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1. My Life as a Quant : Reflections
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2. Quantum Mechanics (Quantum Mechanics)
$60.00 $53.02
3. A First Course in String Theory
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4. Mathematical Methods for Physicists
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5. Quantum Computation and Quantum
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6. Using and Understanding Mathematics
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7. Mathematical Methods in the Physical
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8. Gravitational N-Body Simulations
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9. Python Scripting for Computational
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10. A Course in Modern Mathematical
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11. Probability Theory : The Logic
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12. Quaternions and Rotation Sequences
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13. Geometric Algebra for Physicists
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14. Mathematics of Classical and Quantum
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15. Geometry, Topology and Physics
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16. Understanding Molecular Simulation
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17. The Lady Tasting Tea: How Statistics
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18. Methods of Theoretical Physics,
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19. Mathematical Physics
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20. Lattice-Gas Cellular Automata

1. My Life as a Quant : Reflections on Physics and Finance
by EmanuelDerman
list price: $29.95
our price: $19.77
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Asin: 0471394203
Catlog: Book (2004-09-17)
Publisher: Wiley
Sales Rank: 1360
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Book Description

"Derman’s memoir of his transition from mathematical physicist to expert finance whiz at Goldman Sachs and Salomon Brothers reads like a novel, but tells a lot about brains applied to making money grow."
–Paul A. Samuelson, MIT, Nobel Laureate in Economic Sciences, 1970

"Not only a delightful memoir, but one full of information, both about people and their enterprise. I never thought that I would be interested in quantitative financial analysis, but reading this book has been a fascinating education."
–Jeremy Bernstein, author of Oppenheimer: Portrait of an Enigma

"This wonderful autobiography takes place in that special time when scientists discovered Wall Street and Wall Street discovered them.It is elegantly written by a gifted observer who was a pioneering member of the new profession of financial engineering, with an evident affection both for finance as a science and for the scientists who practice it.Derman’s portrait of how the academics brought their new financial science to the world of business and forever changed it and, especially, his descriptions of the late and extraordinary genius Fischer Black who became his mentor, reveal a surprising humanity where it might be least expected.Who should read this book?Anyone with a serious interest in finance and everyone who simply wants to enjoy a good read."
–Stephen Ross, Franco Modigliani Professor of Finance and Economics, Sloan School, MIT

" … a deep and elegant exploration by a thinker who moved from the hardest of all sciences (physics) to the softest of the soft (finance). Derman is a different class of thinker; unlike most financial economists, he bears no physics envy and focuses on exploring the real intuitions behind the mechanisms themselves. In addition to stories and portraits, the book documents, in vivid detail, the methods of knowledge transfer. I know of no other book that bridges the two cultures. Finally, I am happy to discover that Derman has a third career: he is a writer."
–Nassim Taleb, author of Fooled by Randomness

"The quintessential quarky quant, Emanuel Derman has it all.Physicist, mathematician, philosopher, and poet blend together to produce a narrative that all financial engineers will find worth reading."
–Mark Rubinstein, Paul Stephens Professor of Applied Investment Analysis, University of California, Berkeley ... Read more


2. Quantum Mechanics (Quantum Mechanics)
by B. Dui, Claude Cohen-Tannoudji, Bernard Diu, Frank Laloe
list price: $125.00
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Asin: 047116433X
Catlog: Book (1978-06)
Publisher: Wiley-Interscience
Sales Rank: 507060
Average Customer Review: 4.24 out of 5 stars
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Book Description

Beginning students of quantum mechanics frequently experience difficulties separating essential underlying principles from the specific examples to which these principles have been historically applied. Nobel-Prize-winner Claude Cohen-Tannoudji and his colleagues have written this book to eliminate precisely these difficulties. Fourteen chapters provide a clarity of organization, careful attention to pedagogical details, and a wealth of topics and examples which make this work a textbook as well as a timeless reference, allowing to tailor courses to meet students' specific needs.
Each chapter starts with a clear exposition of the problem which is then treated, and logically develops the physical and mathematical concept. These chapters emphasize the underlying principles of the material, undiluted by extensive references to applications and practical examples which are put into complementary sections. The book begins with a qualitative introduction to quantum mechanical ideas using simple optical analogies and continues with a systematic and thorough presentation of the mathematical tools and postulates of quantum mechanics as well as a discussion of their physical content. Applications follow, starting with the simplest ones like e.g. the harmonic oscillator, and becoming gradually more complicated (the hydrogen atom, approximation methods, etc.). The complementary sections each expand this basic knowledge, supplying a wide range of applications and related topics as well as detailed expositions of a large number of special problems and more advanced topics, integrated as an essential portion of the text.
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Reviews (25)

5-0 out of 5 stars This book is simply amazing!
Complete, pedagogical, and beautiful. These volumes have it all! Now, they might seem disorganised at first, but once you read the "Introduction" and the "Directions for Use" page you will learn how to navigate the book. Don't be intimidated by the thickness of these two volumes; most of it is due to chapter complements, which are wholly optional.

It is highly recommended that you have some previous experience with elementary quantum physics before hitting Cohen-Tannoudji. Eisber and Resnik or French and Taylor (MIT series) are both good starts.

5-0 out of 5 stars quantum mechanics by claude cohen-tannoudji, vols I and II
After years of searching for a really good book on non-relativistic quantum mechanics, I found it in this book. The beginning student can easily understand it and it's comprehensiveness will appeal to the more advanced student. It's use of the Dirac notation makes for a clean and concise treatment. The book is FAR better than most other quantum mechanics books found in university libraries, in my opinion.

4-0 out of 5 stars Cohen is great, but Wiley & Sons could have done better.
Most of what ought to have been said about this book has been said in previous reviews. It is missing a few crucial topics such as group theory, Lie algebras, and the Bell inequality, but it is extremely well-written, and the treatment of topics which are contained is nothing short of thorough. Reading this book is an illuminating experience.

Wiley & Sons (the publisher) fall short in their treatment of the book. This may read like a modern classic, but it is put together like a telephone book. The paper binding is extremely flimsy (given the size of the book, that is to be expected), and the covers are of such low quality that not only do they scuff, crease, and dent easily, but they stick to surfaces when only a bit of dampness is present, and are impossible to remove without damage.

For the price, one ought to expect more. A book like this deserves to be in a rounded, full-cloth, non-acid edition. At the very least, they could have put it in a textbook binding with sturdy cardboard covers. Timeless references ought to take more abuse than the Yellow Pages.

5-0 out of 5 stars THE BEST QM BOOK FOR STARTERS
This is the best book on QM that any person can lay his hands on,and it is a shame it is not introduced as a first cource in QM for every science student interested in the subject.Once you go through the book,you may even be able to solve all classical problems quantum mechanically!!

The plus points of this book which other books lack:
complete and elaborate discussion of all mathematical tricks and tools needed in chapter 2,clear layout of the postulates of QM in chapter 3 so that one faces no conceptual difficulty in the remainder of the book,angular momentum addition and clebsch-Gordan coeeffecient calculation in CH.10,electromagnetic interaction with matter in chapter 13(complement),clearly explained probabaility calculation concepts for identical particles ,Ch14.,and a understandable tratment of scattering ,partial traces and the wigner-eckart theorm with applications.

I would recommend this book for any one who wishes to learn QM without laziness(the book is tiringly comprised of 2 volumes)before touching any other book in this subject(others an only lead you astray).the book is self suffecient in all respects and doesnt make a single step jump(no wonder its shear volume).

Good luck!
ganesh

5-0 out of 5 stars BEST QM BOOK FOR STARTERS
It is a book which every student who needs to master QM sometime should thoroughly read and solve.It is a shame that it is not taught in the very first course of QM that any student comes across in his academic life,since this book clears the very fundamental so much that when you are done with it ,you can even solve any classical problem quantum mechanically yourself.

The second chapter clearly lays down all fundamentalmathematical tricks and tools required to grasp the subject,and chapter 3 has the basic QM postulates so clearly and elaborately explained that one has no problem in understanding the application of quantum mechanical postulates to the problems in the later chapters.

The basic plus points which other popular books lack are,elaborate treatment of angular momentum and Clebsch-Gordan coeffetients,partial traces,scattering,decay of a descrete state resonantly coupled to a continuum of final states and the probabilty calculations when particles are identical.

it is a self consistent book,with exercises which clear the concepts (though not enough always).a major amount of worked out problems with clear explanations for all steps.

it is a book which covers a great deal with no step jumps at all,no wonder it has two tiring fat volumes.
I repeat,a must for any science student willing to learn QM,before he touches any other book of the subject(the rest can only lead you astray).

good luck. ... Read more


3. A First Course in String Theory
by Barton Zwiebach
list price: $60.00
our price: $60.00
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Asin: 0521831431
Catlog: Book (2004-06-28)
Publisher: Cambridge University Press
Sales Rank: 7713
Average Customer Review: 5 out of 5 stars
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Book Description

An accessible introduction to string theory, this book provides a detailed and self-contained demonstration of the main concepts involved. The first part deals with basic ideas, reviewing special relativity and electromagnetism while introducing the concept of extra dimensions. D-branes and the classical dynamics of relativistic strings are discussed next, and the quantization of open and closed bosonic strings in the light-cone gauge, along with a brief introduction to superstrings. The second part begins with a detailed study of D-branes followed by string thermodynamics. It discusses possible physical applications, and covers T-duality of open and closed strings, electromagnetic fields on D-branes, Born/Infeld electrodynamics, covariant string quantization and string interactions. Primarily aimed as a textbook for advanced undergraduate and beginning graduate courses, it will also be ideal for a wide range of scientists and mathematicians who are curious about string theory. ... Read more

Reviews (1)

5-0 out of 5 stars Strings Everywhere
Highly recommended!
Dr. Zwiebach's book is an excellent resource for individuals with at least an undergraduate education in physics who are interested in pursuing string theory and related topics. Advanced students in other disciplines can also benefit with some hard work. It is very well organized, starting with the necessary mathematics and relativistic formalism/notation later used in calculations. The book is very rewarding, leading the student with great detail through derivations and avoiding the common "it can easily be shown that..." statements found in other books. The most enjoyable thing is that you really can begin grasping the basics of string theory and branes. After going through this book (maybe in a one year course) the reader should be prepared enough to start looking at other books such as Hatfield, Polchinski, and Green et. al. ... Read more


4. Mathematical Methods for Physicists
by George B. Arfken, Hans Weber, Hans-Jurgen Weber
list price: $104.95
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Asin: 0120598256
Catlog: Book (2000-10)
Publisher: Academic Press
Sales Rank: 38868
Average Customer Review: 2.84 out of 5 stars
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Book Description

Through four editions, Arfken and Weber's best-selling Mathematical Methods for Physicists has provided upper-level undergraduate and graduate students with the paramount coverage of the mathematics necessary for advanced study in physics and engineering. It provides the essential mathematical methods that aspiring physicists are likely to encounter as students or beginning researchers. Appropriate for a physics service course, as well as for more advanced coursework, this is the book of choice in the field.

