful applications of the theory such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. ... Read more

Customer Reviews (10)

Advanced Undergrad Math Text
This book is concise and straightforward. It serves well as a reference when you're trying to solve problems since it follows the definition, theorem, proof, proposition, lemma, example layout.However the block style writing of the proofs is hard to read.

okay book
I taught a year analysis with this book. The book contains two semesters at least of undergraduate abstract analysis. The first half or so covers a first semester course with the usual things, metric spaces, continuity, sequences and series, and so forth. The second half or so has Lebesgue integration and multivariable analysis. I found it difficult to find another book having both semesters content in one volume, except for Rudin, which I chose not to use due to its price. So it fits a certain need. But I probably will not use this textbook again in my courses. I found the text to be way to concise, which might have been a result of the effort to fit so much into one volume. This is especially hard for the beginning half of the book, since the transition from calculus to abstract analysis tends to be conceptually challenging for students. Rudin is similar in some respect, since it is also concise. However personally I found it very natural to "fill in the blanks" in sketched proofs in Rudin, whereas in Browder I was more likely to develop a headache doing the same. Also I don't like the problems in the text. There's not really that many, and they tend to be multipart, too difficult and time consuming. The book could be improved by increasing the number of shorter exercises.

Concise, rigorous text
This book is for serious students of mathematics. A certain amount of mathematical maturity is needed in order to, fully, appreciate this book. It is also necessary to work through the examples in order to derive the greatest value from this text. Having studied, mathematics, over various years, from texts by Hardy, Rudin, Royden etc.,I feel that this book is a worthwhile addition to the armamentarium of a serious student who is interested in learning the tools of rigorous analysis.

Best Selection of Topics
I've read a few books on Real Analysis.Some attempt to cover too much, some don't cover enough.This book seems to include all of the essential topics without going overboard.It is also very easy to navigate.

Way too dense
The entire book is written in thm. prop. lemma. def. etc... form, with few breaks from this sequence of statements and proofs.While this seems to be the preferred style for a lot of textbooks, frankly I found it boring to read, and difficult to understand.That being said, the book covers a wide variety of topics, and goes into a good level of depth on each.The material is definitely worthwhile, but Browder seems to share the all too common mathematics teachers' curse of poor communications skills. ... Read more

Product Description

Cities can be considered to be among the largest and most complex artificial networks created by human beings. Due to the numerous and diverse human-driven activities, urban network topology and dynamics can differ quite substantially from that of natural networks and so call for an alternative method of analysis.

The intent of the present monograph is to lay down the theoretical foundations for studying the topology of compact urban patterns, using methods from spectral graph theory and statistical physics. These methods are demonstrated as tools to investigate the structure of a number of real cities with widely differing properties: medieval German cities, the webs of city canals in Amsterdam and Venice, and a modern urban structure such as found in Manhattan.

Last but not least, the book concludes by providing a brief overview of possible applications that will eventually lead to a useful body of knowledge for architects, urban planners and civil engineers.

Product Description

This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.

The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.

Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis.

Product Description
This text combines mathematical economics with microeconomic theory and can be required or recommended as part of a course in graduate microeconomic theory, advanced undergraduate or graduate-level mathematical economics, or any advanced topics course. It also has reference value for international, library, professional and reference markets. This revision addresses significant new topics - the theory of contracts and markets with imperfect information - that have recently become prominent in the microeconomics literature. ... Read more

Customer Reviews (13)

Good for PhD level theory supplement
Professor recommends this book for our first year PhD micro econ theory courses.Definatley helps understand the application sides of first year micro theory topics.

don't stupid
how to say that, I paid about 70 dollars for this version,but I just found the hardcover version only need 60 dollars at the same shop(amazon).
BTW, I found that this version is internation version after I reveived it. -_-!! the international version only need 40 dollars at other web site.

so I would suggest buy the hardcover version!!!

Spectacular
I have an ambitious goal for this review. I want this book to become a standard reference for all aspiring economists. If you only "kind of" understand the first several chapters of MWG and it gives you cold sweats at night, read this book as soon as possible. "The Structure of Economics" should be considered a classic and recommended to all graduate students of economics, and to all advanced undergraduates aspiring to graduate study. It is vastly superior to the equivalent sections in MWG (the "time-capsule" approach to economics...).

Every single page of this book gives the reader a fresh and profound perspective on the bread and butter mathematical techniques employed by practicing economists. The author does not wave his hands. Even better, he waves his hands very occasionally in very precise ways, and he tells you up front why it's necessary to do so without resorting to serious mathematical pyrotechnics (and tells you where you can find those pyrotechnics if you're intrigued). He presents the same ideas over and over in waves of increasing sophistication. He provides problems at the end of each chapter that are solvable and genuinely interesting. He is funny. He intersperses the text with jewels of historical context.

