Chemical Applications of Group Theory, 3rd Edition

Book Description

Retains the easy-to-read format and informal flavor of the previous editions, and includes new material on the symmetric properties of extended arrays (crystals), projection operators, LCAO molecular orbitals, and electron counting rules. Also contains many new exercises and illustrations.

Customer Reviews:

this review is for struggling undergrads.......2007-03-29

I used an earlier edition of this book for symmetry/group theory and couldn't figure out what the heck was going on! Fortunately, there are lots of good alternatives:

1. "Molecular Symmetry and Group Theory: A Programmed Introduction to Chemical Applications" by Alan Vincent. This one is Excellent. It takes you by the hand and gives you a tutorial!

2. "Group Theory for Chemists" by George Davidson. Out-of-print now but look for it used.

3. "Molecular Symmetry and Group Theory" by Robert L. Carter, ISBN 0471149551

4. "Group Theory and Chemistry" by David M. Bishop. inexpensive.

5. "Introduction to Molecular Symmetry" (Oxford Chemistry Primers) by J. S. Ogden. inexpensive

Also look at chapter 1 of "Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy" by Daniel C. Harris & Michael D. Bertolucci

For a very nice overview try "Symmetry through the Eyes of a Chemist" by István Hargittai & Magdolna Hargittai

P.S. For a similar book to Vincent's try "Beginning Group Theory for Chemistry" by Paul H. Walton. It's meant to be written in (pencil!).

Look at my other reviews for other chemistry books.

Review nearly 40 years later.......2005-11-21

I read this book in 1965 as a freshman in Chemistry
at UCLA. I had no background in group theory or representation
of groups by characters. It started me on a life long study of groups,
but the wrong way. For someone without the necessary mathematics background
this book is actually harmful.
I think a course in modern algebra should be necessary
to reading this book. In 1965 an understanding of Calculus
wasn't enough even with a little Boolean algebra mixed in.
It came down to us using the book like a recipe book
for the mathematics, following many of the operating blindly.
But I have to say that over the years I have learned more about groups
and that the approach here has grown in my respect with that study.
So I have to say it is an excellent book
for those prepared
and a very poor book for those who aren't.

Good Reference, Poor Textbook.......2004-05-02

This book is a double edged sword. As a reference textbook for a person who has already had a significant introduction to group theory and chemical applications of it, this book can't be beat. It provides some very detailed mathematical derivations of the theoretical formulas used within group theory which one may not find in an elementary inorganic text which skims over group theory. Additionally, Cotton covers organic, organometallic and inorganic examples which allows the reader to have a broad spectrum of systems to learn from. The blurbs about molecular vibrations and crystallography were nice too. Finally, Cotton does not lack in providing journal references to the original research that he covers in the text.

In lieu of all that, this book is a bain to use in order to learn the principles of group theory. Cotton, in his typical fashion, assumes that the reader is well-versed in linear/matrix algebra (and has a very condescending comment for anyone who MIGHT have to read the matrix algebra appendix he has in the back of the text) and that the reader can visualize symmetry operations readily in their head. There are places in the text where he should go into more detail and provide further examples, but he does not. Lastly, anyone who knows anything about group theory knows that it is a pretty dry subject matter. Cotton doesn't enhance the excitement of learning group theory with his dry, humor-less approach to writing the text (not to mention that this 3rd edition is already overdue for another overhauling being over a decade old!). In case you have insomnia while taking your group theory course, attempt to read a full chapter in one sitting, you'll be out cold by the second paragraph!

My final verdict, if you are a graduate student in chemistry who already knows something about group theory and its application, but needs a text to jog your memory now and again, this book is worth your money, but if you have to learn the basics of group theory from this book, RUN! Run as fast as you can! Or if you can't do that, buy this book, but buy another book and learn from that one rather than this one.