* Provides the essential mathematical methods that aspiring physicists are likely to encounter as students or beginning researchers
* *Serves as both text and useful reference for students of physics and applied mathematics
* *Throughout the text the physical relevance of the mathematics is constantly reinforced
... Read more

Reviews (37)

2-0 out of 5 stars A physicists handbook for mathematics -- not a textbook
The lecturer of our undergraduate Mathematical Methods for Physics course said that he recommends Arfken's book because it will be useful also later as a reference book. Hearing those words, I could not help but to think "this is one of *those* books". And indeed, although Arfken's and Weber's book covers quite a wide range of mathematics, it does so by being very concise, e.g. there is usually only one example per topic. This is one example of why it is not a good textbook. Not following Arfken's course, I will give another example: there are no answers and no solutions for any of the problems, making it very undesirable from the viewpoint of the person who cannot attend all the lectures. Finally, text itself is quite concise, and often it stops at telling the things rather than explaining them also. I guess I have to admit that I am not one of the excellent students mentioned by a reviewer, for I liked Kreyszig's Advanced Engineering Mathematics much more. As a contrast to Arfken's book, it offered many examples and helped to understand what the thing was all about. Unfortunately, it does not cover nearly all of the topics covered by Mathematical Methods for Physicists. If Mathematical Methods for Physicists is going to be your first introductory text to these topics and if you are not supported by very good lectures I can only say that may God have mercy on your soul.

3-0 out of 5 stars Needs elaboration: Add 5 pages per page.
I am convinced that the author of this book has made the assumption that the reader has had pretty significant exposure to most of this already. Therefore, this is nothing more than a "all in once place" reference on math methods for physicists. The reason for the diverse range of opinions on this book is due to the various backgrounds of students. For most physic undergrads now taking a grad level math methods course, our exposure to differential eqns, complex functions, tensors, group theory, etc. is superficial. Here is a good entrepreneurial idea for an accomplished physicist that can relate to us mere mortals. For each page that Arfken has provided on a topic, ELABORATE (add 5 pages per page to it and now you have a useful textbook that every graduate student in physics should have). It would save us a fortune in buying the many additional supplemental texts required if you are stuck with Arfken.

2-0 out of 5 stars Not good to learn from
I used this book in a Math Methods 1st year Graduate Physics course, and I dont think I really learned anything from it.
It doesnt do well at TEACHING you anything, you'll have to buy another book with examples or find them somewhere, and that itself can be difficult.

I found myself referring to Mary Boas' book for a few examples if I wanted to learn anything, but when you get to Group Theory you'll end up lost because the professor will run right over the material and textbooks on that subject arent that great.

If i'm looking for an equation or a mathematical rule, this book is great. Ive used it for Quantum and Jackson E&M quite a bit.

1-0 out of 5 stars A salad of typos
I have had the misfortune to teach from several editions of this pathetic textbook. The later printings of the 3d edition, by Arfken alone, were quite free of mistakes and of typos. But the early printings of the 5th edition by Arfken and Weber are loaded with typos and have some errors. Most of these typos are in equations that were correct in the 3d edition.

My students have had a hard time learning from this book.

Also, the binding of this $99 book is cheap cardboard -- the hardcover edition does not really have a hard cover. All in all,
this is a typical Elsevier product: inferior and expensive.

5-0 out of 5 stars Great text for reference and learning
I noticed that most student reviews seemed to disparage this book as a textbook, so I am writing this to provide an alternative veiwpoint. My intermediate Math Methods class used this book and I have not yet enountered a math problem in any of my grad classes that I couldn't use this book as an aide to solve. The book is clear yet concise, which allows for a large breadth of material to be covered in one semester effectively. Yes, some material is not covered with great depth, but I think that Mathematical Methods Books by design are not meant to be thourough, mathematically rigourous books but rather books that will present the method of solving, if not the exact solution, of most problems one might encounter in the physical sciences.

I reccomend this book. Like all other Math Methods books I have seen it will require other texts as supplements if one wants a reference for every problem one could encounter. ... Read more


5. Quantum Computation and Quantum Information
by Michael A. Nielsen, Isaac L. Chuang
list price: $68.00
our price: $68.00
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Asin: 0521635039
Catlog: Book (2000-09)
Publisher: Cambridge University Press
Sales Rank: 211769
Average Customer Review: 4.33 out of 5 stars
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Book Description

In this first comprehensive introduction to the main ideas and techniques of quantum computation and information, Michael Nielsen and Isaac Chuang ask the question: What are the ultimate physical limits to computation and communication? They detail such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error correction. A wealth of accompanying figures and exercises illustrate and develop the material in more depth. They describe what a quantum computer is, how it can be used to solve problems faster than familiar "classical" computers, and the real-world implementation of quantum computers. Their book concludes with an explanation of how quantum states can be used to perform remarkable feats of communication, and of how it is possible to protect quantum states against the effects of noise. ... Read more

Reviews (18)

5-0 out of 5 stars Good for Research and Self-Study
I think that this book is excellent for self-study, and does provide a significant level of rigour.

I believe that the authors do a significantly good job defining their terms and making sure the reader is "with them." For example, just a few lines up from Equation 5.36 on page 226, in fact immediately after the start of Section 5.3.1, the authors make the comment, "For positive integers x and N, x < N, with no common factors,...". Now I would assume that Equation 5.36 would reference these same variables, and thus the restriction would still apply.

This is admittedly rather a specific example, but it illustrates the point: the authors have a well-developed sense of logical flow, and such flow makes it much easier to follow what is rather a difficult subject. The subject is difficult because it spans such a huge variety of disciplines.

My advice is to take courses in mathematics: linear algebra (easily the most important of all the classes), abstract algebra, discrete mathematics, advanced calculus, number theory; in physics: classical mechanics, quantum mechanics, electricity and magnetism; electrical engineering: linear circuits, digital logic, microprocessors; and in computer science: algorithms and data structures, cryptography. Then I think you would have an adequate background to understand this top-notch, advanced book.

5-0 out of 5 stars The Reader Review by Julian Miller is INCORRECT!
Dr. Julian Miller is either an idiot and obviously didn't read the book carefully at all. On page 226 just above the equation Miller talks about it says "For positive integers x and N, x < N, with no common factors, ..." and goes on to clearly define EVERYTHING. I read this book and I disagree 100% with that review and have just proved to you that the reviewer was completely wrong and just didn't read the book carefully on page 226. I had no trouble understanding the topics in this book and don't have PhD in anything, just a Bachelors in Physics and took a couple graduate courses. Everything was very clear in this book to me and I think it is a great book. Don't believe what that reviewers said, if he/she had just read the book more carefully he/she would notice that everything is defined. I bet that reviewer wasn't reading the book carefully at all and was just skipping sections and jumping around from page to page, skimming over certain paragraphs. It's a great book and it's the first one I encountered that was helpful enough to allow me to really make sense of this subject.

5-0 out of 5 stars Essential Quantum Information/Computing
This is *the* book to learn Quantum Information/Computation theory from. I tried others but nothing made much sense until I read and worked through this book, then I went back to the other books and everything made sense to me.

Someone who has been doing research in this area for many years probably cannot use this book for much other than an occasional reference, but for those who want to learn the subject it is a GREAT place to start.

5-0 out of 5 stars Needs solutions to problems!
I have over 3 dozen books on the subject and this is by far the clearest. I believe this book to be extremely well written and much clearer than other texts. In addition, the circuit notation used in the text is BY far easier than what is found in a text on Quantum Physics. Also, the way things are stated about general Quantum Theory is so much kinder and more logical than in any other text I have read, both saying the same things only this text explains this painful subject in a nice clean way.

In any case, I believe this to be the best book on the subject. I also recommend Explorations in Quantum Computing (Williams, Clearwater), it is useful since it has many Mathematica Workbooks to simulate Quantum Circuits and that related. Really you need to read many books to understand this subject, but Nielsen and Chuang make a good foundation.

I do agree that this book could be better, as could all texts, but being the best book in a very complicated new area of study is worthy of 5 stars. Simply, this is the best book on the subject that I have seen. If you are trying to teach yourself this material from any book chances are you will fail, but if you must I would get this one first and then the Williams book. Regards.

