5 comments about Geometrical Methods of Mathematical Physics.

1. This book presents the basic concepts of differential geometry in a clear, concise manner using modern notation. Schutz's writing style is very readable and there is a considerable breadth of coverage. In areas where one might wish for greater depth, Schutz provides excellent references. My only regret is that the physical applications chapters weren't longer. An excellent starter book and a good quick reference if you continue in differential geometry, GR or field theory.



2. This is a very enjoyable and clearly written book. From a physics point of view the approach is rather abstract, so although differential geometry is developed from 'scratch', it is probably better to have studied a more elementary text on the theory of 2-surfaces in 3-space first (eg Faber's book Differential Geometry and Relativity Theory ). The first chapter sets the mathematical background expected of the reader. The rudiments of analysis, topology, calculus of many variables and basic linear algebra is reviewed.The ensuing chapters cover differential geometry from a 'modern' viewpoint but the style is quite relaxed and the links to 'co-ordinate approach' are well explained. The exercises concentrate on the abstract approach. Throughout the book the underlying structure of manifolds is concentrated upon. No extra 'structure' eg connections and 'distance' concepts are added until the final chapter on Riemannian spaces. For example the metric tensor throughout the body of the book is merely used as a map between a tangent space and its dual space. It is only used as a 'distance' operator in the final chapter.For the purposes of independent study this is a sound book, there are hints and partial solutions for many of the exercises, which is always a welcome feature for those studying entirely on their own.



3. I had read first the "first course in general relativity"and was exited,so i fygured out that this book from the same author would reach the same standards,but it didnt.If Ihadnt read the first book from Schutz this book would be incomprenheceble.The greatest problem i think is the lack of exercices.Without them you cant really go anywhere.Another problem ,i believe,is the short space given to analyzeeach topic.Eventhough i understand tensor calculus very well I just cant get anywhere with the differential forms.
   Eventhough its not the worst book out there its not the best either.My advise,buy a better book.



4. Written in a attractive and even seductive way, relying more on Lie algebraic language than is typical, this book is probably as stimulating an intro. to modern geometry as you can find, within certain limits. The section on noncoordinate bases might have been more clearly written, however. Frobenius's theorm is discussed, something that Fomenko et al should have covered, and the section on connections can be worked throuigh independently of the heavy machinery of exterior differential forms, which is attractive for physics students.



5. Advanced mathematics, such as differential geometry and topology, plays an important role in many areas of physics. This excellent book covers one of these topics, differential geometry. This is a topic essential for understanding general relativity and gauge theory. There are several good books aimed at physicists that cover differential geometry. While some of these have a broader scope than this book, nevertheless this book is my favorite one for differential geometry.
   
   The topics covered include those necessary for reading advanced treatments of general relativity (such as Wald or Misner/Thorne/Wheeler). These include manifolds, fiber bundles, tangent/cotangent bundles, forms, Lie derivatives, Killing vectors and Lie groups.
   
   Following this basic material a chapter covering some applications to physics, one example is electromagnetism. Up to this point the consideration of manifolds had been fairly general. In the final chapter the implications of adding a connection, and then a metric, are considered.
   
   Why do I think this book is so good? It's not the breadth of material covered, this book is very focused on a limited range of material. It's the quality of the presentation for what it does cover. The development follows a logical order, the writing is exceptionally clear and the diagrams are very useful since Schutz explains them so well.

5 comments about The Story of Mathematics: From Babylonian Numerals to Chaos Theory.

1. As far as the text goes, this is a pretty nice book. But the publishers have done the author a disservice in how they produced the book (maybe over-produced is a better term). It looks to me as if the book was intended to be a coffee-table sized book, then, when that turned out to be too expensive, the size was reduced. So we get tiny print, small pictures, and an over-dense page layout. Plus, there's one of the most irritating typos I've ever seen: the splash page for chapter three says it is about the Pythagorean "theorum"!!

   The actual content is competently done, for the most part reflecting what is in the standard references and not taking any big interpretive risks. There is more coverage of recent mathematics than is common on books aimed at the "general reader." The bibliography is much too short, but it points to other books that do have more extensive references. There are better short histories of mathematics, but this one won't lead you astray... provided your eyes are good and small sans-serif type doesn't bother you!




