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1. Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics) by William P. Ziemer | |
list price: $69.95
our price: $59.46 (price subject to change: see help) Asin: 0387970177 Catlog: Book (1989-08-01) Publisher: Springer-Verlag Sales Rank: 632264 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (1)
excellent resource |
2. Metric Spaces by Victor Bryant | |
list price: $15.99
our price: $15.99 (price subject to change: see help) Asin: 0521318971 Catlog: Book (1985-05-02) Publisher: Cambridge University Press Sales Rank: 310535 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (3)
Great Introduction to Metric Spaces. Lively, Informal Style Dr. Bryant motivates the reader immediately with a look at iterative techniques, fixed point functions, converging sequences, and approximation solutions - all in an engaging style. Later topics included distance concepts, function spaces, and the relationship between closed sets, complete sets, and compact sets. The fourth chapter was devoted to the contraction mapping principle and its use in solving differential equations. Is this book for you? The author says: "The only prerequisite is to have done a course on elementary analysis: it is not a prerequisite to have understood it nor to have remembered it at all." I personally had no formal courses in real or functional analysis and the highly structured axiomatic approach of analysis texts had never appealed to me. I only had a vague idea as to the properties of a metric space. But I was lured into buying Dr. Bryant's short text by the previous Amazon reviewers. And thankfully so. Dr. Bryant clearly enjoys his subject, but he just as clearly recognizes that not everyone might have such an abiding interest. Throughout the text, he points out opportunities where the reader might skip forward if the going has become less interesting. (For the record I refused to be enticed by these short cuts.) Problems are embedded in the text, one or two at a time, and are used to reinforce points under discussion. Most have clear hints and I found many problems straightforward, but others were more difficult. A few problems were identified as appropriate for the "keen" student. The most abstract mathematics are reserved for the last (optional) chapter, but the author does encourage the reader to stay with it: "It would be a pity to stop ..." Chapter five recasts the first four chapters into a more generalized form of real analysis and addresses the question: "What makes analysis work?" Dr. Bryant had an unusual goal for a mathematics text. "I have tried to provide a readable and natural introduction to an abstract subject in a down-to-earth manner." Also, he says, "My aim is to provide a book which can be read and enjoyed ..." He succeeded in doing just that.
Metric Spaces I believe the author is correct when he recommends the book for people who have already had some exposure to analysis. At best a student should already have completed the standard non-rigorous college calculus sequence to get the most out of this book.
This is a great introduction to fixed-point methods. |
3. An Introduction to Hilbert Space by N. Young | |
list price: $36.99
our price: $29.59 (price subject to change: see help) Asin: 0521337178 Catlog: Book (1988-07-21) Publisher: Cambridge University Press Sales Rank: 132792 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (5)
GOOD for control theory theory
A Tantalizing Introduction to Hilbert Space I must strongly disagree with the reader from Sao Paolo who says that chapters 12 and 13 are poorly motivated. These chapters are crucial for the final theorem of the book in chapter 16. Parrott's Theorem in chapter 12 is the key to the foundational Nehari's theorem of chapter 15. Chapter 13 explores Hardy spaces which are the setting place for the major theorem of Adamyan, Arov, and Krein in chapter 16. In fact, I found the movement of ideas from chapter 12 to chapter 16 to be marvelously compelling. These chapters have extreme importance for theoretically oriented control engineers. Only a modicum of real and complex analysis is necessary to understand the book. Knowledge of measure theory is not required.