5-0 out of 5 stars Good, just advanced enough
This book covers quantum information theory at a level that can be understood by someone who has only had an introductory course in quantum mechanics and the same in basic computability theory. While this still rules out most of the general public, this is an excellent book for anyone seriously thinking of entering the field. The first third of the book reviews the required basics of quantum mechanics, computability, and information theory, and outlines where QIT differs from the classical theory. The rest of the book goes into more specifics.
While this book does cover introductory level quantum circuit design, elementary quantum information theory, and the basics of just about every part of the field, it doesn't go into terribly much depth. This makes it an excellent introductory book (targeted at graduate or upper-level undergraduate physics majors), but if you want something more targeted towards a particular facet of quantum computation and information, you may want to try something else. ... Read more


6. Using and Understanding Mathematics : A Quantitative Reasoning Approach (3rd Edition)
by Jeffrey O. Bennett, William L. Briggs
list price: $101.33
our price: $101.33
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Asin: 0321227735
Catlog: Book (2004-02-17)
Publisher: Addison Wesley
Sales Rank: 94681
Average Customer Review: 3.75 out of 5 stars
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Reviews (4)

4-0 out of 5 stars Good Math Textbook
I used this book for a class I took in college. It was very helpful. Highlights of the book include examples, language, and ease of understanding. I would recommend this book to anyone taking a class that needs it, or even a person just interested in furthering their basic math knowledge. Check this one out!

5-0 out of 5 stars User Friendly 2nd Ed. Essential for Survey of Mathematics
Extremely User friendly text, be sure you are getting 2nd edition and not first, they are not the same!!! Uses real life examples to explain various mathematical models, a book you'll want to hold on to for future use.

1-0 out of 5 stars A Math Book for the Mathematically Inept
There are no numbers in this math book. What kind of math book has no numbers??

5-0 out of 5 stars WoW! A math book for the mathmatically impaired!!!
I bought this book over a year ago for a class I had to take. I would have to say that this book is the best learning tool I have been able to use in understanding mathmatics. I was diagnosed with a math disability. This book has helped me with this disability. I am able to understand concepts and apply my understanding of those concepts.It has given me a self confidence I didn't think I would ever have. I have tried other texts and found them to be either to general in thier knowledge or poor in thier use of the english language. I found this book to be very descriptive and helps the student to paint a picture of what problems they may face in the world of mathmatics. I would highly recommend this book to anyone who has had a hard time with spatial ability. The detailed step by step process is wonderful. It covers an array of subjects. I still use it to help me through other classes. I have found it to be the only book detailed enough to teach me properly. It is the best college book I have ever had to buy. I really have gotten my dollars worth out of it. ... Read more


7. Mathematical Methods in the Physical Sciences, 2nd Edition
by Mary L.Boas
list price: $106.95
our price: $106.95
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Asin: 0471044091
Catlog: Book (1983-04-06)
Publisher: Wiley
Sales Rank: 36598
Average Customer Review: 4.73 out of 5 stars
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Book Description

Updates the original, comprehensive introduction to the areas of mathematical physics encountered in advanced courses in the physical sciences. Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded. ... Read more

Reviews (22)

5-0 out of 5 stars indispensable Mathematical hanbook for physics students
To put it quite simply, if you are a physics student, you must own this book. What does this book do for you? Consider this...

In my school, we do not have a mathematical methods course for science, so I decided to take on a math minor to take all the classes neccesary to do physics "right." This included a class on ODEs, Fourier Series & PDEs, Linear Algebra, and Complex Variables. These classes, although helpful, cover a lot of stuff that is not quite useful for understanding physics concepts, often undermining or dampening the stuff that is actually applicable.

What makes this book so great is that it combines all the essential math concepts into one compact, clearly written reference. If I could do it all over again, I would easily rather take a two semester Math Methods course (like they do in many schools) using a book like Boas than take all these obtuse math courses. With this book, it makes it so handy to review previously learned concepts or actually learn poorly presented topics ( for a physicist anyway) in mathematics classes... (Things like Coordinate Transformations, Tensors, Special Functions & PDEs in spherical & cylindrical coordinates, Diagonilzation, the list goes on.....)

Keep this gem handy when doing homework and studying for exams, learning the math tools from this book enables you to concentrate squarely on the physics in your other textbooks... (since mathematical background information, understandably, is often cut short...)

5-0 out of 5 stars Boas is the best math methods book
It is not only well written, it has lots of worked examples! It is not as comprehensive as some "standards" such as Arfkin or Butkov, but it is much more useful for mastering the basics. No physics student should be without this book.

5-0 out of 5 stars Clearest and most comprehensive book on Math for Physics
I'm a physics undergraduate. Out of all my books on math, this is far and away the most comprehensive and useful book! It has supplanted my other, thicker books and is the one thing I turn to whenever I need to refresh myself on a math method.

It covers practically every useful math technique for physics, and never assumes that you're a genius (unlike other books). Each step is explained in clear, refreshing language and in a very logical order. From Laplacian transforms to Fourier series to ODEs, each subject is introduced so well that, even when I've missed a lecture, I can understand the topic just from reading it.

Highly recommended and worth the price, this is one book physics undergraduates should have. The only thing else needed with it is the solutions manual.

5-0 out of 5 stars A book that has everything.
This book has a bit of everything from Linear Algebra, Calculus, Analysis, Probability and Statistics, ODE, PDE, Transforms just to name a few. If you get a chance to study everything from this book, you will probably learn more from this book than all your undergraduate math courses combined. Some concepts on this book may be difficult to understand due to the lack of in depth coverage. But I guess the main intention of this book is to focus on the applied side and cover as much material that is relevant to physics and engineering as possible and not go into much detail on the theory side.
If you are a graduate student in physics or engineering and want to buy this book for reference, it will be a good start for the first year courses but won't help you much after that.
Readibility of this book is excellent. You will understand most of the concepts and examples presented.
Bottomline: This is a must have book for engineers and physicists.

3-0 out of 5 stars This is not the best math methods book
Boas is overrated. The book "Mathematical methods for Physics and engineering" by Riley, Hobson, and Bence is much better. ... Read more


8. Gravitational N-Body Simulations : Tools and Algorithms (Cambridge Monographs on Mathematical Physics)
by Sverre J. Aarseth
list price: $110.00
our price: $110.00
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Asin: 0521432723
Catlog: Book (2003-10-23)
Publisher: Cambridge University Press
Sales Rank: 444361
Average Customer Review: 5.0 out of 5 stars
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Book Description

This self-contained book presents basic methods of numerical simulation of gravitational systems, with applications in astronomy and cosmology. The first half of the book presents and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model known planetary and astrophysical phenomena such as Hubble motion. The second half of the book demonstrates how to develop clear and elegant algorithms for models of gravitational systems. ... Read more

Reviews (1)

5-0 out of 5 stars What we have been expecting!!!
This is an excellent book on simulation of n-body systems. The
author gives a very good description of several techniques and
algorithms together with some theoretical background. This is
the book to have on your desk if you don't want to have a pile
of pappers and other books. ... Read more


9. Python Scripting for Computational Science (Texts in Computational Science and Engineering)
by Hans Petter Langtangen
list price: $69.95
our price: $69.95
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Asin: 3540435085
Catlog: Book (2004-10-01)
Publisher: Springer-Verlag
Sales Rank: 45153
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Book Description

The goal of this book is to teach computational scientists and engineers how to develop tailored, flexible, and efficient working environments built from small programs (scripts) written in the easy-to-learn, very high-level language Python. The focus is on examples and applications of relevance to computational science: gluing existing applications and tools, e.g. for automating simulation, data analysis, and visualization; steering simulations and computational experiments; equipping programs with graphical user interfaces; making computational Web services; creating interactive interfaces with a Maple/Matlab-like syntax to numerical applications in C/C++ or Fortran; and building flexible object-oriented programming interfaces to existing C/C++ or Fortran libraries. In short, scripting with Python makes you much more productive, increases the reliability of your scientific work and lets you have more fun - under Unix, Windows and MacIntosh. ... Read more


10. A Course in Modern Mathematical Physics : Groups, Hilbert Space and Differential Geometry
by Peter Szekeres
list price: $65.00
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Asin: 0521829607
Catlog: Book (2004-12-16)
Publisher: Cambridge University Press
Sales Rank: 266188
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Book Description

Presenting an introduction to the mathematics of modern physics for advanced undergraduate and graduate students, this textbook introduces the reader to modern mathematical thinking within a physics context. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book also includes exercises and proofed examples to test the students' understanding of the various concepts, as well as to extend the text's themes. ... Read more


11. Probability Theory : The Logic of Science
by E. T. Jaynes
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Asin: 0521592712
Catlog: Book (2003-04-10)
Publisher: Cambridge University Press
Sales Rank: 23824
Average Customer Review: 5 out of 5 stars
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Book Description

Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information. ... Read more

Reviews (7)

5-0 out of 5 stars Ontological and Epistomological Probability
I read this book before it was published; I downloaded it from a WU website. It has been of immense use to me in my career, it is a very practical book. Other reviews that say Dr. Jaynes' ideas are at odds with traditional measure theoretic probability are mistaken. Dr. Jaynes is a true Baysian. A Baysian is one who believes that probabilities do not model serendipity in nature, but do model subjective certainty. The Bayesian concept of probability is epistomological, i.e. the uncertainty is in our minds, not in objective reality. Traditional probability takes the reverse view: probabilities model unpredictable events, they are a model of objective reality like any science, i.e. probabilities are ontological. The trick is to realize the two are not mutually exclusive! There can be true ontological randomness in nature, and our minds can have uncertainty from incomplete knowledge as well. Probability theory as a branch of mathematics makes no claim what it models. The beauty is that probabiltity distributions integrate the two seamlessly. Thus, it is perfectly valid to put a distribution on an unknown parameter, epistomologically unknown, and derive that distribution from an experiment with, presumably, ontological randomness. Dr. Jaynes' book is well worth reading for the many case studies he presents. His background as a physicist is key to understanding some of the esoteric philisophical points.

