Book Description

All the tools necessary to understand the concepts underlying today's statistical physics

A Modern Course in Statistical Physics goes beyond traditional textbook topics and incorporates contemporary research into a basic course on statistical mechanics. From the universal nature of matter to the latest results in the spectral properties of decay processes, this book emphasizes the theoretical foundations derived from thermodynamics and probability theory that underlie all concepts in statistical physics. Each chapter focuses on a core topic and includes extensive illustrations, exercises, and experimental data as well as a section with more advanced topics and applications. This comprehensive treatment of traditional and modern topics:
* Covers equilibrium and nonequilibrium thermodynamics
* Presents the foundations of probability theory and stochastic processes
* Derives statistical mechanics from ergodic theory
* Examines the origin of thermodynamic and hydrodynamic behavior
* Emphasizes equilibrium and nonequilibrium phase transitions
* Presents theories of random walks and Brownian motion
* Discusses hydrodynamics and transport theory of chemical mixtures and discontinuous systems
* Presents transport theory on microscopic and macroscopic levels
* Includes thermodynamics of biophysical processes

Comprehensive coverage of numerous core topics and special applications gives professors flexibility to individualize course design. And the inclusion of advanced topics and extensive references makes this an invaluable resource for researchers as well as students-a textbook that will be retained on the shelf long after the course is completed. ... Read more

Reviews (5)

Cumbersome
I found this book to be clumsy in its notation and sloppy in its delivery. The information presented in the book is more than comprehensive, however. Each chapter ends with a "special topics" section that covers new and old ideas in the field. Yet the book manages to fall short with its organization and presentation. When new concepts are introduced, very little background is given, and steps in calculations are often bypassed. There are many examples to follow, but even the examples seem pointless when the next step in the derivation has been skipped and it takes the reader several minutes to find the connection. In addition, the book is a somewhat poor reference in the way that many chapters cannot stand alone, due to the quirky notation that is scattered all over the book. If one is not familiar with this notation, then if one wishes to reference the book, he or she will have to waste time finding out why the author uses a capital N there and a small n here, a "mu prime" there and a "mu" here, or a vector k there and an apparently scalar k here.

In summary, the book is comprehensive, covering a wide range of ideas both new and old, but it fails in the fact that it cannot present the information in a clear manner.

The best grad-level book on this subject I've seen
This is not a book for total beginners, but those with a good math background and at least a rudimentary understanding of thermodynamics should be able to bring their knowledge to a very high level by diligently studying Reichl's text.

The book starts out with a couple of chapters on "non-statistical" thermodynamics and a few chapters on probability and stochastic processes; this provides a firm foundation for the equilibrium and non-equilibrium statistical mechanics to which the latter two-thirds of the book is devoted. Throughout the book the explanations and derivations are very clear, and the inclusion of worked sample problems is a definite plus. Highly recommended for any grad student (or advanced undergrad) in physics, materials science, etc.

an excellent textbook for graduate students
I'm glad that there's "eventually" a stat-mech textbook that takes from grads' points of view. It starts from a undergrad level of thermodyanmics and ends to somewhere close to renormalization group. It's a book with clear examples, figures, and explicit derivation of equations for average grad students rather than particular flock of "genius". I gave it two thumbs up.

Good introduction to Statistical Physics
I own the first edition of this book, which I enjoyed thoroughly. Clearly written, it steers a course between introductory and advanced. Whether an owner of the first edition should also buy the second edition, may be doubted, as is clear from the 1 star comment below, but a physics student looking for a good "more advanced" book after having followed an introductory university course, would certainly appreciate this second edition, which is a stepping stone between the basic intro books and the specialized monographies on e.g. phase transitions or hydrodynamics. I have given 5 stars to compensate maximally for the 1 star review below, which does not do justice to the book.

somewhat disappointing second edition
This book used to be really modern and avant garde in its first edition, but the second edition somehow doesn't make upwith the first one. There are quite a few misprints and it looks as if the concise style of the first edition had been abandonned for a more talkative, but confusing style. Also, J. Wiley really overmarket their products in recent times. The jacket of the book is just full of rubish publicity about the merits of the book. ...... ... Read more

Book Description

This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, a detailed treatment of Markov chains, continuous Markov processes, and more. 150 problems, many with answers. Indispensable to mathematicians and natural scientists alike.
... Read more

Reviews (3)

The best introductory probablity book for a serious reader
It is amazing that a 148 page book can cover so much with such clarity. Even more amazing is the way it covers all basics, going from combinatorial problems to limit theorems in the first half, with a measure of relevant examples and a good selection of problems. It makes an equally excellent choice of "additional topics": Markov chains and processes, information theory, game theory, branching processes, and optimal control.