Good book for its intended purpose and audience.......2003-06-05

Professor Cotton's book is a well written introduction to the theory of group representations for chemists. It is appropriate for chemical experimentalists and beginners with a more thoeretical bent. It was NOT INTENDED to be a book of algebra for mathematicians or physicists interested in Lie groups. The pure rotation group is not covered, representations of space groups are not mentioned, ray representations are not used, etc. Many of the reviewers below seem to think they will need one and only one book that deals with applications of group theory - not likely! For a beginner with a background typical of a 1st year grad student in physical or inorganic chemistry at an American university, the book is good. If the complainers below ever tried to teach a course to such students using the more rigorous books they are clamoring for, they would be hung in effigy (if they were lucky).
However, even for the intended audience, there are things that could be improved. Most glaring in my opinion is the treatment of electronic states, as opposed to orbitals. Even "mathematically-challenged chemists" have to face up to Slater determinants as basis functions for multi-electron wavefunctions. The spectroscopy and ligand-field theory topics are obscure if you don't introduce this concept. Symmetry with respect to interchange of particle labels is not that difficult to teach, and is essential for understanding the symmetry requirements that must be placed on electronic and vibrational wave functions.

Bad expectations => Bad reviews.......2003-03-19

So if you are a mathematician or a physicist, don't whine if this book isn't for you. It's for chemists, specifically inorganic ones, who use group theory to analyze ligand chemistry and spectroscopic measurements. It is also useful for those who utilize computational chemistry programs like Gaussian and need to know the basics of orbital and molecular symmetry.

This book contains only point group symmetry and none of the SO, SU, U, etc. groups used in physics. There is also no coverage of Lie algebras.

Average customer rating:

Heavy on the Math . . .
Good for the Undergrad Students.
Most accessible of the useful physics texts
A must for every grad student
Group Theory and Quantum Mechanics

Group Theory and Quantum Mechanics
Michael Tinkham
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486432475

Book Description

This graduate-level text develops aspects of group theory most relevant to physics and chemistry and illustrates their applications to quantum mechanics: abstract group theory, theory of group representations, physical applications of group theory, full rotation group and angular momentum, quantum mechanics of atoms, molecular quantum mechanics, and solid-state theory. 1964 edition.

Customer Reviews:

Heavy on the Math . . ........2007-09-10

This book is an excellent reference for group theory. It gives you the detailed math behind group theory (which is great for me). It also gives you a brief introduction so you can work with molecular group theory. This was the recommended text in my chemical group theory class. It serves as a good mathematical reference. Also, see Cotton's group theory book, and Carters group theory book.

Good for the Undergrad Students........2007-08-27

This book has the advantage of applying group theory directly to solvable physical problems. In most areas of applied physics it is
very important to know the basics concepts of group theory, but
there is no need to have a deep knowledge as well as to know how to
proof all the main theorems. As an introductory course for undergrad
students this book is well recommended.

Most accessible of the useful physics texts.......2006-08-11

My background is that of theoretically inclined inorganic chemist and this review is intended for those with interests in inorganic and physical chemistry or solid-state chemistry/physics.

Tinkham's text is the first textbook one should go to for a reasonably rigorous introduction to the theory and use of group representations in physics and theoretical chemistry. Modern theoretical chemists should become familiar with all of this book, with the possible exception of the some of the material in Chapter 5 that will be applicable only to physicists (and not a lot of that, actually). The pervasiveness of band theory, even in general inorganic chemistry journals now, should convince chemists who teach this subject to include a lot of Chapter 8 (Solid-State Theory) and chemical theorists will even have to go beyond the symmorphic groups treated here.

The purely mathematical aspects of the subject are treated briefly, but much more completely, than "chemical group theory books" like Cotton's, for example. Naturally, this comes at a price of more mathematical abstractness, but that is unavoidable. These sections, like the rest of the book, are very well written.

