Product Description
Famed mathematical scholar’s concise exposition of the mathematical basis of tensor analysis, integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity and Dirac’s matrix calculus. Exercises. Index. Bibliography. Notes.
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Customer Reviews (3)

An abridged version of Schouten's earlier treatise
In recent times it has become fashionable to derogate the classical tensor analysis cultivated by such pioneers as Levi-Civita, Schouten and Eisenhart.Modern critics refer to such works as a "sea of indices", the reading of which is likened to "chasing shadows".It is true that this style of tensor analysis does not uphold the standards of rigor set forth by the Bourbaki school of presentation, but, in light of the fact that the language has changed so drastically since the writing of this book, it would be fair to treat the classical theory as a separate subject, of interest in its own right.

This book offers a valuable, yet not entirely self-contained, introduction to classical tensor analysis.As a beginner, I found the text to be too terse and was forced to consult other sources, such as Levi-Civita's "Absolute Differential Calculus" and Eisenhart's "Riemannian Geometry".Once I had gained some familiarity with the basic notions, Schouten's book became the preferred reference.The author develops an extremely precise notation which he calls the "kernel-index method" and systematically applies it as a problem solving tool throughout the book.Looking back, it is difficult to say how I ever got along without it.

Unfortunately, the book's terseness is due in part to the fact that the first five chapters are basically abridged excerpts from the author's lengthier 1954 treatise, "Ricci-Calculus".In nearly every respect, the aforementioned title is more complete than the present book.In the interest of saving space for the physical applications in the second half of the text, the author omitted important details, such as an adequate definition of manifold and the role of the vector field which generates the infinitesimal transformations used in discussing Lie derivatives.

For classical tensor analysis, Schouten's "Ricci-Calculus" (1954) and "Pfaff's Problem and its Generalizations" (1949, but still in print) are both excellent.For the modern theory, I have found Noll: Finite Dimensional Spaces; Choquet-Bruhat et al: Analysis, Manifolds and Physics, Part I and II; Spivak: A Comprehensive Introduction to Differential Geometry, Volume 1; Loomis: Advanced Calculus; and Helgason: Differential Geometry, Lie Groups and Symmetric Spaces all to be exceptionally well written.

This is a no easy book!
First that everything should have present that this it is not an introduction book. Don't hope to learn tensor analysis in this book. From the first chapter it begins to demand you and to tell you what you should know and to understand the subject to follow their reading. Definitively you have to have the clear subject in your mind to enjoy the book. But that doesn't mean that it is bad book, or that the book takes a lie title : the book is for exact science graduates (or science advanced undergraduates). The notation, inclusive, you will notice it heavy, difficult. You can divide the book in three parts: the part corresponding to the chapters 1-5 where it introduces all the elements of the tensor analysis . A second part, the chapter 6, dedicated to the study of the physical objects and their dimensions, and a third part that it includes the remaining chapters, dedicated to applications. It is not an easy book. This is a book on tensors where you won't learn on tensors. It is a beautiful synthesis of the content of the tensor analysis (chapters 1-5). The rest, obviously is impossible to find everything in a single book. Not yet it is enough with to have a general knowledge of the topic for this book. You have to have a solid one.

Possible books that you can read before being faced with this book: A. I. Borisenko (Classic, elementary), Synge, Goldberg, Levi-Civita, Akivis (Elementary, very elementary), Kreiszig (differential Geometry, elementary to intermediate level), etc.

Great Book
I would suggest this book for relativity lovers, who loves to undrestandGeneral relativity deeply. This book is easy to learn and it takes verylittle time to read but the benefits are very large. ... Read more

Product Description
Here is collection of writings that bridges the gap between science and religion.Quantum Questions collects the mystical writings of each of the major physicists involved in the discovery of quantum physics and relativity, including Albert Einstein, Werner Heisenberg, and Max Planck. The selections are written in nontechnical language and will be of interest to scientists and nonscientists alike. ... Read more

Customer Reviews (14)

The Greatest Physicists were Mystics, Militant Atheists Beware
American philosopher Ken Wilber has done a great service by bringing together in a single volume excerpts from the mystical writings of the world's greatest physicists.Six of the eight men included were Nobel laureates including Einstein, Heisenberg, Schroedinger, Plank, de Broglie, and Pauli.

These are the intellectual giants who gave us the twin pillars of modern physics, relativity theory and quantum mechanics, upon which all of contemporary science rests. Given the popular view that they must have been atheists it is astonishing to learn that all of them were quite explicit in expressing the need for a mystical outlook extending beyond the physical world.