This book is not for everyone, as it does require a small degree of mathematical sophistication. But it will prove most useful for a very large audience. For serious beginning mathematics and science students it will provide the quickest way to learn the subject. For lecturers devising an introductory probability course it will make an excellent textbook. And, most importantly, for mathematicians and scientists of all kinds it will serve as an indispensable concise reference book.

Excellent Pocket Reference
This is not meant as an introductory text--rather, it's a very handy reference for major concepts needed in probability and stochastic calculus. It was one of the few places where I could find a proof of the DeMoivre-Laplace theorem.

The examples are also very good--they touch upon basic problems in the field without being overly trivial.

not a good first book on probability
The problem with this book is that there is no way you can understand the later chapters based on the earlier chapters. This is a more like the survey of the important topics in probability and stochastic processes. There are appendices on information theory, game theory, and branching processes. The book includes basic concepts of probability, random variables, and Markov chains. Feller has a better introductory book on probability. ... Read more

Reviews (1)

A beautiful work by a great writer and mathematician.
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. ... Read more

Book Description

The Mathematics of Relativity for the Rest of Us provides a detailed explanation of relativity, particularly its mathematics, designed for the non-professional audience. The subject is developed from basic principles and observations in physics and mathematics, starting with algebra and geometry as taught in thorough high school courses. On the premise that this background suffices to build an appreciation and understanding of the subject, the crucial concepts are spelled out, and the key derivations are disclosed step-by-step.

The relativity of time, space, and mass is covered first, giving some attention to the history of the two main divisions of relativity, the special and the general. Once special relativity and its mathematics are established, general relativity is covered, beginning with its relationship to Newton's laws and advancing through its revolutionary concepts as well as its mathematics.

This process is carried all the way to the level of tensor equations. The Mathematics of Relativity for the Rest of Us treats topics such as: The constant speed of light, the invariant laws of physics, the basis and meaning of the equation E = mc2, the nature of curved four-dimensional space-time, the importance of non-Euclidean geometry, the gravitational bending of light, experimental confirmation of relativity, the philosophical and intellectual appeal of relativity, the nature of black holes, and the cosmologic significance of relativity -- both as concepts and as mathematical issues.

As a result the sufficiently attentive reader is set at ease with the reputedly incomprehensible but essential details about relativity. Even subjects such as "tensor calculus" and the "covariant partially differential field equations of general relativity" will be clear. For instance such a reader will know just what a "tensor" is, why the equations are "covariant," why they are "partially differential," why they are "field" equations, why relativity can be "general," and most importantly just what is meant by "relativity." Furthermore, if a reader is shown the fundamental equation of general relativity,

Rik - 1/2gikR = -XTik

he or she will understand what every term of this equation means, why each is included, what obstacles Einstein and his colleagues overcame to derive each term, what impact this equation has on modern science, and why this equation revolutionized our understanding of our universe.

The Mathematics of Relativity for the Rest of Us also devotes a chapter to the relationship between relativity and quantum mechanics. It reveals the limitations of relativity and the direction of future work in this branch of science. The chapter concludes with the role of string theory in reconciling relativity and quantum mechanics. ... Read more

Reviews (2)

Relativity review
Makes topic seem fairly simple. Much math, but most of it pretty basic. Explains well. Makes you think! Might be good as a text for a course on special and general relativity.

Relativity's not so bad after all
First time I finally see a book on relativity math that I think can be understood by just about anyone. Very clear. Diagrams a bit amateurish. Good English. Good index. Best feature I like is Q & A summary of general relativity and table pages 336 to 344. Never seen anything like this. ... Read more

Book Description

A comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research, is provided in two volumes. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to-the-fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. ... Read more

Reviews (3)

