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    Stochastic Processes (Wiley Classics Library)
    by J. L.Doob
    Paperback (11 January, 1990)
    list price: $126.00 -- our price: $110.55
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    Isbn: 0471523690
    Sales Rank: 342978
    Subjects:  1. Mathematics    2. Probability & Statistics - General    3. Science/Mathematics    4. Stochastic Processes    5. Mathematics / Statistics    6. Stochastics   


    $110.55

    Probability, Random Variables and Stochastic Processes
    by Athanasios Papoulis
    Average Customer Review: 3.0 out of 5 stars
    Hardcover (01 February, 1991)
    list price: $100.94
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    Editorial Review

    This text is a classic in probability, statistics, and estimation and in the application of these fields to modern engineering problems. Probability, Random Variables, and Stochastic Processes assumes a strong college mathematics background. The first half of the text develops the basic machinery of probability and statistics from first principles while the second half develops applications of the basic theory. Topics in the first section include probability distributions and densities, random variables and vectors, expectations, covariance, correlations, functions of random variables and vectors, and conditional distributions and densities. In this third edition of the text, the second half of the book has been substantially updated and expanded to include new or revised discussions of the following topics: mean square estimation, likelihood tests, maximum entropy methods, Monte Carlo techniques, spectral representations and estimation, sampling theory, bispectra and system identification, cyclostationary processes, deterministic signals in noise, and the Wiener and Kalman filters. Probability, Random Variables, and Stochastic Processes covers a remarkable density of material and the clarity of both presentation and notation make this book invaluable as a text and a reference. ... Read more

    Reviews (19)

    2-0 out of 5 stars Too elementary
    This book lacks rigor, and contains horrendous typos (but there is an errata sheet available) although makes a nice effort to "engineerize" the topic for the dumb reader (i.e. engineers).
    Not meant for the mathematician, it makes no use of measure theory, and so you have to believe the results at face value.
    On the positive side, it contains tons of worked-out examples, the chapters on distribution functions are quite nice and contain nice applications of calculus.
    Other than that, it is a bit too elementary and avoids any of the interesting topics dealt with in more rigorous courses such as the stochastic integrals.

    Did I already mention this is an easy book? I don't see why the other reviewers complain it is hard, it must be due to their low IQ, so I wouldn't worry about their comments too much. These engineers want the answer ready to copy down on their homework sheets, this book almost gives you the answer if you're able to do changes variables etc., although this is sometime a difficult task for freshman engineers.

    5-0 out of 5 stars Not easy but worth the effort
    This is a book which definitely requires diligence and effort to get through.The excercises are also not trivial to say the least.However, if you have the energy and patience to actually slug through this text, in the end you will discover that you have actually learned something.Something which is profound and difficult to understand.This book is definitely not recommended as a casual reference.

    1-0 out of 5 stars Not a good textbook
    IMO, this is not a good textbook. On one hand, it never explains the purpose of the materials. I know it elaborates on the random variables and different distributions and a lot of materials in detail, but I don't know where can I use these things. On the other hand, it omits the mathematical details, too. So when I read this book, I found unclear points everywhere. Someone else recommended this book as a good engineer reference. I think that might be true if there were less errors. I find errors in the equations every two or three pages. Engineers may not need to know the details, and they know what they need to model their designs. But they need the "correct" thing to do that. Maybe that is not the author's fault but McGraw-Hill's, but to me, a reader of the textbook, it is the same. No recommendation of this book. ... Read more

    Isbn: 0070484775
    Subjects:  1. General    2. Mathematics    3. Probabilities    4. Probability & Statistics - General    5. Random variables    6. Reference    7. Science/Mathematics    8. Stochastic processes    9. Stochastics   


    Mathematical Analysis (2nd Edition)
    by Tom M. Apostol
    Average Customer Review: 4.5 out of 5 stars
    Paperback (01 January, 1974)
    list price: $119.40 -- our price: $119.40
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    Reviews (15)

    5-0 out of 5 stars 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.

    5-0 out of 5 stars 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'.

    5-0 out of 5 stars 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.

