Reviews (9)

Wonderfully written, straight-to-the-point book
Whenever I want to brush up my ODE and PDE skills, I will reach out to this one. It is like instant "stock-up", refresh my memories very fast. Good buy.

Good, to-the-point, well-balanced.
I like this book a lot more than my Diff. Eq. textbook, mostly because it focuses on application rather than abstraction. Bronson does a good job of explaining the mechanisms and applications of DE, while cutting through most of the kludgy rhetoric and laborious explanations of my course textbook. The examples are straight-forward without too much of a stretch to see how they work, while the explanations are quick and to-the-point.

I would thoroughly recommend buying the Schaum's Easy Outline for DE in addition to this book, since I find the Easy Outline to be easier to pick up quickly on a first read. The Easy Outline is essentially the Outline, boiled down to the bare essentials and re-written to be easier to absorb quickly. The regular outline (this book) does a good job of filling in the gaps and providing more examples on top of the Easy Outilne.

My copy (2nd edition, current) shows an original copyright date of 1973, with another in 1994 to reflect the Library of Congress title update (the title change was minute, and not worth repeating). I was surprised by the extreme similarity between some examples in the Ouline versus those in my course textbook (carrying a 2003 copyright in its 7th edition). It makes you wonder if this is the reference for the textbook writers!

My only criticism of this book is that it is not a textbook. If it were, I wouldn't have to spend four times as much on another book which I use for not much more than the exercises. Oh, and the Outline HAS plenty of problems, both solved and not.

Reviews (8)

As an Outline...
This is not a book to learn tensor calculus from.It is an outline only, no greath depth or insight is presented.This book works perfectly as a supplement to a course in tensor calculus, or as a quick reference for the various techniques and concepts involved, provided one is already somewhat familiar with the material.It would be possible to learn the basics of tensor calculus from this book with some effort, and reflection on the implications of the concepts dealt with, however as a complete course in the subject it is insufficient, and I believe intentionally so.
The more modern aspects of tensor analysis on manifolds are largely ignored in this treatment, but also intentionally so, an approach which I found useful practically.
The book does not aim to be an all-inclusive course in the applications of tensor concepts to all areas of mathmatics, but rather a quick-reference guide supplementing more complete treatments, and as such, is largely successful.

Disappointed.
This book is substandard for the Schaum's Outline Series. The descriptions for the techniques are much too brief, and as a result, it's hard to follow what's going on. The summaries are so thin that it's even difficult to learn how to do the mechanics of tensor operations, a real deficit for an outline book! I have a pretty good background in advanced math, but I don't think I could learn tensor analysis from this book. I was especially disappointed because I have had good luck with other books in the Schaum's series. I'm planning on looking for a more traditional book with more discussion and background of the different techniques.

Reviews (6)

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.

A wonderful text -- Highly recommended!
I purchased this book as a reference book for my first analysis course.It is very well written, and easy to follow.Dr. Shilov has a very nice way of organizing this text:He puts all the definitions at the beginning of the chapter and the subsequent sections are results of those definitions.It makes for a very quick reference.His presentation of the included proofs is also very nice.There were several occasions I found myself thumbing through it for a second perspecitve.

As far as the actual material presented, Dr. Shilov starts off with funtions of one real variable, then rather quickly generalizes to complex variables and N dimensional functions, so you'll quickly see metric theory and some topology.He does keep in mind this is intended for undergrads and first year grads though.

Reviews (10)

Very bad book
If you want to study differential geometry for the first time, I would recommend the book "Differential geometry of curves and surfaces", by M. do Carmo, instead of this one. I bought Kreyzig's book for self-study but gave up after a few weeks. I then bought do Carmo's book and felt relieved that it was totally different from Kreyzig's.

Kreyzig's book has several issues, especially when compared to do Carmo's book: it is too small for the number of topics it deals with, it has few exercises and the notation is cumbersome. Part of these issues is probably due to the fact that this book was first published in 1959, and though I have seen older math books which haven't fallen behind, this one seems to have suffered from this. It took me a lot of time to understand some of the sections because of the bad notation, and the lack of some good exercises contributed to this problem. The book does cover the standard material that is expected of it and has a reasonable number of exercises, but, still, the exposition is very bad, and you get the feeling that the book could have been much better.

Despite the (important) fact that it costs about 10 times less than do Carmo's book, I strongly recommend that you save your time and enhance your learning by buying do Carmo's book instead.

Agree -- one of the best; elegant; beautiful
I had been seeking a book on differential geometry for self-study, as a preface to learning general relativity. A seasoned mathematics friend recommended Kreyszig.

