No comments about II: Fourier Analysis, Self-Adjointness, Volume 2 (Methods of Modern Mathematical Physics).

No comments about Twentieth Century Harmonic Analysis -- A Celebration (NATO SCIENCE SERIES: II: Mathematics, Physics and.

1 comments about Introduction to Fourier Analysis.

1. Throughout my graduate career, I searched desperately for a book that covered Fourier Analysis in a manner that would be lucid to a novice. Of all the books that I've seen dealing with the subject, I rank Morrison's as the best in this category.

   Most books dealing with Fourier Analysis appear to be written for someone with a degree in mathematics. Although I would say that this book is an excellent introduction to Fourier analysis and the Fourier transform, the reader must possess a strong working knowledge of calculus at the least.

   The book is presented in the classic textbook format, where each section is introduced and explained with examples, then a series of problems are presented to reinforce the concepts presented.

   The first half of the book covers continuous Fourier analysis, and the second half of the book covers discreet Fourier analysis. Some may argue that these two concepts could have been introduced simultaneously, however I found this dichomtomy to be an effective way of presenting the material. The book is geared towards undergraduate students of electrical engineering, but I think that it is appropriate for anyone wishing to learn Fourier analysis. The book is replete with exercises to be completed with the accompanying diskettes (both Mac and PC are included), but I never used them.

   This book is the best I've seen dealing with the subject, but I did have to proceed very slowly. I did not understand all of the concepts presented, perhaps because of my limited mathematics background (as high as calculus). For this reason, I rate the book a seven.

3 comments about First Course in Wavelets with Fourier Analysis.

1. At the time of writing of this review (October 2001), a standard academic search procedure
   produces about twenty references per week of scientific papers using wavelet analysis in a very wide spectrum of sciences. More than 160 english language books have been published on wavelets since the first books appeared around 1990. Yet even now it is rare to find a book on this subject which is aiming at undergraduate students and yet is mathematically responsible, without being heavy going. Boggess and Narcovich have tried to do just that, and to my mind have admirably succeeded.
   Assuming a standard background knowledge in calculus and linear algebra that many science and engineering students acquire in their first two years at university, they present the basics of Fourier analysis and wavelets in eight brief chapters. To prepare the way, they start in chapter 0 with an introduction to inner product spaces, without using advanced analysis, and building on the experience with ordinary vector spaces.
   Also a sniff of linear operator theory is offered.
   Chapter 1 introduces Fourier series in real and complex form. These originated in the eighteenth century study of vibrations and in the theory of heat, made famous by Fourier's classic book of 1808: Analytical Theory of Heat. The mathematical claims Fourier made, but which he could not all prove himself, gave the impetus to an enormous development of both mathematical theory and applications in all fields of natural science, which is still going on today. The applications briefly mentioned here are denoising and compression of signals, and finding the solution of partial differential equations. Various aspects of the convergence of Fourier series are dealt with. All concepts are illustrated with a good set of clear figures, and the chapter finishes with exercises that are going from very elementary to a little more ambitious, sometimes involving the use of simple computer algebra tasks. This format is maintained thorugh the entire text, except for the last chapter.
   Chapter 2 proceeds with the Fourier Transform, including the important theory of linear time invariant filters. The existence of the impulse response function and its convolution character are shown. As an example the noise reducing Butterworth filter is presented. Sampling and the Nyquist frequency are touched upon, and a derivation of the uncertainty relations, originally coming from quantum mechanics, is given.
   To analyse discrete data, one needs the discrete Fourier Transform, which is the subject of chapter 3, including of course the Fast Fourier Transform. Also the z-transform is introduced. Examples given are elementary cases of parameter identification in vibration, numerical solution of ordinary differential equations, as well as in the exercises: noise reduction and data compression.

