A text full of symmetries and witting
351929
This text shows extensive textual analysis and revealing nexus between two major figures of Spanish literature: a definite must have.
135381
The Particle Explosion (1987) by Oxford University Press tells the story of particle physics from the unexpected discoveries of electrons, x-rays, and radioactivity in the 1890s to the meticulously planned, large scale experiments nearly a century later that detected the W and Z particles, thereby confirming the Standard Model.

The three authors - Frank Close, Michael Marten, and Christine Sutton - should be commended for the exceptional set of photos that make this book so fascinating.  The target audience is the enthusiastic layman, but this account should also appeal to all science students, especially undergraduate physics majors.

Even numbered chapters focus on the researchers and their massive machines. Odd numbered chapters describe the subatomic particles. This unusual even-odd arrangement is surprisingly well-integrated and does not attract attention to itself.

The Particle Explosion is true to its title. The reader encounters neutrinos, muons, pions (pi-zero, pi-plus, pi-minus), kaons (K-zero, K-plus, K-minus), J/PSI, D (D-zero, D-plus), upsilon, lambda, sigma (sigma-zero, sigma-plus, sigma-minus), xi (xi-minus, xi-zero), omega minus, and charmed lambda. And don't forget, there is an antiparticle for every particle as well as resonance states for many particles.  Fortunately, Murray Gell-Mann and others bundled these bewildering particles into well-behaved symmetry groups.

Rather unexpectedly, I actually developed some skill at deciphering images of particle tracks from cloud chambers, bubble chambers, and various electronic detectors. I found that I could even recognize indications of missing particles.  Nonetheless, complicated images revealing quarks and gluons remain intimidating. Computer processing is needed to remove unrelated low-momentum tracks, and thereby expose the unique signatures of high energy quarks.

As fate would have it, I no sooner completed this book review than I learned that a 2002 edition with the title The Particle Odyssey (same three authors) was available. The new layout is quite similar. The material has been updated to cover the years 1987-2002 and the graphics are even better.

Recommendation: Deep Down Things (John Hopkins Press, 2004) by Bruce A. Schumm offers a more technical look at the Standard Model. Five stars.
105950
Students plod through Applied Math graduate courses with desk tops groaning under many supplementary texts - linear algebra, Functional Analysis and some Upper-level Physics/ Electrical Engineering books. Learning a new topic often involves frantic hunting through numerous texts to refresh one's memory of the underlying concepts. The primary strength of Hassani's book is to spare the reader of this "where is Waldo?" tedium.

Hassani first introduces the concept of a vector space and gives numerous examples including the less "intuitive" function spaces and matrix spaces. He quickly builds upon this idea to encompass linear operators, algebras and functions defined in terms of them. Hassani's sweep of basic concepts is comprehensive and thorough while seamlessly weaving in ideas from many different branches of mathematics that provide the edifice for much of modern physics. The side notes enable one to browse through the book and find a particular topic.  Interspersing the text with short biographical sketches of mathematicians who made important contributions to the field within the past three centuries adds further interest to the book.

The author has devoted much of the book to those special functions that emerge as solutions to the prototype differential equations of Physics. These functions are presented at a more generalized and rigorous mathematical setting than in many Mathematical Physics books aimed at beginning graduate students while sparing the more tedious proofs all too common in books on Functional Analysis, for example. In particular, his exposition of Green functions and Operator Theory are much more comprehensive and easy to follow than comparable treatment in other texts targeting the same readership.

Hassani continues on through Lie Groups to end this tome with a look at symmetries and conservation laws. The latter are especially relevant in Quantum Field Theory and HEP. Topics given cursory treatment in texts on these subfields of Physics are presented by Hassani in greater detail, again sparing the reader the mathematics that often serve more to sidetrack that edify.

Given the subject matter, it is no easy task to produce such a user-friendly tome, but Hassani has admirably risen to the task. I look forward to more texts by the author, perhaps one with more emphasis on Measure Theoretic approaches?
3783432
The main public of the book is the undergrad (or grad) physics student who wants to make a tour of these functions. The approach, at least during the first 7 chapters is mainly through Series. The required knowledge is minimal (math 201) and whatever is needed is nicely introduced at the begining.

