Reviews (17)

Lack of answers
Good book but the greatest fault with the book is its lack of anwsers to the end of chapter questions. If it did have anwsers this book will definetly be worth a five star rating

An excellent book
This is an excellent book for the early undergraduate student.It is actually two books in one.The first half is a careful review of Logic and the essentials of Set Theory with an emphasis on precise language. Thereafter a structured development of proof techniques is clearly presented using these tools. The second half of the book is a detailed presentation of introductory material about functions, relations, and a few aspects of more advanced set theory.These chapters serve as a wonderful introduction and show applications of the proof techniques developed earlier.
I have referred back to this book often in my own study of analysis and number theory.I recommend it highly.It will be very useful to any undergraduate proceeding through a mathematics curriculum.I recommend studying it early in the first semester, and re-reading it as time goes on.

Reviews (15)

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.

The Cat's Meow
As stated by prior reveiwers, this books does assume that the reader is Mathematically mature (a saying most young Mathematicians despise), in the sense that he/she must be able to follow the logical development of any given arguement, be able to 'see' where and how topics are related as well as fill in any blanks that may present themsevles in a given definition/proof.Apostol, as compared to Rudin, does a nice job of filling in these blanks by adequately providing all of the necessary details within a proof.This book will provide the willing student with a solid foundation in elementary analysis as well as the confidence to persue higher analysis.The only draw back to Apostols book, aside from cost, is that the constant Theorem - Proof - Theorem format can be overwhelming at times and cause some readers to cover material too quickly.Despite the book's cost I would highly recommend this book over "baby" Rudin (that is, Principles of Mathematical Analysis) since Rudin is notorious for not filling in the blanks within a given proof and instead provides seemingly 'slick proofs'.

A cut above the rest...
I am currently studying from Apostol's book, completeing a year-long course with his treatment of the Lebesgue integral. While my experience with comperable analysis texts is not exhaustive, I am familiar with the more notable: "Baby" Rudin, Marsden,... So, I can confidently say that Apostol's text is among best covering the subject. His treatment is well modivated with examples, and his proofs, while not as not as "elegant" as those of Rudin, are surely more pedagogical in nature. Apostol has included a large amount of exercises that range througout the gamut of difficulty, and the material is peppered with a treatment of complex varaibles. Also, the readability is something to be attained by all authors of mathematics texts.

One drawback to the text is a too abstract approach to the Implict and Inverse Function Theorems. I found these to be the most challenging in the text, and I was forced to return to my copy of Stewart's Calculus text to re-acquiant myself with each concept. Also, at times Apostol falls into the pattern of Definition, Theorem, Definition, Theorem,..., but this seems to be only in the cases when ample preparation is needed to provide noteworthy examples; eg. Lebesgue integration.

Editorial Review

Reviews (5)

All new but just as good
This book seems to have been completely rewritten by the new author, only keeping the outline of the original, and it's for the better. The writing is as careful as the original, and as economical, so you have to master the early chapters or the rest is hopeless, as things start off slowly but quickly become difficult. A few nuclear decay experiments provide examples throughout, and the author shows how to calculate many quantities manually. Some background topics like matrix algebra appear in the appendix too.

misprint and misleading!!
There are lots of misleading in Ch. 3. - Specific error formulas. See the original Bevington's 1st ed., and compare the formulas. I think this misleading should be corrected. Standard deviation is ALWAYS positive!!..

Great Book
I make measurements frequently and this book is great for providing the background to analyze your data.

I took undergraduate level statistics and it never really gave the practical applied background in how to analyze data.It merely presented concepts and presumed you knew how and why to apply them.This book is very good at helping you to understand the how and why.

I have read a number of other statistics book in search of the practical applied information provided in this book and did not find it in the other books.

The writing is clear and consice.There is enough background provided for even those unexposed to statistics.

I have not tried the software.Most of the formulas are easy to apply and can be implemented in simple programs or spreadsheets in very little time.

Reviews (12)

A little off the top, please...
But how much is 'a little'?

I first encountered this book when I was a physics and astronomy major in college, a major that changed over time to include mathematics proper, then political science, then other humanities such as religious studies, history and philosophy.Strange as it may seem, this text has been one of the few constants that has been helpful in almost every field.For physics and any of the natural sciences, the content of this book is highly necessary - be in chemistry, physics, astronomy, geology, or biology, all sciences depend upon observation and analysis, both of which are far from perfect.The task of ever-increasing observational and analytical precision is both an art and a science in and of itself, and one of the tasks of any scientist is to discover where errors might lie.

Interestingly, this also occurs in political science and sociology, economics and history, and even philosophy (logic can incorporate ideas from error analysis, as can epistemology).Error analysis is primarily a statistical tool, and those who have had statistics will find this very familiar.The first part of the book is very simple - Taylor assumes no background, so gives an introduction to the simple reading of charts, graphs, scales and other such things, with plenty of examples.He talks about estimating, significant figures, fractional uncertainties, and how uncertainties can accumulate.How can 2 + 2 = 5?Well, if you round to the highest or lowest whole number, 2.49 and 2.49 will both be rounded down to 2 (under many normal rounding procedures), yet if the underlying calculation or data include the 'real' information, 2.49 + 2.49 in fact equals 4.98, very close to 5.If you think that's confusing, you ain't seen nothing yet...