Let's be clear. Wilber as editor has not pulled a few paragraphs out of context.Erwin Schroedinger for example writes of"the mystic vision",De Broglie writes that "the mechanism demands a mysticism", and Wolfgang Pauli speaks of "embracing the rational and the mystical."

None of these men were particularly 'religious' however.The popular religions of today (Christianity, Judaism, Islam, Buddhism, etc.), may be viewed as specific theories of Ultimate Reality (this reviewer's characterization).They all make specific statements - some empirically testable, many others not - about people and events in the physical world and how these related to God, or Allah, or All That Is, or some similar term.

Mysticism on the other hand is not a religion but a path to understanding.It has nothing to do with religious creeds or doctrines, or whether or not there is a personal God, and certainly nothing to do with science which is something else entirely. Mystics simply believe on the basis of personal experience that there is likely to exist another level or levels of consciousness beyond that of the five senses.Through rigorous mental practice they believe that it is possible to access wisdom and insight from that level which represents the highest or ultimate reality.

Individual mystics may personally identify with one religion or another but the practice of mysticism as a path is found in all the major religions and is, in and of itself, areligious.This point is unfortunately muddied in Wilber's otherwise quite interesting introduction where he equates religion with spirituality (p.18), something most thoughtful people would probably strongly reject.One can be deeply spiritual without committing to any specific set of religious doctrines.

Finally, I feel compelled comment on Wilber's assertion that the physicists would reject so called New Age books like "The Tao of Physics" and "The Dancing Wu Li Masters".The key argument of such books is less that physics "proves" Taoism or Buddhism or some other form of Eastern esoteric thought but rather that seemingly bizarre and unbelievable statements about the nature of space and time and reality made by practitioners of these traditions appear to be supported by the findings of modern physics. (Cf. for example G. Zukav, "Wu Li Masters", p. 256 and especially p. 331).

For the last hundred years or so science and religion have declared a truce in their war for the allegiance of the mind of Man.Science would to stick to matters of the physical world while religion would stick to matters of the world beyond the senses.However much both sides, including Ken Wilber, would like to keep it that way, the march of scientific knowledge takes us ever forward toward a world view that challenges our most basic assumptions about the nature of human reality.

I am speaking here specifically of entanglement, the now widely accepted principle in physics that particles really do influence each other without regard to distance or time, that is, they interact instantaneously even if they are separated by billions of light years.This was scientifically demonstrated in 1982, the year before Quantum Questions was originally released, and has been confirmed repeatedly since then.Even more disconcerting are recent experiments which seem to imply that actions in the present (as we perceive it) can actually alter events that have already been recorded in the past.(Cf. Amir D. Aczel, "Entanglement: The Greatest Mystery in Physics", 2003).

However troubling such findings may be to our everyday conception of 'reality', they merely confirm Max Plank's famous statement that "those who are not shocked when they first come across quantum theory cannot possibly have understood it."

The shocks keep coming and they are getting stronger whether we like it or not. Will they lead to a total paradigm shift in our conception of reality?

The deeper significance of this book is that it shows all scientists and those who someday will be scientists that being a mystic is okay.Want to argue with Heisenberg and Plank and Einstein and Schroedinger and....?

brought clarity to my internal debate
Any book that can end, by the introduction, an internal debate that has raged for years in my own mind all the while providing an entirely new perspective on some of the most brilliant minds of modern times deserves the highest mark.

I have struggled for years to come to terms with the balance of physics and mysticism.The Tao of Physics and such never really rung completely true for me, and I had resided myself to accepting that perhaps someday physics would explain my experiences.

This book brings so much clarity to my perspective on this matter and how they are traveling in two different directions.The critical reviews either sought something different or completely misunderstood the book (if they read it at all).

I can't get over how mystical our most brilliant scientists were.I suddenly don't feel so alone ... or insane.

A Philosophical Perspective Never Hurt Anyone;
Ken Wilber takes us back to the early turn of the Twentieth Century, in this work, but remember, it is not his work but the work of some of the greatest scientists of the last century. This book is an anthology that includes original works from Heisenberg to Eddington. Uniquely, they are not theoretical works by these authors(the scientists), but enters into the classification of Philosophy of Science. As a Philosopher in train-ing, this is what I bought the book for, and already familiar with Ken Wilber, this was an easy decision. So, for anyone who is an avid reader of Philosophy, this is for you! Though the title alludes to the mystical perspectives held by say, Einstein and Plank, for instance, it does so by way of philosophical speculations about the Universe.