    So, in spite of the cost, I highly recommend this text for the study of real analysis (even for self study), although at [this price] there are bound to be others that have a higher value to cost ratio. Having completed the text (almost), I feel prepared to begin a more abstract study of analysis. ... Read more

    Isbn: 0201002884
    Sales Rank: 338513
    Subjects:  1. General    2. Mathematical analysis    3. Mathematics   


    $119.40

    Functional Analysis
    by WalterRudin
    Average Customer Review: 4.5 out of 5 stars
    Hardcover (01 January, 1991)
    list price: $131.56 -- our price: $131.56
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    Reviews (4)

    3-0 out of 5 stars Decent book, if you can get it cheap
    I strongly urge any serious math student to own a copy of both Rudin's Principles ("Baby Rudin") and his Real and Complex Analysis ("Adult Rudin").The former is absolutely essential- without completely mastering continuity and convergence on the basic metric space topology on R^n, higher math is going to be quite a pain.The second is good because it puts the major ideas of basic analysis- Radon measures, L^p spaces, rudiments of Hilbert and Banach Spaces, differentiation and integration, Fourier and Harmonic Analysis, Holomorphic and meromorphic functions, etc. all in one nice volume, although the problems may be too challenging or tangential to master the material by doing them.

    With that said, I don't like this book as much.Perhaps because the problems don't provide great movitation for the theorems- in any event, I would recommend using at least two books to understand functional analysis.One that emphasizes a rigorous approach to the theory involved, and another more applied book that allows you to play with the new tools to solve the problems functional analysis was invented to solve; quantum mechanics, for example.

    Reed and Simon is a good book, although I'm sure physicists or physics students would probably complain about it for the same reason I like it- its very mathematically rigorous and has a ton of problems- 30 to 60 on average at the end of each chapter, with only a few digressions into applications into quantum physics or elementary QFT.Get this with some Springer text, like Elements of Functional Analysis.

    One more note- Rudin's book is broken up into three parts- one on TVS (Topological vector spaces) that combines topological properties of a space (for example, local convexity or local compactness) with the usual vector-space operations to set the spaces where operators act.

    The second section deals with distributions- I regret that one failure of "Adult Rudin" was to emphasize the abstract integral as a linear functional, because this would have helped to make the concept of a distribution more clear.

    While the introduction to distributions and their connections to Fourier analysis and differential equations is nice, the text gets bogged down with proofs about convolutions that are highly technical (and make either good practice or a good time for Rudin to actually use, for once, "The details are left to the reader...").

    Finally, Rudin introduces operator theory, although it could go much more smoothly- the proofs come off as way too technical, a far cry from the "slickness" his proofs are often accused of being in the graduate analysis text.

    All in all, there's some interesting problems to do, but you're not going to understand the applications of Functional Analysis to quantum mechanics or PDE (other than distributions a little), where other, more applied (read: easier) books may give nice problems about applications of Hilbert space methods, such as variational techniques or Fredholm theory.

    5-0 out of 5 stars Modern topics in math.
    "Modern analysis" used to be a popular name for the subject of this lovely book. It is as important as ever, but perhaps less "modern". The subject of functional analysis, while fundamental and central in the landscape of mathematics, really started with seminal theorems due to Banach, Hilbert, von Neumann, Herglotz, Hausdorff, Friedrichs, Steinhouse,...and many other of, the perhaps less well known, founding fathers, in Central Europe (at the time), in the period between the two World Wars. In the beginning it generated awe in its ability
    to provide elegant proofs of classical theorems that otherwise were thought to be both technical and difficult. The beautiful idea that makes it all clear as daylight: Wiener's theorem on absolutely convergent(AC) Fourier series of 1/f if you can divide, and if f has the AC Fourier series, is a case in point. The new subject gained from there because of its many sucess stories,- in proving new theorems, in unifying old ones, in offering a framework for quantum theory, for dynamical systems, and for partial differential equations. And offering a language that facilitated interdisiplinary work in science! The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor in theories surprisingly far from the original roots of the subject. The topics in Rudin's book are inspired by harmonic analysis. The later part offers one of the most elegant compact treatment of the theory of operators in Hilbert space, I can think of. Its approach to unbounded operators is lovely.

    5-0 out of 5 stars The Bible on Distributions
    No other book covers the elements of distributions and the fourier transform quite like Rudin's Functional Analysis.This is a must for every budding PDE-er! ... Read more

    Isbn: 0070542368
    Sales Rank: 201282
    Subjects:  1. Advanced    2. Functional Analysis    3. Mathematics    4. Science/Mathematics    5. Mathematics / Functional Analysis   


    $131.56

    Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics)
    by WalterRudin
    Average Customer Review: 4.5 out of 5 stars
    Hardcover (01 January, 1976)
    list price: $138.13 -- our price: $138.13
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    Reviews (73)

    5-0 out of 5 stars 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.

