1 comments about Monte Carlo Simulation in Statistical Physics: An Introduction (Springer Series in Solid-State Sciences).

1. This is a nice little book written by two experts of the field. This edition is only an expanded version of earlier editions (by addition of two new chapters, the core of the book chapter 1 to 3 hasn't change at all). The book covers monte carlo techniques through various well-known examples (Ising model, random walk, percolation, self-avoiding random walk). I enjoyed reading the first 3 chapters of the book. In particular, chapter 3 guides the readers and gives them the chance to practice what they should have learned in previous chapter (through 53 exercises). The following 2 chapters (chapter 4 and 5) are not as nicely written. Moreover, there are some serious shortcoming in the book. (1) All codes are written in Fortran. While everyone who can program can easily understand the codes, Fortran belongs to the past and could have been ok for physics students during late 80's (first edition) but not for those at 2006. (2) The guide (chapter 3) should have been the last chapter and have covered subjects in chapters 4 and 5 (3) As I mentioned before, chapter 4 and 5 are not well-organized. (4) The book in general stresses too much on finite-size effects. However, it is an important subject and it tells us how we can scale our simulation result to more realistic cases. By my judgement, the book gives wrong impression about the degree of its importance.
   
   I recommend graduate students who are serious about learning monte carlo methods to read Newman and Barkema book (Monte Carlo Methods in Statistical Physics) instead since it provides a broader view about the subject. Although I highly recommend those who are interested in the subject to go through chapter 3. It is fun and very instructive.

5 comments about Statistical Mechanics.

1. The reviewer below who said that this book pursues primarily a kinetic theory - Boltzmann Transport Equation approach, got it right. It really is a fearsome, and by and large, pointless read. Our professor used this book in our stat. mech. class back in 1992. He also used Mahan's Many Particle Physics book in our solid state course and de Genne's Superconductivity text in our superconductor course, so that gives you an idea of what kind of person likes Huang. Most students I've talked to feel that this text is the worst sort of student pain. The pain you feel when after exerting colossal effort trying to understand, you realize at the end of the semester that you didn't learn anything, and that you could have, if only the instructor had chosen one of any number of better books. I am completely mystified as to why and how this book has reached a 3rd edition. Perhaps there are too many physics professors out there who don't care about pedagogy.



2. Huang approaches the subject as a series of proofs: he does not make physical arguments, and his writing is wooden. Instructors--avoid this book!

   Some have said that this book approaches stat mech from the refreshing view of kinetic theory. But it leaves out the Fokker-Planck and Langevin approaches, by which the Boltzmann equation is usually solved. Anyone interested in this approach would be *far* more rewarded by Landau's Physical Kinetics.

   Anyone interested in Gibbs theory should consult Landau or Sommerfeld.

   Anyone who wants good problems (and real applications) would be better served by the canonical McQuarrie.

   Anyone who wants a feel for what the subject *actually now is* should see Kadanoff or Chandler. Actually I think allowing students to leave stat mech without seeing the monte carlo algorithm or solving a stochastic equation is a crime.




3. As repeated by reviewers below, this is NOT STANDARD textbook on statistical mechanics because it stresses the kinetic theory. If reader would like to learn the equilibrium theory, this book might be embarassing. However, this book is recommended to anyone who is interested in "unusual" viewpoint. I prefer Huang to other numerous too standard textbooks. But I am a little disappointed that some interesting topics are removed in the new edition, such as the Chapman-Enskog method.

   Now, it is NOT SO BAD.




4. I learned statistical mechanics from `Statistical Mechanics' by K. Huang and `Statistical Mechanics' by S.K. Ma. In my opinion, most books on the elementray principles, including the book by K. Huang, are too complicated for beginners. The best treatments as far as I know are given by `Statistical Physics, part I' by Landau and Lifshize and the one by S.K. Ma. Another weak points in Huang's book are the discussions about ideal quantum gases. It presents formal mathematical methods to study this problem. I think that this approach is also too complicated for beginners and sometimes bury the relevant physical ideas. In this part, the best treatment for the ideal Bose gas is given by `Statistical mechanics' by T.D. Lee (in Chinese), and for the ideal Fermi gas given by S.K. Ma.
   
   For these parts, I should give 3 stars. However, the strong parts of Huang's book is the chapters on the advanced topics. The writting is compact and clear. They can be served as a good introduction to the modern theory of critical phenomena and superfluidity. Further, they are useful references for research. In addition, the formal manipulation for quantum ideal gases is necessary for research though it seems a little bit complicated for students. For all these, I gave 4 stars to this book.
   
   Finally, I should say that the approach of Huang's book is not based on the kinetic theory though it spends a few chapters on this aspect. The reason why the kinetic theory is put before the chapters on SM, in my opinion, is to emphasize the important role played by collisions between particles to establish thermal equilibrium and the validity of the basic assumption of SM, as indicated by S.K. Ma in his book. I think previous reviews about this are misleading.



5. This is the worst book I have ever had the displeasure to encounter in any field.
   
   Ever.
   
   Is there any way I can possibly be any more clear?
   