Some of the main lessons are: the meaning of Lagrangian objective functions and multipliers, the meaning and omnipotence of the envelope theorem, the sources of prediction and ambiguity in economic models, the sources and meaning of duality theory, the unity of most economic models...if you have seen these ideas all over the place and wished you understood them well enough to employ them yourself, this book is for you.

This book is not all you need, of course. But I think it delivers a bigger intellectual reward per unit time than MWG, Varian, Deaton and Muellbauer's "Economics and Consumer Behavior" (a great treatise on the consumer's optimization problem), Dixit's "Optimization in Economic Theory" (also a superb book, and a nice prelude to Silberberg). Even if you think you already knew something in the table of contents, Silberberg will make you see it in a cleaner, more general, more useful way. I keep thinking I can skip a section but then, nope, Silberberg has something to teach me.

Maybe I've been duped, but I don't understand why this book is not more widely read. The above reviews which claim the text is too arduous must have come from students without any prior exposure to basic mathematical economics. Perhaps you do need some preparation before tackling this book. But I am not very mathematically-inclined and I think this book is crystal-clear.

In summary: Buy it. Read it. Assign it to your students. Spread the word.

Perfect!!
The book arrived in a timely manner and the condition was just as described. Very satisfied!

Excellent book
Excellent book for micro economics, from intermediate to advanced level, allows for excellent undersatnding although as some point out in other reviews it can be at times complicated, but so is the nature of the subject it explains. In use with an additional text covering the more theoretical approach it is key to understanding the analytical part of microeconomics. A parallel could be established to some extent to Alpha Chiang's Fundamental Methods of Mathematical Economics. ... Read more

Product Description
In contrast to traditional textbooks for students and professionals in the physical sciences, this book presents its material in the form of problems. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. The book can be used by undergraduates and lower-level graduate students. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks. First Edition Hb (2001): 0-521-78241-4 First Edition Pb (2001): 0-521-78751-3 ... Read more

Customer Reviews (6)

Terrible book for undergraduates, impossible to use for a class
This book might be educational or enlightening if you had a year (or long leisurely summer) and nothing to do but read the book and take your time going through page by page at your own pace.The reality, however, is that college professors will assign this book to unsuspecting undergraduates, and then jump around from chapter to chapter following a syllabus.

This doesn't work, because this book:

-- Is arbitrarily self-referential
-- Has NO WORKED EXAMPLES
-- Has terribly drawn and worthless diagrams and illustrations

Overall this is one of the worst textbooks I've ever had to work with, and my physics study groups all agree.

TERRIBLE BOOK.Do not assign.Do not buy.

Great physical insight
This book by Roel Sneider provides a solid foundation of various physical (geophysical) problems in a unified mathematical framework and complements many other excellent books on mathematical physics. It takes a mathematical equation and explains the physical insight in terms of known observational physics and identifies questions at various steps (in form of excercise) which is very important. The objective of these questions are to introduce complexity in a stepwise manner which is often hard to do. The solution treatment of the problem are primarily in analytical form using vector calculas in most part, Green's function and transform calculas. I particularly like the chapters on conservation laws, scale analysis and Green's function. I am using this as a text to teach a course on Properties and Processes of the Earth for first year geophysics graduate students at Boise State University.

APPLIED Physics: Practical yet theoretically advanced
The book was excellent and extremely practical while avoiding mathematical obfuscation common to such books. Yet it did not sacrifice more advance theoretical concepts, a truly remarkable achievement. A wonderful book for self-learning, easily in the same league as "Div, Grad, Curl and All That" and similar excellent books, but more advanced. Also great for "cleaning up" and "pulling together" that sketchy undergrad education in mathematics and its use in physics and engineering. I also appreciated the very strong and coherent treatment of wave propagation in general. While pulling from the literature in seismology, it also generalizes to other fields such as electromagnetics. Its use of examples from seismology and earth science are very fascinating, and inherently practical. Highly recommended. Having written my own textbook, I appreciate even more Prof. Snieder's accomplishment.

Michael W. Burke, Lawrence Livermore National Lab

THE BOOK OF ONLY PROBLEMS.
i just don't understand the name of this book.
guided tour means i guide someone to do some thing or to know it
but this book is just the opposite it does not guide u to do anything except of problems without answers..good luck.
the introduction preceding every problem is very short and always misty and definitly not enough to solve most of the problems there , which makes the book very unsuitable for self
learning like in my case..because if you stuck ...-> no help.
2 b ohnest here i purchased 2 books with the name mathematical
methodes and both are just useless from educational point of view..

but this book could have been marvelous if it were written like
normal books because it is full of very nice math. but the approach of the book is really bad.
because there is no much of explanations,no examples ,no techniks how to solve problems ...just u and the problems alone
vois la.