    5-0 out of 5 stars 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 ;)

    4-0 out of 5 stars Great analysis...
    This book is tough to learn from (because it has almost no motivation), but the text is clearly written and easy to understand.

    The proofs are elegant and easy to follow.The construction of the reals using dedikind cuts along the rationals is the only construction I've found in introductory books.Other books I used as suplementary to this (Rosenlicht and Bear) did not have this in their texts.

    After learning analysis, I find this book to be an excellent reference for anything that I might have forgotten or just didn't understand the first time around. ... Read more

    Isbn: 007054235X
    Sales Rank: 29749
    Subjects:  1. Advanced    2. Mathematical Analysis    3. Mathematics    4. Science/Mathematics    5. Mathematics / Advanced   


    $138.13

    Real and Complex Analysis (Higher Mathematics Series)
    by WalterRudin
    Average Customer Review: 4.5 out of 5 stars
    Hardcover (01 May, 1986)
    list price: $140.94 -- our price: $140.94
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    Reviews (16)

    5-0 out of 5 stars A start in math.
    I am a fan of Rudin's books. This one "Real and Complex Analysis" has served as a standard textbook in the first graduate course in analysis at lots of universities in the US, and around the world.

    The book is divided in the two main parts, real and complex analysis. But in addition, it contains a good amount of functional and harmonic analysis; and a little operator theory.

    I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and it is still my favorite. I have to admit that it is not the favorite of everyone I know.

    What I like is that it is concise, and that the material is systematically built up in a way that is both effective and exciting.

    Some of the exercises are notoriously hard, but I think that is good: It simply means that they serve as work-projects when the students use the book. And this approach probably is more pedagogical as well.

    After surviving some of the hard exercises in Rudin's Real and Complex, I think we learn things that stay with us for life; you will be "marked for life!"

    Review by Palle Jorgensen, September 2004.

    5-0 out of 5 stars Welcome to the self-service analysis center!
    This year we have been using Walter Rudin's treatise as the main text for a standard first-year graduate sequence on real analysis, backed up by Wheeden/Zygmund's book on Measure and Integral, and the two seem to complement each other quite nicely. Rudin writes in a very user-friendly yet concise manner, and at the same time he masterfully manages to maintain the high level of formality required from a graduate mathematics text. To be totally honest, a few years ago my very first attempt at learning graduate-level real analysis in a classroom setting (via Folland's book) was not successful, as I found the exposition in Folland very dense and rigid, and the homework problems too difficult to do. Rudin's book however is a lot more accessible for the beginning graduate students who may not have had any more than some basic exposure to measure theory in their upper division analysis classes. One point to keep in mind is that Rudin developes the measure in the more formal axiomatic way, instead of in the more concrete constructive approach. In the constructive approach, one first introduces the "subadditive" outer measure as a set function which is defined on the power set P(X) of a nonempty set X. One then proceeds by showing that the restriction of the domain of the outer measure to a smaller class of subsets of X (a sigma algebra M), obtained via applying the Caratheodory's criterion, results in a "countably additive" set function which is called a measure on (X,M). (The latter is the approach taken in both H.L. Royden and Wheden/Zygmund). The formal approach is not very intuitive and is less natural for a beginning graduate student who might not have developed a certain level of mathematical maturity yet.

    Also, Rudin does not discuss some of the more advanced or interdisciplinary topics such as distribution theory (Sobolev spaces, weak derivatives, etc.) or applications of measure theory to the probability theory, both explored in the book by Folland. Last but not least, it's worth noting that contrary to the common practice, Folland includes many end-of-chapter notes where he outlines some important historical aspects of the development of the topics, and also gives a few references for further study. For example, in the notes section at the end of the chapter on Lebesgue integration, he mentions --and briefly outlines-- the basics of the theory of "gauge integration" (also called Henstock-Kurzweil theory) which serves to construct a more powerful integral than that of the Lebesgue's. As another instance, having already defined and used "nets" within the chapter on topology, in the end-notes Folland also introduces "filters" and "ultrafilters". These are all machineries which have been developed to play the role of the metric space sequences in general (locally Hausdorff) topological spaces, but for some historical reasons, ultrafilters have nowadays taken a backseat to the nets (the older general topology books usually prove the Tychonoff theorem using ultrafilters). All said, I can recommend taking up Royden as your very first approach to measure theory, then based on how well you think you have learned the first course, move on to either Rudin or Folland for a more advanced treatment. Please note that the other books I have mentioned above do not discuss complex analysis, a subject which is also masterfully presented in Rudin. There are however a few other equally well-written complex analysis books to pick from, for example John B. Conway's classic from the Springer-Verlag graduate series, or L.V. Ahlfors' masterpiece, to name just a couple.