5-0 out of 5 stars The most important book on probability theory in decades
Reading this book is an exhilarating intellectual adventure. I found that it shed light on many mysteries and answered questions that had long troubled me. It contains the clearest exposition of the fundamentals of probability theory that I have ever encountered, and its chatty style is a pleasure to read. Jaynes the teacher collaborates fully with Jaynes the scientist in this book, and at times you feel as if the author is standing before you at the blackboard, chalk in hand, giving you a private lesson. Jaynes's advice on avoiding errors in the application of probability theory -- reinforced in many examples throughout the book -- is by itself well worth the price of the book.

If you deal at all with probability theory, statistics, data analysis, pattern recognition, automated diagnosis -- in short, any form of reasoning from inconclusive or uncertain information -- you need to read this book. It will give you new perspectives on these problems.

The downside to the book is that Jaynes died before he had a chance to finish it, and the editor, although capable and qualified to fill in the missing pieces, was understandably unwilling to inject himself into Jaynes's book. One result is that the quality of exposition suffers in some of the later chapters; furthermore, the author is not in a position to issue errata to correct various minor errors. Volunteer efforts are underway to remedy these problems -- those who buy the book may want to visit the "Unofficial Errata and Commentary" website for it, or check out the etjaynesstudy mailing list at Yahoo groups.

5-0 out of 5 stars Truthful
it offers a mathematical discussion of probability
from the point of view of information theory. It argues
against the frequentist approach. The author is absolutely
right: probability has meaning only as incomplete
knowledge (but still objective). Any frequentist approach
is problematic. A real diamond.

5-0 out of 5 stars Invaluable
This book has been on the web in unfinished form for a number of years and has shaped my scientific thinking more than any other book. I believe it constitutes one of the most important scientific texts of the last hundred years. It convincingly shows that "statistics", "statistical inference", "Bayesian inference", "probability theory", "maximum entropy methods" , and "statistical mechanics" are all parts of a large coherent theory that is the unique consistent extension of logic to propositions that have degrees of plausibility attached to them. This is already a theoretical accomplishment of epic proportions. But in addition, the book shows how one actually solves real world problems within this frame work, and in doing so shows what a vastly wider array of problems is addressable within this frame work than in any of the forementioned particular fields.
If you work in any field where on needs to "reason with incomplete information" this book is invaluable.

As others have already mentioned, Jaynes never finished this book. The editor decided to "fill in" the missing parts by putting excercises that, when finished by the reader, provide what (so the editor guesses) Jaynes left out. I find this solution a bit disappointing. The excercises don't take away the impression that holes are left in the text. It would have been better if the editor had written the missing parts and then printed those in different font so as to indicate that these parts were not written by Jaynes. Better still would have been if the editor had invited researchers that are intimately familiar with Jaynes' work and the topic of each of the missing pieces to submit text for the missing pieces. The editor could then have chosen from these to provide a "best guess" for what Jaynes might have written.

Finally, there is the issue of Jaynes' writing style. This is of course largely a matter of taste. I personally like his writing style very much because it is clear, and not as stifly formal as most science texts. However, some readers may find his style too belligerent and polemic.

5-0 out of 5 stars Brilliant but attended by many misunderstandings
To "pure" mathematicians, probability theory is measure theory in spaces of measure 1. To the extent to which you remain a "pure" mathematician, this book will be incomprehensible to you.

To frequentist statisticians, probability theory is the study of relative frequencies or of proportions of a population; those are "probabilities".

To Bayesian statisticians, probability theory is the study of degrees of belief. Bayesians may assign probability 1/2 to the proposition that there was life on Mars a billion years ago; frequentists will not do that because they cannot say that there was life on Mars a billion years ago in precisely half of all cases -- there are no such "cases".

To _subjective_ Bayesians, probability theory is about subjective degrees of belief. A subjective degree of belief is merely how sure you happen to be.

"Noninformative" _objective_ Bayesians assign "noninformative" probability distributions when they deal with uncertain propositions or uncertain quantities, and replace them with "informative" distributions only when they update them because of "data". "Data", in this sense, consists of the outcomes of random experiments.

"Informative" _objective_ Bayesians -- a rare species -- ask what degree of belief in an uncertain proposition is logically necessitated by whatever information one has, and they don't necessarily require that information to consist of outcomes of random experiments.

Jaynes is an "informative" objective Bayesian. This book is his defense of that position and his account of how it is to be used.

"Pure" mathematicians will not find that this book resembles that branch of "pure" mathematics that they call probability theory.

Jaynes rails against those he disagrees with at great length. Often he is right. But often he simply misunderstands them. For example, writing in the 1990s, he said that pure mathematicians reject the use of Dirac's delta function and its derivatives, and related topics. That is nonsense; the delta function has long been considered highly respectable, and required material in the graduate curriculum. Unfortunately Jaynes's misunderstandings may cause some others to misunderstand him when he is right. Statisticians are more informed than "pure" mathematicians and will disagree with Jaynes for better reasons. _Some_ statisticians will agree with him.

Jaynes has many flaws, made all the more annoying by the fact that we need to overlook them in order to understand him. His message is important. ... Read more


12. Quaternions and Rotation Sequences : A Primer with Applications to Orbits, Aerospace and Virtual Reality
by J. B. Kuipers
list price: $35.00
our price: $29.05
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Asin: 0691102988
Catlog: Book (2002-08-19)
Publisher: Princeton University Press
Sales Rank: 92635
Average Customer Review: 4.72 out of 5 stars
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Book Description

Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations.

The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality. ... Read more

Reviews (18)

5-0 out of 5 stars An oustanding work on rotations for the practitioner
My graduate school work was in theoretical quantum mechanics, and was especially concentrated in the group properties of rotations. I can honestly say that I would have been twice as effective if I had this reference available then.

Kuiper does an outstanding job of pulling together the traditional matrix-based approach to describing rotations with the less-frequently encountered quaternion approach. In doing so, he clearly shows the benefits of the quaternion algebra, especially for computer systems modeling rigid body rotations and virtual worlds. The exposition is clear, concise, and aimed at the practitioner rather than the theoretician. The examples are taken from classical engineering problems -- a refreshing change from the quantum-mechanical problems I was used to from previous works on the subject.

Despite the practical foocus, though, there is plenty of material here for those more interested in understanding the minutia of the SO(3) symmetry group. And unlike most work in this field, he doesn't stop with algebra, but includes the calculus of rotation matrices and quaternions using material on kinematics and dynamics of rigid bodies, celestial mechanics, and rotating reference frames.

I give the book my highest recommendation. It should be considered an essential reference work for anyone who encounters rotational problems with any frequency.

--Tony Valle

4-0 out of 5 stars Good beginning, not enough for most applications
The book delivers exactly what it promises, an in-depth study of rotations using quaternions. However, if you are looking for a complete description of how to use quaternions, it is missing a lot.

Specifically it doesn't explain anything about interpolating rotations, which is absolutely required in the field of animation. After reading this book, I would recommend finding a copy of Ken Shoemake's article "Animating Rotation with Quaternion Curves", which explains slerp and squad, there are many references available on the Internet. The Flipcode.com site has some code by Tim Sweeney (lead programmer for Unreal) under "Vector Math and Quaternions", which explains how to use quaternion logarithms to handles higher-order (Hermite, Bezier, TCB) interpolations. It could be argued that this is out of the scope of the book, but I suspect many people interested in buying this book will need this information. This is the main way quaternions are used in game programming, for example.

Still, this book gives you a good starting point and its explanation of Euler angles and conversion to/from is about the best I have ever read. The derivation of quaternions as an extension of complex numbers is quite easy to follow and has a very easy-going style, which still giving a firm mathematical basis.

5-0 out of 5 stars I am the Quaternion Book's Author
I merely want to share with you an excellent review of my Quaternion Book. The review appeared in the Nov/Dec'03 issue of Contemporary Physics, vol6., and was written by Dr Peter Rowlands, Waterloo University, UK. The review is herewith attached (if I may) otherwise I'll paste the text). It's probably too long --- but you now know where to find it. Here goes:

The following Book Review Appeared in Journal: Contemporary Physics},
Nov/Dec 2003,
vol 44, no. 6, pages 536 - 537 · · ·
Quaternions & Rotation Sequences
A Primer with Applications to Orbits, Aerospace, and Virtual Reality
by JACK B. KUIPERS
Princeton University Press. 2002, £24.95(pbk), pp. xxii +
371, ISBN 0 691 10298 8.
Scope: Text.
Level: Postgraduate and Specialist. }

Quaternions are one of the simplest and most powerful
tools ever offered to the physicist or engineer. Unfortunately,
they are relatively little known because a centuryold
prejudice (the result of a family feud involving vector
theory) has been responsible for keeping them out of
university courses. The fact that quaternions have never
really found their true role has become a self-fulfilling
prophecy, despite their reappearance in various disguised
forms such as Pauli matrices, 4-vectors, and, in a complex
double form, in the Dirac gamma algebra. The straightforward
manipulation of this relatively simple formalism,
however, means that, to a quaternionist, such things as

Minkowski space-time and fermionic spin are no longer
mysterious unexplained physical concepts but merely
inevitable consequences of the fundamental algebraic
structure, while even ordinary vector algebra as David
Hestenes has shown (Space-Time Algebras, Gordon and
Breach, 1966) is much better understood in terms of its
quaternionic base. The immense value of the quaternion
algebra is that its products are ordinary algebraic products,
not the dot or cross products of standard vector algebra,
although they also include these concepts.

