Reviews (21)

Wedderburn, Waring and Hamilton
Not necessarily in that order.President McCosh of Princeton
waxes eloquent in his Scottish Philosophy book somewhere on
the internet, re: Dugald Stewart, Kant and Hamilton.

Hamilton is a strong vice, but clearly represented in Herstein.

Good Introduction, useful for self study
I am an engineer by training and a sales man by profession, with a a strong liking for mathematics.
I found this book to be an very readable introduction to a subject (abstract algebra), I had never been exposed to during my engineering math - other than matirx theory, which was obviously taught extensively.
The proofs are generally easy to understand, but certainly not trivial.
A pleasure to read

Reviews (19)

Not really helpful
I tried to use this book as a supplement text for my multivariable calculus class. I found it to be very useless even as a supplement, let alone a main source to rely on. The main problem with this book is the fact that it is very short (Can I say way overpriced? Good thing I got it for free) and it doesn't explain the concepts properly. It is theoretical, but also in my opinion too far out there. I have nothing against theory, in fact I think its great to have theory in a math book. But in this case the material presented very tersely and unclearly. In my opinion books should explain concepts nicely and clearly with a proper use of examples. I do not wish to spend hours trying to understand what an author tried to say, especially when a concept is a really easy one. Another annoying thing about this book is the notation. Author uses "modern" notation for partial derivatives, but for some reason not many other people use it. It is found mostly in the 1950s era math books. This archaic approach to math is devastating to a student. Avoid at all costs.

Must be written by Spivak's evil twin
Spivak's other books are quite good, but don't let that fool you into getting this one. This is a horribly dry and terse text of the type which is convenient for authors and lecturers but hopeless to learn from. The object of Bourbakian worship is of course "the modern Stokes' Theorem", but, Spivak says in his preface, "Yet the proof of this theorem is, in the mathematician's sense, an utter triviality - a straight-forward computation. On the other hand, even the statement of this triviality cannot be understood without a horde of difficult definitions from Chapter 4. There are good reasons why the theorems should all be easy and the definitions hard." Perhaps these "good reasons" are that lazy authors can throw together unhelpful books where everything is "left to the reader".

Reviews (12)

Quite Dry
This is the second book that I have read beside the Vector Calculus by Marsden and Hoffman.This book rushes you through with an introductory chapter and go right into the heart of complex analysis.The author assumes you to have a great professors that can explain things in detail when you can't quite understand what is written in the text.Unfortunately I did not have a great instructor.

The examples of the book are quite simple, compare to some end of section problems.

Overall this book has no surprises as it is quite dry, got bored from reading it.If it was not a required text book for a 3rd year complex analysis course, i wouldn't recommend it to anyone.There are many other books out there that are better written.

A versatile introduction to the subject.
I used an earlier edition of this text as an instructor 20 years ago.The students in my class at the time were equally divided among the fields of mathematics, physics, and engineering.The book proved to be quite useful for all of them.Marsden skillfully strikes a balance between the needs of math majors preparing for graduate study and the needs of physics and engineering students seeking applications of complex analysis.

The book is clearly written and well-organized, with plenty of examples and exercises.My only significant criticism of the first edition was the author's tendency to label many examples of contour integration as theorems.Technically, there is nothing wrong this, but I found that some of my students tended to memorize the statements of these "theorems" rather than focus on the methods of integration discussed (for example, "Pac-Man" integrals with branch cuts along rays other than the positive real axis).Nonetheless, this is a fine text that has--not surprisingly--continued to be widely used for over two decades.

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 ;)

Reviews (16)

Lots of description... a bit too much
The book is excellent for self-study with its in-depth descriptions.The reader should look out for the occasional misprint (even in definitions, which makes it a bit more difficult), but if the book is read carefully these errors expose themselves.The reader should highlight definitions for later reference (since they are sometimes within the text).

In use for a class or for reference, this book is too wordy.Definitions are difficult to spot in many cases (some are written directly within the text).Descriptions also drag on too long in many cases, making it difficult to read the entire text.The book is by no means concise, which, after sitting in a lecture on the topic, makes much of the description too repetitive.

The problems the book offers are very good, in that they require thought but are also possible for someone fairly new to analysis (although this isn't unique to this book).The proofs are clear and many are quite elegant.They need no explanation other than what is in the text (how it should be).

One last comment on the book itself -- this book is too big to be a paperback and hold up under typical use.Look for this one in a hardcover edition, if you can find one.

Recommended instead of this book: "Principles of Mathematical Analysis," by Walter Rudin.This book is concise and clear and most appropriate when taken with a course, but must involve careful reading for self-study in comparison of Strichartz's book.

Very lucid and ideal material for learning real analysis
Most books on mathematics simply dump concepts,equations and examples and let you figure out what to do. Not this one. The book is written in a passionate manner where the author takes pains to explain why we are going in a particular direction and the goals. The style is extremely lucid and informal, something unusual for a subject that is steeped in formal mathematics. Yet the author presents, explains and covers all the formal theorems, concepts etc . The book also has excellent exercises. A truly noteworthy achievement. I would highly recommend this to anyone (especially self-study) trying to learn this subject.

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.

Isbn: 0486658465
Sales Rank: 392544
Subjects:  1. Differential Equations    2. Mathematics    3. Science/Mathematics    4. Stability