Learn Math and Physics by doing
I'm a 1st year graduate student at UC - Riverside studying Physics. I struggled throughout my undergraduate curriculum trying to master the vector calculus, complex math, and the miscellaneia of techniques that physical scientists need.

Reading the book and outlining just doesn't cut it... No matter how well you study the lecture notes and books, you must apply the language you are learning, i.e. mathematics.

This book covers the fundamental techniques one must have to study the physical sciences by explaining theory and having you prove the theory as you read in the book. So in order to learn the Cauchy-Riemann condition, you must take the derivatives from the real direction and then the y direction. The book coaches you through the logic and you do the grunt work.

Literally, you cannot go to the next page without solving a few problems, to come to the next idea which you must prove. Therefore, the book reinforces the material as you learn. What, I guess, we should all be doing when we read a textbook, rederiving the results as we read without using anything but the results that we had proven before.

Anyways, there is no solutions provided, but the questions flow so well with the book that they can be answered within a few minutes or an hour at worst...

So, in conclusion, this is an excellent book to review or self-teach yourself the fundamentals. Also a good price! ... Read more

Product Description
First course in mathematical analysis, for students who are already familiar with calculus. ... Read more

Product Description
A self-contained introduction to the fundamentals of mathematical analysis

Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis.

Mathematical Analysis is composed of three parts:

?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces.

?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem.

?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method.

Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics. ... Read more

Customer Reviews (2)

OUTSTANDING AND COMPREHENSIVE ANALYSIS TEXT
I completed a bachelor's degree in math twenty years ago, and my favorite course was Real Analysis; however, the text I used was very poor in nearly every way.Over the years, as I have continued to study analysis (real and complex), I have found texts which were mediocre, at best.Professor Schroder's text is the absolute finest on analysis I have read.Professor Schroder is from Germany and was educated, in part, there; and, to beat a stereotypical drum, his text rings through with the thoroughness and clarity (and precision) for which Germans are oft celebrated.His command of English is superb, and this is seen in his lucid explanations of abstruse theorems and concepts.The text is arranged intuitively logically, such that topics are covered in an organic, holistic way.Schroder not only provides the logic behind the proofs of the theorems (never any 'hand-waving' in this able text), but he also provides detailed paragraph explanations about the 'reasoning' of the proofs.There are plenty of exercises which allow practice, and this text develops the student's aptitude for proving theorems from an inductive basis of logic.A major strength of the book is that the author invited student input (and criticism) during the text's development, and his incorporation of the suggestions makes the text exceptionally student-friendly.This text can be used fruitfully in undergraduate and graduate courses, for its layout, or format, presents the elementary aspects of the theory of functions of real (and complex) variables, first, and then builds (as I stated, inductively) to greater complexity.Another great strength (probably its greatest) is the comprehensiveness with which all the major branches of math are treated.Professor Schroder infuses abstract algebra, linear algebra, topology and the theory of differential equations into analysis in a seamless, disarming way, such that the reader is able to see the way in which, for instance, the concept of a 'space' shares domain with algebra and point-set topology.A clear, comprehensive and extremely well-written mathematics textbook is a true blessing for a math nerd.Therefore, the nerds of math can stop digging round amid poor imitations of readable analysis books; this book is the golden chalice par excellence.

An excellent introduction to mathematical analysis with a different focus
Writing a new book on mathematical analysis takes courage: the field is crowded and there are several well-known classics that are the focus of attention. My fascination with mathematical analysis (and advanced calculus, which is essentially the same area of study but with a focus on the theoretical underpinnings of calculus) has led me to collect more than 40 books on the subject. A good grounding in real analysis will provide a sturdy backbone for further study in key fields such as complex analysis, differential equations, differential geometry, functional analysis, harmonic analysis, mathematical physics, measure theory, numerical analysis, partial differential equations, probability theory, and topology.

Thus, it is hardly surprising that the author, Professor Bernd Schroder, points out that upon completing this text, readers will be ready for all analysis-based and analysis-related subjects in mathematics. That is not hyperbole: this new analysis textbook is wide-ranging in its areas of interest yet concise in implementation, thorough yet crisply focused, well written and clearly presented even while using an axiomatic approach to mathematics. Most important for the author's stated purpose, the book is a self-contained introduction to the fundamentals of analysis. The only obvious prerequisite is some experience with mathematical language and proofs. Also useful is a familiarity with the nature and structure of mathematical statements and proof methods, such as direct proofs, proofs by contradiction and induction. With a little assistance in the beginning, this textbook can be used without prerequisites in a first proof class. Standard proof techniques are discussed early in the text and they are explicitly analysed. Proofs are detailed and handwaving is minimal. Exercises have varying degrees of difficulty. Some problems require adapting arguments from the text. Fortunately, the book guides the reader through the process of making a critical analysis of an argument before adapting it, an especially useful skill. This textbook also guides the development of proof writing techniques, essentially from scratch. All of this material can be found in part one, whose primary focus is on the analysis of functions of a single real variable.