   These first 153 pages serve as a good undergraduate introduction to Fourier analysis.
   The second half of the book is devoted to wavelets. Chapter 4 deals exclusively with Haar wavelets which are the oldest wavelets because they date from 1910! These wavelets constitute an orthonormal basis of functions, which makes for fast calucation, a very important aspect for many applications. The core ideas of the central concept of a "multiresolution analysis" of a signal, can be demonstrated with these simple wavelets. All of this is already understandable without the machinery of the preceding Fourier analysis, so you could jump into the book here and start reading about wavelets right away, picking up the Fourier analysis from the first part bit by bit as the need arises. As applications denoising and compression are mentioned again, as is the detection of a discontinuity in a signal.
   The general case of a multiresolution analysis is the subject of chapter 5. Again a large part of the discussion can be swallowed without the need of the Fourier transform point of view. The explanation of the structure of a multiresolution analysis leading to an orhtonormal basis of wavelets is straightforward and clear. It is only when we want to go into more detail about the precise characteristics of the underlying wavelet and scaling function that the Fourier point of view is introduced. This then leads up to the presentation of the famous Daubechies wavelets in chapter 6. These wavelets revolutionised the field after their publication in 1988.
   Chapter 7 which closes the book, gives several short remarks about various other topics among which are two-dimensional wavelets, and the continuous wavelet transform.
   This chapter is more sketchy than the others, and left me much less satisfied. Also the motivation why these subjects are chosen was lacking almost completely, and there are no exercises. I was particularly disappointed not to find any discussion of the relative merits of the continuous versus the discrete wavelet transform, and there is no mention of any application of the continuous case. Yet the latter is also used frequently in many important scientific applications, and it started the modern wavelet endeavour in the early eighties in France.
   That being said I still think this is a very useful book for anybody wanting to start with wavelets at an undergraduate level. A few helpful Matlab Codes are collected in an appendix as well as the more difficult parts of some proofs. The exercises make this good course material, but as a text for self study it will also be quite satisfactory for many newcomers that find most of the existing books too demanding.




2. ...this book is one of most informative and legible books on wavelt theories and applications.

   The author paves the theoretical development about wavelets and multi-resolution analysis EXCELLENTLY. With this book, you can construct wavelets for your own applications in engineering and science disciplines.

   This book is very good for first year engineering-majored graduate students and all engineering scholars.




3. If you want to learn Wavelet theory in a easy way like reading a story book then this is the book. It deals with the most complicated thing in the easiest way.

No comments about Harmonic Analysis and the Theory of Probability (Dover Books on Mathematics).

3 comments about The Fft, Fundamentals and Concepts.

1. Of the half-shelf of books in my library related to signal processing, this one by Ramirez is part of a highly valued subset. The author achieves an artful balance of the theoretical with the practical. Given that my emphasis is on applying the principles of FFT processing in a manufacturing environment, his approach proved quite helpful.

   Throughout the book, basic concepts are initially presented within a mathematical context. Subsequently, they are reinforced with examples. Often, hardcopies of traces from a signal processor's monitor are provided--these are effective in driving home key points.

   After reading this book over two days' time, I was left wishing to see a companion volume that adds more on real-life problem solving, plus material on advanced techniques (e.g., cepstrum). This thirst for more knowledge says a lot for the way in which Ramirez motivates.




2. This book is a great way to realize that theoretical murmurings can mature into intuitive processes that can be used as guides to self-check new ideas. While FFT theory is necessary, if you like that kind of thing, a good grasp of what may be accomplished is often left out or buried. This book provides a great way to get perspective on rigorous frequency domain textbook theory and make the necessary textbook search for detail much more meaningful. I highly recommend this book for anyone who has to deal with signal processing.



3. Too simplistic. Perhaps good for newbies. But anyway there
   are better books on FFT, e.g. Brigham. This one is not for
   professionals! You've been warned. For beginners I would recommend books by Zonst. They are much more to the point.
   And cheaper! Thanks god I didn't buy it myself!

2 comments about A First Course in Fourier Analysis.

