5 comments about Introduction To Fourier Optics.

1. This is the best book on Fourier Optics that I'm aware of. There is sufficient detail that you can follow the math, but also has well written text explaining concepts. The problems are sometimes trivial and sometime challenging, but they are very much an integral part of the book and doing them is necessary to get a full understanding of the material. There is a 3rd edition of the book with an additonal chapter, which is available at a much lower price, but Amazon does not seem to be carrying it yet. Hopefully they will soon. (...)



2. For the last month, I have been using this book for self study to aid me in my work with lasers. Originally, I was working from the 1st edition (borrowed from a co-worker), but decided to buy my own copy. I wound up buying the 3rd edition, a significantly expanded version of the original.
   
   Goodman's writing style is conversational and his treatment of the subject is thorough. I appreciate his inclusion of enough optics/E&M background within the text that I am not constantly having to go to my bookshelf to consult other references. Note, the 3rd edition has several helpful appendices not found in the 1st edition.
   
   There are also many instructive problems given throughout the text to help students solidify their understanding of the material.
   
   This is an excellent book for self study, and would certainly make a fine text for a senior undergrad course on the subject. I recommend it highly.
   
   Charlie.



3. Overall I like the book for it is clear, the mathematics is lucid and has all the essentials in a comprehensive way. I have found it quite useful for research. In addition, for the most parts it is quite accurate.
   
   Some criticisms though:
   Contains everything from a more mathematical point of view. By that i mean, problems are usually not very physically motivated and some of the conclusions drawn are not very physical. that is you are given at the end of a discussion only an integral. It would have been nice if there were more discussions on the physics of Fourier Optics, for example pictures of actual experimental results or clear diagrams that show for example how does the diffraction pattern for a given input looks like. So getting an intuitive grasp of the subject at a pictorial level, where you can 'see' the results is a bit challenging to get out of this book. also very expensive.



4. Only the best will do - and this is it.
   
   Mandatory reading for anyone involved in optics. Goodman's books are treasure troves.



5. I took a class in Fourier Optics and found this text to be indispensable. It explains everything very clearly and concisely, which is a minor miracle for a text at this level. I didn't have any particular background in optics, and was able to pick this up and understand every word.
   
   I do agree with the earlier poster that more 'physical' or graphical representations of concepts would have been useful as I tend to be a visual learner.

No comments about Invariant Subspaces of Matrices with Applications (Classics in Applied Mathematics).

No comments about The Metric Theory of Tensor Products.

1 comments about Classical Banach Spaces I and II: Sequence Spaces; Function Spaces (Classics in Mathematics).

1. This book is an excellent survey of Banach Space Theory, and an invaluable resource. It's too terse, but then again, most reference books are.

1 comments about A Hilbert Space Problem Book (Graduate Texts in Mathematics).

1. This book should have been titled "A Hilbert Space Idea/Problem Book" as it not only challenges the reader to work out interesting problems in operator theory and the geometry of Hilbert space, but also motivates the essential ideas behind these fields. It is definitely a book that, even though out-of-print, will be referred to by many newcomers to operator theory and quantum physics. The insight one gains by the reading of this book is unequaled in any other books in existence on operator theory. It is becoming more rare as mathematics advances, to find books that attempt to explain the intuition behind the abstractions that are manifested in any area of mathematics. The problems in the book deal with both concrete examples and general theorems, and the reader should attempt to try and solve them without looking at the hints. The solutions found by the reader can then be compared with the author's, and some interesting differences will occur.

   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 states most 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.

1 comments about Vector Measures (Mathematical Surveys, Number 15).

1. Vector Measures is the best book on this subject! The general treatment is very nice...this book is perfect if you know the book "Linear Operators, vol I" of Dunford and Schwartz.

No comments about A Short Course on Banach Space Theory (London Mathematical Society Student Texts).

3 comments about Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms (Computational Mathematics Series).

1. If you need this book, you already know it. You barely remember what the Fourier transform does, let alone how it works, and you need to implement it from scratch. This book is for you.
   
   Most programmers never need to use Fourier transforms. Most of the ones who do will get by quite nicely on black boxes from Mathematica, Matlab, or Numerical Recipes. Data goes in, answers come out, and "a miracle occurs" somewhere in between. There are those times, however, when you can't use the canned routines. You just have to write your own.
   