The book is well written and  easy to read

In the first chapter, the author shows how to solve linear second order differential equation by power series and obtain directly the power serie expansion of the solution.

Second Chapter is devoted to the differential equation defining hypergeometric function and its solution in power series. Generalizing this expression gives rise to "generalized hypgeos" and "confluent hypgeos".

The next 3 chapters are variations around this theme, begining with various equations of mathematical physics (penduluum, harmonic oscillators of quantum mechanics, wave equation with cylindric symetry, ...), obtaining the power serie solutions and the defining functions (elliptic, hermit, bessel,...) and show their relation to heyper gemotric functions.

Chapter 7 and 8 introduce complexe numbers and contour integration, which allows the author to come back and define the various functions by definitie integrals, rodriguez formula, generating functions, recursion formula and so on.

In conclusion, this is a pretty complete overview of special functions and easy to read.
492379
The book has 3 parts: 50 pages of basic introduction to general group theory including matrix Lie groups, 50 pages on vector spaces including infinite dimensional Hilbert spaces, and 50 pages on group representations and characters. Also there are 40 problems (at the necessary beginner level to help you digest the new concepts) with detailed solutions. The material was selected as a preparation to group theory in Quantum Mechanics. It is NOT a discussion of the usage of groups in QM and Elementary Particles.

Amazingly, the book combines rigor (almost all theorems are proven, also you are asked to construct proofs in the exercises) with a  human-language motivation of the definitions. Thus, the typical dryness of a mathbook or the typical hand-waving of a physics book have been avoided.

Before reading that book, I have had a one quarter course in group theory that covered approximately the same topics. Compared to the course, the book not only gives you the definitions but also makes you understand why a concept is important, thus beating the hell out of the course.

If you learned about Hilbert spaces from a Quantum Mechanics course and you think you know everything about them - you are deeply wrong - read and see ...

You can read that slim book and solve all the problems in a reasonable pace for one month - 3 times faster than a course and you will know the same material at better level.

I am amazed that nobody has written a review on that book before but as usually happens good things are not necessarily well known.
567046
Written in a attractive and even seductive way, relying more on Lie algebraic language than is typical, this book is probably as stimulating an intro. to modern geometry as you can find, within certain limits. The section on noncoordinate bases might have been more clearly written, however. Frobenius's theorm is discussed, something that Fomenko et al should have covered, and the section on connections can be worked throuigh independently of the heavy machinery of exterior differential forms, which is attractive for physics students.
2396263
The authors are college professors in mathematics who also have extensive experience with sudoku puzzles. In this book, they cover a range of mathematical considerations from quite elementary to advanced, discussing sudoku puzzles from a number of different perspectives and drawing many interesting conclusions. In several cases, they analyze a smaller sudoku-like grid that uses entries only from 1-6 to simplify the math.

Also enjoyable are a number of unsolved puzzles of various sorts, some quite unusual or advanced versions of the sudoku puzzles published in daily newspapers, etc. (with complete solutions provided at the end of the book).

Anyone interested in the mathematical underpinnings of these ubiquitous puzzles will find this book a worthwhile read.
545658
Very good text if you want to learn Poincare duality and cohomology rings of spaces. Fundamental theorems of homological algebra such as Kunneth's theorem and universal coefficient theorems are also thouroughly discussed. I think a good strategy is to use Hatcher's book for Fundamental groups, covering spaces, homology and cohomology before Poincare duality and move to Munkres for cup product, cap product and Poincare duality.
890706
An interesting combination of an autobiography and the latest developments in the unification of branches of mathematics and their potential application in theoretical physics. The biographical aspect of the book are fun to read, the unification of mathematics require more concentration and I found more interesting.
4284466
Whereas the only way that you'll be able to fully understand this author's enigmatic style and classical education is to read his other works more than once and parse his keyed language, at least in this instance there are clear visual references for the lattice of his cards after having been painted so beautifully by Lady Frieda Harris. Descended of the Golden Dawn and blinded by correspondence confusion, this work, one of his last, includes esoteric and rudimentary oracular instruction for any usage. It has minimum value without the deck for which it is a manual, excepting that one would seek to assimilate the abstruse knowledge and understanding of the Master. Helpfully organized by conventional and symbolical categories, it is festooned occasionally with confounding and arcane diagrams perhaps designed or organized so as to confuse the non-initiate to his cults (see a minor example below from page 284, wherein some reshuffling of the the data has obviously occurred during handling, initiate notes included).