The worst text-book on theoretical physics I ever read
This book is simply awful.
I couldn't understand a lot of derivations.
Before buying this book I studied the standard course on QFT by Peskin and Schroeder.(I solved 95% of its problems, so I'm not stupid!).
The reason I bought the book by Itzykson and Drouffe was to study some interesting advanced topics in QFT.
I began with Ising model and immediately got stuck.
I read previous reviews on this book. The authors praised it.
I wonder if any of them could proceed from formula 65 to 66?
(first volume)
Did any of them understand the derivation of Szego lemma?
What about Kac determinant?
I found that even original article by Itzykson was written better
and with more care than this book.(!)
Still it's worth buying as the source of references.
That's why one *.

first vol only
i think the first chapter is a b---- to get through, but after i did that i found the entire book either particularly useful or insightful. volume two never motivated it's own purchase.
I read it in frech, so i cant talk about how well things are explained in english, just in case anything was lost in translation, but with something like chapter two on grassman variables i dont think it's such a big deal. to put it succintly chapter 2 makes berezin's book obsolete to me and i feel that way about the whole book.

First rate presentation
This first volume of a two volume set serves a wide audience. Themonograph will prove to be indispensible primary or secondary material forthose whose interests cover quantum fields in minkowski space, quantumfields in euclidean space, constructive field theory --- particularly`triviality' related matters --- critical phenomena, dimensional regulatedrenormalization,the renormalization group, andlattice QCD. As asecondary source, the monograph is particularly well suited when coupled totexts such as J. Zinn -Justin's `QFT and critical Phenomena', Peskin andScroeder's `Intro to QFT', or Itzykson's own `QFT'; by combining one ofthese texts with vol I of Statistical Field Theorystudents preparing forresearch will find themselves with more then enough material to begin theirwork.

But the real pleasure of this text is in its writing style andpresentation. Here the text is a true jewel amongst lesser competitors.Manysubtle points --- frequently obscured elsewhere in the literature ---are presented sharply in Statistical Field Theory. This is accomplished bya *thoroughly* readable prose, clear presentation of material's motivation,aconcise and consitent manner for presenting points, and many examplesand excercises that truly illuminate the reading.

Overall, this is atext that anyone with even a passing interest in quantum fields will berewarded by. ... Read more

Book Description

Wavelets analysis--a new and rapidly growing field of research--has been applied to a wide range of endeavors, from signal data analysis (geoprospection, speech recognition, and singularity detection) to data compression (image and voice-signals) to pure mathematics. Written in an accessible, user-friendly style, Wavelets: An Analysis Tool offers a self-contained, example-packed introduction to the subject. Taking into account the continuous transform as well as its discretized version (the ortho-normal basis) the book begins by introducing the continuous wavelets transform in one dimension.It goes on to provide detailed discussions of wavelet analysis of regular functions, tempered distributions, square integrable functions, and the continuous wavelet transform.Throughout, the language of group theory is used to unify various approaches.Profusely illustrated and containing information not available elsewhere, this book is ideal for advanced students and researchers in mathematics, physics, and signal processing engineering. ... Read more

Reviews (1)

All the proofs:wavelets....Fourier methods.
This is a great book from which students, instructors, math researchers, signal processing workers,and communications engineering, can pick
up the rigorous tools from Fourier analysis and sub-band filtering theory;-- and see in full mathematical detail how they are used in the study of wavelets in their traditional settings (from the 1980ties)of scaling of multiresolutions, spectral estimates, orthogonality,
Cohen's condition, tilings, and a priory regularity...The proofs are complete, crisp and elegant. The book can now be supplementedwith newer ones that emphasize algorithms more. And others with a more applied bent!
But Holschneider's book will likely remain a classic. ... Read more

Reviews (2)

Mathematical Modelling Genius
One thousand word limit to this review, eh? Well, I could do it in one word: Fantastic.

This book approaches mathematical modelling from a conceptual level, with Rutherford explaining how to make numbers dance through equations any which way you want them. His depth of knowledge as a Chemical Engineer, combined with his fantastic mathematical skills means that he has knows what needs to be done in various situations and how best to do it.

The attribute that makes this, and all of Rutherfords work stand out from the rest of the pack, is his undeniable presence when writing. Rhetoric, personal insights and may the dry-and-dusty-academic world forgive him, humour (!) can be found throughout this book, making its reading quite pleasurable.

Finally, a number of thoughtful articles of his have been bound into the back of this edition, providing useful "food for thought" for those people for whom modelling is a way of life. If you are considering any of the finer points of mathematical modelling (I was doing a PhD on the subject), this book is a must-have (not just a must-read). You'll come back to it time and time again for the articles, long after you've digested the rest of the book.