Will Blow Your Freakin' Mind!!!
I was ready to hate this book, ready to do battle with another soft-headed New Ager who, in a mirror image of the lab coat creationists, wants to bend science to their will, to appropriate its authority to help sway, even coerce, for the sake of their grand cause.Was I surprised!Wilber's introduction is a pellucid repudiation of The Toa Of Physics and The Dancing Wu Li Master and a devestating blow to the even less legitimate "What The Bleep Do We Know."Wilber even abandons his own earlier views on physics supporting his mysticism.Why?Because he read these founders of New Physics, and not one of them believed that their work supported it.And this wasn't out of their ignorance of Eastern thought.No,in fact, each of these great thinkers is well versed in mysticism and, ultimately, they are mystics themselves!Wilber makes it clear that (opposed to my belief that science can only become mysticism henchman if you lessen science) that only by lessening your mysticism can you claim it's proven in the lab.And pragmatically he argues that by hitching your mysticism to the science wagon, you are (as was the case with Capra) subject to the further results of experiments that might disprove your theory.Science is, after all:provisional, changing, abstract and only intelligible in the language of mathematics.Mysticism, on the other hand, is unmediated, absolute and ever-true.Not that Wilber walks away from his dialogue with these great scientists disillusioned.His Mysticism is firmly intact.He just admits that science is not the way to get there, except in the sense that a profound understanding of physics gives you a profound understanding of its limits, of its failure to address being as such.And it is this deep understanding that lead all these scientists to their mysticism.Science should be left to scientists and Religion to the religious.Why would you want to mix the two?Only if you want to coerce, only if you are too weak to look Shiva in the eyes.This book changed me, I hope you can read the introduction with an open mind.

Interesting
I read one reviewer, an academic I suspect (perhaps in a religion/philosophy dept.), refer to Quantum Questions as ... Read more

Product Description
This essential new text by Dr. Susan Lea will help physics undergraduate and graduate student hone their mathematical skills. Ideal for the one-semester course, MATHEMATICS FOR PHYSICISTS has been extensively class-tested at San Francisco State University--and the response has been enthusiastic from students and instructors alike. Because physics students are often uncomfortable using the mathematical tools that they learned in their undergraduate courses, MATHEMATICS FOR PHYSICISTS provides students with the necessary tools to hone those skills. Lea designed the text specifically for physics students by using physics problems to teach mathematical concepts. ... Read more

Customer Reviews (5)

Awesome
It is one of the best books I hv ever come across. The pedagogy is excellent. The best part is that every topic is followed by examples which makes it so easy to understand.I would advice every physicist , undergrad to Phd scholar, to read this book.

So-so text for basic physics math
I am a former physics graduate student.I used this book for a class on mathematical physics, as is to be expected.

Strong and lucid treatment of vector calculus review, in particular with the diagrams of volume elements.Concise and clear presentation of complex analysis in as much detail as physicists typically need.Same goes for Laplace and Fourier transforms.These three chapters, put together and given a little bit more theory on meaning of Laplace and Fourier transforms, could make a high quality small textbook.

Sometimes it spent too much time doing trivial algebra and not enough talking about ideas.Congruent transformations and generalized eigenvalues are treated as a given, surprising given how much less advanced stuff is derived.It is almost as if the book says it is too hard -- then why cover it in this book?A lot of the material on linear algebra is never used again, and the review of differential equations is weak -- if the student does not know the material, they will not learn it, and if they know it, they can review more efficiently from an old textbook.The numerical integration section in particular is awful -- seriously, tables of numbers in the 21st century?Programming in Excel for a physicist?This section should probably just be omitted and left to a different book.

Would recommend as a supplement for students weak in algebra in a course on partial differential equations assuming knowledge of complex analysis.The tone is at times pedantic but it's not a huge deal.Doesn't work well as a reference text on mathematics -- not really complete enough.As another reviewer mentioned, mathematical strictness is hit and miss.It's surprising it's cared about so much in some sections of the book and not at all in others.

I think this book work fairly well for someone studying out of a textbook, as well.It's pretty readable by a non-expert, unlike half the other texts on the subject.You'll want something more dry to sum things up for you and keep perspective, but it'd be a great addition to that.