I obtained a new copy of this edition recently to supplement my 1970s tattered and worn, heavily-marked-up, book. It was helpful to see the original text without the haze of scribbles and annotations. It is a classic text well-suited for those who plan to submit to the arrogance and outrageous opinions of the Beast 666, Aleister Crowley (amongst his numerous other pseudonyms, nomes de plume, and initiatic conceits). The egyptomania inherent to the presentation should not overly-persuade the interested to fall under the spell that this is some genuine "Book of Thoth" such as may be spoken of in hushed tones by mystics and magicians after the very deities like Tahuti-Thoth. That would best be reserved for some tarotic implement, perhaps inclusive of the one for which this is a Large White Book.
333
4436594
I love this little guy. Written by two students of the eminent theoretical physicist Chen-Ning Yang, it captures all the essential features of Yang's (and Mills') beautiful idea: the deep and powerful geometrical  interpretation of general (classical and quantum) fields derived from the  deceptively simple principle of gauge invariance. Although it requires some  knowledge of field theory, it doesn' t force the reader to study hundreds  of pages of prerequisites to understand the topics treated. It follows a  very wise philosophy about the maths of gauge theory, by not slaughtering  the reader's mind with lots of differential geometry right at the beginning  of the book, although it accomplishes to discuss even some quite esoteric  topics, as how Alain Connes' noncommutative geometry may arise in  non-conventional field theories (e.g., string theory). Even people already  acknowledged with gauge theories may learn one or more things from this  book.
609792
This book consists of an interesting assortment of articles all presented in honor of the scholar V.H. Viglielmo. In the preface the editors note that festschrifts such as this are often criticized for being a mixed bag and then argue that this one is different in having a unifying theme. Hmm. Maybe, but as a glance at the article titles below will show, the mixed bag effect is still pretty strong--which is just fine with me anyway. I rather enjoy an eclectic mix. The unifying principle really is the various contributors' deep respect and affection for Viglielmo, which is the way it should be in a work of this nature. Still, Viglielmo's influence as a mentor is apparent in a number of the articles, and the impact of his highly important, pioneering work in the literature of Natsume Soseki and the philosophy of the Kyoto School is especially clear.

Like I said, I don't mind the "mixed bag" effect, but other things did annoy me slightly. The second article is in German, for instance, which seems silly to me in an American publication predominantly in English. What I can make of the title sounds quite intriguing, too, but not so much so that I'm willing to learn a whole language from scratch. I found the other articles generally interesting and full of neat insights, even the ones not dealing with Soseki or Watsuji (my own pet interests), but sometimes the quality was a bit uneven and a few in particular seemed not quite ready for prime time, if you get my drift. A couple of instances of mild Japan-essentializing were rather jarring in this regard, as was an odd scorn for Japan's indigenous poetic tradition and hints of a patronizing attitude on the part of one contributor who otherwise makes some good observations. In the case of a partially informal publication such as this, though, it would be mean-spirited to dwell too much on these lapses, most of which are minor bumps anyway--easily outweighed by the overall fine scholarly quality of the collection as a whole, a fitting tribute to an excellent scholar.