Very Clear,short and useful
An unusually readable book on Hilbert space
Concise and accurate introduction to Hilbert space |
4. Elements of Mathematics: Chapters 1-5 by N. Bourbaki, H. G. Eggleston, S. Madan | |
list price: $54.95
our price: $54.95 (price subject to change: see help) Asin: 3540423389 Catlog: Book (2002-12-16) Publisher: Springer Verlag Sales Rank: 477744 US | Canada | United Kingdom | Germany | France | Japan | |
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5. Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms by Eleanor Chu, Alan George | |
list price: $99.95
our price: $99.95 (price subject to change: see help) Asin: 0849302706 Catlog: Book (1999-11-11) Publisher: CRC Press Sales Rank: 713568 US | Canada | United Kingdom | Germany | France | Japan | |
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6. Applications of Orlicz Spaces (Pure and Applied Mathematics (Marcel Dekker)) by M. M. Rao, Z. D. Ren | |
list price: $185.00
our price: $185.00 (price subject to change: see help) Asin: 0824707303 Catlog: Book (2002-02-01) Publisher: Marcel Dekker Sales Rank: 1212045 US | Canada | United Kingdom | Germany | France | Japan | |
7. A Hilbert Space Problem Book (Graduate Texts in Mathematics) by P.R. Halmos | |
list price: $54.95
our price: $54.95 (price subject to change: see help) Asin: 0387906851 Catlog: Book (1982-11-08) Publisher: Springer Sales Rank: 324484 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Reviews (1)
Deserves 10 stars There are so many interesting discussions in this book that to list them all would probably entail listing everything in the book. The reader will find excellent discussions of the origin of normal operators on infinite dimensional Hilbert spaces as analogs to matrices on finite dimensional spaces; why the weak topology in infinite dimensions is not metrizable; the non-emptiness of the spectrum and why the spectral radius can be computed even though the spectrum cannot; the impossibility of isolated singular operators; the non-continuity of the spectrum: the existence of an operator with a large spectrum and the existence of operators with small spectra in every neighborhood of the large spectrum. The author then goes on to show that the spectrum is an upper semicontinuous function, thus preventing the existence of small spectra arbitrarily close to large spectra. This is an excellent discussion on the meaning and intuition behind semicontinuity; the result that every normal operator is unitarily equivalent to a multiplication and its equivalance to the spectral theorem. The author goes on to explain how one gives up the sigma-finiteness of the measure when doing this, and the origin of functional calculus; the difference between infinite and finite dimensions when attempting a polar decomposition for operators and its connection with partial isometries; the origin of compact operators and their connection with integral equations. The author shows how even the identity operator is not an integral operator on the space of square-integrable functions with Lebesgue measure. In discussing the spectral theorem in chapter 13 the author statesmost profoundly: "In some contexts some authors choose to avoid a proof that uses the spectral theorem even if the alternative is longer and more involved. This sort of ritual circumlocution is common to many parts of mathematics; it is the fate of many big theorems to be more honored in evasion than in use. The reason is not just mathematical mischievousness. Often a long but 'elementary' proof gives more insight, and leads to more fruitful generalizations, than a short proof whose brevity is made possible by a powerful but overly specialized tool." In these few sentences the author has characterized the problem with current methods of teaching advanced mathematics. Too often the formalism masks the true meaning and intuitive motivation behind the mathematics. And even though mathematics is being applied to many different areas at an unprecedented rate, pure mathematics seems to be trapped in a local minimum, and I beleive this is due to the reluctance of authors to explain in detail the essentials of their ideas. This book is a perfect example of how mathematics can be taught that requires much thought and creativity on the part of students, without spoon-feeding them and thus encouraging a passive attitude to the learning of mathematics. I salute the author in his achievements in research and in teaching...one can only hope that his approach will be followed in all future works of mathematics. ... Read more |
8. Non-Linear Elastic Deformations by R. W. Ogden | |
list price: $17.95
our price: $12.57 (price subject to change: see help) Asin: 0486696480 Catlog: Book (1997-06-01) Publisher: Dover Publications Sales Rank: 163308 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (3)
A defense of Ogden
If you can't teach it, you don't understand it. If you are interested in learning continuum mechanics, I recommend starting with Introduction to the Mechanics of a Continuous Medium, by L. E. Malvern. Then continue with Nonlinear Solid Mechanics: A Continuum Approach for Engineers, by G. A. Holzapfel.
Not good. |
9. Theory of Linear Operators in Hilbert Space by N. I. Akhiezer, I. M. Glazman | |
list price: $17.95
our price: $12.21 (price subject to change: see help) Asin: 0486677486 Catlog: Book (1993-12-16) Publisher: Dover Publications Sales Rank: 67094 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description This classic textbook by two mathematicians from the U.S.S.R.’s prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition. ... Read moreReviews (2)
A Dover classic.
Such an easy book to read! |
10. Introduction to the Analysis of Metric Spaces (Australian Mathematical Society Lecture Series) by John R. Giles | |
list price: $31.99
our price: $31.99 (price subject to change: see help) Asin: 0521359287 Catlog: Book (1987-09-03) Publisher: Cambridge University Press Sales Rank: 1360947 US | Canada | United Kingdom | Germany | France | Japan | |
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11. Transform Circuit Analysis for Engineering and Technology (4th Edition) by William D. Stanley | |
list price: $130.00
(price subject to change: see help) Asin: 0130200352 Catlog: Book (1999-06-24) Publisher: Prentice Hall Sales Rank: 588745 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Reviews (1)
Excellent Electrical Engineering Reference Book |