This book is an excellent introduction to the area.
This book gives an amazing introduction to mathematical modelling techniques for engineers and scientists along with excellent useful tools for model development. Further, the appendices provide very illustrative example cases of the methods developed. ... Read more

Book Description

For some people, driving is an art; for others, it's a science. At the Isaac Newton School of Driving, though, every car is a laboratory on wheels and every drive an exciting journey into the world of physics. As explained by renowned science writer and physics professor Barry Parker—whose father was a car mechanic and garage owner—almost every aspect of driving involves physics. A car's performance and handling relies on fundamental concepts such as force, momentum, and energy. Its ignition system depends on the principles of electricity and magnetism. Braking relies on friction—yet another basic scientific concept—and if the brakes fail, the resulting damage, too, can be predicted using physics.

Parker's first lesson describes the basic physics of driving: speed and acceleration; why you get thrown forward while braking or outward while turning; and why car advertisements boast about horsepower and torque. He goes on to discuss the thermodynamics of engines, and how they can be more fuel efficient; and what friction and traction are and how they keep a car's tires on the road, whether it's dry, wet, or icy. He also describes how simple laws of physics enable scientists to design aerodynamic cars and high-tech steering systems. Parker then explores the high-performance physics of auto racing, outlines how traffic accidents are reconstructed by police, uses chaos theory to explain why traffic jams happen, and describes what cars of the future might look like. Whether you drive a Pacer or a Porsche, The Isaac Newton School of Driving offers better—and better-informed—driving through physics. ... Read more

Reviews (3)

Too Much Math For Me, But Still a Good Informative Book
Barry Parker has written a book that gets down to the nitty gritty of how a car actually works. All the way down to the physics of it. There is actually alot to be learned from his book even if you're not a physics buff. For example, I now understand the difference between a 2 and a 4 stroke engine. I still can't explain the physics behind any of this stuff, but then again, I don't really want to. If you have an interest in understanding cars, or an interest in physics, this book will keep you interested with Barry's down-to-earth writing style. But if you don't like physics or math, it's not a total loss. Those parts are easily skimmed or even skipped entirely.

Good but could be better
In short, the idea of writing this book was an excellent one. The book's potential is tremendous. However, rating it fairly is a more difficult matter. On the positive side, the writing style is very friendly, engaging and clear; a few of the author's personal experiences are peppered throughout - a big plus. The topics include: driving, most if not all of the various systems in cars, as well as the road-tire interface. It even covers car racing and theories of traffic congestion. A lot of interesting, indeed fascinating, information is presented. On the negative side, however, although some items are discussed clearly and as thoroughly as one might expect in such a book, other items are briefly glossed over while some seem to come to an abrupt end. The physics in each case is discussed to correspondingly varying degrees. Some equations are incorrect due to errors in subscripts and some graphs' axes are mislabeled, i.e., editorial mistakes requiring more careful editing. Some equations are magically presented out of thin air, while the derivations of others are are briefly discussed before presenting them. I would hope that, in the future, a second edition of this book would appear in which the various shortcomings would be corrected and additional material added to even out the physics, the various explanations and include a few formula derivations (or recommend references if the derivations are too involved). In other words, perhaps 50 to 100 additional pages may be appropriate. Should such a second edition of this book appear, I would be among the first to get a copy. As it stands, it is valuable reading for any driver; however, a revised edition, as discussed above, could satisfy the needs of the more scientifically curious as well. I am giving the book as much as four stars mainly because of its concept, its tremendous potential, its excellent writing style and the interesting information that it contains. An appropriate second edition would earn an easy five stars.

