The World According to Wavelets: The Story of a Mathematical Technique in the Making

Barbara Burke Hubbard, AK peters, Wellesley, Massachusetts, 1996

A very good book written by a professional public science writer. Barbara admitted she is not a mathematician, while she holds a BA of English. No wonder there were so many words that I did not know.

She interviewed many important mathematicians and scientists for the invent and development of wavelets, maybe all in America and French. The book covered the underlying ideas for developing wavelets and introduced the applications of wavelets in diverse fields. The first part of the book is brilliant. It is really a joy to take a journey with her to gain a panoramic view of the wavelets. The second part presented the relevant mathematical theories to wavelets, according to Barbara’s claim. However, the mathematics is obviously too elementary to give a general description of the wavelets. Perhaps I am developing more and more of the type who can understand mathematical equations better than text explanations.

Parallel Programming with MPI

Peter S. Pacheco, Morgan Kaufmann Publishers, San Francisco, California 1997

“E Pluribus Unum”, in the dedication page, this Latin motto is first time encountered. Quite similar, I was my first time to read a book on MPI. There is not much to say about MPI, which I am not grasped yet. However, it seems there is not too much to grasp either, simply some basic ideas about parallel computation (many are new) and programming functions.

Wavelet Theory Approach to Pattern Recognition

Yuan Yan Tang, World Scientific, Singapore, 2009

A book in English written by a Chinese! The English itself is very easy to understand, but there is always a feeling it is not written by a native speaker. I am curious how long would it generally take a Chinese to learn and practice English after he can use idiomatic English.

I guess the author majored in math, since he used so many professional math jargons. And there are lengthy math equations throughout the book. However, there are also a huge number of pictures and numerical data. Besides, the resolution of the pictures scattered broadly, some are fine quality vector graphics, while some are very low resolution bitmap graphics.

A Panorama of Harmonic Analysis

Steven G. Krantz. The Mathematical Association of America, Washington, DC, 1999

Yes, it is really a panorama of harmonic analysis. I feel much more confident about harmonic analysis after reading the book, although I cannot understand nearly half of the contents. It seems that the key topics in the classical harmonic analysis are several convergence theorems. Despite of the technical difficulties to grasp the details, the basic ideas are not too difficult. I also feel much more comfortable with the space, which once was so abstruse to me.

The book closed with a discussion about wavelet, and regards wavelet as the reinvent of the Fourier analysis. I also understand more about wavelet, and want to apply wavelet to my research in some recent day.

The Art of Probability: For Scientists and Engineers

Richard W. Hamming, Addison-Wesley Publishing Company, Inc., Redwood City, CA, 1991

This is a very good book. I have carefully read every sentence, of course, not including all the equations. The author provided a panoramic view of probability, from pure mathematics, from practical applications, and even from philosophy of mind. Generally, the contents are easy to follow, although the style of writing is somewhat tautological.

Once I believed that the measure theory is the substantial foundation of the probability theory, furthermore, I had the vision in mind that math is omnipotent to understand and model the nature. However, I gradually change my mind, and my favor for pure math is fading away. I am getting more and more “practical”, meanwhile, some long cherished ideals are not so charming any longer. 

Methods of Theoretical Physics

Philip M. Morse and Herman Feshbach, Part 1 & Part 2, McGraw-Hill, 1953

I have not read through the two big books. In fact, I only finished several ten pages of the Part 1. I have tried finding the electronic contents to paste here, but failed. The books cover many aspects of mathematical physics. But I guess some methods are becoming out of fashion. However, I have been interested in all “classical” methods and dream to master all of them. From a pragmatic point of view, to learn so many methods is a waste of time, if they are no used in a paper. At this moment, I am tired to learn more.

Adventures of a Currency Trader: A Fable about Trading, Courage, and Doing the Right Thing

Rob Booker, John Wiley & Sons, Inc., 2007

Definitely, this is not a how-to book about Forex trading. As the title suggested, it is an adventure story, about money. The story is like a fable, where I found much the same as I did. The story has a happy end, just as most of the Hollywood  movies. However, I don’t my end yet, whether happy or disastrous.

The book is full of an optimistic attitude, perhaps it originates from the nature of Americans. I seldom feel so optimistic about the unknown future, and always in a slightly upset mode. When Harry, the protagonist, lost his job, and lost almost all the money in his Forex account that he couldn’t afford, I felt really sorry about him, about his wife and children. I couldn’t help thinking what about me if in the same circumstance. However, I did find an exciting idea on trading from the book. Arbitrage between two brokers when one of them does not charge/pay rollover! I was so excited, and thought that it is the reward of reading so many books. Every dog has its day. However, the excitement did not last long, when I realized that the idea is so popular that it is hard to practice in real market any longer. There exists no broker that does not take account of rollover or swap, except some small brokers. Putting money into their bank account is rather risky, it is not arbitrage any more. Oops, it seems there is no easy money at all, at least from my point of view.

Forex Wave Theory: A Technical Analysis for Spot and Futures Currency Traders

James L. Bickford, McGraw-Hill, New York, 2007

It is another book that I could skim through in a few hours. Many “theories” were introduced, but none impressive. The theory part is like a report composed by a busy student after searching the relevant topics in internet. The main part of the book was to define several patterns and then investigate the frequencies from market data. This “academic” style is much familiar to me. So, I hardly believe in the analysis and evaluation.

Boundary Integral and Singularity Methods for Linearized Viscous Flow

C. Pozrikidis, Cambridge University Press, New York, 1992

This is another book on linear problem. I have a “better” understanding about Green’s function. “In mathematics, a Green’s function is a type of function used to solve inhomogeneous differential equations subject to boundary conditions.” (from Wikipedia). This is what I obtained after reading the book. I used to think the Green’s function is a strange function that I could not remember always. Now, it seems that a Green’s function is barely a name of a function introduced in the specific solving procedure of the linear boundary value problem.

Singularity methods seems to be the singularity image method I learned many years ago in university.

The original objective to read the book is to find out the analytical solution of a Stokes flow around a prolate spheroid, and compare the solution with my numerical simulation. Finally, I found the expected solution, but doubt the correctness of the expression. Some different references are required to tackle the issue. 

Random Integral Equations

A. T. Bharucha-Reid, Academic Press, New York, 1972

This is another mathematics book I have finished and could understand 50 percent, perhaps. No direct application of the theories is possible at present.