So, I waded in, and patiently made my way through every page of the first six chapters, working the problems along the way, at a pace of a few pages per day.Now that the journey is behind me, I can say that I appreciated this book. It compares favorably to some other texts I had tried reading, with less success.

I realize that the author's approach is an old-style classical one, with a reliance on specific coordinate systems and transformations between coordinate systems.To work the problems requires a fair amount of paper and pencil work.Nonetheless, this approach worked well for me. On those occasions when my reading bogged down, inevitably there was a good reason. If I went back carefully, re-read and pondered, doodled on paper, and tried to visualize what Kreyszig was describing, it always worked!The light would soon go on, usually with a pleasurable sense of discovery.

I went back to re-read certain sections of the book to refresh my memory, and realized how elegant the writing is.Crystal clear, right to the heart, and always trustworthy. Everything follows in a gentle persuasive way; there are no jarring leaps or gaps.

Additionally, I had a nice sense of the different flavor brought to the field by the French geometers who made many of the key advances around the turn of the 19th-20th century.

Finally, the summary of key results and equations at the end is very smart and helpful.

Since finishing Kreysig, I did find it helpful to push on and try to grasp these same ideas from the standpoint of one-forms and the coordinate-free approach to tensors. But I'm not sorry I came at the subject this way first.

I do recommend this book, and think that a beginner needs only a moderate amount of stamina and patience here.

A postscript -- the book is also beautiful. I like that in a math book.

Reviews (2)

Good Introductory Book
This was the book that I learned Complex Analysis from. Definitely made the subject accessible to pretty much any reader. Plenty of exercises: some more theoretical, some more applied. It skillfully straddles the gap between being a theoretical math book and a math book for people with more applied aims (such as engineers). Most topics are covered thoroughly, though certain more complicated subjects such as winding number are left out for simplicity.

This book definitely prepared me for tackling the dense, theoretical, and exceptional "Complex Analysis" by Ahlfors. I'd recommend it as an introductory book for anyone trying to get into the subject who is intimidated by Ahlfors, as well as for anyone who is only interested in the essential commonly-applied tools.

Reviews (12)

too many wrong solutions
too many wrong solutions and typo~~~~
I don't recommend ppl buy this study guide!!!
This book confused ppl even more!!

Good for all science/Linear Algebra courses and exams
This study aid provides information about all possible content on linear algebra courses. I passed all algebra tests with the help of this and other nessecary books. Everyone should have material such as this piece. Not only do I reccomend this book, but it also works for everything possible. The guidelines in this book help you know the subject, and this book is easy and hard. For excellent knowledge of mathematics, natural sciences, computer science, etc. you can count on this.

Reviews (4)

Not a 5 star!
I waited several weeks for this book to arrive, and was disappointed to see that its 'just another maths book', nothing special. I didn't find this book any easier to understand than any other maths book, I ended up refering to my other book more.

Too Simple
I bought this book to help me survive my Discrete Math class, and ended up thoroughly disappointed. It's just too simple to be of any use. The examples it goes over are the obvious ones I've never had any trouble with, but more involved problems or complex proofs are nowhere to be found in the text. In the end I ended up relying on my course text much more than this, and I already had that book to begin with.

Reviews (2)

Riddled with errors
A good intro to Number Theory for non-mathematicians. (Specfically, excellent for anyone who wants to pick up cryptography.)
However, the numerous errors found throughout the book take away from it's impact. Not to mention some outdated algorithms in Chapter 5.
A lower price would make this a better buy.

Reviews (6)

Good foundational text for Cryptography
I bought this book as a supplemental study guide - my course was a mix of Number Theory, Abstact Algebra, Finite Fields and Probablility (pre-requisites for Cryptography study).The professor used lectures with hand-written supplements as primary study media.

I found this text to be well-written, each concept was dealt with separately and concisely, then later assimilated with others to form broader ideas.Even though the text is directed at Number Theory,many of the other related concepts I studied were mentioned or covered in this text.

This book will stay on my bookshelf for quite a while.

Very helpful resource
I'm currently taking a Discrete Mathematics class that is a stew of number theory, abstract algebra and probability.

This books has been very helpful as a reference as my professor teaches the course from his own lecture materials that often do not provide enough examples or coherent explanations.

The chapters on cryptography add a welcome flavor to the material.

Reviews (7)

An irritating book.
The strongest point of the book is the exercises.They force you to reread and understand the proofs and they build a foundation for material that is to come.