    5-0 out of 5 stars A Comprehensive Guide to Analysis
    Rudin's Real and Complex Analysis is an excellent book for several reasons.Most importantly, it manages to encompass a whole range of mathematics in one reasonably-sized volume.Furthermore, its problems are not mere extensions of the proofs given in the text or trivial applications of the results- many of the results are alternate proofs to major theorems or different theorems not proved.With that in mind, this book is not appropriate for a course where the instructor wants students to merely understand the theorems well enough to develop applications- the structure of the book is far better suited for a more theoretical course.

    For example, the construction of Lebesgue measure is considered one of the most important topics in graduate analysis courses.After this construction, more abstract measures are developed, and then one proves the Riesz Representation Theorem for positive functionals later.

    Conversely, Rudin develops a few basic topological tools, such as Urysohn's Theorem and a finite partition of unity, to construct the Radon measure needed in a sweeping proof of Riesz's Theorem.From this, results about regularity follow clearly, and the construction of Lebesgue measure involves little more than a routine check of its invariance properties.

    Another example of where Rudin takes a more theoretical approach to provide a more elegant, yet less intuitive proof, is the Lebesgue-Radon-Nikodym theorem.Other books generally introduce signed measures with several examples, and use this result, along with properties of measures to derive the proof.On the other hand, since the first half of the book contains an intermission on Hilbert Space, Rudin uses the completeless of L^2 and the Riesz Representation Theorem for a more sweeping proof.

    In the real analysis section, Rudin covers advanced topics generally not covered in a first course on measure theory.The chapters on differentiation and Fourier analysis are key examples of this.Rudin uses maximal functions to develop the Lebesgue Point theorem and results from complex analysis, and provides an incredibly thorough proof of the change-of-variables theorem.The ninth chapter, on Fourier transforms, relies heavily on convolutions, which are developed as a product of Fubini's theorem.This, in turn, is used to prove Plancherel's theorem and the uniqueness of Fourier transforms as a character homomorphism.

    The tenth chapter, on basic complex analysis, essentially covers an entire undergraduate course on the subject, with added results based on a solid knowledge of topology on the plane.Once a solid foundation on the topic is laid, Rudin can develop more advanced topics from Harmonic analysis using general results from real analysis like the Hahn-Banach theorem and the Lebesgue Point theorem (for Poisson integrals).

    Most of the basic results from the power series perspective are covered in the text, but while the geometric view is examined, it is still done in a very analytic, formula-based way that does not allow the reader to gain too much intuition.Nonetheless, all the basic results are covered, and Rudin uses these to develop the main theorems, such as the Mittag-Leffler and Weierstrass theorems on meromorphic functions, and the Monodromy Theorem and a modular function used to prove Picard's Little Theorem.

    As an introductory text, even for advanced students, Rudin should probably be accompanied by more descriptive texts to develop better intuition.In fact, I would recommend Folland's Real Analysis and Ahlfors' Complex Analysis for self-study, because the problems are easier and one can learn better through those.With a good instructor, though, Rudin's text is concise and elegant enough to be both useful and enjoyable.It is also a good test to see how well one REALLY knows the subject. ... Read more

    Isbn: 0070542341
    Sales Rank: 196045
    Subjects:  1. Advanced    2. Mathematical Analysis    3. Mathematics    4. Science/Mathematics    5. Mathematics / Advanced   


    $140.94

    Probability Theory One
    by M. Loeve
    Average Customer Review: 4.0 out of 5 stars
    Hardcover (29 March, 1977)
    list price: $69.95 -- our price: $69.95
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    Reviews (1)

    4-0 out of 5 stars Dense Reference Book
    Probability Theory I is a very dense reference book.It contains a large amount of useful specific results, but the scarcity of explanatory remarks makes it a difficult casual read. ... Read more

    Isbn: 0387902104
    Sales Rank: 733244
    Subjects:  1. History    2. Mathematics    3. Probability & Statistics - General    4. Mathematics / Probability    5. Probability    6. Wahrscheinlichkeitsrechnung   


