GOLSCO Books Online Store | UK | Germany |
books | baby | camera | computers | dvd | games | electronics | garden | kitchen | magazines | music | phones | software | tools | toys | video |
Help |
Books - Science - Mathematics - Mathematical Analysis - Analysis |
1-8 of 8 1 |
Featured List | Simple List |
Go to bottom to see all images
Click image to enlarge
Undergraduate Analysis (Undergraduate Texts in Mathematics) by Serge Lang Average Customer Review: Hardcover (May, 2005) list price: $69.95 -- our price: $59.48 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (4)
Just like every other Lang text
Solid, complete reference to basic analysis topics
okay Isbn: 0387948414 |
$59.48 |
Real Mathematical Analysis by Charles Chapman Pugh Average Customer Review: Hardcover (01 March, 2002) list price: $59.95 -- our price: $59.95 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (5)
Would be better if solutions are provided
Very good exposition, great problems 1.) Why purchase this book rather than the classic of the genre? 2.) Is this book appropriate for me? So why buy this book rather than Rudin? It has great exposition (as does Rudin), very well chosen problems (as does Rudin), but Pugh manages to improve on the standard by supplementing his written explanations with diagrams and pictures that Rudin mostly lacks. Additonally, the price stands at something less than half the cost of Rudin's book. Who is this book appropriate for? This text delves into the topological underpinnings of analysis. It is not an "analysis-lite" textbook a la Ken Ross's Elementary Analysis. It is a rigorous treatment of the subject, and it has a comprehensive feel to it, covering topics like Lebesgue measure and integration, and multivariable analysis in addition to the normal topics one would expect. In short, it is appropriate for somebody who is seeking the challenges and rewards of a full treatment of what for many is a difficult subject. It is a very good book that does not shy away from difficult material that no amount of explanation or good writing will make easy to learn, but of all the analysis books I've seen, this comes the closest.
6 star Isbn: 0387952977 |
$59.95 |
Yet Another Introduction to Analysis by Victor Bryant Average Customer Review: Paperback (28 June, 1990) list price: $32.99 -- our price: $32.99 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (4)
Great Introduction
Basic Real Analysis unleashed
Exposes Mathematical Analysis Without Set Theory Background One of the most important considerations prior to taking an analysis course is the level of background and understanding of mathematical logic. Set theory, a branch of mathematical logic, is in fact the basis of calculus as well. Due to an emphasis upon computations, however, the highest grades in calculus are possible without understanding, or even knowing of, this underlying foundation. This work is unique among those introducing analysis, in that it does not require a background in set theory. It in fact teaches numerous fundamental concepts of set theory, without stating that it is doing so. Examples provided are based on daily concrete experience, yet are altered for purposes of mathematical instruction. These descriptions are sufficiently general as to prepare the reader for when formal set theory is introduced in more rigorous textbooks. In addition to being an extremely readable and accessible work,solutions and hints are provided for every review question for every section of the book. This is in stark contrast to textbooks on the subject, which, while costing several times more, are typically designed for a classroom setting, and so leave all questions unanswered. This self-testing of the understanding of each section is crucial for subject matter requiring such attention to detail and precision. The numerous illustrations throughout the book are rendered clearly and with instructional purpose, yet are often drawn by hand, adding to the sense of familiarity with the author. All of the basic subject matter for a course on analysis is provided, yet has been specifically tailored for a reader in the stages of preparation, of review after completion, or one who is simply inquisitive as to what is required to comprehend analysis successfully. The softcover edition is durable and portable, and the book remains in excellent condition through numerous readings, which it will almost certainly go through. If you have been required to take an analysis class but left it with only a vague sense of its underpinnings, you may wish to go through this work when time permits. For the price of the book, the information and instruction provided is truly outstanding. This text receives the highest marks in all categories. ... Read more Isbn: 052138835X |
$32.99 |
Elementary Real and Complex Analysis (Dover Books on Mathematics) by Georgi E. Shilov, Richard A. Silverman Average Customer Review: Paperback (01 February, 1996) list price: $19.95 -- our price: $13.57 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (6)
Getting started in math analysis
Possibly too simple 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! 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. Oh, another nice feature is the price!I'd recommend this book to any math enthusiast as a reference, or to someone going through an early analysis course. ... Read more Isbn: 0486689220 |
$13.57 |
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 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.
Modern topics in math.
The Bible on Distributions Isbn: 0070542368 |
$131.56 |
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 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.
Welcome to the self-service 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 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.
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 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 |
$140.94 |
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 |
Functional Analysis (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) by Peter D.Lax Average Customer Review: Hardcover (22 March, 2002) list price: $105.00 -- our price: $91.71 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (2)
Excellent
Brings the subject to life! quantum theory, for dynamical systems, and for partial differential equations. The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor Isbn: 0471556041 |
$91.71 |
1-8 of 8 1 |
Books - Science - Mathematics - Mathematical Analysis - Analysis (images) |
Images - 1-8 of 8 1 |
Images - 1-8 of 8 1 |