12. Invariant Subspaces by Heydar Radjavi, Peter Rosenthal | |
list price: $19.95
our price: $13.57 (price subject to change: see help) Asin: 0486428222 Catlog: Book (2003-07-15) Publisher: Dover Publications Sales Rank: 709356 US | Canada | United Kingdom | Germany | France | Japan | |
Book Description This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces, and a selection of unsolved problems. 1973 ed. New appendix on recent developments. ... Read more |
13. Theory of Hp Spaces by Peter L. Duren | |
list price: $10.95
our price: $8.21 (price subject to change: see help) Asin: 0486411842 Catlog: Book (2000-08-01) Publisher: Dover Publications Sales Rank: 537699 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (1)
This book is a classic |
14. Introduction To Fourier Optics by Joseph W Goodman | |
list price: $120.63
our price: $120.63 (price subject to change: see help) Asin: 0070242542 Catlog: Book (1996-01-01) Publisher: McGraw-Hill Science/Engineering/Math Sales Rank: 59574 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (4)
A good path to physical optics and imaging theory
optics
Clearly the Best Fourier Optics Book
A classic made better. |
15. An Introduction to Hilbert Space and Quantum Logic (Problem Books in Mathematics) by David W. Cohen | |
list price: $64.95
our price: $64.95 (price subject to change: see help) Asin: 0387968709 Catlog: Book (1989-06-01) Publisher: Springer-Verlag Sales Rank: 770408 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (1)
Effective introduction This is followed by an elementary introduction to Hilbert space in Chapter 2. This is standard material and most of the proofs of the main results are omitted and left to the reader as projects. Chapter 3 is more controversial, and attempts to formulate a logic of experimentation for "non-classical" systems. This is done by use of what the author calls a "manual", which is viewed as an abstraction of the experimenters knowledge about a physical system. A manual is a collection of experiments, and an "event" is a subset of an experiment. Orthogonality of events is defined, along with the notion of a collection of events being "compatible", meaning that there is an experiment that contains all of these events. A manual is called "classical" if every pair of events is compatible. The author then exhibits systems that are not classical via the double-slit and Stern-Gerlach experiments. A logic of events is then developed in the next section, where quantum logic is defined explicitly. The author defines a pure state that is not dispersion-free as a state of ontological uncertainty as opposed to "epistemic" uncertainty. Quantum systems have states that are ontologically uncertain according to the author. The author chooses not to engage in the debate about the actual existence of these states and, accordingly, no real-world experiments are given to illustrate the relevance of the concepts and definitions. The next chapter covers the geometry of infinite-dimensional Hilbert spaces. The structure of the collection of these subspaces is defined in terms of the quantum logic defined earlier. This is followed by a discussion of maps on Hilbert spaces, as preparation for defining observables in quantum systems. The important Riesz representation theorem is stated but the proof left to the reader. Projection operators are defined also with the eventual goal of relating them to the compatibility of two propositions. Gleason's theorem is discussed in Chapter 6, along with a discussion of the geometry of state space. The proof of Gleason's theorem is omitted, the author emphasizing its difficulty. The proof in the literature is non-constructive and thus the theorem is suspect according to some schools of thought. The spectral theorem, so important in quantum physics, is discussed in the next chapter. Once again the proofs are left to the reader for most of the results. The spectral theorem allows the author to define another notion of compatibility in terms of the commutativity of two Hermitian operators. The books ends with a overview of the EPR dilemna and is naturally more controversial than the rest of the book. This topic has provoked much philosophical debate, and the author gives the reader a small taste of this in this chapter. The book does serve its purpose well, and regardless of one's philosophical position on quantum physics, the mathematical formulations of quantum physics and measurement theory are nicely expounded in this book. ... Read more |
16. Introduction to Operator Space Theory (London Mathematical Society Lecture Note Series) by Gilles Pisier | |
list price: $55.00
our price: $51.15 (price subject to change: see help) Asin: 0521811651 Catlog: Book (2003-08-25) Publisher: Cambridge University Press Sales Rank: 972865 US | Canada | United Kingdom | Germany | France | Japan | |
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17. An Introduction to Models and Decompositions in Operator Theory by Carlos S. Kubrusly | |
list price: $64.95
our price: $64.95 (price subject to change: see help) Asin: 0817639926 Catlog: Book (1997-03-01) Publisher: Birkhauser Boston Sales Rank: 1429460 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Reviews (1)
Nice and well organized introduction to a difficult subject |
18. Classical Banach Spaces I And Ii: Sequence Spaces; Function Spaces (Classics in Mathematics) by Joram Lindenstrauss, Lior Tzafriri | |
list price: $49.95
our price: $36.46 (price subject to change: see help) Asin: 3540606289 Catlog: Book (2001-12-30) Publisher: Springer-Verlag Sales Rank: 443997 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (1)
Great Book |
19. Integral Transforms, Reproducing Kernels and Their Applications by S. Saitoh | |
list price: $99.95
our price: $99.95 (price subject to change: see help) Asin: 0582317584 Catlog: Book (1997-05-28) Publisher: Chapman & Hall/CRC Sales Rank: 1348917 US | Canada | United Kingdom | Germany | France | Japan | |
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20. Function Spaces, Entropy Numbers and Differential Operators (Cambridge Tracts in Mathematics) by D. E. Edmunds, H. Triebel | |
list price: $80.00
(price subject to change: see help) Asin: 0521560365 Catlog: Book (1996-08-28) Publisher: Cambridge University Press Sales Rank: 2057717 US | Canada | United Kingdom | Germany | France | Japan | |
Book Description |
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