Despite many statements to the contrary, quaternions
are by no means short of serious applications, either. Often
in highly practical contexts, and, in every application that I
know of, where a quaternion formulation is possible, this
formulation is invariably superior to any more 'conventional'
alternative. Kuipers, in his splendid book, effectively
shows this in the eminently practical case of the aerospace

sequence and great circle navigation by demonstrating how
the same calculations are done, first by conventional matrix
methods, and then by quaternions. Rather than abstractly
defining quaternion algebra and then seeking possible
applications, he prepares the ground well by describing
the application first, and then developing the quaternion
methods which will solve it. It is not until chapter 5, in fact,
that quaternion algebra is seriously introduced. However,
Kuipers sets this on a
firm basis by establishing early on the connection with
complex numbers, matrices and rotations. These subjects
are discussed with great thoroughness in the early chapters.
The work is avowedly a primer, and so nothing is taken for
granted. The student can begin at the beginning and follow
the argument through stage by stage, with virtually no
prior knowledge of the subject. The real core of the
mathematical analysis comes in chapters 5 to 7, with solid
and relatively easy to follow treatments of quaternion
algebra and quaternion geometry, together with an algorithm
summary, relating quaternions to such things as
direction cosines, Euler angles and rotation operators. The
superiority of quaternion over, for example, matrix
methods is demonstrated by Kuipers' statement on p. 153
that the quaternion rotation operator (unlike the matrix
one) is 'singularity-free'. Following the main application to
the aerospace sequence and great circle navigation, there
are further chapters on spherical trigonometry, quaternion
calculus for kinematics and dynamics, and rotations in
phase space, with two final chapters devoted to applications
in electrical engineering (dipole radiation signals sent by a
source to a sensor, and then correlated using a processor)
and computer graphics.

The final application is especially interesting as quaternions
have been behind much of the rapid development of
computer graphics. One role that quaternions have always
fulfilled is their applicability to 3-dimensional structures,
and the otherwise difficult problem of rotation, especially
when time-sequencing is involved. Computer software
engineers have exploited this while physicists have missed
out. The creation of a 'natural' 3-dimensionality, using the
'vector' or imaginary part of quaternions was, of course,
the original reason for their creation; but, while the
remaining 'scalar' or real part was originally thought of
as a problem by the proponents of vector theory, it is now
seen as a bonus, allowing the incorporation of time as a
natural result of the algebra. We cannot escape the fact that
we live in time within a 3-dimensional spatial world, and
quaternion algebra appears to be the easiest way of
comprehending and manipulating this 3-or 4-dimension-
ality. Kuipers shows us examples of the exploitation of the
technique in aerodynamics, electrical engineering and
computer software design, but it also has relevance in
topology, quantum mechanics, and particle physics.

It is frankly as absurd for physicists and engineers to
neglect quaternions as it would be for them to disregard
complex numbers or the minus sign. It is important that
students get to learn about this spectacularly simple and
powerful technique as early as possible, and Kuipers has
provided us with the perfect opportunity of remedying a
massive defect in our technical education. His book has

everything that one could wish for in a primer. It is also
beautifully set out with an attractive layout, clear diagrams,
and wide margins with explanatory notes where appropriate.
It must be strongly recommended to all students of
physics, engineering or computer science.

DR PETER ROWLANDS
(University of Liverpool)

4-0 out of 5 stars A good introduction to quaternions
Is it possible to recommend a book and still say that it needs revision? It needs revision precisely because it is a good book and may well find more readers. The book does what no other does as far as I know; it introduces quaternions in elementary terms and shows some, at least, of how useful the concept is. The topic is neglected in textbooks for students at this level and probably even more generally. And yet I do think that the author could revise this book substantially and produce a better one.

3-0 out of 5 stars A word of caution
I was very disappointed when I started reading the book and immediately noticed a number of errors in the formulae. These were most likely typos but still can be confusing at times. As the other reviewers mentioned, the book has a very interesting, and in my opinion very good, teaching sytle, but don't take all the formulae by heart if you are going to use it as a reference book.

(PS. My comments are on the first print of the book, I hope the errors have been corrected in the later prints.) ... Read more


13. Geometric Algebra for Physicists
by Chris Doran, Anthony Lasenby
list price: $95.00
our price: $85.50
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Asin: 0521480221
Catlog: Book (2003-05-01)
Publisher: Cambridge University Press
Sales Rank: 108947
Average Customer Review: 5 out of 5 stars
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Book Description

As leading experts in geometric algebra, Chris Doran and Anthony Lasenby have led many new developments in the field over the last ten years. This book provides an introduction to the subject, covering applications such as black hole physics and quantum computing. Suitable as a textbook for graduate courses on the physical applications of geometric algebra, the volume is also a valuable reference for researchers working in the fields of relativity and quantum theory. ... Read more

Reviews (2)

5-0 out of 5 stars Compared to what ?
This is truly a great book for any one who is interested in not just physics, but physical reality. Although the ideas expressed therein have a long history and are by no means as uniquely those of its authors as were Albert Einstein's in his day, I believe that they will have comparable lasting value. Moreover the synthesis presented in this book, which builds pre-eminently on the work of Hestenes, is absolutely superb. Interested readers need not take my word for these claims, but are invited to prove it to themselves.

Although the above should be a sufficient review, my experience nevertheless indicates that it is a good idea to warn potentially enthusiastic readers against several common semantic misconceptions, lest they jump to conclusions which prevent them from ever taking that vital first step. Thus let it be clearly understood that Geometric Algebra is NOT:
(1) A replacement for linear/matrix/tensor algebra (on the contrary, it is a very nice complement to these formalisms).
(2) Identical, or even very close, to Emil Artin's earlier excellent book on bilinear forms with the title "Geometric Algebra".
(3) Another name for the enormous field "algebraic geometry" (it is indeed appropriate that the word stemming from "geometry" comes first in "geometric algebra").
(4) Just another reformulation of complex / quaternion / octonian analysis; for it connects all these purely algebraic objects, and many generalizations thereof, to Felix Klein's Erlangen Programme and Sophus Lie's theory of continuous groups.
(5) The ultimate theory of everything (although it probably will eventually be found to have something to do with it).

Geometric algebra IS a practical and natural (canonical) tool for formulating physical and mathematical problems in homogeneous spaces in a fully covariant fashion. But more importantly, you do not need to understand all those words in order to benefit from it, and this book is an excellent place for physicists of all stripes to start.

5-0 out of 5 stars Articulate Path to the Future
The quality and importance of this book could hardly be overstated. Geometric algebra might casually be considered the "correct" generalization of linear algebra. By considering, for a start, directed line segments, the linear algebra courses presently taught in some high schools and all universities achieve miracles. Although viewed by a few of the slower students as merely unpleasant bookkeeping systems, linear algebra derives its power from allowing algebraic manipulation of sophisticated aggregate objects, namely vectors. The benefits are not just computational, but stem more importantly from a more powerful and more unified, although slightly more abstract point of view than a student had before studying. Geometric algebra is all that and much more. By extending consideration from directed line segments to the inclusion of direct plane segments, directed elements of three space, etc., an extremely flexible and elegant mathematical tool arises. It allows a deeper, quicker, and more concise treatment of essentially all of modern differential geometry. Its applications throughout physics are at once simplifications of ordinary matrix treatments and occasions to allow much greater insight.

Geometric algebra is a great theory, one of highest importance. It will, undoubtedly, find a dominant place in our mathematics curriculum at the highest speed allowed by our educational systems (the highest speed being actually quite slow). This book is an especially good place to begin study. It starts from the most elementary principles, and exposes the material with very thoughtful, clear presentation. The economy and elegance of the geometric algebra itself allows this one substantial but not enormous book to reveal great insights into many branches of study, from differential geometry and its applications to gravity theory to quantum mechanics and classical mechanics.

If I had no books in my library, I would purchase a Bible. If I had only the Bible in my library, I would purchase this book next. I would certainly study this book in all detail before making a third purchase. My library already has several books in it. None of them will be read further until I finish every line, every exercise of this book. It's an important theory, and it is explained in a very useful and articulate way. This would, of course, be entirely expected if the authors were from Oxford University. Since they are only from Cambridge, we might not have expected as much, but we got it, nonetheless. ... Read more


14. Mathematics of Classical and Quantum Physics
by Frederick W. Byron, W. Fuller Robert
list price: $22.95
our price: $15.61
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Asin: 048667164X
Catlog: Book (1992-08-20)
Publisher: Dover Publications
Sales Rank: 24845
Average Customer Review: 4.83 out of 5 stars
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Book Description

Well-organized text designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism and quantum mechanics. Topics include theory of vector spaces, analytic function theory, Green’s function method of solving differential and partial differential equations, theory of groups, more. Many problems, suggestions for further reading.
... Read more

Reviews (12)

5-0 out of 5 stars An introduction to the basic mathematics of physics
This book introduces the reader to the basic mathematical structures of theoretical physics: mainly Quantum Mechanics, Electromagnetic Theory, And Classical Mechanics. I used this at UC San Diego for a year long graduate course on Mathematical methods in physics and engineering. If one has the time, there is really a lot to be gained by carefully studying this book. A big part of the book is geared toward developing in detail the mathematics of the Quantum Theory. This is a good thing because in my experience most QM books are too eager to "get to the physics". It is true that you can get by with a superficial understanding of functional analysis and still do QM, but this book will give you an immensely deeper understanding of the underlying structure of the theory. In particular, the treatment of Green's functions and integral equations is good. There is chapter on Group Theory and it's uses in QM. Also is a chapter on Complex analysis, although it is a wise idea to read a book entirely devoted to this subject. Overall, I like this book very much.