Taylor's first part concludes by looking at the basics of simple statistical analysis - standard deviations, normal distributions, justification of the mean as best estimate, and a brief introduction to the concept of confidence.Part two gets into more detailed analysis, including least-squares fitting, correlation coefficients, binomial distributions, Poission distributions, and the chi-squared test.The mathematics requirement goes up as the chapters progress - the early chapters only require an elementary knowledge of algeba; as the text continues, knowledge of differentiation, integration and exponential functions are necessary.A first-year course in calculus should be sufficient for easy understanding here; it is possible to get through the material without this background, but it will be more difficult.

This text is designed to be a self-study for the students; it can be introduced in lectures prior to lab work, but can also be used easily for the independent reader to understand.This book is really intended for the physical scientist - most of the examples come from problems in optics or mechanics (physics problems).Useful, helpful, and a good introduction to error analysis.

Read and understand.

Excellent desktop reference
As a professional engineer with a recurring need to crunch large amounts of statistical data, I find that this book is the perfect quick guide to things that forget and don't use that often.If has easy to follow language, and the best part about it is that I don't need to reread the whole thing to get a good explanation of a topic in the last chapter.

I had to knock it down a star because it is a touch out of date.The math is fine, but I wish that there was a companion that explained how to do some of the more uncommon operations using common spreadsheeting or data analysis software.Sometimes, figuring out how to get MS Excel to do what Taylor recommends that I do can be more cumbersome than anything else.

If nothing else, it has a great picture on the cover.

Isbn: 047186174X
Sales Rank: 2109645
Subjects:  1. Mechanics    2. Unassigned Title    3. Classical mechanics   

Reviews (27)

Unclear spoon feeding
Way overpriced and tooooo overrated; although, maybe not for my taste, but... ........This is like an excellent reference book for engineers -- a collection of recipes to use without thinking. Now thinking is indeed important and this book is very far from stimulating thinking. However, the problems do contain "proofs" (the quotes must be used) -- probably, as an attempt to make up for lack of precision. It seems like a good book to use in high school, but definitely not for college. I really am being very generous with the 2 stars. Let's see, what else.............There really isn't anything very good to say I'm afraid....

Clear and Understandable!!
Why can't all college textbooks be like this book? Many times authors write over your head to make themselves feel superior or to ensure they will still have a job explaining things to the student. Not this book. It is extreamly clear and highly understandable. I actually read the book to understand the professor instead of the usual practice of listening to the instructor to understand the book. Mary Boas did an awesome job with this book. I am more than pleased with it. It just because the number 1 book for me to recommend and you will darn sure find it in my office from now on!!

Reviews (73)

An excellent textbook
I think mathematics is a part of our culture.That's why, as a non-math major, I wandered into a very serious analysis class for mathematics majors.That might have been a disaster for me.Luckily, we used this book as a text, and it saved me.I read the whole book and diligently did all the exercises (of course, back then, it was the first edition, with only 227 pages and 140 exercises; it's somewhat more now).And that is my recommendation today.Read the book carefully and do as many exercises as you can.It certainly isn't easy.But it isn't, um, countably hard either.

The material in the book is self-contained.I guess that in theory, it could be mastered by any bright 14-year old who had learned some high school algebra and geometry.But I would surely recommend having much more mathematical sophistication than that as a prerequisite!

If you haven't learned the language of mathematics before, you'll enjoy the use of terms such as "countable," "real," "rational cuts," "measure," "ring," and "complete." By the end of the book, when the author claims that a proof (involving Cauchy sequences no less) is complete, you'll barely be able to suppress a desire to ask "Does every Cauchy sequence in the proof converge?"

In the first edition of this book, Rudin did mess up a little in his section on "the integral as a limit of sums." His theorem as stated was false.We cruelly dubbed it "Rudin's Last Theorem."Worse, he had used it "to prove some elementary properties of the Stieltjes integral."But that was all straightened out by the second edition.

I especially like the first couple of chapters.They give most readers the confidence to continue.And the final chapter, on Lebesgue integration, is very well written.One note of warning, though.Rudin begins this chapter by saying, "Some of the easier propositions are stated without proof.However the reader who has become familiar with the techniques used in the preceding chapters will certainly find no difficulty in supplying the missing steps."That is an exaggeration.It takes work.After all, this is, um, real mathematics you'll be doing!

I'm thankful that I was assigned this as my textbook.

A masterpiece
I absolutely agree with Professor Jorgensen.

I loved it when I was a student of physics, and I still love it because I tend to consider it as my personal standard in Classical Mathematical Analysis (and not only): sort of a "pacemaker" which sets the qualitative level to go back to just every time one is a little confused about what to do and where to go ;)