A Century's great Inventions
Barry Parker's book The Isaac Newton School of Driving is one of the few whose underlying message transcends the scope of the subject matter. Like the tale of the sorcerer's apprentice who remembers the charm for hauling water from a nearby river into his master's bathtub, but has forgotten the magic words to timely stem the flood, so could Parker's writings be taken as the reminder of not to make the road of technological achievements into a one way street.
In the fairy tale, only the timely interfering of his master saves the apprentice from drowning in the waters he himself has conjured, and us from missing out on his story altogether. Likewise, Parker shows us the way to upgrade our consumer knowledge into solid know how.
Sorcerers haven't made it into our times, but we, their apprentices, are blooming. We know all the charms that transmute our former hand-tools into vacuum cleaners, television sets, and self-propelled vehicles, to name only a few. But did we follow up in learning the "undo" commands?
The abundance and sophistication of technological contraptions within reach of our pocket books calls for an understanding of not alone what they do, but principally how they do it, and reading instruction sheets alone will not help.
The Isaac Newton School of Driving opens up with a crash course on the physical principles of maneuvering animated objects, vulgo automobiles. We recall the basics of the four-stroke engine, the machine some of us remember as the light-weight primary mover which made aviation possible.
While the Carnot Cycle is introduced as the thermodynamic principle behind it all, a glimpse at the Wankel rotary engine and the Volkswagen W engine conclude the introductory chapters. What follows are easily understandable presentations of a car's electrical, mechanical, and hydraulic elements. Of special interest are the author's applications of probability calculus, Mandelbrot's theory of chaos, and the Complexity Theory, on the flow of traffic and the preconditions on traffic congestion.
We cannot thank authors like Barry Parker enough for their efforts to open peoples' eyes to the underlying principles of those engineering wonders we take for granted, and in particular the ones we operate on our daily trips to the office. ... Read more

Book Description

As the twentieth century closed, Fred Adams and Greg Laughlin captured the attention of the world by identifying the five ages of time. In The Five Ages of the Universe, Adams and Laughlin demonstrate that we can now understand the complete life story of the cosmos from beginning to end.

Adams and Laughlin have been hailed as the creators of the definitive long-term projection of the evolution of the universe. Their achievement is awesome in its scale and profound in its scientific breadth. But The Five Ages of the Universe is more than a handbook of the physical processes that guided our past and will shape our future; it is a truly epic story.

Without leaving earth, here is a fantastic voyage to the physics of eternity. It is the only biography of the universe you will ever need. ... Read more

Reviews (27)

Four and the 1/2 Stars about The Five Ages of the Universe.
I love and collect books about cosmology since many years. This one was a great reading. Not only about the beginning and current state, but also about the fate of the Universe in the future.
Time will show how these computer simulated predictions are accurate. But it will not be you or me of course to observe it.
Book as for today is a bit outdated, does not take under consideration new discoveries like dark energy and acceleration of the Universe.
I have asked Professor Adams about it and he e-mailed: "the biggest change to our vision of the future comes in the Dark Era; positronium formation will be less likely, and a vacuum phase transition will be more likely if the Universe has a component of this dark energy. The basic picture however is still correct". What I really like about this book is that it gets even more interesting in the end. Explanation of quantum mechanical tunneling and possibilities of sudden cosmic scale phase transition is so vivid that I had a hard time to fall a sleep. My imagination was running wild ignited by description of space-time foam and multiverses. Summarizing: it was easy, quick and enjoyable learning about not so easy subjects. "References and further reading" list included in this book is worth to have a look as well.
Professor Adams is currently working on his new book.

INSIGHTFUL!
"Five Ages" provides a very comprehensible summary of the extraordinary events from the birth of our universe to its ultimate "end". In the introduction the authors provide an overview of each of the five ages, and also introduce benchmarks and standards for coping with the incredibly large numbers required for such a discourse.

With each successive chapter an in-depth, insightful and clearly understandable discussion of each age includes the relevant subatomic/particle physics and their formed macrostructures. Of equal intrigue, and perhaps what sets this book apart from many others, are the theoretical constructs for present and future life forms, and potential sources of energy for future civilizations.

While the authors presume the universe to be open (and flat) they do not deprive the reader of a fantastic, fast paced scenario describing a "big crunch". The emphasis, however, is to describe the later ages as somewhat stagnant and dull. When even matter, as we are familiar, ceases to exist (proton decay becoming complete by 10e38 cosmological decades) except for the matter "protected from time" by the strong gravitational fields of black holes.

Ultimately this book includes information including particle physics, nuclear physics, relativistic theory, astronomy, biology, thermodynamics & energetics and provides the reader with a comprehensive evaluation of each of the "Five Ages."

One of the laymen
This book describes what I hope is the ultimate fate of the universe, that is, a gentle, long-lasting slip into beautiful quiescence. Alas, we are only babies in this universe, and should this prove to be true, all our offspring, and their offspring, and so on shall continue to be babies in this increasingly grandiose yet dimming universe. Then, maybe, intelligence shall cease and true existence, that is, non-existence, will prevail into the dark eternity...far out man:)

It's a gloomy future but great to read about.
This book will make you think. It will make you think about the purpose of life if the universe will eventually decay into a bleak black empty desolate emptiness.

