John Allen Paulos, Viking, London, 1989
At first sight, I though the book is too simple and is not worth reading. Soon, I changed my mind after reading the following joke:
A man who travels a lot was concerned about the possibility of a bomb on board his plane. He determined the probability of this, found it to be low but not low enough for him, so now he always travels with a bomb in his suitcase. He reasons that the probability of two bombs being on board would be infinitesimal.
Marc Baus and Carlos F. Tejero, Springer, Berlin, 2008
This is the first book in statistical physics that I have almost read through. It’s very easy to read, both contents and language. Only after reading the book, I can distinguish various Ensembles: microcanonical, canonical and grand canonical.
Errata:
The double integral with respect to p and q was missing in equation (4.44).
Richard L. Liboff, Springer-Verlag, New York, third, 2003
I first encountered this book several years ago. The contents were so new to me and I was impressed. But it was hard to grasp the contents also. I have been hoping to read through the book one day.
In order to figure out the clear relation between viscosity and conductivity of fluid and the particle kinetics, I pick up the book again.
“A distribution function is worth a thousand macroscopic variables.” The quip is excepted from the footnote 5 of page 162.
Errata:
It seems from page 29 on all the references to (4.20) should be (4.23).
The subsection 3.3.4 title “Temperance: Variance of the Velocity Distribution” is so weird, perhaps “Temperance” should be “Temperature”. But this kind of error is unimaginable, except the word was automatically chosen by the word processor through the auto-correction function, which I encountered several times.
Page 169, the second sentence was repeated.
Page 181, “+” in equation (4.18) should be “=”.
Mark Kac with special lectures by G. E. Uhlenbeck, A. R. Hibbs, and Balth. van der Pol, American Mathematical Society, Providence, Rhode Island, 1959
It is too hard to follow the author’s derivation owing to very subtle math, and there was any subsections at all which made the context more difficult to grasp. In conclusion, I learned almost nothing new. However, I do respect Kac’s math ability, and appreciate the style to solve a concrete physical problem by presenting a math model and then analyzing the model. The style is not unfamiliar, but the author’s ability is admirable. There are special lectures appended in the book by Uhlenbeck and van der Pol (I have not heard about Hibbs.), but I did not read them. So many famous names in a single title page reminds me of the saying birds of a feather flock together!
The book contains too much on the topic of irreversibility from the Boltzmann standpoint to be of much interest today, excepting one chapter: the one by Kac on functional integration and partial differential equations.
Above is the review by professor Joseph L. McCauley in Amazon.com. I cannot judge professor McCauley’s review either, since I do not know the popular point of view on the paradox of Boltzmann’s irreversibility.
Alexander Elder, John Wiley & Sons, Inc., New York, 1993
If I become half of a percent smarter each year, I will be a genius at the time I die!
The book was referred a few times when reading about trading. I have been scared about trading for one year, since the big loss in Forex market. My confidence is coming back little by little as the frustration is fading away. The book increases my confidence even. Dr. Elder was a psychiatrist, and he did show his profession in the book from the beginning which I just finished reading. The author explained why to trade, one reason is for self-fulfillment. I like the excuse! It makes me feel more comfortable to spend time on trading, other than feel not to attend my proper works or duties. The author further claimed that making money is just a afterthought of successful trading. What similar to my once hold believing that wealthy will be byproduct of academic success! However, I care about money much more often than academic research now. In “beautiful” words, I am getting more practical. In other words, I am falling into the mundane world inevitable for the great majority of people. Luck or pity?
Ole Christensen and Khadija L. Christensen, Birkhäuser, Boston, 2004
Completely as the authors said in the preface, the contents about polynomial approximation is elementary and easily to understand. Also I am so familiar with Taylor expansion, yet the book provides me many interesting and counter-intuition examples about polynomial approximation. I have neglected, or have never noticed, many subtle premises of the validity of these approximations. One astonishing example is that the infinite sum of a series of continuous functions is not continuous! Example 2.5.3
$$! \begin{cases} \frac{1}{x} \mbox{for} 0<|x|<\sqrt{2},\\ 0 \mbox{for} x=0.\end{cases}$$
Ingrid Daubechies, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992
Nyquist frequency is a term I have met many times. In Daubechies’s book, which is one of the classics about wavelets, I obtained a “natural perception” of it for the first time, which means a kind of assuring understanding. Meanwhile, I got a better understanding about the aliasing phenomenon. Perhaps it is just one interesting fact among the myriad in the nature, under sampling a signal can still get some bona fide portion of frequency spectrum of the signal, other than aliasing every frequencies.
Lars V. Ahlfors, McGraw-Hill, New York, Third Edition, 1979
Ahlfors was emeritus professor in Harvard university, and his book “Complex Analysis” is considered a classic in the field.
I have not spent much time on the book. The reading experience is so so. Many times I found difficulties to follow the author’s ideas, which contrasts the joyful experience during studying several books on heat equations and integral equations. However, I did find an interesting theorem, the lemma of Schwarz:
If
is analytic for
and satisfies the conditions
,
then
and
.
If
for some
, or if
,
then
with a constant
of absolute value 1.
The proof is not hard to understand, but the conclusion is really amazing. There is so few limitations on the function 
David Porter and David S. G. Stirling, Cambridge University Press, Cambridge, 1990
I am trying to solve the Burgers equation with specified boundary and initial conditions through the Hopf-Cole transformation. However, I don’t know how to transform the boundary/initial conditions for the Burgers equation to those for the heat equation. There are a few papers focused on the problem. But I can’t totally grasp the techniques involved. It clues that some theories about integral equations are necessary.
I encountered the jargon like Fredholm or Volterra integrals occasionally. It was so daunting that I never tried to understand them. Quite surprisingly, I found the integral equations are not difficult to understand at all, when reading the beginning of the book. The idea behind a resolvent operator is also interesting. I anticipate it is a very useful systematic solution process, although I don’t the underlying mathematical theory yet, perhaps the spectral theory.
Sheldon K. Friedlander, Oxford University Press, New York, Second Edition, 2000
Nearly five years ago I touched the book first time when I set about the research on vehicle exhaust pollution, where aerosol dynamics is applied. I had known nothing about aerosol dynamics before reading the book. It was the right first introduction book. And the relevant research, although not very successful then or even now, was started from the General Dynamics Equations proposed by the author.
When I reread the book, I learned much more, and admired the author’s profound knowledge. The book almost covered every aspects that aerosol dynamics involved, and provided abroad research results. It can be seen as the classics in aerosol dynamics!