2. I read this book because math is one of my favorite subjects and it seemed to be full of inforamtion. And it was full of information which stretched from discussing math in Pythagoras's times all the way up to modern chaos theory, but as I read it I just didn't find that it captured my attention as I had hoped. As I read through this novel I felt that only a small portion of what I was reading was really going to stay with me. I often felt my mind wandering as I just didn't find myself completely interested and sometimes I had to remind myself to pay attention. I would have liked a little bit more discussion on the importance and applications of the mathematics that was being developed. There wasn't as much depth as I yearned for, but perhaps this can be forgiven to some extent considering how much the author was attempting to discuss.

   Despite all of the aforementioned, I'm still giving this book 3 stars(although I'd prefer to give it 2.5 if I could). It was a very easy read and certainly didn't get particularly complicated. Plus, there were some pretty nice illustrations. Overall, I'd say that although I don't regret having read the book, I probably wouldn't read it again.




3. As another of the reviewers remarked, this book was obviously originally designed to be a "coffee-table" book on math for casual browsing... lots of beautiful illustrations (ranging from Michaelangelo pictures employing the use of perspective, right through to computer-generated fractal patterns), a chatty but superficial perusal through the history of mathematics, and very little in the way of actual mathematics content.
   
   Unfortunately it seems the publisher slashed the printing budget for this book, and instead of being published in its originally designed "coffee-table book" dimensions, the book has been reduced in physical size with the result that the text is pretty small, and the print on the pages looks very cramped.



4. Mankiewicz has given his readers exactly what the title promises -- The *Story* of Mathematics. As such the book doesn't bog itself down with illustrating the very mathematics it talks about. This might seem like a major absence for a book about mathematics, and maybe it is, but I get the feeling that the book assumes that the reader doesn't need or want a refresher. I appreciate the approach taken by Mankiewicz because it successfully keeps the story moving forward...as all good stories are inclined to do.
   
   More commendable is that Mankiewicz's book gives the most historically balanced view of the early origins of mathematics that I've yet encountered. I am, of course, referring to the controversy that still surrounds Egypt's influence in the subject. I've read an entire spectrum of biased claims. Some of them over-crediting Egypt's contributions, but most of them under-crediting her legacy. Mankiewicz's view that "Our knowledge of Egyptian mathematics is necessarily limited by a genuine lack of artefacts" resonates as both sincere and true. He goes on to write that "It is therefore tempting to see the mathematics of the Egyptians as a step backward from the level reached by the Babylonians. But this probably unwarranted, especially given their precision in pyramid-building and their management of such a vast empire....the ancient Greeks widely acknowledged that their mathematics, especially their geometry, originated in Egypt." Those words seem to avoid the usual sensationalizing that I've encountered in other works on the topic.
   
   This balanced reportage precipitates throughout the rest of the book, giving due space to all the key players, regardless of their geographic origins, in the story of numbers. The writing style is very accessible and, thankfully, with personality. Hopefully, this book is a hallmark of more to come. I think the world deserves a proper and balanced view of mathematics.



5. Light mathematical history is the best phrase to describe this book; it has too much math to be considered as mere history and not enough to be described as mathematics. It begins with the earliest of representations of mathematics, which was of course numbers. After that came the geometry of area representations for land surveying and the beginning of abstraction, where the idea became the mathematical concept traded rather than physical objects.
   Most of the general ideas of mathematics developed since antiquity is at least mentioned, and Stewart is to be commended for including formulas when needed. His style of exposition is effective in presenting complex ideas in a manner that makes it very readable. Any reader with knowledge at the level of high school algebra will be able to understand the fundamentals of the concept even if the particular details are beyond their grasp.
   This book could also serve as a text for a college level history of mathematics class for the elementary or middle school education major. If used as a source of ideas for classroom presentation, it could also be used as a text in a history of mathematics class for the math major.

4 comments about Old Physics for New: a worldview alternative to Einstein's relativity theory.