4-0 out of 5 stars A lot of fun!
The Byron & Fuller provides a serious introduction in mathematics of classical and quantum physics. This book is designed to complement graduate-level physics texts and one of its goal is to introduce the physicist to the language and style of mathematics. Consequently, this book may be really useful to people with strong skills in physics and maths. No doubt that they will have fun reading the theory of vector spaces.
For the others, just like me, not really specialized in physics and maths, but maybe just curious, this book can bring you a lot of fun too. It reminds you of what you may have studied a few years ago... And more than that, you cover with this book other fields of mathematics that are not taught to non specialized students like Hilbert space, quantum physics, theory of analytic functions, Green's functions and integral equations.

To conclude, if you're curious about mathematics and physics, you should buy this book. If you're good at maths and physics, you should already own this book.
And now, with this special price, do the maths!

5-0 out of 5 stars Terrific book to ramp up and read original papers
If you're tired of reading descriptive physics like Paul Davies' books and want to be able to read the original papers and follow the math, this is the book. It presumes a strong undergraduate math background in some areas but the explanations are clear and the proofs are easy to follow. If you want to read quantum physics, the chapters on vectors and operators will give you the math foundations.

4-0 out of 5 stars Important Information
This book is not, and I repeat, IS NOT for the inexperienced. This book is a GRADUATE LEVEL TEXT on mathematical physics. If you are an undergraduate student taking a physics class, this book will be of no use to you. I recommend that anyone interested in purchasing this book have a somewhat decent amount of mathematical background. I personally recommend Calculus I-IV, Advanced Calculus and Linear Algebra.
If, though, you have this background, then this book is may just be for you. It is concise, to the point and presents a clear and well written discussion of mathematical physics.
I just felt that before you dive, head first, into the world of mathematical physics, somebody needed to warn you about what you were getting yourself into.

5-0 out of 5 stars Fantastic
Concise and complete. I find myself coming to this book not only for Physics courses and Physics research, but I find it helpful in most Math courses. This book is a must for anyone in Physics and applied mathematics. ... Read more


15. Geometry, Topology and Physics (Graduate Student Series in Physics)
by Mikio Nakahara
list price: $55.00
our price: $55.00
(price subject to change: see help)
Asin: 0750306068
Catlog: Book (2003-10-01)
Publisher: Institute of Physics Publishing
Sales Rank: 71824
Average Customer Review: 4.29 out of 5 stars
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Reviews (7)

4-0 out of 5 stars Flat spheres and more
Highly stimulating and extremely hard to read, written for mathematicians in physics. However, the chapter on Riemannian Geometry can be worked through, up to a point, without any knowledge of exterior differential forms, and is notable if for only one fact alone: a simple calculation is provided that explains explicitly that spheres in four and eight dimensions (3-spheres and 7-spheres) are flat with torsion! I don't know another reference that a physicist without special background in math can consult to understand this highly nonintuitive fact.

2-0 out of 5 stars Just a "better than nothing" book
It's not the best way to learn geometry / topology for physics. It's better than nothing, though, if you are familiar with the topics already. There are many "holes" in Nakahara's book, which you would spend much more time and hard working in a "big" library. than you should to fill in. It's not worth that money and struggle. It's the last one you should consider about owning.

If you are a physics graduate who needs a nice guide to "understand" the aspects and skills of geo / top, I would recommend the following: (1) Milnor's Topology from the Differentiable Viewpoint, and (2) Kreysig's Differential Geometry. The first one was old, and so it does not assume much knowledge about the topic. The latter is a kind-of-Bible for the topic, and all solutions are provided for the problems. These two books will help you a lot if you care about the meaning, not only for those classroom exams or just showing off that you know something about it. Frankel is the next to put on your bookshelf as a detailed and rigorous development for your preparation to be a theoretical physicist.

If you have only a rough idea about topology, Hocking and Steen are the best choices, and they are Dover!!

Anyway, if I could find a cheap used Nakahara, I would get it as a reference.

5-0 out of 5 stars Best in its genre
I suppose I should preface this by saying that I read this book *after* reading similar books, so my ability to understand this book is probably better than others, but that said, I think that my comparative evaluation is free from this bias...

There seem to be a few books on the market that are very similar to this one: Nash & Sen, Frankel, etc. This one is at the top of its class, in my opinion, for a couple reasons:

(1) It's written like a math text that covers physics-related material, not a book about mathematics for physicists. I prefer this; you may not. As a consequence, this book is more rigorous than its alternatives, it relies less on physical examples, and it cuts out a lot of lengthy explanation that you may not need. Of course, there are drawbacks to all of these "features" -- you need to decide what you need and what's best for you.

(2) It's most comprehensive, with Frankel coming in second, and Nash & Sen least comprehensive (though they have quite a bit on Fibre bundles and related topics). Nakahara has a chapter on complex manifolds, which is absent from the other two. Nakahara also concludes with a nice intro to string theory, which is absent from the other two as well (though nothing you couldn't find in Polchinski or the like). Actually -- I modify this slightly. Frankel covers less subjects than Nakahara, but with more depth (though also more wordiness -- I quit Frankel about 2/3 through because it wasn't succinct enough and I got tired of it).

Depending on your tastes, I would recommend this book before the other two.

It presupposes that you have an understanding of algebra (groups, rings, fields, etc.) but it has an introduction to the necessary components of topology within. Frankel has presupposes both algebra and topology; Nash & Sen presupposes only algebra.

5-0 out of 5 stars Excellent book
A very nice blending of rigor and physical motivation with well chosen topics. Plenty of examples to illustrate important points. Especially noteworthy is its description of actions of lie algebras on manifolds : the best I have read so far.

Most of the topics are intepreted in terms of their topological/geomtrical structure (and the interplay between those two), but that's what the title of the book says. So you will learn things again in new ways, and gain a powerful new set of tools. If nothing else, it gives you a nice warm fuzzy feeling when you read other field/string theory books that glosses over the mathematics.

One minor rant : the notation of the book can be better. I personally uses indices to keep track of the type of objects (eg. greek index=components of tensors, no index=a geometrical object etc..), but Nakahara drops indices here and there "for simplicity". But that's my personal rant.

Good book. Buy it.

5-0 out of 5 stars A must for any theoretical physicist
With an excellent balance between mathematical rigor and pedagogical simplicity, Nakahara remarkably captures in a single volume much of the mathematics a physicist will ever need. (If he wrote a few chapters on group theory, 'much' might be replaced with 'all'). Containing as much as it does, it is not something to breeze through. Depending on your mathematical background, you may only want to read a few chapters (and if the Homology chapter is tripping you up, just keep moving). But invest the time with it, and you will be rewarded with a solid grasp of the mathematical pictures underlying most modern physics. And once you read it and see physics from this perspective, you'll be amazed you had ever thought you understood the physics it describes. It should be said, though, that some of the latter chapters, in particular 12, are horribly sloppy. There are dozens upon dozens of errors, many at a deep conceptual level. Nonetheless, it is a monumental text, and I recommend it heartily. ... Read more


16. Understanding Molecular Simulation
by Daan Frenkel, Berend Smit
list price: $70.00
our price: $57.40
(price subject to change: see help)
Asin: 0122673514
Catlog: Book (2001-10-15)
Publisher: Academic Press
Sales Rank: 131235
Average Customer Review: 4.75 out of 5 stars
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Book Description

Understanding Molecular Simulation: From Algorithms to Applications explains the physics behind the "recipes" of molecular simulation for materials science. Computer simulators are continuously confronted with questions concerning the choice of a particular technique for a given application. A wide variety of tools exist, so the choice of technique requires a good understanding of the basic principles. More importantly, such understanding may greatly improve the efficiency of a simulation program. The implementation of simulation methods is illustrated in pseudocodes and their practical use in the case studies used in the text.

Since the first edition only five years ago, the simulation world has changed significantly -- current techniques have matured and new ones have appeared.This new edition deals with these new developments; in particular, there are sections on:

ú Transition path sampling and diffusive barrier crossing to simulaterare events
ú Dissipative particle dynamic as a course-grained simulation technique
ú Novel schemes to compute the long-ranged forces
ú Hamiltonian and non-Hamiltonian dynamics in the context constant-temperature and constant-pressure molecular dynamics simulations
ú Multiple-time step algorithms as an alternative for constraints
ú Defects in solids
ú The pruned-enriched Rosenbluth sampling, recoil-growth, and concerted rotations for complex molecules
ú Parallel tempering for glassy Hamiltonians

Examples are included that highlight current applications and the codes of case studies are available on the World Wide Web. Several new examples have been added since the first edition to illustrate recent applications. Questions are included in this new edition. No prior knowledge of computer simulation is assumed.
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Reviews (4)

5-0 out of 5 stars Perfect for New Grad Students
This book is how I bootstrapped my way into being a molecular simulationist. Anyone who can program in some language can get started writing simple routines for the basic MD and MC simulations.

I do Monte Carlo simulations at Princeton, and found this book to be the most helpful available for getting my research started. It is my most common reference, and is used extensively in writing background information for various research documents.

However, after you have written your first few codes, you will pass the level of this book and need to move on. I use it less now than I did my first year.

Every student in my group (Panagiotopoulos) has this book I think. And like me, they started with it, but moved on.

