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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 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Isbn: 0471523690 
$110.55 
Probability, Random Variables and Stochastic Processes by Athanasios Papoulis Average Customer Review: Hardcover (01 February, 1991) list price: $100.94 US  Canada  United Kingdom  Germany  France 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)
Too elementary 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.
Not easy but worth the effort
Not a good textbook Isbn: 0070484775 
Mathematical Analysis (2nd Edition) by Tom M. Apostol Average Customer Review: Paperback (01 January, 1974) list price: $119.40  our price: $119.40 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (15)
One of the best I own...
The Cat's Meow
A cut above the rest... 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 reacquiant 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 
$119.40 
Functional Analysis by WalterRudin Average Customer Review: Hardcover (01 January, 1991) list price: $131.56  our price: $131.56 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (4)
Decent book, if you can get it cheap 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 vectorspace 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.
Modern topics in math.
The Bible on Distributions Isbn: 0070542368 
$131.56 
Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by WalterRudin Average Customer Review: Hardcover (01 January, 1976) list price: $138.13  our price: $138.13 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (73)
An excellent textbook
A masterpiece
Great analysis... Isbn: 007054235X 
$138.13 
Real and Complex Analysis (Higher Mathematics Series) by WalterRudin Average Customer Review: Hardcover (01 May, 1986) list price: $140.94  our price: $140.94 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (16)
A start in math. 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 workprojects 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.
Welcome to the selfservice analysis center! 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 endofchapter 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 HenstockKurzweil 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 endnotes 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 wellwritten complex analysis books to pick from, for example John B. Conway's classic from the SpringerVerlag graduate series, or L.V. Ahlfors' masterpiece, to name just a couple.
A Comprehensive Guide to Analysis 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 LebesgueRadonNikodym 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 changeofvariables 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 HahnBanach 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, formulabased 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 MittagLeffler 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 selfstudy, 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 
$140.94 
Probability Theory One by M. Loeve Average Customer Review: Hardcover (29 March, 1977) list price: $69.95  our price: $69.95 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (1)
Dense Reference Book Isbn: 0387902104 
$69.95 
Probability Theory II (Graduate Texts in Mathematics) by M. Loeve Hardcover (12 August, 1994) list price: $59.95 US  Canada  United Kingdom  Germany  France Isbn: 0387902627 
An Introduction to Probability Theory and Its Applications, Volume 2 by WilliamFeller Average Customer Review: Paperback (1971) list price: $102.95  our price: $102.95 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (9)
daunting, very duanting
what is a title?
A Reference in Probability Theory Whatever your preferred writing style is, Feller is probably a "mustread" 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 
$102.95 
An Introduction to Probability Theory and Its Applications, Volume 1 by WilliamFeller Average Customer Review: Hardcover (1968) list price: $102.95  our price: $102.95 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (9)
daunting, very duanting
what is a title?
A Reference in Probability Theory Whatever your preferred writing style is, Feller is probably a "mustread" 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 
$102.95 
Functional Analysis by Frigyes Riesz, Bela Sz.Nagy Average Customer Review: Paperback (01 June, 1990) list price: $19.95  our price: $13.57 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (2)
The standard work, but there are better
Very readable classic Isbn: 0486662896 
$13.57 
Elements of the Theory of Functions and Functional Analysis by A. N. Kolmogorov, S. V. Fomin Average Customer Review: Paperback (17 February, 1999) list price: $14.95  our price: $10.17 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (10)
It's a classic
Four stars for the content, five stars for the price.
My math master Isbn: 0486406830 
$10.17 
Introductory Real Analysis by A. N. Kolmogorov, S. V. Fomin Average Customer Review: Paperback (01 June, 1975) list price: $15.95  our price: $10.85 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (22)
Are all Silverman's "translations" like this one?
Not so "introductory" 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 downtoearth 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 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 
$10.85 
Real Analysis (3rd Edition) by Halsey Royden Average Customer Review: Hardcover (02 February, 1988) list price: $114.67  our price: $114.67 (price subject to change: see help) US  Canada  United Kingdom  Germany  France Reviews (17)
Standard Analysis Text; Necessary, but not Sufficient!
this book is just plain good.
Not bad for selfstudy, excellent for reference Isbn: 0024041513 
$114.67 
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