1. For those who are interested in views contrary to Einstein's theories of relativity, this book is a "MUST-HAVE." Phipps is without a doubt the most entertaining writer who disagrees with Einstein and his followers. Phipps appears to be someone who really and truly understands what he is talking about.
   
   If your special interest is the topic of "time," you simply must read this book.
   
   Highly recommended.
   
   If you are a die-hard Einsteinian, why not read the book and then post your critical review here for people like me? I would love to see what the official response is to ideas like these.



2. Phipps has the good fortune to actually have been a practicing Phd physicist. Having been forced into the mold of lock step physics, he has, upon retirement, let loose pent up frustrations that must have festered over time.
   
   Fortunately for us, he is a master at the use of the language and this artifice allows a rather uncharacteristic eloquence to his verbage that would attract any reader in search of english written in a form that is all but dormant. The book would be a pleasurable read from this point alone were it not for the pressing need to have things put aright by the author in the areas of physics not so deeply trodden in our modern age.
   
   Phipps doesn't attack relativity directly, as so many do in a rabid fashion of late, but does us the honor of showing how much of its "bed rock", Maxwellian electrodynamics, was allowed to lead physics off track. This bed rock did not get fully corrected by the time Einstein did his work. Phipps gives us a much needed history lesson which is so often overlooked in modern science. He shows errors in many works, and later attempted corrections that ultimately went begging or that complicated, needlessly, issues that might have been handled in a wiser, more direct fashion.
   
   He does not let words alone speak for physics, but involves us in the mathematics to a level that only those deeply involved might follow to full advantge. Yet as an electrical engineer, I perservered and gained real insights to work that normally is left to higher level physicists.
   
   Phipps takes a delightful relish in pointing out issues that are just not right on the path to modern accepted relativistic physics. The reader will love his powerful use of the language in finger pointing and following up on faux pas on the part of his fellow physicists.
   
   The book is a must read for those willing to think a bit deeper and allow a physicist to reveal that the veil of physics is a bit tattered and shop worn and, to its detriment,loaded with all manner of operable but poorly conceived patchwork attempts.
   
   A real eye opener, regardless of your thoughts on the matter in the end.
   
   Intellectually stimulating, eloquent, humorous in places, and very thought provoking.



3. Phipps has done great work here. Set aside, for a moment, what you may think of consensus science
   versus 'fringe' work. Set aside, too, your beliefs about the verities of Relativity, Maxwell's
   equations, and the like. This book is important because it's written as a conversation between the
   reader and a very bright and passionate man, a man who knows physics well, mathematics well, and
   history very well. I learned things here that were never even hinted at in 4 years of education in
   physics. Even the revealed history here is worth the price of admission.
   
   OK, pick up your beliefs about consensus science and relativity now. Worst case: you buy this
   book, find fault with it, and use it in your classroom to exercise the students' minds. It will
   certainly do that, regardless of the stance of the author!.
   
   I recommend this book enthusiastically for teachers, science historians, science buffs, and very,
   very especially, current physics students (sophomore level, who have taken at least a year of
   statics/dynamics, a year of EM, a year of quantum, and a semester or two of relativity theory.)



4. Although Einstein said his theory could be overthrown by a single experiment, his current followers heed him not.
   As but one of numerous delightfully interesting discussions, Phipps shows how the GPS system is exactly that experiment, in that it establishes that the Now is NOT relative, as Einstein asserted to be the inevitable conseqence of his time-rate symmetry. This symmetry, and its attendant Twin Paradox, was necessary to justify the biggest Procrustean bed of all, Lorentzian SpaceTime, which spatializes time through the Lie of Universal Covariance. Phipps' book proves there is no SpaceTime, only Space and clocks. The central distinction between Einstein's relativity and this, correct one by Phipps is Einstein's denial of a Common Now throughout the Cosmos. GPS couldn't possibly work if that were so, but Einstein is both the Prophet and the Pope of the Church of Physics, and heretics will not be tolerated.
   Phipps brilliantly explains the root error behind Einstein's folly, the partial derivatives in the standard exposition (by Heaviside) of Maxwell's Equations are in truth total derivatives. They were only made partial by, in a most Procrustean manner, excluding Faraday's experiments that generated voltage when a wire loop changes shape. Only a total derivative can handle that.
   This is a wonderful book, well worth many times its price, but bring some calculus with you.