    $69.95

    Probability Theory II (Graduate Texts in Mathematics)
    by M. Loeve
    Hardcover (12 August, 1994)
    list price: $59.95
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    Isbn: 0387902627
    Sales Rank: 1050039
    Subjects:  1. General    2. Mathematics    3. Science/Mathematics    4. Mathematics / Probability    5. Probability    6. Wahrscheinlichkeitsrechnung   


    An Introduction to Probability Theory and Its Applications, Volume 2
    by WilliamFeller
    Average Customer Review: 5.0 out of 5 stars
    Paperback (1971)
    list price: $102.95 -- our price: $102.95
    (price subject to change: see help)
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    Reviews (9)

    5-0 out of 5 stars daunting, very duanting
    This book is one of the tomes of probability theory.The material covered is not for the faint of heart though.The text explains things as do most graduate level math texts, in proofs and theory.

    5-0 out of 5 stars what is a title?
    This is a GREAT book.
    Unfortunately, I lost mine.
    I wanted to buy volume 1, third edition, to replace the lost book but I got volume 2, second edition. Because volume 1 is SO GREAT book, I decided to keep volume 2 as well. How can be sure I ordered the needed one?

    5-0 out of 5 stars A Reference in Probability Theory
    Although people often recommend K.L. Chung at our math department as an introduction to probability theory, i think that Feller is just another view of the problem. If you prefer a concise writing style then Chung is better. On the other hand, Feller's books are full of examples so that you cannot go through this book without having an accurate picture of the historical developments of probability theory and its many applications (even if sometimes applications are driving the need for theory...). This is anyway something you must have read if you want to get an intuitive understanding of probability theory.

    Whatever your preferred writing style is, Feller is probably a "must-read" if you're involved on probability theory, just because of its importance in the literature, not because you like it. Maths are not just about formalism, they're also a matter of culture. ... Read more

    Isbn: 0471257095
    Sales Rank: 344434
    Subjects:  1. Mathematics    2. Probabilities    3. Probability & Statistics - General    4. Mathematics / Statistics    5. Probability & statistics   


    $102.95

    An Introduction to Probability Theory and Its Applications, Volume 1
    by WilliamFeller
    Average Customer Review: 5.0 out of 5 stars
    Hardcover (1968)
    list price: $102.95 -- our price: $102.95
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    Reviews (9)

    5-0 out of 5 stars daunting, very duanting
    This book is one of the tomes of probability theory.The material covered is not for the faint of heart though.The text explains things as do most graduate level math texts, in proofs and theory.

    5-0 out of 5 stars what is a title?
    This is a GREAT book.
    Unfortunately, I lost mine.
    I wanted to buy volume 1, third edition, to replace the lost book but I got volume 2, second edition. Because volume 1 is SO GREAT book, I decided to keep volume 2 as well. How can be sure I ordered the needed one?

    5-0 out of 5 stars A Reference in Probability Theory
    Although people often recommend K.L. Chung at our math department as an introduction to probability theory, i think that Feller is just another view of the problem. If you prefer a concise writing style then Chung is better. On the other hand, Feller's books are full of examples so that you cannot go through this book without having an accurate picture of the historical developments of probability theory and its many applications (even if sometimes applications are driving the need for theory...). This is anyway something you must have read if you want to get an intuitive understanding of probability theory.

    Whatever your preferred writing style is, Feller is probably a "must-read" if you're involved on probability theory, just because of its importance in the literature, not because you like it. Maths are not just about formalism, they're also a matter of culture. ... Read more

    Isbn: 0471257087
    Sales Rank: 307069
    Subjects:  1. Mathematics    2. Probabilities    3. Probability & Statistics - General    4. Mathematics / Statistics    5. Probability & statistics   


    $102.95

    Functional Analysis
    by Frigyes Riesz, Bela Sz.-Nagy
    Average Customer Review: 4.5 out of 5 stars
    Paperback (01 June, 1990)
    list price: $19.95 -- our price: $13.57
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    Reviews (2)

    4-0 out of 5 stars The standard work, but there are better
    This is the "standard" book on the subject. It is referenced everywhere. It has a lot in it. I have not read it cover to cover, just used it for reference, but if you are new to the subject I think Kolmogorov and Fomin looks beeter, and Shilov's books look better too.