The authors extrapolate the potential future of the universe and it is a dark one. One of the more interesting aspects is learning how life as we know it- animals & plants living on planets - will cease to exist fairly early in the lifetime of the universe. But at the same time the book paints a picture about possible future life forms inhabiting the universe many, many years in the future.

The book however, is not mainly about life but about the decay of the universe as it ages billions, trillions, quadrillions of years. It specifically details how stars will die, protons will decay and eventually after a googol (10 to the 100th power) number of years, how black holes decay. It is impossible to fully grasp the size and enormity of these numbers but the authors make a good attempt.

Suprisingly, the book is a somewhat light read, which is a good thing. It won't bog you down with equations and abstruse theories. I read the entire book on a flight from NYC to SF and was immersed throughout trying to imagine the universe as it will be.

Fascinating theories about universe
I thought this book was very fascinating! I enjoyed reading not only about theories regarding the past and present eras of the universe, but also about future eras. As the title implies, authors Fred Adams and Greg Laughlin divide the lifetime of the universe into five eras, and we're living in the second. It was fun to imagine what the night sky should look like trillions of years into the future, and many more. It was also fun to read about the time when it can be expected that only black holes will be left, and to go even beyond that. This is the only book I know that deals much with the question of the far future of the universe.
The authors also brings up questions which are probably beyond our ability to know the answer to(for example, whether our universe is one of many), but such an idea is interesting to think about. They do mention a few ideas that I'm skeptical of (for example, the idea of a "Darwinian view of universes"), though they also acknowledge that this remains speculative.
Although this is a scientific (not a theological) book, I will also mention that I am a believing Catholic. So I believe that God created all things, including the whole universe. However, I also believe that the scientific theories mentioned in this book are compatible with Catholic Church teaching, provided we understand that everything that happens is in the providence of God. Of course we should also understand that theories are not doctrines, and so theories could be subject to change upon future discoveries.
I highly recommend this book, at least for those who have some general knowledge of astronomy and physics. ... Read more

Book Description

Applies successive bifurcations approach to complex time-dependent processes in large scale atmospheric dynamics, geomagnetism, and theoretical climate dynamics. Presentation of results on planetary-scale phenomena in the earth's atmosphere, ocean, cryosphere, mantle and core provides an integrated account of mathematical theory and methods together with physical phenomena and processes. Brings together modern tools of nonlinear mathematics and the problems of global change in the environment. ... Read more

Book Description

Reviews (1)

Prof. Boyd's book is a gift from the sky
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. ... Read more

Book Description

This book treats a wide variety of topics systematically by constructing time-dependent Ginzburg-Landau models for various systems in physics, metallurgy, and polymer science. Beginning with a summary of advanced statistical-mechanical theories including the renormalization group theory, the book reviews dynamical theories, and covers the kinetics of phase ordering, spinodal decomposition, and nucleation in depth. The phase transition dynamics of real systems are discussed, treating interdisciplinary problems in a unified manner. New topics include supercritical fluid dynamics, stress-diffusion coupling in polymers, and mesoscopic dynamics at structural phase transitions in solids. ... Read more

Book Description

This book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived. ... Read more

Book Description

This book is a comprehensive and coherent introduction to the role of cosmic strings and other topological defects in the universe.After an introduction to standard cosmological theory and the theory of phase transitions in the early universe, the book then describes, in turn, the properties, formation, and cosmological implications of cosmic strings, monopoles, domain walls and textures. It concludes with a chapter considering the role of topological defects in inflationary universe models. Ample introductory material is included to make the book readily accessible. It will be of interest to graduate students and researchers in particle physics, astrophysics and cosmology. ... Read more

Reviews (1)

Good book, though dated
With so much having happened in cosmology in the past several years, pretty much any book not written very recently or about intro topics has lost some of its relevence. With that restriction in place here, one still finds this book to be very informative and useful. Many pioneering efforts are encapsulated here, and although alternative theories have surpassed some of the theories presented in this book any cosmologist should have this book on his/her shelf. ... Read more

Book Description

This book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which spinors behave. The book concentrates on the algebra and calculus of spinors connected with curved space-time. Many of the well-known tensor fields in general relativity are shown to have spinor counterparts. An analysis of the Lanczos spinor concludes the book, and some of the techniques so far encountered are applied to this. Exercises play an important role throughout and are given at the end of each chapter. ... Read more