Not mathematical strict enough
I used this book in an applied math for physicists course. The book is generally easy to read and starts with a short summary of vector calculus, complex analysis and linear algebra. However I'd say that this is only usable for brushing up, and shouldn't be used to learn the stuff from scratch. The rest of the book is not too challenging and contains many examples.

My main problem with this book, however, is that it is not strict enough when it comes to the math. She often assumes that a variable or a function is real, without stating it and not considering the general case of a complex function. I'm really glad I had another book on real analysis to get the mathematical foundation to really understand the subjects.

Good examples but careless
This book is intellectually slovenly but has many interesting examples in it. It is useful in the hands of an experienced instructor. I would rate it ahead of Arfken's well-known manual. It is a pity that Margenau and Murphy is so out of date.

THE NEW STANDARD IN MATH PHYSICS!
As a physics graduate student, I cannnot say
enough good things about this book. Professor Lea
has written what is perhaps the ONLY user-friendly
textbook in mathematical physics!

The book begins with an extremely well-written
review of basics such as vector calculus and
matrix algebra. The discussion then turns to
a very thorough exploration of complex analysis.
Then we take a delightful tour through the marvels
of differential equations, Fourier analysis, special
functions, group theory, tensors, and many other wonderful,
relevant, and challenging topics.

Entire generations of physics grad students have had
to suffer through dry tome-like math
physics books. No longer! Professor Lea has given
physics grad students everywhere what we've long wanted:
a lucid, clear math physics textbook filled with worked
examples and, most critically, clear explanations of
challenging topics.

This book will make Arfken obsolete. ... Read more

Product Description
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Product Description
The advent of powerful desktop computers has revolutionized scientific analysis and engineering design in fields as disparate as particle physics and telecommunications. This up-to-date volume provides the essential mathematical and computational education for students, researchers, and practicing engineers. The author begins with a review of computation, and then deals with a range of key concepts including sets, fields, matrix theory, and vector spaces. He then goes on to cover more advanced subjects such as linear mappings, group theory, and special functions. He concentrates exclusively on the most important topics for the working physical scientist or engineer with the aim of helping them to make intelligent use of the latest computational and analytical methods. The book contains well over 400 homework problems and covers many topics not dealt with in other textbooks. It will be ideal for senior undergraduate and graduate students in the physical sciences and engineering, as well as a valuable reference for working engineers. ... Read more

Customer Reviews (2)

Not for the non-expert
I took the class under this author and this book was the required textbook. I had some background in numerical methods, but this book does not lead you to the advanced topics starting from the basics. It seems to jump to very specific topics directly, with no apparent progression. I did not find the book very useful, due to my limited background. If you are an expert in these topics, you might find it good as a quick reference.

Highly recommended
Of all the "mathematical methods" or "applied mathematics" books
on my shelf, this is the one I find myself turning to most often.

There are many other books where you can look up, say, the
orthogonality properties of some "special function," but for an
authoritative explanation of fundamental mathematics as used
in physics today -- especially computational physics -- Cantrell
is excellent.

I often have to check with Cantrell to get an answer to questions
like "Is this result in this other text true in general, or only
in the special case that its author describes?".I never have
to double check to see to what extent the results in Cantrell
apply -- he makes things like that quite clear.

Cantrell has included a healthy dose of linear algebra and
functional analysis in his text, at the expense of some of the
chapters in more traditional mathematical physics texts, such as
those on contour integration or special functions.

However, examples of the use of special functions are sprinkled
liberally thoughout the text.And although the chapter on that
subject is mostly about Bessel functions, Cantrell's discussion
of Bessel functions is, typically, different from and more
insightful than conventional treatments.

My quibbles with the book have to do not with its content, but
with "first edition" glitches -- a figure here or a typo there.
And some sort of bug in the index preparation process left many
of the page numbers referred to in the index "off" by a page
or two.On the other hand, the hardcover edition that I have
lays open nicely on my desk, and after heavy use the binding
has not broken, and no pages have fallen out.

It would be nice if there were an appendix of "Answers to Exercises,"
or maybe a "Student's Guide."However, many of the exercises
are of the "Show that ..." variety, so the lack of such an appendix
is not nearly the drawback that it might be.

Overall: Excellent book, highly recommended. ... Read more

Product Description
Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This 2006 textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses. ... Read more

Customer Reviews (5)

Excellent reference for self study
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 hadunderstood 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.

Fairly good content, very bad exposition
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.

The best book on the subject
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.