Chapter 1 (2nd edition) need a complete rewrite.How can you obfuscate something as simple as the Archimedean property in all its forms?Chapter 8 on Euclidean spaces needs to be better integrated with what the student should know from the first linear algebra course.

The author's proofs are not clear and I found myself rewriting many of them in my own words or turning to other references.

The core chapters 2-7 and 11-13 are fine - especially if you buy the approach of doing analysis first in R and then doing it a second time in R^n.This may be especially appropriate in an environment where most of the students are future high school teachers and will only take 1 advanced calculus course.

There are an unusual number of typos in the second edition. They are no longer accessible on the author's website.But hey, the 3rd edition is available, just throw out the 2nd and get the latest.

Nice intro, but could use some improvements
I used this book for my first analysis course.Over all, I think it does a nice job, but it could use a little tweeking.Let's start with the good...

First off, Wade understands the difficult time most students have with the transition from the early calculus courses to the higher, more abstract classes.Several proofs in this text are a little more drawn out than in others, and this is to aid the in the understaning of the art of proof writing (and it really is an art).

Another think I liked is the variety of exercises.They range from relatively easy to rather difficult (I was unable to solve some...).

Now for the bad...

I really didn't like the layout of some of the material.Especially in chapter 1.He states a definition, and then it's results.Another definiton will be thrown in along with more results.Especially in chapter 1, it would be nice if all the definitions and axioms are put into one place, and the results to follow in a later section (Shilov does this, and I used his book a lot as well during the course).I find that referencing definitions that are organized in such a fashion much nicer.

If you're a budding mathematician, and would like to get a better understanding of analysis, I'd feel confident about adding this one to your collection.

Reviews (9)

Don't see why its used in so many classrooms
I am currently taking a course in analysis, and our instructor is using this book as his primary teaching material. I have to say that I am not impressed with this book at all. There are parts where the author goes to great lengths explaining things that seem may evident (to me at least) for any student familiar with calculus, and then there are times I feel helplessly lost in his lack of explanation. The only positive thing about this book is its excercises and problems, they are placed strategically in the book, meaning that the easier problems and the hard ones are placed in the book appropriately. The easy problems inject confidence for beginners while the tougher ones will, no doubt, challenge even the most confident students.

Not So Hot.
Unevenly written. Full of typos. Some sections, like the one describing types of matrices, are so incompetently worded as to defy complete comprehension, even with repeated readings. Although some of the coverage of topological material is good, overall the informal explanations don't really do much to supplement the rigorous proofs -- they're just sort of... verbose. Not recommended. (Instead, try "Yet Another Introduction to Analysis" by Victor Bryant, as a fine introduction to the subject.)

An excellent introduction to Real Analysis
Marsden and Hoffman have done an admirable job combining clarity and rigor in a book appropriate to the level of an advanced undergrad class at a good university. The organization and tone of the work set it apart from the alternatives. The authors proceed from lesser rigor to greater within each chapter, presenting definitions, theorems, and worked examples before the proofs, which are placed at the end of each chapter. The authors address this somewhat unusual organization in their introduction:

"We decided to retain the format of the first edition, which gives full technical proofs at the end of each chapter but presents some idea of the main point in the text. This seems to have been well-received by the majority of readers... and we still believe that it is a sound pedagogical device for a course like this. It is not meant as a way to shun the proofs; on the contrary it is intended to give to views of the proof: on in the way working mathematicians think about it, (the trade secrets, so to speak), and the other in the way mathematicians write out formal proofs."

Marsden Hoffman is written in a slightly more conversational tone than other rigorous introductions to analysis. However, as a math major at Stanford, I felt like this only made the text more readable.

Reviews (1)

Reviews (1)

Isbn: 1852330562
Sales Rank: 516154
Subjects:  1. Categories (Mathematics)    2. Category Theory    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematics    7. Science/Mathematics    8. Set Theory    9. Mathematics / Logic   

Reviews (1)

Not Just for Linguists
Mathematical Methods in Linquistics is far more about mathematical methods than about linguistics, although in many places linquistics is used as a source of examples.

Instead it covers such mathematical topics as sets (including infinite sets), relations, a good deal of mathematical logic,
automata (up to turing machines), the lambda calculus, lattices and more.