4 comments about The Quantum Theory of Fields, Volume 2: Modern Applications.

1. This is another gem of a book by Weinberg. The discussion is fairly modern at places (for instance nice discussion of BRST, BV Formalism, RG and Anomalies), but could have been more modern and compact in certain other places (like chiral lagrangians, standard model etc.). However, even those parts are a pleasure to read. It is just that some other aspects could have been discussed (as I hope he does in the third volume), such as SUSY, especially QFT dualities. Anyway, an excellent book!



2. This book has some of the most exquisite expositions on the theoretical aspects of quantum field theory that you are ever likely to run into, i.e. Weinberg's name is literally stamped on every page for brilliance. There are topics treated here that are not likely to be found anywhere else, for instance Batalin-Vilkovisky Quantization. Weinberg's treatment of the proof of renormalizability is compact and yet very readable. And his chapter on anomalies is simply speaking the authortiative treatment. This book is a must have for anyone interested in the more theoretical aspects of Field Theory. Though I would recommed a few months with Peskin & Schroeder, and volume 1 of Weinberg to get the full flavour of Weinberg's treatment.



3. I have found this text extremely useful as a guide to the essentials of modern renormalization theory, as well as modern quantization techniques for Non-abelian gauge theories. The chapter on extended field configurations is nice, though it is meant as an overview and guide to the literature. What I like most about this volume is the discussion of experimental or phenomenological issues that complements many of the discussions. He has a broad base of knowledge in particle physics, as well as field theory. If you don't have volume 1, get that first.



4. Before Weinberg's books, a typical graduate student in theoretical physics would study the standard textbooks (e.g. Itzykson-Zuber, Peskin-Schroeder) to pass QFT courses. When confronted with actual research problems, he would discover that all he has learned is how to do calculations in perturbation theory, that he is unfamiliar with a host of ideas and techniques that are widely used in the present-day research literature and that he has to resort to original papers and reviews to learn them.
   
   Weinberg's three-volume set drastically changed this situation, giving the most authoritative and complete presentation of QFT to appear in a textbook. Although it is not suitable for beginning graduate students, it is invaluable for covering all these topics that are typically omitted in QFT courses and for providing valuable insight missing from other textbooks.
   
   The highlight of the set is Volume 2, which includes most topics where Weinberg has made his own invaluable contributions. In his inimitable style, Weinberg guides us through the great developments in QFT from the 1960's to the 1980's, including most topics that are essential for a working knowledge of modern QFT. The presentation is crystal clear throughout and every topic is presented in as much detail as it deserves. In particular, the chapters on spontaneously broken symmetries are simply masterpieces, the treatment of anomalies is the most complete ever, while the chapter on extended objects is a thorough overview of an ever-expanding subject. This book is a must for everyone working on theoretical physics.

4 comments about Mathematical Foundations of Statistical Mechanics.

1. A Y Khinchin was one of the great mathematicians of the first half of the twentieth century. His name is is already well-known to students of probability theory along with A N Kolmogorov and others from the host of important theorems, inequalites, constants named after them. He was also famous as a teacher and communicator. The books he wrote on Mathematical Foundations of Information Theory, Statistical Mechanics and Quantum Statistics are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour.

   In his "Mathematical Foundations" books Khinchin develops a sound mathematical structure for the subject under discussion based on the modern theory of probability. His primary reason for doing this is the lack of mathematically rigorous presentation in many textbooks on these subjects. I can remember the vague feeling of dissatisfaction I felt as a student with some of the mathematics in Frederick Reif's "Fundamentals of Statistical and Thermal Physics" and other texts. Khinchin's little book puts everything on a firm mathematical foundation and yet is very readble.

   I liked all three of these books but I think I liked this one best. The English translation was done by the eminent physicist and writer George Gamow. Nicely typeset in modern notation with index. This book is also a real bargain.