Differential geometry
Marian Fecko's textbook covers well fundamental elements of modern differential geometryand 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.

not for starter or self-learning
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.



... Read more

Customer Reviews (1)

Understand Quantum Mechanics and Solid State Theory
Group theory... Ever heard about it? Want to understand what reallyhappens, from the mathematical standpoint of view, in quantum mechanics,crystallography, symmetries and solid state physics? Ever found some bandstructure graphic and had no idea of its meaning? Tired of computersimulation without knowing the 'guts' of that first-principles? I foundwhat I needed in terms of group theory in this book. The undergraduatecourse of chemistry, and perhaps physics as well, just give us hints aboutsolid state. But this book have much to offer for any reader. Starting withabstract group theory from the very basic ending in solid state physics,going through extensive but not exhaustive analysis of quantum mechanics,it is a must read not just for all who deal with theory but also to anyonewho really want to understand energy bands, level splitting, and aninfinite number of must-know topics in today's thin border betweenchemistry and physics. ... Read more

Product Description
This volume shows how the analytic properties in the complex energy plane of the Green's functions of many particle systems account for the physical effects (level, shifts, damping, instabilities) characteristic of interacting systems. It concentrates on general physical principles and, while it does not discuss experiments in detail, includes introductions to topics of current research interest, such as singularities (X-ray, Kondo) associated with transient perturbations in an electron gas, the Mott metal - insulator transition in correlated electron systems, and the phenomenon of high T0 superconductivity. This work grew out of a course of graduate lectures given by S. Doniach at the University of London. It will appeal to beginning graduate students in theoretical solid state physics as an introduction to more comprehensive or more specialized texts and also to experimentalists who would like a quick view of the subject. A basic knowledge of solid state physics and quantum mechanics at graduate level is assumed. ... Read more

Customer Reviews (2)

good companion
I liked this book a lot because it teaches this stuff through examples of when some seemingly abstract quantities are actually observables, but this approach is not always as lucid as a formal text because the general results need sometimes be distilled from the examples. I think it makes a great companion (esp. since it's not terribly expensive) to like a Fetter/Walecka or Abrikosov et al. or whatever more general text you like.

Good for a grasp of the essential physics.
When I was learning many body physics course one years ago, I found this book is very hopeful because it is clearly written and is focused on essential physics instead of rigorous mathematics.
Of cause Mahan¡¯s book is better for a big reference book. And Fetter¡¯s book is better if you want more mathematics. ... Read more

Product Description
Applications from condensed matter physics, statistical mechanics and elementary particle theory appear in the book. An obvious omission here is general relativity--we apologize for this. We originally intended to discuss general relativity. However, both the need to keep the size of the book within the reasonable limits and the fact that accounts of the topology and geometry of relativity are already available, for example, in The Large Scale Structure of Space-Time by S. Hawking and G. Ellis, made us reluctantly decide to omit this topic. ... Read more

Customer Reviews (6)

Excellent overview and graphical explanation
This book shows you the geometric view of some advanced mathematical topics. It can greatly assist your intuition of what is going on in a mathematical setting when reading a true mathematics book. Armed with this book the other advanced text in Topology, Algebraic Geometry and Differential Geometry make more sense from a Physics point of view.

Excellent overview and graphical explanation
This book shows you the geometric view of some advanced mathematical topics. It can greatly assist your intuition of what is going on in a mathematical setting when reading a true mathematics book. Armed with this book the other advanced text in Topology, Algebraic Geometry and Differential Geometry make more sense from a Physics point of view.

Good attempt
When reading this book one can both admire these authors and feel sympathy with them. They have made an honest effort to explain the conceptsof differential geometry and topology in a way that is understandable and appreciated by the physicist reader. But the book falls short in many places, although there are some places where they do a fine job. They have taken on a very difficult project in this book, for it is quite straightforward to expound on the formalism of mathematics, but explaining it in a way that grants insight into its conceptual meaning is another matter altogether. Many physicists complain, with justification, that the way mathematics is presented in textbooks is not sufficient for giving them a deep appreciation of the underlying ideas involved. This, they argue, is what is needed for devising new physical theories and results based on these ideas. Physicists must assimilate very complex mathematical ideas very quickly in order to formulate these theories in a reasonable time frame. This is especially true in high energy physics, which in the last two decades has used mathematics like it has never been used before. Indeed, the mathematical complexity of high energy physics is dizzying, and if progress is going to be made in this field by the students of the 21st century, they are going to need mathematics books and documents that are more than just formal expositions. But, again, writing these kinds of books is very hard to do, and has yet to be done in a book to this date, although there are helpful discussions scattered throughout the mathematical literature.