Book Description

The use of symmetries and conservation laws in the qualitative description of dynamics has a long history going back to the founders of classical mechanics. In some instances, the symmetries in a dynamical system can be used to simplify its kinematical description via an important procedure that has evolved over the years and is known generically as reduction. The focus of this work is a comprehensive and self-contained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail. The exposition reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. This is followed by a discussion of momentum maps and the geometry of conservation laws that are used in the development of symplectic reduction. ... Read more

Book Description

Quantum field theory forms the present theoretical framework for our understanding of the fundamental interactions of particle physics. This updated and expanded volume examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. A new introductory chapter gives a systematic overview to classical field theories and a short discussion of their canonical quantization and the discrete symmetries C, P and T. Coverage provides a brief exposition of perturbation theory, the renormalization program, and the use of the renormalization group equation. It then explores topics of current research interest including chiral symmetry and its breaking, anomalies, and low energy effective Lagrangians and some basics of supersymmetry. A chapter on the basics of the electroweak theory is also new to this edition, as well as an appendix that contains a complete set of Feynman rules for the Standard Model. This volume will be ideal for graduate students and researchers in theoretical physics, condensed matter physics, and applied mathematics. ... Read more

Reviews (3)

From Fair to Good
Pokorski starts the book with a very pedagogical spirit, giving an overview of classical field theory needed for the sequel and providing detail in his presentation. His treatment of functional integrals is one of the best I've seem in a field theory textbook and he does a better job of deriving the Feynman rules for QCD than I have seen elsewhere. But somewhere around half-way to two-thirds into the book it seems as though the author starts to get a little lazy, applying a more descriptive approach to the material rather than careful derivations. More is left to the reader to work through and his discussions tend to give one a sense of knowing about the material more than the actual material itself.

Its not that self contained. For instance scattering problems are presented without the development of a scattering formula and are very sketchy. Knowledge of group theory and spinors is required although they are discussed briefly in an appendix.

For a book of this level it would have been nice to see some topics included that were not covered: a deeper treatment of renormalization, proof of Coleman's theorem, proof of BRS invariance, derivations for asymptotic freedom of QCD.

Topics I thought were handled well are: the proofs of Goldstone's theorem and the treatment of spontaneous symmetry breaking in general, development of the non-abelian gauge theory, renormalization group and the general Ward identities.

swell
I learned from cheng and li, which aint bad itself, but i found myself frequenting this book because of it's structure.

basically, i think that the path integral viewpoint should be stressed because of renormalizing gauge theories and more advanced topics. If i taught field theory i think this would be an ideal second semester book, first semester something more mundane.

it's strong points are
1) this approach i like
2) starting with basically no prereqs
3) details that cant be found elsewhere (theta vacua, some calculations in GWS theory that others dont do).

weakness: no traditional operator-style QFT, not a lot on representing groups.

A quantum field theory book
This book covers the following subjects: 1. A brief introduction to QFT formalism 2. Feynman rules for YM thy 3. RG 4.QED 5. OPE 6. QCD 7.Spontaneous and explicit symmetry breaking 8. Higgs mechanism 9. SM of EW interactions 10. Chiral anomalies 11. Eff. Lagrangians and 11. a brief introduction to susy. The derivations are in general very detailed. At the end of every chapter, there are exercices (without solutions). The appendices are very useful, specially appendix C, which collects the SM feynman rules in a concise manner. ... Read more

Amazon.com

The search for infinity, that sublime and barely comprehensible mystery, has exercised both mathematicians and theologians over many generations. Jewish mystics, in particular, labored with elaborate numerological schema to imagine the pure nothingness of infinity, while scientists such as Galileo, the great astronomer, and Georg Cantor, the inventor of modern set theory (as well as a gifted Shakespearean scholar), brought their training to bear on the unimaginable infinitude of numbers and of space, seeking the key to the universe.