Walter Rudin's Principles of Mathematical Analysis (known as 'Baby Rudin') and his Real and Complex Analysis ('Papa Rudin') are the gold standard. This textbook's subject matter and approach falls between those two legendary books. In its axiomatic style, it is reminiscent of Tom Apostol's superb Mathematical Analysis. It also resembles Introductory Real Analysis by the great Russian mathematician A. N. Kolmogorov, which is available as an inexpensive Dover reprint. A unique aspect of Schroder's book is that it features an intense focus on the practical use of mathematics with part three's emphasis on applied analysis. This section of the book offers the practically-minded mathematics student the opportunity to develop a strong physics backgound. It discusses harmonic oscillators, Maxwell's Equations, heat and diffusion, ODEs, and the finite element method. Part two of the book, on the other hand, takes a purist's approach, focusing on analysis in abstract spaces. Topics include integration on measure spaces, L^p spaces, topology of metric spaces, an introduction to differential geometry, Hilbert Spaces, measure, topology and tensor algebra, multidimensional substitution and differentiation in normed spaces.

With its well written clarity, its eclectic nature and its steady development of proof writing skills, this is not merely another book on mathematical analysis. As an adjunct to some of the other great books on analysis, it is extremely helpful in mastering the very first baby steps leading to mathematical maturity. Read it slowly and always with a pencil in your hand ('To read without a pencil is daydreaming'). The author often provides hints for his exercises, allowing you to slowly build your expertise until hints are no longer necessary for success. By the end of the text, your grasp of mathematical analysis should be solid and deep. This is a fine textbook, multidimensional in its aspect and broad in its scope. It is certainly recommended for classroom usage but it is especially useful for self-study.

Mike Birman ... Read more

Product Description
For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation. ... Read more

Customer Reviews (4)

Analysis book with answers to excersises
I'm reading Walter Rudin's "Principles of Mathematical Analysis" along with this one.If I cannot follow Rudin's exposition, I refer to this book and try to get at least one version of the exposition that I can understand.Then, tackle again what Rudin has to offer.Binmore's explanation is easy to follow.On the other hand, Rudin's is a bit more abstract and has more surprisingly elegant proofs (and you have to fill in the gaps if they don't strike you as logical).

Good Deal!
This is almost same as it was described except some black shade on the back cover. Inside the book, everything is OK. Moreover, it is a recent reprinted edition.

Ideal for self-study
This book is ideal for self study.It has complete solutions to all the exercises in the book.A very good introduction to real analysis.Basic calculus is all that is needed to understand the book.Stirling's approximation, Gamma and Beta functions are some of the topics in the book that are not generally found in a book at this level.This is an elementary book - but rigorous, in my opinion.If you want to get started in analysis this book would be an ideal place to start.And given the current price of the book, it is a steal.There are some typos but none too serious.

Entertaining, instructive
Brief, entertaining and quite instructive. And what's more, it gives solutions to all problems at the back. The coverage is unusual (e.g. there is a chapter on the Gamma Function, something one usually encounters in a book on complex variable theory.) but the book makes an excellent first course in analysis. There are extra unsolved exercises in the appendix which is a very useful innovation. ... Read more

Product Description

Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying.

The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it intends to stimulate its readers to independent thought in discovering analysis.

Prerequisites for accessing this book are a robust understanding of calculus and linear algebra.

Customer Reviews (2)

good practice, nice book
My math teacher recommended I buy this book for extra practice. There are a ton of problems, and the solutions are usually easy to follow. Also, although this is not that important, the book is really well bound, has a hardcover, and seems more like a textbook than a problem book. A little pricey, but well worth it..

REALLY useful book!
I am taking an analysis this quarter, and this book is helping me survive the course. Analysis is all about writing proofs, and there is really no other way to learn how to write proofs other than to try problems and compare your answers to the solutions. This book has many problems, and the solutions are broken down step by step so that they are really easy to follow. An extra bonus was that certain problems I did in this book showed up on homework assignments and the midterm. It seems the authors have a good sense of the types of problems featured in a standard analysis course, and the types of problem's analysis teachers like to ask on exams and homework. Especially if you find your primary textbook hard to follow (like I did), I highly recommend this book. ... Read more