1. I have been interested in the Mathematics of Fourier Series/Fourier Transform methods for well over 15 years. I own already well over 10 books on this subject. The book by David Kammler strikes me as having a particularly good balance between theory and applications as well as taking a modern computer approach to this ever relevant subject. Important topics such as sampling theory and the Fast Fourier Transform (FFT) are well covered and explained in detail. Also, chapters that apply Fourier Analysis to important physical areas (heat conduction, light diffraction, wave propagation, musical sound, etc.) illustrate and higlight the relevance of Fourier Methods in the real worls. There is also a nice summary at the end of the book that explains the histoy and most important application of Fourier Analyis (very nice). Ample computer excerices and the traditional proof/derivation homework problems are included. The book also seems to prepare the reader well for the increasingly subject of Wavelets and applying them musical sound. Also, what makes the book stand out from more traditional ones is the emphasis on Numerical Method and using the computer to solve or illustrate some of the powers of Fourier Analysis. Readers considering using this text should best have a background in calcus, differential equations and Matrix methods. This probably puts it at the junior/senior undergradudate level. 1st year graduate students might also benefit from the text.

   In a nutshell this is an excellent textbook for anyone serious about Fourier Analysis and applying those methods via computer (or pencil) to real world situation. This is probably one of the best books yet on this very important subject. Highly Recommended!




2. I am taking this class as an undergraduate course with Dr. Healy at University of Maryland at College Park. This is an elegant, thoughtful book that provides a rich math course that is a welcome alternative to run-of-the mill engineering math classes lacking in intangible qualities. Many of the problems are tough and require some rigorous math at an advanced, math-major level (real analysis would be helpful) but are overall accessible to engineering seniors with strong math skills and office hours support from the professor, and the problems are well-geared to illustrating and exploring the topics in the text. As another benefit to the student, the examples definitely help one warm up for the problem solving at the end of the chapters. In addition to the richness and elegance of the subject as presented, this is a thoughtfully constructed and presented text.
   
   The first several chapters introduce fourier transforms and related math such as convolutions as a set of operations in a variety of spaces, including continuous, discrete and periodic spaces. Then the text goes into the theory of distributions/generalized functions and solutions of differential equations. Several additional chapters take the subject into wavelets. The presentation of the Fourier transforms having a variety of manifestations in different kinds of spaces unifies in a fundamentally harmonious (no pun intended!) and beautiful way the disjoint and arbitrary Fourier processing taught to engineering undergraduates.
   
   Five years after writing the above review, I want to update it: I associated with Dennis Healy in a funded program and was subjected by him to a lot of inappropriate behavior. The beauty of the Mathematics is in no way representative of the ugly, personally underdeveloped behavior of the male mathematicians. There was only one female with a PhD remotely associated with Dennis Healy and John Benedetto's MAIT (Mathematics of Advanced Industrial Engineering Technology) Math program at the University of Maryland, and she was doing the males. Presumably, I was taken on to fill just that same kind of role. I regret and retract my earlier praise, especially where I included wording like "elegant". The qualities of Mathematics far outstrip the qualities of the personally undeveloped and egotistical men who engage in it! Kammler, I love your book, disdain those who teach from it!

3 comments about The Mathematics of Infinity: A Guide to Great Ideas (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts).

1. An excellent book with a slightly misleading title. A better title might be "Sets and Proofs and their Applications to Infinity".
   
   The book is well organized and well written, although the author's assumptions concerning his target audience appear slightly inappropriate. The back cover recommends the book as recreational reading for the mathematically inquisitive. The material presented is certainly accessible to a highly motivated reader. However, the level of mathematical maturity needed to maintain the interest and understanding of the reader appears more realistically targeted for an audience at the college level or the equivalent self-educated reader.
   
   This concise presentation is dense in mathematical symbols. Fortunately for the reader, the examples and proofs give all the appropriate steps so that there are rarely any mathematical gaps to close. The book introduces some substantial mathematical concepts and ways of thinking. This is one of those math books that holds and sustains your interest throughout.
   