    5-0 out of 5 stars Very readable classic
    This book is a bargain ... in these days of $100 paperbacks ! The foreign authors, who 1st published this in the early 50s, write in a very readable way as opposed to most US profs. The book starts with an example of a continuous function which is not differentiable and then proves Lebesgue's theorem which tells you when a function does have a derivative.The 2nd part of the book is about Integral equations which again starts with some examples of problems the early 19th century mathematicians solved. Particularly interesting to me was Fredholm's method which was to replace the integral with a series. The book covers all the topics you would expect in a very readable form. ... Read more

    Isbn: 0486662896
    Sales Rank: 282933
    Subjects:  1. Calculus    2. Functional analysis    3. Mathematics    4. Science/Mathematics    5. Mathematics / General   


    $13.57

    Elements of the Theory of Functions and Functional Analysis
    by A. N. Kolmogorov, S. V. Fomin
    Average Customer Review: 5.0 out of 5 stars
    Paperback (17 February, 1999)
    list price: $14.95 -- our price: $10.17
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    Reviews (10)

    5-0 out of 5 stars 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.

    5-0 out of 5 stars 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.

    5-0 out of 5 stars My math master
    I am electrical eng who study math all of my life. I had the Arabic version of it which cover more than the Englishone.I start reading it after Krewsiq book of advance functional analysis. I really like Krewsiq because it is so easy so I cover itwithin 1 year but I need 2.5 year to finish off this one which isfantastic, I really can't compare it with other books, it is a school of functional analysis and master book that you can'treally understand functional analysis without it. ... Read more

    Isbn: 0486406830
    Sales Rank: 16150
    Subjects:  1. Calculus    2. Functional Analysis    3. General    4. Mathematics    5. Science    6. Science/Mathematics    7. Mathematics / General   


    $10.17

    Introductory Real Analysis
    by A. N. Kolmogorov, S. V. Fomin
    Average Customer Review: 4.5 out of 5 stars
    Paperback (01 June, 1975)
    list price: $15.95 -- our price: $10.85
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    Reviews (22)

    3-0 out of 5 stars 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.

    3-0 out of 5 stars 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.

    2-0 out of 5 stars Siverman spoiled Kolmogorv
    This is one of many Dover's book where the editor Silverma tryed to ''improve'' the original version of a book.

    Not having the stature of the authors, the editor failed to understand that no one should try to mess with other's people book. ... Read more

    Isbn: 0486612260
    Sales Rank: 44607
    Subjects:  1. Algebra - General    2. Calculus    3. Functional analysis    4. Functions    5. Mathematics    6. Mathematics / General   


    $10.85

    Real Analysis (3rd Edition)
    by Halsey Royden
    Average Customer Review: 3.5 out of 5 stars
    Hardcover (02 February, 1988)
    list price: $114.67 -- our price: $114.67
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    Reviews (17)

    4-0 out of 5 stars Standard Analysis Text; Necessary, but not Sufficient!
    Very useful textbook, easy to follow.
    A little over-simplified though.
    Doesnot leave a lot of gaps, but then that doesnot leave a lot of room for imagination either.
    At times it gets toooo wordy, if you know what I mean. Less ideas and more talk.
    A stark contrast to Rudin, but can be very useful if both are used together. However, if you need to choose between those two, go with Rudin.

    5-0 out of 5 stars this book is just plain good.
    I began as a graduate student in applied maths less than a year ago; all of the students that I spoke with prior to that said that real analysis with rudin's book was their worse & hardest class..
    So when I walked into MTH 5111 Real Variables I thought oh *&^% what am I in for?? but then I picked up the Royden book and I understood the way he was presenting the materail.. the book is very stright to the point + leaves channelgning problems to the HW sets but the autor clearly outlines. I have learned more from this book and course than any other...

    4-0 out of 5 stars Not bad for self-study, excellent for reference
    I used Royden (2nd edition) as a graduate student over 30 years ago, and have been away from real analysis pretty much ever since (not because of the book(!), but because of being in computers).I've taken a renewed interest in the subject (I'm a pretty random person) and have been surprised at how the material has come back to me, I think because of the readability of the text.It's true, Royden challenges the reader at every turn, but if one has acquired the level of mathematical maturity commensurate with strong interest in analysis, the challenges are appropriate, in my opinion ... Read more

    Isbn: 0024041513
    Sales Rank: 151717
    Subjects:  1. Advanced    2. Functional Analysis    3. Functions Of Real Variables    4. Mathematical Analysis    5. Mathematics    6. Measure theory    7. Science/Mathematics    8. Mathematics / Advanced   


    $114.67

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