   I'm not going to parse the book for you. But, I will tell you a few things which might come in handy:
   
   The book is utterly confusing and baffling. While most other physics textbooks explain things poorly, you can usually still pick up at least a few things from them. As you can see by my review of Jackson's "Electrodynamics", I have no love for that book.
   
   This book makes Jackson look like Shakespeare.
   
   I used the book in a one-semester graduate level class while I was working on my PhD at one of the top ten physics programs in the US.
   
   I don't know how to explain this, but let me try:
   
   Physics is hard, OK? Typically, you might read something in a grad level textbook and not get a darn thing the first time. Then you start slowly and go line by line, and slowly understanding comes upon you. The reason it happens this way is because you, the reader, don't understand the physics at first, but the author of the book does. As you focus and think on the text, you gradually understand.
   
   With this book, it doesn't matter how long or how diligently you focus on the text--- you won't understand. The reason for that in this case is because the text is utterly illogical, pedagogically terrible, filled with baffling nonsequiturs, and so disconnected from physical reality that it seems like a math textbook.
   
   See, the thing is, though, it's NOT a math textbook-- because math textbooks use logic and deductive reasoning. This book is just a bunch of really badly-done math-like gibberish, both disconnected from physics as well as logic.
   
   It is utter garbage.
   
   Please, professors, the only reason you should be assigning this book to your students is if you all need some kindling for the end of semester bonfire. That way you can at least use it to demonstrate an experimental example of Thermodynamics and Statistical Mechanics.
   
   That is the only useful purpose to which it can possibly be put.

3 comments about Mathematics for Physics.

1. This book has nice sections on signals and noise and digital filtering, which are important topics but usually left unaddressed in standard mathematical physics books. I think the book is well done, but a good part (a quarter or so) of the book is at a 2nd year calculus review-type level, much more so than most mathematical physics books (e.g. Boas or Arfken). The encyclopedic book by Riley-Hobson-Bence, which I like except for its sheer size, does also have review chapters, but most of that book is still at a higher level. If you want something about signals and noise in the text, this is the book, otherwise, I think the others may be a better choice for advanced undergraduates.



2. O got this book as a refresher course in mathematical physics since I left grad school almost 10 years ago. I wanted to get straight to the basics and then build from there and also cover the gaps that I had in my math background since I am think about applying to grad school to study Operations Research.
   
   Overall, it seems to be meeting my needs.



3. I had high hopes for this book. It has an attractive layout and an encyclopedic range of topics. Unfortunately, in a mere twenty minutes of perusal I discovered factual errors:
   1. In the treatment of Stoke's Theorem, the authors neglect to state the very important condition that the surface must be simply connected.
   2. The authors claim that the central limit theorem hold with "no restriction on the nature of the individual distributions..." which is untrue. The distributions must have non-diverging moments (i.e., long-tailed distributions), otherwise one ends up with a generalized central limit theorem for which the Levy distributions are stable.
   3. The authors lead one to believe that the angular momentum vector is parallel to the angular velocity vector. The discussion of the moment of intertia (tensor) assumes that one already knows what the principal axes are. It is a shoddy treatment.
   
   Finally, in the preface, the authors say that their textbook was "designed for the twenty-first century". Yet they present computer programs in Fortran and C which in my opinion are obsolete languages. The authors should be encouraging the use of Mathematica or Maple.
   
   Given the number of mistakes turned up in so short an inspection, I consider this an unreliable text.

5 comments about Differential Geometry and Lie Groups for Physicists.

1. The book covers a good range of topics in Differnetial geometry with lots of exercises. One literarily has to do the exercises to develop the concept. Ecah chapter ends with a concise summary of the key equations. The problem is that all the exercises are mixed with the main context. It lacks any exposition or concept development for most of the topics, no definition, no prove, and every page is filled with exercises. This style make it difficult for someone to learn the subjects the first time or to use it as a reference.
   
   Separately, there are too few graphs to assist the reader to visualize the ideas. The prints are also small making it hard to read.
   
   Nakahara's book (Geometry, topology and physics) is a much better choice on the same subject.



2. Marian Fecko's textbook covers well fundamental elements of modern differential geometry and introduction to the Lie groups (not only) from geometrical point of view. Geometrical formulations of the classical mechanics, gauge theory and classical electrodynamics are discussed.
   
   The textbook expects the reader to be familiar with mathematical analysis on the level of the standard course usual in the physics undergraduate study programs. Understanding of the parts dealing with physical applications (classical mechanics and electrodynamics) expects knowledge of fundamental principles of these subjects. Organization of the book allows the reader to concern on particular part, i. e. understanding of later parts doesn't require reading of all previous parts (reading of parts concerning on the classical dynamics does not require reading of parts dealing with electrodynamics). However, relations between different subjects of the theory are explained instructively.
   
   The main advantage of this textbook is that reader "builds" the subject himself by solving the exercises usually appended by hints. It makes all the elements of the theory natural to the reader during study. This way is a little bit more time consuming when compared with other textbooks dealing with this subject. It provides good starting point for study of mathematical aspects of the general relativity and field theories. I recommend this book to everybody who wants to understand fundamental concepts in differential geometry in detail.