   This book isn't for the faint-hearted, but really does give everything a non-specialist needs for creating a competent implementation. There's no cut&paste code here, but this is for people with unique needs. It presents a number of basic variations, with clear illustrations and pseudocode. It even discusses 2D transforms, but most of that discussion centers on how to transpose the 2D matrix between 1D transforms.
   
   The discussion of parallel implementation was the only section I found weak. It's aimed at standard sorts of multiprocessors, with specific kinds of connection networks between processors. First, those networks are rare in commercial multiprocessors or are so deeply embedded that the topology is not accessible to the application writer. Second, those networks and architectures miss a lot of important computing environments completely - including the ones important to me.
   
   I don't wish it on anyone, but it might happen - you might have to implement a FFT for yourself. If it does happen, this book may be your most effective tool. It will probably take the non-specialist (like me) time to get past some of the notation, but the answers here are worth the effort.
   
   //wiredweird



2. While I'm positive that this book will serve engineers well, I cannot recommend it to practitioners of pure mathematics, videlicit those who are not comfortable with the bloodied abortion that is mathematics to the engineer. It blows my mind that we ever got a man on the moon! A good example can be found in the first line of page 7. omega^l=omega^(l+(2*n+1)). Keep in mind that n is an element of the set of positive integers, their claim not mine. Now, if you solve for n you'll find that this equation can only be satisfied for n=-1/2, clearly not an element of Z+! (Perhaps rational numbers are included in the set of "integers for engineers.") And yet they seem to indicate that it holds for all n in the aforementioned set! I pray that I've missed something and that someone will embarrass me by pointing out my mistake because as irate as I am right now, blood will likely shoot out of my nose in the next 5 minutes and they'll find me dead in my office at day's end.



3. Personally, I am satisfied with what I bought. I wrote an uninspired fast fourier transform from its mathematical formula and it took 30 seconds to execute. I knew I could do better. After buying the book I learn to play close attention to the bit reversal on the twiddles (trig functions). I also learned how to do the split-radix. I also learned that each calculation yields two terms. Also, I gained emough of a sense of how the fft works that I was able to successfully create threads and try parallel processing. All totalled, I reduced the run time from 30 seconds to 1 second.
   
   The book was not as well written as I would have liked. The formula for the split-radix was screwed up. Using the form of the formula and the suggestion of what it represented I was able to derive the formula. It would have been nice if they had written out each term of each iteration for a 64-term fft. That is what I did to see with my own eyes what was happening. The text is too abstract.
   
   All-in-all it was worth the $100.

5 comments about Conduction of Heat in Solids.

1. This book is a masterpiece of a collections of all the known analytical method applied to heat conduction. A must buy and collectable classic.



2. This classic should be on every science and engineering bookshelf. The wealth of elegant analytical solutions is an invaluable resource for analysis as well as for informing numerical solutions.



3. on time, great quality for the money. Would most certainly purchase from this seller in the future



4. This is THE REFERENCE book in Heat Conduction which is a must to any Engineering or Science researcher. It covers a wide range of topics related to Heat Conduction. It is necessary to have even if one has other more modern books covering the topic such as the excellent Ozisik textbook on Heat Conduction.



5. I found the book interesting and challenging to read at the same time. The concepts are old but it presents them in a different format.

1 comments about Best Approximation in Inner Product Spaces.

1. Frank Deutsch writes this remarkably self-contained work on the most fundamental aspects of approximation theory in vector spaces with inner products.
   
   Deutsch starts this work by describing the basic problems of approximation theory: what is the best line fit (linear regression), what is the best solution to an over-determined system of equations, how to approximate a real continuous function with a polynomial, how to solve basic control system problems, and computing the best approximation to a surface with convexity constraints. He simply explains how to characterize and solve these problems with approximation theory while gently introducing graduate level analysis. The reader will learn the basics of orthogonality, Hilbert Spaces, compactness, dual spaces, Fourier analysis, Gram-Schmidt orthonormalization, Zorn's Lemma, and dual spaces with applications of all these concepts to concrete approximation problems. He concludes the text with four chapters of very recent research on common computer algorithms, strong CHIP, and the convexity of Chebyshev Sets. This book is a great introduction to approximation theory and modern analysis. I highly recommend it to any advanced undergraduate mathematics student or to any graduate student studying operations research, electrical engineering, or computer science (esp. numerical analysis).