The articles are as follows:

1. "Brief Memoir of a Japan Basher" by Edward Seidensticker

2. "Tariki--Uber Shinrans und Tanabes Verstandnis des 'Wirkins' der 'Anderen Kraft' in der metanoetischen Wandlung des Selbst" by Johannes Laube

3. "Shinran: Religious Consciousness and True Individuality" by Alfred Bloom

4. "The Phenomenology and Logic of Interpresence in Watsuji Tetsuro and Nishida Kitaro" by David A. Dilworth

5. "On Nature" by Nisitani Keiji (translated by Setsuko Aihara and Graham Parkes)

6. "The Influence of William James and Henri Bergson on Natsume Soseki's 'Higan Sugi Made'" by Harue Summersgill

7. "Natsume Soseki's 'Mon' (The Gate) and Dostoevsky's 'Crime and Punishment': Understanding Soseki's Sokuten Kyoshi" by Nakayama Etsuko

8. "Natsume Soseki's 'Nowaki', A Novella" by William Ridgeway

9. "The Twelve-Part Story of Lady Joruri" by Frederick Kavanagh

10. "Higuchi Ichiyo's 'Wakaremichi', Modern Punctuation, and Genbun Itchi" by Kyle Ikeda

11. "Grief and Guilt: A Study of Hagiwara Sakutaro's 'Night Train' (1913)" by Robert Epp

12. "Kawabata Yasunari's Concept of Beauty" by Gladys Nakahara

13. "Nakajima Atsushi's 'Gojo Tan`i': An Intertextual Reading in Relation to 'Faust' and 'Zarathustra'" by Nobuko Miyama Ochner

14. "Oe Kenzaburo and the Fifty-Year Postwar Period" by Nobuko Pugarelli Aoshima

15. "William Faulkner's Visit to Nagano" by Travis Summersgill

16. "Japan and Japanese in Brazil's Literature" by Edgar C. Knowlton, Jr.

17. "'Boku' in Edo Epistolary Texts" by Katsue Akiba Reynolds

18. "Synthesis of Modern Japanese Literature and Philosophy in the Writings of Valdo H. Viglielmo" by Steve Odin

(In addition, the book also includes a good biography of Viglielmo and a useful bibliography of his publications)
4631750
This book is great for the Pre-K/K level when teaching about symmetry.  Great pictures and text. Go for it! This book is a great addition to a lesson.
2154312
Readable, has a simple chapter on continuous groups that (implicitly) introduces the notion of global integrability. Discusses and uses Fuch's theorem (classification of singularities of linear ode's, basis for 'guessing' the right form of the series solution in terms of singilarities of coefficients), easy group theoretic discussion of singularities in the complex plane. Stage 2: see Arnol'd's Ordinary Differential Equations for theory, Bender and Orszag for approximation methods.
3502908
for anyone interested in the subject. The author treats both the
native tradition and the reception of Western mathematics with
the highest scholarship. One of the most significant themes is
the conflict between the combinatoric spirit of Chinese mathematics,
akin to modern group theory and algebra, and the synthetic
Euclidean system introduced by European missionaries.
The initial Chinese puzzlement at what seemed an artificially
contrived structure will amuse those who have endured traditional
geometry and those struggling with Chinese itself.
2473802
This an excellent classical physics book. It explains many approaches that your typical University Physics textbook leaves out, including Lagrangian and Hamiltonian Mechanics, Symmetry, and Poisson Brackets. It also reviews the math necessary to carry out the physics problems.
4386201
While some of the examples in the text need to be fleshed out a bit, and the problems at the end the of the chapters are somewhat too oriented toward programming problems, on the whole I am finding this to be an extraordinary text.  I am teaching it to freshman physics majors, and even those who've had significant high school physics (includng AP) have never really seen a physics course like this, and it seems to be keeping them excited.  Unlike the standard freshman college texts, which simply reiterate the high school curriculum at a slightly higher level (and makes them do blocks on planes and pulleys ad nauseum), Matter and Interaction introduces classical mechanics alongside modern, alongside relativity.  I have also found it a useful jumping-off point to discuss oscillators and circuits.  Though the authors will need to do a bit of fine-tuning in future editions, I highly recommend this as an excellent freshman physics curriculum.