3. Before discovering the new book my Marian Fecko I thought I know all that I need about differential geometry (I co-authored a monograph on this subject myself). I had my favorite books: Kobayashi-Nomizu, Bishop-Crittenden, Sternberg, Michor, Abraham and some more. Yet "Differential Geometry and Lie Groups for Physicists" was a completely new experience. It is written with a "soul" and covers topics that are important but missing in other books. As I was working on a paper dealing with torsion, I emailed the Author with some of my ideas and questions and got an instant answer.
   
   Readers looking for explanations and geometrical interpretations of the abstract concepts will certainly find this book irreplaceable. Lie and covariant derivatives, parallel transport, Hodge operator, Cartan's moving frame method, Laplace-Beltrami operator, Lie groups, Maxwell equations, Clifford algebras and spin bundles, SL(2,C), Dirac operator, Momentum map etc. etc. - all introduced and explained in a concise yet clear way, with exmaples and exercises.
   
   This book should find its place on the bookshelf of everyone interested in geometrical concepts required for understanding contemporary theoretical physics.
   
   I recommend this book to all students and professionals. It should find its place in every university library.
   
   Just one warning: certain mathematical symbols did not find their way to the "Index of frequently used symbols" at the end of the book. The reader trying to read the book starting from p. 600 may find it necessary to spent some time going through the earlier chapters to find out the meaning of a given symbol.



4. There's no doubt about it: the material in this book is incredibly interesting and important for an ambitious physics student. The organization of the book is fairly good: informal passages relating the necessary theory alternate with exercises which are all written as "Check that..." or "Prove that...", which allows you to choose which results to prove and which to take as given facts if you -- for any reason -- don't feel like proving them.
   
   However, the book also has some serious shortcomings. The most important one seems to be the horrid style. A book of mathematics for physicists should not be written just like a standard math textbook without proofs -- and this is exactly what this book is like. The definitions that are given are "mathematical" at heart; very rarely can one find an intuitive picture of what is going on immediately after a concept is introduced. On the other hand, the propositions that are not left as excercises are never proven. Granted, they might be intuitively clear, but that doesn't mean that their proofs are obvious. Due to all this, I have always felt a bit confused and certainly not comfortable with new concepts. The author's occasional attempts to "raise morale" by inserting jokes would always backfire because these jokes are so trivial that they seem offensively condecending. Take, for example, the sentence that finishes the introduction of a vector as the equivalence class of tangency of curves:
   
   "And a good old arrow, which cannot be thought of apart from the vector, could be put at P in the direction of this bunch, too (so that it does not feel sick at heart that it had been forgotten because of some dubious novelties)." (p. 25)
   
   So... first of all, this is probably not particularly funny. But more seriously: are we to conclude that the notion of vectors as "directed lines" is important only because otherwise the "good old arrow" (and the reader alike) would feel "sick at heart"? This is an example of a concept so intuitive that a joke like this is generally harmless; however, trouble arises when the same kind of explanation is applied to more abstract concepts (e.g. why not study non-Hausdorff spaces? The explanation given on p. 4 relates to Amazon Basin Indians).
   
   Another important issue is that a large part of this book teaches you the principles of the mathematics behind the physics. This is fine, provided you learn how to operate with these principles; however, the book seldom teaches you how to *work* with the most basic concepts, and that's what the author promises to deliver in the preface.
   
   Unfortunately, there are other issues as well. Introducing new, vital ideas in exercises *only* is one of them. Also, one would desire to know which ideas are crucial or well-worth meditating upon, and this is generally not given in the text. Finally, the excessively informal style prevents this book from being even a good reference.
   
   All in all -- it is possible to learn a lot of new things from this book, but the effort probably isn't worth it.



5. An excellent reference for self-study. Four stars not five, because contrary to its claim, a reader with an undergraduate physics background cannot read it from the start to end without referring to other books. I decided to learn some General Relativity after hearing Smolin talk better smack than Triple H, and encountering Penrose's intriguing Road to Reality. Fecko logically and succintly weaves together many possible views of each subject he discusses. He clarified for me, for example, the links between the approaches taken by the texts of d'Inverno and Ludvigsen. Many of these links are given as well-structured exercises, so the book is best used when one has an uneasy suspicion that something might be true. Fecko also gives outstanding motivations and intuitive pictures for many definitions. Even after I had understood pull-backs and differentials, it was a delight to discover that putting a shoe on my foot was as good as putting my foot in the shoe.

No comments about Lie Groups, Lie Algebras, Cohomology and some Applications in Physics (Cambridge Monographs on Mathematical Physics).

No comments about Synergetics: Introduction and Advanced Topics (Physics and Astronomy Online Library).

No comments about The Dynamics Of Particles And Of Rigid, Elastic And Fluid Bodies.

No comments about Probability and Mathematical Physics (Crm Proceedings & Lecture Notes).

No comments about From Quantum Cohomology to Integrable Systems (Oxford Graduate Texts in Mathematics).

No comments about Relativistic Fluids and Magneto-fluids: With Applications in Astrophysics and Plasma Physics (Cambridge Monographs on Mathematical Physics).