2. To read this book one needs some fundamental knowledge of mechanics and probability theory. The great author builds the foundations of statistical mechanics on these two pillars. Throughout the book the author develops the statistical theory of mechanics using an axiomatic approach and tries to invoke as few assumptions as possible.
   If you like the language of mathematics, this is the most elegant and concise book on classical equilibrium statistical mechanics. J.W.Gibbs's pioneering book, elementary principles of statistical mechanics, is not as readable as this one, in my opinion.
   In the appendix there is author's extension of the central limit theorem as a bonus!



3. This text will be of interests for people wanting to increase their knowledge in conceptual aspects of statistical mechanics. To read it ideally you should have a level of preparation comparable to Landau's book,but that's just ideally. In reality curious student interested in subject and having solid background in just basics of undergraduate level math being taught in physics departments could get most out of book.
   The book contains careful discussion of ergodic theory, topology of phase space and couple of important probabilistic theorems in a clear and elegant way. Name of the author is indicating that quality of book should be very high in terms of mathematical rigor and conceptual richness. Khinchin is one of the famous figures of last centuries brilliant mathematicians, who had contributed greatly to foundations of statistical mechanics and theory of stochastic processes. Despite the small size, this book requires some serious amount of mental work to fully grasp the content, so prepare your best pencil and clean papers and dive into mysterious world of statistical mechanics.



4. This book gives an excellant review of the theory behind statistical mechanics. This is a topic that is often left out of more popular books on statistical mechanics. It is a great companion to those other books.

5 comments about Mathematical Methods for Physics and Engineering: A Comprehensive Guide.

1. I've been teaching an upper-level course in math methods of physics on and off for thirty-five years or so. This is as good a text as I've found. In fact, I've been using this book since it began life as a much smaller volume by Riley alone. It has always provided a down-to-earth exposition of applicable mathematics. Now it provides more than ever, include two nice chapters on group theory, with more problems than the previous editions.
   
   Despite its broad coverage, it is not an encyclopedia. Individual sections are thorough, well illustrated by examples, and comprehensible. Yes, I might have organized some of the material somewhat differently. But that is largely a matter of taste.
   
   The reviewer who alleges that one must have mastered a lot of math to benefit from this book clearly has not read the first chapter. The book by Boas with which he compares it is a) less comprehensive, b) at a lower level overall, c) and a lot more expensive.
   
   At $63, this volume is a real bargain.



2. Beautifuly organized compendium of mathematical tools which are daily bread and butter of every theoretical physicst. Excellent for first year graduate students wanting to pursue career in any branch of theoretical physics.
   The main advantages which distinguishes this classic from others is clear and conscise pedagogical style and excellent selection of topics which are being discussed fully and without sacrifising mathematical rigour.
   However for advanced students this text may sometimes bore with overdetailed explanations and minor details.
   Summing up everything, if you wanna learn mathphys and want to start you are in the right place.



3. The book was in excellent conditions and its content have been very useful. This is the book with a high level but at the same time easier to follow and understand. The examples shown are illustrative enough to consider that the topic was completely covered and understood.



4. Very good book. Wide range of contents and written in British style, which may seem strange to some.



5. I bought this book a few years ago when I was studying physics in University, I've now switched to engineering and I still use this book regularly. I wouldn't think it a very good book for a text, but it is a wonderful reference book. The entries are short(generally a couple of pages) but in depth with references to other sections to lean more. The book is full of examples and uses straight-forward explanations of techniques and their physical interpretation. I highly recommend this title for anyone looking for a good quick math reference.

3 comments about Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences (Springer Series in Synergetics).

1. This is a great book. The different chapters are very clearly written and each of them could be applied as a tool for solving similar problems, one may encounter in his (hers) research. Although the text is not introductory, with some effort, the reader could avoid going through more elementary books on the subject first.



2. This is a great book on stochastic processes. The author has a unique perspective on the subject and elegantly moves from one topic to the next. A great help in understanding difficult concepts.



3. "Handbook" is a fitting title. It reads more like a collection of solution techniques than like a book meant to actually teach the subject to someone, which is perfectly acceptable for a reference book but not really suitable for a textbook.
   
   Unfortunately for this book, however, van Kampen's book is better as both a reference and a textbook. While generally written with a somewhat higher degree of sophistication, van Kampen is organized so much more logically and is so much more complete in its development of the subject that it is far easier to read, even as (or maybe especially as?) an introductory book.
   