4-0 out of 5 stars A nice disappointment
The title of the book is overly ambitious and falls short on its promises. The book is a good introduction to Molecular Mechanics (MM), Molecular Dynamics (MD) and Monte Carlo (MC) methods, with detailed descriptions of the methods used and FORTRAN (pseudo)code, covering from the basics to some middle-level and some advanced algorithms.
But it does NOT cover all the fields of Molecular Modelling, just the three mentioned (MM, MD and MC), there's no coverage of quantum mechanics methods, nor QSAR or other technologies. And, while it described the algorithms, I can't think of it going all the way through up to building applications. For this, Rapaport's makes a better job, and for a general intro to Molecular Modelling, Grant & Richards' Computational Chemistry is more comprehensive (albeit at a more superficial level). Nor does it provide much detail on the methods used in modelling biological macromolecules, an increasing application field for the methods discussed in the book.
All in all, this book fails to satisfy its cover title, it won't introduce to the whole field (just the areas of MM, MD and MC) nor does it go up to application level. But it IS a REAL GOOD introduction to the subjects covered and their basic algorithms,
with sample code, detailed descriptions and plenty of references to specialized articles, texts and resources.

5-0 out of 5 stars An excellent introduction
This book is an excellent introduction to the field of molecular dynamics simulation. It is easy to follow for a scientist entering the field and at the same time contains overview of most critical topics in MD simulation. The book's major goal is to describe how to simulate liquids, however it also mentions briefly the methods for gas and liquid simulations. List of references for further readings is very useful and complete.

5-0 out of 5 stars A great book for begginers.
This book covers many interesting topics in molecular simulation, both Monte Carlo and M.D. It focuses on understanding the main ideas rather than giving long codes. It's a good place to start, but it also covers some ideas not found in many other books. When I try to extend my molecular dynamics program I always check what Frenkel and Smit have to say about it. ... Read more


17. The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
by David Salsburg
list price: $16.00
our price: $10.88
(price subject to change: see help)
Asin: 0805071342
Catlog: Book (2002-05-01)
Publisher: Owl Books (NY)
Sales Rank: 20927
Average Customer Review: 4.14 out of 5 stars
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Book Description

An insightful, revealing history of the magical mathematics that transformed our world.

At a summer tea party in Cambridge, England, a guest states that tea poured into milk tastes different from milk poured into tea. Her notion is shouted down by the scientific minds of the group. But one man, Ronald Fisher, proposes to scientifically test the hypothesis. There is no better person to conduct such an experiment, for Fisher is a pioneer in the field of statistics.

The Lady Tasting Tea spotlights not only Fisher's theories but also the revolutionary ideas of dozens of men and women which affect our modern everyday lives. Writing with verve and wit, David Salsburg traces breakthroughs ranging from the rise and fall of Karl Pearson's theories to the methods of quality control that rebuilt postwar Japan's economy, including a pivotal early study on the capacity of a small beer cask at the Guinness brewing factory. Brimming with intriguing tidbits and colorful characters, The Lady Tasting Tea salutes the spirit of those who dared to look at the world in a new way.
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Reviews (22)

5-0 out of 5 stars Wonderfully well written, entertaining, and informative
The intense media attention given to the proof of Fermat's Last Theorem a few years ago was followed by the publication of many books on mathematics for non-mathematicians. Dr. Salsburg's book is arguably among the best of them. It has many interesting and illuminating anecdotes about the most influential statisticians in the early 20th century, which is when the Statistical Revolution (as aptly called by the author) took place. Important developments are clearly explained in their historical context, and their implications for current (i.e., 21st century) scientific research are given. The student of Statistics will get to know the people behind the names mentioned in the textbooks. The book is non-technical and written for the general public, but as a statistician myself I can say that I was no less than delighted reading it. In fact, two chapters (on probit and sample selection) deal with concepts I'm using in an epidemiological manuscript!

5-0 out of 5 stars great look at statistics in the 20th Century
The Lady Tasting Tea is a new book by David Salsburg (a Ph.D. mathematical statistician, who recently retired from Pfizer Pharmaceuticals in Connecticut). The title of the book is taken from the famous example that R. A. Fisher used in his book "The Design of Experiments" to express the ideas and principles of statistical design to answer research questions. The subtitle "How Statistics Revolutionized Science in the Twentieth Century" really tells what the book is about. The author relates the statistical developments of the 20th Century through descriptions of the famous statisticians and the problems they studied.

The author conveys this from the perspective of a statistician with good theoretical training and much experience in academia and industry. He is a fellow of the American Statistical Association and a retired Senior Research Fellow from Pfizer has published three technical books and over 50 journal articles and has taught statistics at various universities including the Harvard School of Public Health, the University of Connecticut and the University of Pennsylvania.

This book is written in layman's terms and is intended for scientists and medical researchers as well as for statistician who are interested in the history of statistics. It just was published in early 2001. On the back-cover there are glowing words of praise from the epidemiologist Alvan Feinstein and from statisticians Barbara Bailar and Brad Efron. After reading their comments I decided to buy it and I found it difficult to put down.

Salsburg has met and interacted with many of the statisticians in the book and provides an interesting perspective and discussion of most of the important topics including those that head the agenda of the computer age and the 21st century. He discusses the life and work of many famous statisticians including Francis Galton, Karl Pearson, Egon Pearson, Jerzy Neyman, Abraham Wald, John Tukey, E. J. G. Pitman, Ed Deming, R. A. Fisher, George Box, David Cox, Gertrude Cox, Emil Gumbel, L. H. C. Tippett, Stella Cunliffe, Florence Nightingale David, William Sealy Gosset, Frank Wilcoxon, I. J. Good, Harold Hotelling, Morris Hansen, William Cochran, Persi Diaconis, Brad Efron, Paul Levy, Jerry Cornfield, Samuel Wilks, Andrei Kolmogorov, Guido Castelnuovo, Francesco Cantelli and Chester Bliss. Many other probabilists and statisticians are also mentioned including David Blackwell, Joseph Berkson, Herman Chernoff, Stephen Fienberg, William Madow, Nathan Mantel, Odd Aalen, Fred Mosteller, Jimmie Savage, Evelyn Fix, William Feller, Bruno deFinetti, Richard Savage, Erich Lehmann (first name mispelled), Corrado Gini, G. U. Yule, Manny Parzen, Walter Shewhart, Stephen Stigler, Nancy Mann, S. N. Roy, C. R. Rao, P. C. Mahalanobis, N. V. Smirnov, Jaroslav Hajek and Don Rubin among others.

The final chapter "The Idol with Feet of Clay" is philosophical in nature but deals with the important fact that in spite of the widespread and valuable use of the statistical methodology that was primarily created in the past century, the foundations of statistical inference and probability are still on shaky ground.

I think there is a lot of important information in this book that relates to pharmaceutical trials, including the important discussion of intention to treat, the role of epidemiology (especially retrospective case-control studies and observational studies), use of martingale methods in survival analysis, exploratory data analysis, p-values, Bayesian models, non-parametric methods, bootstrap, hypothesis tests and confidence intervals. This relates very much to my current work but the topics discussed touch all areas of science including, engineering in aerospace and manufacturing, agricultural studies, general medical research, astronomy, physics, chemistry, government (Department of Labor, Department of Commerce, Department of Energy etc.), educational testing, marketing and economics. I think this is a great book for MDs, medical researchers and clinicians too! It will be a good book to read for anyone involved in scientific endeavors. As a statistician I find a great deal of value in reviewing the key ideas and philosophy of the great statisticians of the 20th Century.

I also have gained new insight from Salsburg. He has given these topics a great deal of thought and has written eloquently about them. I have learned about some people that I knew nothing about like Stella Cunliffe and Guido Castelnuovo. It is also touching for me to hear about the work of my Stanford teachers, Persi Diaconis and Brad Efron and other statisticians that I have met or found influential. These personalities and many other lesser-known statisticians have influenced the field of statistics.

The book includes a timeline that provides a list in chronological order of important events and the associated personalities in the history of statistics. It starts with the birth of Karl Pearson in 1857 and ends with the death of John Tukey in 2000.

Salsburg also provides a nice bibliography that starts with an annotated section on books and papers accessible to readers who may not have strong mathematical training. The rest of the bibliography is subdivided as follows: (1) Collected works of prominent statisticians, (2)obituaries, reminiscences, and published conversations and (3) other books and article that were mentioned in this book.

The book provides interesting reading for both statisticians and non-statisticians.

4-0 out of 5 stars What happened to Frank P. Ramsey?J M Keynes?
Salsburg(S) does an excellent job discussing the historical development of the field of statistics in the 20th century.He has a way of writing that blends current statistical theory with the development of statistics over time from a historical perspective with the individuals who made it all happen,such as Neyman-Pearson and Sir Ronald Fisher.In this book he is close to Ian Hacking in the manner in which he weaves his story.This reviewer has a few quibbles.First,in S's discussion of the personalist(subjectivist)theory of probability,only de Finetti and Savage are covered.Since Frank Ramsey's 1922 and 1926 contributions to the subjective theory of probability,unfortunately combined with error filled critiques of John Maynard Keynes's logical theory of probability,were published BEFORE the work of de Finetti and Savage,he definitely deserved to have a prominent place in any book dealing with the history of probability and statistics.Second,there are a number of errors made in the all to brief discussion of Keynes and his logical theory of probability in his 1921 book,A Treatise on Probability(TP).Contrary to S(p.112,p.305),Keynes never received a doctorate in philosophy for writing the TP because the TP is not a doctoral dissertation.The TP was a thesis submitted for a fellowship, successfully, in 1909 at Cambridge.Keynes added a Part V to his thesis in the period from 1910-1914 to complete his TP.S commits another error when he chacterizes Keynesian economic policy as the manipulation of monetary policy.It is the manipulation of both fiscal and monetary policy.Finally,Keynes's probabilities are primarily intervals with a lower and an upper bound,not ordinal rankings as suggested by S.S's flawed appraisel involves a failure to translate Keynes's definition of the term "nonnumerical",which means"not by a single numeral but by two numerals".Finally,S is in too much of a hurry to take the side of Neyman,a deductivist, in his debates with Fisher,an inductivist,about significance levels(p-values) and confidence intervals.Neyman's justification for confidence intervals is badly flawed.It essentially boils down to an arbitrary "act of will" on the part of the researcher.Fisher,who was well acquanted with Keynes's logical theory of probability,realized that Neyman's "reasoning" was actually an evasion.Unfortunately,Fisher never was clear about his reservations .Fisher simply needed to come right out and say that a 95% confidence interval means that the researcher is 95% confident that the particular parameter,say the mean,lies in that interval.Of course,this conclusion follows from the proportional syllogism,which is part of the logical theory of probability.Neyman,who was a frequentist,ends up in a quagmire of his own creation because he did not want to allow any "inductive" concepts into his theory.