Reviews (22)

Are all Silverman's "translations" like this one?
First, let us be precise in reviewing this book. It is NOT a book by Kolmogorov/Fomin, but rather an edited version by Silverman. So, if you read the first lines in the Editor's Preface, it states, "The present course is a freely revised and restyled version of ... the Russian original". Further down it continues, "...As in the other volumes of this series, I have not hesitated to make a number of pedagogical and mathematical improvements that occurred to me...". Read it as a big red warning flag. Alas, I would have to agree with the reader from Rio de Janeiro. I've been working through this book to rehash my knowledge of measure theory and Lebesgue integration as a prerequisite for stochastic calculus. And I've encountered many results of "mathematical improvements" that occurred to the esteemed "translator". Things are fine when topics/theorems are not too sophisticated (I guess not much room for "improvements"). Not so when you work through some more subtle proofs. Most mistakes I discovered are relatively easy to rectify (and I'm ignoring typos). But the latest is rather egregious. The proof of theorem 1 from ch. 9 (p.344-345) (about the Hahn decomposition induced on X by a signed measure F) contains such a blatant error, I am very hard pressed to believe it comes from the original. That book survived generations of math students at Moscow State, and believe me, they would go through each letter of the proofs. Astounded by such an obvious nonsense, I grabed the only other reference book on the subject I had at hand, "Measure Theory" by Halmos. The equivalent there is theorem A, sec. 29 (p.121 of Springer-Verlag edition), which has a correct proof.
For those interested in details, Silverman's proof states that positive integers are strictly ordered: k1Unfortunately, I don't have the Russian original. Instead, I'm trying to get the other, hopefully real translation, "Elements of the Theory of Functions and Functional Analysis". BTW, this is the actual title of the original, not "Introductory Real Analysis". Which apparently is causing significant confussion amoung past and present readers. To give you a background info, the Russian original is (or has been, at least) used as a textbook for a third-year subject for (hard-core) math students. Meaning, in the preceding two years they would complete a pre-requisite four-semester calculus course. For example, criteria of convergence of series and their properties is an assumed knowledge in presentation of Lebesgue integral. So, I think most of the critique from earlier reivews is a bit misdirected. The original book is a great starting book into functional analyis/Lebesgue integration and differentiation, but proofs require solid understanding of fundamentals of calculus.
The best part about Kolmogorov's text is the clarity of conceptual structure of the presented subject a reader would gain, if he/she puts some effort. You would gain a thorough understanding, not just a knowledge of the subject. There is quite a difference between the two, and not that many authors succeed in delivering that.
But to gain that from Kolmogorov, I would suggest the other, "unimproved" but real, translation.

Not so "introductory"
This textbook has several major virtues: it is dirt cheap, it is concise, and it touches on many advanced topics. Unfortunately, it has equally major flaws.

Many of the "proofs," especially in the first few chapters, are simply vague outlines of proofs. New notation is introduced without formal definition, terminology is used sloppily (sometimes even inaccurately), and explanations are invariably terse.

Before reading each chapter, I found it was necessary to first consult a more down-to-earth text. Sometimes I got the impression that the authors were more interested in showing off their brilliance than teaching me about analysis.

If you want to learn analysis, I would recommend first working through Rudin's Principles of Mathematical Analysis, then using this book as a source of challenging problems and interesting remarks.

Siverman spoiled Kolmogorv
This is one of many Dover's book where the editor Silverma tryed to ''improve'' the original version of a book.

Reviews (10)

It's a classic
I own the book in Spanish language. Some content in the book is not easy stuff, if you study by others books, but Kolmogorov has the gift to make easy things that aren't quite so easy. Perhaps some theory is "old", because all the new books use some diferent approach to the subject, like the chapter dedicated to the Lebesgue integral, the book give the definition of a simple function in a different manner that we use today. The book is a must to have in your library, when you need to work with Functional Analysis.

Four stars for the content, five stars for the price.
This book is not quite up-to-date, but still very good as a starting point in (functional) analysis. The virtue of Kolmogorov and Fomin is their user-friendly writing style. I am delighted to find their book being available for less than ten dollars.

Editorial Review

Could it be true that Whitehead and Russell's Principia Mathematica is the most influential book written in the 20th century?Ask any mathematician or philosopher--or anyone who understands the impact these fields have had on modern thinking--and you'll get a short answer: yes. Their goal, to set mathematics on a firm logical foundation, was revolutionary, and their tools and rigor continue to influence modern professionals. Using Peano's symbolic logic, they formalized axioms and produced theorems (including the famous "1 + 1 = 2") in orderings, continuous functions, and other areas of mathematics.

Isbn: 0156016095
Sales Rank: 719595
Subjects:  1. Fourier Analysis    2. Mathematical Analysis    3. Study Guides