Some of the concepts that need more in-depth explanation include: the theory of characteristic classes, sheaf theory, the theory of schemes in algebraic geometry, and spectral sequences in algebraic topology. There are of course many others, and some of the ones that the authors do a fairly good job of explaining in this book include: 1. the reason that the continuity of a function is defined in terms of inverses of open sets; 2. The orientability of a manifold; 3. The fundamental group and its relation with the first homology group. 4. The discussion on Morse theory.

Covers a lot of ground . . . but not always well
Unlike many physics students, I grant a lot of leeway to books on mathematics for physicists.I think it's all right for an author to engage in hand-waving arguments if this enhances physical intuition or even to make the occasional statements without proof if this allows more ground to be covered.However, if a proof actually is presented, I expect this proof to be correct.In this book, proofs are sometimes only for special cases of theorems stated more generally and often contain logical errors.

flawed and incomplete
Nash's book commits the sin many mathematical physics textbooks out there commit: "oh, we're writing for dimwit physicists, lets just give them a few scrawny examples and assure them everything else works alright." I'm sorry but writing for physicists is NOT an excuse for writing a sloppy textbook. Would you feel alright not knowing how an integral is defined? Would you use a numerical evaluation software to calculate integrals in serious research without understanding the algorithm it uses? If you do then you're a pretty shoddy physicist. I'm not saying this out of some "macho" sentiment many purist physicists have - I'm simply saying this because I feel the way this book teaches you diff. geometry is wrong - it teaches you to draw pictures and go by the pictures. When the pictures run out, so does your understanding.

This book is supposed to teach differential geometry. However, very little can be learned from it unless one already knows differential geometry: definitions are sometimes not general and sometimes not present at all, theorems are often stated only for special cases and even more often than that not proved at all. Sure, the book offers nice geometrical intuition, but this is not enough. An example: the book "proves" Stoke's theorem around page 40. Now, even a rigorous and condensed book would have problems doing that, considering the amount of "machinery" one needs to build up for it (tensors, differential forms, manifolds and so forth). This means the book makes a mess of it - big time.
There are many fine diff. geometry books out there, some for physicists, some not, which you should check out - Nakahara's text is so much better. For geometrical intuition I suggest picking up Schutz's book. Several books from the GTM (Graduate texts in mathematics series, the yellow ones) are really very accessible, such as Introduction to Topological Manifolds/Smooth Manifolds. Another good one is Allen Hatcher's Algebraic Topology for homotopy, homology and cohomology. For a good and responsible exposition, do yourself a favor and look for something else. ... Read more

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Outstanding, still fresh after a generation
It was a bit of a shock for me to read this book, because I had already been exposed to the random walks idea long before I found it.I had already learned about Black-Scholes-Merton and had read about "The Holes in Black-Scholes" (that's the name of a paper by Fischer Black).But here we have a physicist who dissected the ideas of economists (mostly statistical ideas) in the 1960s and 1970s, and anticipated a lot of what has been done since.

Osborne repeatedly picks at assumptions that have tripped up those who blindly misapply BSM, such as the idea of "continuous markets".His section on market making is better than anything else I have read on the subject (though I have not been able to find much on this subject).It illustrates that market makers create the illusion of continuity on a price chart, and for them to function the way they do, the market either must have "down time" or they must be able to halt the market occasionally and restart it (or both).

This book is very rough: it's a collection of lecture notes, and the pictures are drawn by hand.This will make any reader uncomfortable who insists on having everything look like it came out of PowerPoint or Mathematica.Younger readers who don't remember what life was like before computers were common would probably find it quaint.

Careful empiricism instead of the usual 'econo-logic'
Osborne was a physicist who observed that stock prices appear to be distributed lognormally. Mandelbrot pointed out a year later (1963) that this can't be true, that price distributions look Paretian, haveexponentially decaying tails with infinite standard deviation. However, noone has yet been able to turn Mandelbrot's observation about asymptotics ofmarket prices into trading rules (what are the dynamics?). In contrast, theBlack-Scholes model, the mathematics of derivatives and option-pricing,follows from the lognormal approximation (see Hull, e.g.). Traders who makemoney apparently don't use academic option pricing theory (it underpricesout of the money trades), but texts and scads of academic papers arewritten using it because no one knows how to do anything else yet.