   There are some slight flaws, such as editing errors, as early as the preface's first paragraph. In a few instances there are factual errors in the mathematics, e.g., on page 21 the author asks the reader to identify the 11 missing sets, when there are actually 13 missing sets. The most unfortunate gap, in light of the intended audience, is the author's request that the reader provide their own proofs for a number of problems, for which Dr. Faticoni fails to provide solutions.
   
   This book should be interesting to the mathematically mature reader, and help the motivated budding mathematician gain insights to prepare them for more advanced material.
   
   Overall, in spite of some minor flaws, this is an interesting and substantive book by a master teacher. It is one I enjoyed and, except for its price which seems somewhat inappropriate considering its size and intended audience, one I can recommend.



2. For the mathematically naive this book is highly misleading. For the Mathematically literate this book is a waste of time.



3. First of all the price for this book is way to high, but really this is my only major objection. I have seen allot of books on set theory. As an introduction that aims to give insight into how set theory is handled, and exactly what it does, this book is top notch.
   
   I also found typos in the book. For someone that does not know enough to sort the typos from author intentions this can be a real pain. Of course the way around this is to have at least one other book on set theory around. If something looks odd, then check the other text.
   
   Summary
   -------
   cost: 1 star
   content: 5 stars
   typos present: 2 stars
   readability: 5 stars (font metrics, printing, page size)
   overall: 4 stars

1 comments about Automatic Sequences: Theory, Applications, Generalizations.

1. In 1983 Lothaire's "Combinatorics on Words" became the definitive resource on the area of stringology. 20 years later, Jean-Paul Allouche and Jeffrey Shallit's "Automatic Sequences" is set to be its heir. Pulling in countless concepts from many seemingly dissimilar disciplines, Allouche and Shallit are successful in bringing them together in an extremely informative and concise way. With detailed chapter notes and an immense bibliography the possible areas of exploration on each topic prove endless. A great resource for everyone from the serious researcher to the casually interested, this text is applicable to almost every area of mathematics and computer science. As the authors put it, "Sequences, both finite and infinite are ubiquitous in mathematics and theoretical computer science." If quality were synonymous popularity then this book will be equally ubiquitous.

2 comments about Uses of Infinity.

1. This book was my first introduction to the infinite. Although it is easy enough for undergraduate study, all will find Zippin's book scintillating and fascinating. A great read for anyone interested in this subject!



2. Zippin's engaging text examines how infinity arises in mathematics. It requires only a solid grounding in high school mathematics and a willingness to think. However, it will most profitably be read by those who are familiar with calculus.
   
   After a brief overview, Zippin begins within the natural numbers. He shows how inductive reasoning is used to search for patterns that can be used to prove results about infinite sequences and series. He examines limits of sequences and series from a geometric point of view. In particular, he considers geometric series and the Fibonacci sequence, using the latter to explore the properties of the golden rectangle. He concludes the text by discussing recursive definition, proofs by mathematical induction, and the pigeon hole principle.
   
   I found the material intriguing and the exposition generally clear. However, there were places where I felt that definitions were imprecise. His proof that the square root of 2 is irrational, while elegant, is harder to generalize than other proofs of that result. Zippin uses numerous examples to illustrate the results that he proves.
   
   Zippin's decision to examine limits from a geometric standpoint provides an interesting alternative to the analytical approach taken in calculus courses. It also helps the reader understand his arguments in his chapter on how the golden rectangle is related to the golden mean and the Fibonacci numbers.
   
   The exericses, for which answers are provided in the back of the text, are thought-provoking and some are quite challenging. I found reading his solutions instructive.
   
   Zippin provides a now dated (the text was published in 1962) bibliography so that the reader can explore the topics he discusses further. The reader may wish to consult the texts Invitation to Number Theory (New Mathematical Library) by Oystein Ore and Numbers: Rational and Irrational (New Mathematical Library) by Ivan Niven while reading this text.