4-0 out of 5 stars Noble effort, and entertaining.
It should come as no surprise to any reader that a 300 page collection of anecdotes might fall a bit short in realizing the implied goal in Salsburg's subtitle. He attempts to explain the paradigmatic shift in science from a Newtonian determinism to a probabilistic worldview by focusing on the statisticians themselves. The reader is often left with a desire for more - either more explanation of the paradigm shift or more anecdotes.

Nonetheless, I found this volume entertaining. I was fascinated by the newness in this field. Certainly nothing in my education led me to believe that virtually every aspect of social science research and statistical analysis is a 20th century invention. Who would have thought that the essence of 21st century social science research would be so well-anchored in agricultural studies and, perhaps most importantly, in the quality control efforts by master brewers at Guinness?

Salsburg intends to write to a non-statistical audience in language that can be understood without mathematic symbols. In this he is only partly successful. He does avoid technical symbols and most technical jargon, but in doing so he is often too vague to make his point clear. Even with three years of graduate statistics (from a social science perspective), I often found myself unsure of his explanations.

In the final analysis, Salsburg's description of the "statistical revolution" in science is really more of a sketch than a portrait. The significances of a shift from certainty to probability cannot be easily explained, but I will give him credit for trying to do so. That he is able to deal with this shift without explicitly commenting on the implications of this shift for religion, values, meaning, and justice is perhaps one of this book's major strengths.

Unfortunately, Salsburg concludes with a critique of the statistical revolution that may weaken the impact of his stories. Those desperately holding onto a Newtonian worldview could use this critique to discount 20th century science, especially social science. If, as Salsburg suggests, we are on the cusp of another paradigm shift, any post-statistical revolution is unlikely to be advanced by those continuing to resist the statistical one.

5-0 out of 5 stars Pleasing intro to statisctics for lay(wo)men
An intriguing story based introduction to the fast field of
statistics. No formulas but still plenty of math terms explained
as easily as possible. The life stories of many statisticians
are combinded with the history of certain statistical problems.
This book showed me how huge the field of stastics is.
Statistics and Probability seem now to be scientific issues
on not just ways for politicians to cheat the public. In
everyday life, any mention of a statistic result causes at best
a compasionate smile. But this book changed that for me and I'd
like to learn more about this topic. ... Read more


18. Methods of Theoretical Physics, Part I
by Philip McCord Morse, Herman Feshbach
list price: $220.10
(price subject to change: see help)
Asin: 007043316X
Catlog: Book (1953-06-01)
Publisher: McGraw-Hill Science/Engineering/Math
Sales Rank: 560910
Average Customer Review: 4.67 out of 5 stars
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Reviews (3)

4-0 out of 5 stars A Classic but dated & expensive - paperback coming soon
In response to questions from colleagues and students i'm posting this review.
This was the standard text many years ago.
Many current topics on mathematical Quantization and Stochastic Optimization are conspicuously abscent.
The publisher is working on a two Volume Paperback edition that will be available shortly, so save your money and buy this 2-vol set for one fifth the price.

5-0 out of 5 stars A hard but superb book.
Current physics students had less mathematical trainings than those did several decades ago, when computer wasn't popular. So this book is probably too hard to read through and to work on its problems. But if you force yourself, you will begin to appreciate the beauty of mathematics. The chapter about Green's function is escpecially good, never had a so vivid lecture on Green's function before. Actually, when I read this book, I felt Green's function is the kernel and the main bone of this book. It appears almost in every chapter.

The price is pretty high, but if you choose physics as your career, it's worth to have this book, both for academic and entertaining purposes.

5-0 out of 5 stars THE classic text
The classic text, still excellent, tho' somewhat dated. Well worth having because (a) the physical viewpoint is helpful for theorists and easier for experimentalists, (b) the older viewpoint is different from that of more modern texts, and still worthwhile; multiple viewpoints increase understanding. ... Read more


19. Mathematical Physics
by Sadri Hassani
list price: $89.95
our price: $89.95
(price subject to change: see help)
Asin: 0387985794
Catlog: Book (1998-12-21)
Publisher: Springer-Verlag
Sales Rank: 334663
Average Customer Review: 4.4 out of 5 stars
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Book Description

This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained. The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws. Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.

FROM THE REVIEWS:

PURE APPLIED GEOPHYSICS "This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear...The typesetting standard is one of the best I have ever seen...The book should already be accessible to advanced undergraduates. It can be used both as a textbook or as a reference book (to some extent)...As a supplementary textbook I believe this book should be sufficient for most physics courses...Among all the available book treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."

LIBRARY OF SCIENCE "MATHEMATICAL PHYSICS will benefit two different classes of readers: first, physics students who are interested in the mathematics they use; and second, math students who are interested in seeing abstract ideas some alive in an applied setting. Unlike many books with the same subject and scope, Hassani's text manages to strike a successful balance between formalism and application, and between the abstract and the concrete...A further notable feature of the book is its success in exhibiting the interrelations among various topics. Indeed, Hassani uses the underlying theme of a vector space, which surfaces throughout the book, to alert readers to the connection between various seemingly unrelated topics...A further benefit concerns Hassani's presentation of biographical details of the men and women of mathematics and physics. Doing so defies the current trend of 'ahistoricism' in many mathematical and physics texts, and pays fitting tribute to the life stories of the people behind the ideas...Impressive in breadth and scope, [this book] may become the definitive text in this profoundly important area." ... Read more

Reviews (5)

4-0 out of 5 stars Comparison with Cantrell's book
Has anyone looked at the difference between Hassani's and C. D. Cantrell's book (Modern Mathematical Methods for Physicists and Engineers)? They seem to cover the same topics.

4-0 out of 5 stars A pleasure to read
I agree with other reviewers that this book is the first choice if you want to get a handle on mathematical methods of theoretical physics at advanced undergraduate / beginning graduate level. The nearest competitor is Byron & Fuller's "Mathematics of Classical and Quantum Physics" which has been around a long time and has many good points; but having used both I prefer this. The level and philosophy is about the same but the coverage is wider and the presentation clearer and cleaner. It's a pleasure to read.

The book is divided into eight parts, each comprising three or four chapters, on: Finite-dimensional Vector Spaces, Infinite-dimensional Vector Spaces, Complex Analysis, Differential Equations, Operators on Hilbert Spaces, Green's Functions, Groups and Manifolds, Lie Groups and Applications. Fear not: although it isn't designed for freshmen, it emphatically isn't the sort of math book where you have to crack the code to get any benefit.

The layout is excellent, there are many, many worked examples, and I found very few slips or typos. One black mark, the reason I don't give it 5 stars: although there are a massive 850 problems, there are no solutions (just like Byron & Fuller). Unless you're confident in your mathematical ability, you may find that a drawback for self-study. Finally, a word to the wise: check out this title at amazon.co.uk (provided you aren't in a hurry).

5-0 out of 5 stars A must for a serious student of theoretical physics.
I have never seen an excellent and well written math book like this. It includes all topics you can think about of mathematical physics in a clear and elegant presentation. A generous amount of solved examples are disscused through the book and a huge number of problems at the end of each chapter. It includes topics which you can not find in any similar graduate math-physics text. It really worth its price.

5-0 out of 5 stars Outsdanding. Highly recommended.
This is by far the best written book on the subject that I've seen. It is very clear and comprehensible. Modern and up-to-date, it is destined to become the standard book in its field.

4-0 out of 5 stars Possibly one of the best of its kind
Up-to-date, thorough, clear and reasonably rigorous, this volume sets a new standard in mathematical physics textbooks. It is so good that the reader can only hope for a few more pages (path integrals, topology) in a new edition or another book. ... Read more


20. Lattice-Gas Cellular Automata : Simple Models of Complex Hydrodynamics (Collection Alea-Saclay: Monographs and Texts in Statistical Physics)
by Daniel H. Rothman, Stiphane Zaleski
list price: $65.00
our price: $65.00
(price subject to change: see help)
Asin: 0521607604
Catlog: Book (2004-12-23)
Publisher: Cambridge University Press
Sales Rank: 471050
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Book Description

The text is a self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases. Lattice-gas cellular automata are discrete models of fluids. Identical particles hop from site to site on a regular lattice, obeying simple conservative scattering rules when they collide. Remarkably, at a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes equations of fluid mechanics. This book addresses three important aspects of lattice gases. First, it shows how such simple idealised microscopic dynamics give rise to isotropic macroscopic hydrodynamics. Second, it details how the simplicity of the lattice gas provides for equally simple models of fluid phase separation, hydrodynamic interfaces, and multiphase flow. Lastly, it illustrates how lattice-gas models and related lattice-Boltzmann methods have been used to solve problems in applications as diverse as flow through porous media, phase separation, and interface dynamics. Many exercises and references are included. ... Read more


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