Lognormality is the last part of Osborne's book. The first chapters areeven more interesting. There, Osborne tears the `mathemology' ofSamuelson's Economics text to shreds by pointing out that the famoussupply-demand curve can't be constructed from any sort of data. The mainpoint is that price does not exist as a function of either supply ordemand. Example: suppose that 25 tomatoes are available (supply). What'sthe price? Answer: anything or nothing (nonuniqueness). Even better,Osborne shows that one can obtain data on both supply and demand as afunction of price, so that discrete (noncontinuous) supply and demandcurves can be plotted for a given commodity in a given market. What a pitythat Osborne did not set his mind to discussing `utility', because (asMirowski points out in "More heat than light) the differential form thatdefines utility is generally nonintegrable, meaning that utility dooes notexist. Samuelson wrote papers trying to get around this in the 50's, butthe correct underpinning of General Equilibrium Theory was neverestablished. Osborne rightfully points out that people who believe in theapproximation of continous price changes and efficient markets are gristfor the mill of traders who use just the opposite assumptions to make moneyoff them every day.

I wish that economics students would be required toread Osborne and Mirowski, but that isn't likely to happen. Meanwhile, theFed keeps hiring those guys to crunch questionable numbers using the CAPMand similar stuff. ... Read more

Product Description

This textbook offers an accessible and highly-effective approach which is characterised by the combination of the textbook with a detailed study guide on an accompanying CD. This study guide divides the whole learning task into small units which the student is very likely to master successfully. Thus he or she is asked to read and study a limited section of the textbook and then to return to the study guide. Through interactive learning with the study guide, the results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. Since the degree of difficulties is slowly rising, the students gain confidence and experience their own progress in mathematical competence thus fostering motivation. Furthermore in case of learning difficulties, he or she is given supplementary explanations and, in case of individual needs, supplementary exercises and applications. So the sequence of the studies is individualized according to the individual’s performance and needs and can be regarded as a total tutorial experience.

More than that, the study guide aims to satisfy two objectives simultaneously: firstly it enables students to make effective use of the textbook and secondly it offers advice on the improvement of study skills. Empirical studies have shown that the student’s competence for using written information has improved significantly by using the combination of textbook and study guide.

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Introduces systematically the eigenfunction method used in quantum mechanics. Textbook serves as a handbook for researchers doing group theory calculations and for undergraduate and graduate students who intend to use group theory in their future research careers. ... Read more

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Peter Russell went from being a strict atheist and scientist to discovering a profound personal synthesis of the mystical and the scientific. That transition is the basis of this book. In From Science to God, he blends physics, psychology, and philosophy to reach a new worldview in which consciousness is a fundamental quality of creation. Russell shows how all the ingredients for this worldview are in place; it remains only to put the pieces together and explore the new picture of reality that emerges. Integrating a deep knowledge of science with his own experiences of meditation, Russell arrives at a universe similar to that described by many mystics — one in which the inner and outer worlds no longer conflict. The bridge between them, he shows, is light, and this book invites readers to cross that bridge to find new meaning in God and a deeper significance in spiritual practice. ... Read more

Customer Reviews (27)

The Mystery of Consciousness
Peter Russell is an experimental psychologist who studied mathematics and physics under Stephen Hawking. In this little book Russell covers an amazing range of topics around the subject of consciousness and how it help us to bridge spirituality with science. A former atheist, now apparently in tune with pantheism and certain eastern philosophies, the seemingly iconoclastic Russell shows little regard for any particular dogma or doctrine of religion or spirituality.

Committed to science, Russell nonetheless notes that "when it comes to the inner world of the mind - to our thoughts, feelings, sensations, intuitions, and dreams - science has very little to say. And when it comes to consciousness itself, science falls curiously silent. There is nothing in physics, chemistry, biology, or any other science that can account for our having an interior world." He augments this with a quote attributed to Christian de Quincey: "Scientists are in the strange position of being confronted daily by the indisputable fact of their own consciousness, yet with no way of explaining it."

There's a very good discussion of what Thomas Kuhn dubbed "paradigms" and how wrong ideas can remain simply because they fit the existing paradigm or model. And Russell makes no secret of an area where he believes the current scientific paradigm mistaken. "I now believe that rather than trying to explain consciousness in terms of the material world, we should be developing a new worldview in which consciousness is a fundamental component of reality. ... Everything we know, perceive, and imagine, every color, sound, sensation, thought, and feeling, is a form that consciousness has taken on. ... The human mind is so constituted that it is forced to construct its experience within the framework of space and time. Space and time are not, however, fundamental dimensions of the underlying reality. They are fundamental dimensions of consciousness."