In this sometimes technical but always accessible narrative, Amir Aczel, author of the spirited study Fermat's Last Theorem, contemplates such matters as the Greek philosopher Zeno's several paradoxes; the curious careers of defrocked priests, (literal) mad scientists, and sober scholars whose work helped untangle some of those paradoxes; and the conundrums that modern mathematics has substituted for the puzzles of yore. To negotiate some of those enigmas requires a belief not unlike faith, Aczel hints, noting, "We may find it hard to believe that an elegant and seemingly very simple system of numbers and operations such as addition and multiplication--elements so intuitive that children learn them in school--should be fraught with holes and logical hurdles." Hard to believe, indeed. Aczel's book makes for a fine and fun exercise in brain-stretching, while providing a learned survey of the regions where science and religion meet. --Gregory McNamee ... Read more

Reviews (49)

An excellent combination of math, psychology, and Cabalah
This is easily the best book on mathematics this year. Amir Aczel has done it again, after Fermat's Last Theorem and God's Equation. Here he tackles one of the most difficult areas in mathematics--set theory--and weaves a very readable narrative including elements of Jewish mysticism and psychology. This book deals with the tormented life of Georg Cantor, the first person in history to understand the nature of infinity. Read it! I will say no more, so I don't spoil your enjoyment.

A delightful guide to the foothills of a huge subject
This delightful little book is a Cook's Tour of some very important personalities in mathematics and their work on the concept of Infinity (actually various magnitudes of infinities, I guess), the Continuum Hypothesis, and the Axiom of Choice. While the author takes us back to the ancient Pythagoreans and their determination to keep irrational numbers secret knowledge, the story really centers around Georg Cantor and his struggles in founding the study of mathematics in this field. Cantor was a mystic as well and there is also more than one appearance of the Kabbalah.

Certainly, you can't learn the subject from this book. However, like visiting some vast architectural wonder that you can only take in as a big view, this book places lots of Post It notes on important points if you want to begin reading more deeply about these profound ideas. And if you don't, it is certainly a fund way to spend a few hours.

The author provides four pages of references for further reading, but if, like me, you don't know the field you will likely have to do preliminary studies to just get to the foothills of really taking on the subjects studied in this book. If you already understand the math then this book is likely too light for you unless you somehow missed out on the history of your field.

I enjoyed the book and if you are interested in how serious thinkers learned to think about Infinity and what it actually means, then this book is a fine initial guide.

Interesting book, but not necessary
Aczel wrote this book in layman terms and he did a good job explaining the concept of transfinite numbers.
However, the association of the concept of infinity with another concept, God, is totally nonsense. (Same with the application of the Incompleteness Theorem to god.)

Complete Nonsense
Although the book's content about mathematics is informative, its association of abstract mathematics with Judaism is completely ridiculous. The author tries hard to establish a link between the ponderings of some ancient Rabbis and Cantor's astonishing accomplishments and between some religious concepts and mathematical infinity. Please do not read this book if you are in any way serious about mathematics or science. Over and over again, the author promotes god and the Jewish religion whereas I was just interested in the exciting mathematics of the period. I consider this book propaganda for Judaism and mysticism. It is one of those instances where a religious zealot tries to cast his absurd views into science.

On the inifinity that comes next...
I would never have imagined that a quest this abstract could entail a story so human. Yet, that is exactly what Amir Aczel provides in this smooth tale of the many humbling encounters with the realm of infinity.

There are two lessons from this compact survey on the effort expended and the toll imposed on those bold enough to go where no person can go. First, the urge to comprehend infinity is an ancient quest and inextricably tied to the effort to ascertain the nature of God. Second, getting to know infinity can be massively bad for one's mental health. Mr. Aczel manages an almost impossible task (infinity tends to do that) in this text. He is (a) attempting to survey an enormous amount of the history mathematics and, to some extent, religion, and (b) providing a glimpse into the lives of those mathematicians that have ventured into this field. At the heart of this book is Georg Cantor, founder of modern set theory. Cantor sought to transcent an intuitive understanding of infinity. He sought an ordered system; specifically he sought to prove what became known as the continuim hypothesis: basically, that the lowest order of infinity (some cardinal numbere) was followed by the cardinal number, c (thus permitting Cantor to give ordere to his transfinite numbers). Against this hypothesis stood the possibility, urged by any number of Cantor's opponents, of infininty somewhere before one reached c. The search to prove what Godel later demonstrated to be an undecidable hypothesis may well have led Cantor (and Godel for that matter) to madness. At minimum it may have activated any underlying predisposition to mental illness in both men. They were not, as Aczels's discussion of the Kabbalists shows, inifinity's first victims. Aczel has provided a balanced and very human exploration into a topic that draws its victims as a moth to the flames. ... Read more