   Gardiner is a good book, and there are things that it has over van Kampen: a chapter on approximation methods, a chapter on simulation methods, and a little bit more detail on certain topics. However, van Kampen's is a phenomenal book and really should be chosen over this one except by those readers with very specific needs.

3 comments about Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition.

1. The book was in excellent conditions and its content have been very useful. This is a book with a high level but at the same time easier to follow and understand. The examples shown are illustrative enough to consider that the topic was completely covered and understood.



2. The solutions manual of a very good book. Useful for instructors and students as well.



3. The book is excellent not only for giving the solution, but explaining the problem, clarifying what exactly is being asked and giving major guidelines for how to solve the problem. Thank you very much!

2 comments about Chebyshev and Fourier Spectral Methods: Second Revised Edition.

1. Prof. Boyd's book is god-sent,

   I discovered it during a self-embarked journey in the blooming world of spectral methods. Unfortunately,
   these very potent and promising techniques have only recently
   escaped the confines of the field of Applied Mathematics where
   they were first developed. Thus, most existing literature is too
   mathematically oriented and rather opaque to the engineer and
   applied scientist, as it does not offer them the basic
   operational knowledge that they would require. This book is
   one of the first to overcome this chasm. It provides
   a survey of all the necessary fundamentals for the application
   of spectral methods to various disciplines of computational
   engineering but also delves deep into various advanced topics.
   At the same time it provides one with sufficient ammunition
   to explore, otherwise intimidating, more theoretically-oriented
   texts. The text, reflecting the author's extensive knowledge
   on the subject, has an unusually flowing writing style to it
   and throughout it are interspersed some quite entertaining
   snippets of the author's humor.

   I recommend this book to all students of spectral methods, regardless
   of level of expertise.




2. Spectral methods, as presented by Boyd, are techniques for numerically solving differential equations. His book is a collection of A LOT of practical information presented mostly through a mathematical frame work. Practical means different things to different people; in Boyd's case, he discusses the details of what happens in putting the mathematics to use (the pitfalls), and when each technique should be used. Supporting numerical methods, such as matrix techniques, are discussed where needed. Example computer code is scarce. Worked examples are inconsistently used, and sometimes abstract.
   
   As a novice to the field, I found the level of presentation a notch too high to be able to put it to use. It was more abstract than applied. I'm not saying it is not informative, only that this is not a good first book on the topic. I might get this as a second or third book.
   
   I give it 4 starts due to two complaints. There are not a lot of illustrations, and moreover those that are included are often too simple or need more annotation. A little more thought should go into them, and there should be a more of them for some of the more abstract topics. Additional thought should go into the organization too. Information at different levels of expertise are scattered throughout so you either (a) need to know the answers already, (b) skip ahead several chapters, or (c) go on an aside in another text.

2 comments about Statistical Physics of Particles.

1. M. Kardar is simply phenomenal, probably the best teacher I've ever seen in the Institute.



2. Perhaps I am a bit biased as I took Mehran Kardar's statistical mechanics class, but this is the best graduate-level statistical mechanics textbook I have looked at (including Pathria, Huang, and Landau). In the tradition of Landau's excellent mechanics textbook, Kardar is a master of statistical physics who starts with only basic assumptions about the nature of the physical laws in each chapter, and derives wonderful results elucidating the nature of statistical physics. The meat of the textbook is less than 200 pages and includes all of the basic results of thermodynamics, a section on probability, an introduction to kinetic theory, and the bulk of classical and quantum statistical mechanics; brevity is the soul of wit, as they say. A few areas could have used a little more elaboration (the derivation of the Boltzmann equation seemed to skip a few important steps in implementing the streaming collision terms, and a better explanation for the basics of diagrammatical techniques would have been nice), but none of the other books I have looked at even broached these topics in any depth. Unlike Landau's excellent statistical physics book, very little assumed knowledge is required to follow this textbook; obviously, skill in elementary algebra, calculus, differential equations, and a bit of Hamiltonian mechanics and a few very basic results of quantum mechanics are prerequisites. Recommended!