Russell's ideas, like those of David Bohm, are not mainstream; also like Bohm, Russell has spent much time studying and meditating among eastern influences. His style is compelling and it is easy to see why he has a following as a lecturer. This is a splendid little book for removing the cobwebs from one's brain and making one think about aspects of consciousness that seldom get a hearing.

Man is a star's way of knowing about stars (George Wald)
I was writing about the experiences ofthe historical Jesus and asking "What did He see?""Who was He speaking with?""Is there a God?""Can we trust the messengers?" Evolution vs. Creationists... are there any right answers, or can Evolution and God exist naturally in our Universe?

I am searching for an explanation of consciousness, God, and soul. I found much in this book that leads me further along the path.I have to agree with other critics here that the book did not quite go far enough.However, science has not gone far enough to comprehend what 'thinking' is. How, from inert dust and mud did consciousness arise? From where do we have a sense of ourselves?

"Out of the cradle, on to dry land
Here it is standing, atoms with consciousness, matter with curiosity,"(Feynman)

Peter Russell touches on these questions but not with the depth I was hoping for.Yet, how can we expect him to do this for us when all mankind still has not come far enough to 'knowing'?This is a great little book but serves more as an introduction to what questions we should be asking and what answers we might expect in the future.My next book to read is:

"Physics of the Impossible: A Scientific Exploration into the World of Phasers, Force Fields, Teleportation, and Time Travel" by Michio Kaku.

I think these two books will work well when read together. I am glad that I read "From Science to God" first, and I recommend that you do the same, knowing with certainty that this little book will only serve to whet your appetite for more.

Liked It
Perfect introduction for a young introspective like me. I highly recommend this for anyone who is at constant struggle with their religious background and not-so-religious intuition. This book introduced the idea to me that there can be a harmonious relationship between God and my gut feeling. It is a very quick read and is put together like a lecture that I would stay up all night to hear. Hope this helps!

Awesome
This is a great book from a Scientist turned spiritual in his search for answers. Awesome.Uses light to link the two subjects.

A book for our time
In this era when people begin to ask questions and take responsibility for their life, it is time to enreach one self with wider understanding about what it is all about out there. Nothing is clear and clean cut. ... Read more

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The purpose of the book is to give a survey of the physics that is relevant for biological applications, and also to discuss what kind of biology needs physics. The book gives a broad account of basic physics, relevant for the applications and various applications from properties of proteins to processes in the cell to wider themes such as the brain, the origin of life and evolution. It also considers general questions of common interest such as reductionism, determinism and randomness, where the physics view often is misunderstood. The subtle balance between order and disorder is a repeated theme appearing in many contexts. There are descriptive parts which shall be sufficient for the comprehension of general ideas, and more detailed, formalistic parts for those who want to go deeper, and see the ideas expressed in terms of mathematical formulas.

- Describes how physics is needed for understanding basic principles of biology
- Discusses the delicate balance between order and disorder in living systems
- Explores how physics play a role high biological functions, such as learning and thinking ... Read more

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A biography profiling the life of Italian astronomer Galileo Galilei, who shared the beliefs of the controversial astronomer Copernicus that the Earth revolved around the sun. Eventually Galielo was found guilty of heresy by the Roman Catholic Church, and forced to live under house arrest for the final years of his life. Includes source notes and timeline. ... Read more

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A book everyone should read
This is the life of one of the greatest minds ever lived on earth:Lomonosov. Polyvalent as Newton or DaVinci this man is the first physical-chemist. He was also a man of letters and art. Many things were assigned to Lavoisier and others, but belong in fact to him. It is an example of how a simple man can overcome its limitations. Menshutkin rediscovered his work, locked by the imperial authority in the academy's basement. Amazing ... Read more

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Nikola Tesla is a Capstone Press publication.

... Read more

Customer Reviews (1)

Fascinating and informative read
As a biography fan and former teacher I really appreciated this book, which we purchased for my 4th graders report.I loved the format--sidebars with relevant historical information, time lines, and excellent photos and images.The information was totally age appropriate without being totally basic.We got a lot out of it.I had no idea how fascinating Tesla was and how much he contributed to our modern lives. ... Read more