Chapter 7, on applications to molecular quantum mechanics, is now quite dated. It was quite incomplete even when written, since it did not include any discussion of ligand-field theory. The effects of antisymmetric wavefunctions for electrons are touched on briefly in Chapter 5 (atoms), but are not adequately accounted for in discussion of molecules. (Incidentally, the failure to use Mulliken notation in molecular QM is an unfortunate annoyance.)

These objections aside, this book is an excellent buy for the price of a Dover edition. Indeed, if I'd included price in my rating, it would be 5 stars - easily!

A must for every grad student.......2005-12-27

I began reading this book having just finished a course on Abstract Algebra through my school's math department, and the semester before I took a graduate course on the exact subject.

After taking the math course, I was presented with group theory as if it were some muddled mix of facts, and the course came across as a poorly taught class on number theory. After reading just the first chapter of Tinkham's book, I developed a new, deeper understanding of group theory as a whole. For example, the way that Tinkham presents normal subgroups makes vastly more intuitive sense than the presentation I received in my math course.

The first two chapters alone are probably worth 80% of the book's sale price. The rest is made up entirely of the fact that the book does not piddle around with trivial examples, but genuinely frames quantum mechanics in the language of group theory, and the most important part is that Tinkham does it well.

This book, along with his book on superconductivity, are must-haves for any serious condensed matter person, and this book should be at least read (if not owned) by any physics grad student.

Group Theory and Quantum Mechanics.......2005-07-19

Both the content of the book and service of amazon are wonderful

Group Sequential Methods: Applications to Clinical Trials (Chapman & Hall/Crc Interdisciplinary Statistics Series)

Average customer rating:

clear coverage for practicing biostatisticians

Group Sequential Methods: Applications to Clinical Trials (Chapman & Hall/Crc Interdisciplinary Statistics Series)
Christopher Jennison , and Bruce W. Turnbull
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0849303168

Book Description

Group sequential methods answer the needs of clinical trial monitoring committees who must assess the data available at an interim analysis. These interim results may provide grounds for terminating the study-effectively reducing costs-or may benefit the general patient population by allowing early dissemination of its findings. Group sequential methods provide a means to balance the ethical and financial advantages of stopping a study early against the risk of an incorrect conclusion. Group Sequential Methods with Applications to Clinical Trials describes group sequential stopping rules designed to reduce average study length and control Type I and II error probabilities. The authors present one-sided and two-sided tests, introduce several families of group sequential tests, and explain how to choose the most appropriate test and interim analysis schedule. Their topics include placebo-controlled randomized trials, bio-equivalence testing, crossover and longitudinal studies, and linear and generalized linear models. Research in group sequential analysis has progressed rapidly over the past 20 years. Group Sequential Methods with Applications to Clinical Trials surveys and extends current methods for planning and conducting interim analyses. It provides straightforward descriptions of group sequential hypothesis tests in a form suited for direct application to a wide variety of clinical trials. Medical statisticians engaged in any investigations planned with interim analyses will find this book a useful and important tool.

Customer Reviews:

clear coverage for practicing biostatisticians.......2000-06-28

Advances in the theory of repeated significance testing in the 1980s and 1990s has made sequential methods practical by identifying stopping rules for data collected sequentially but in groups. This material is now used to plan interim analyses and both safety and efficacy group sequential trials for clinical trials. This text provides for the first time thorough coverage of these advances with suitable references to the literature.

Book Description

A Thorough But Understandable Introduction To Molecular Symmetry And Group Theory As Applied To Chemical Problems! In a friendly, easy-to-understand style, this new book invites the reader to discover by example the power of symmetry arguments for understanding theoretical problems in chemistry. The author shows the evolution of ideas and demonstrates the centrality of symmetry and group theory to a complete understanding of the theory of structure and bonding. Plus, the book offers explicit demonstrations of the most effective techniques for applying group theory to chemical problems, including the tabular method of reducing representations and the use of group-subgroup relationships for dealing with infinite-order groups. Also Available From Wiley:
* Concepts and Models of Inorganic Chemistry, 3/E, by Bodie E. Douglas, Darl H. McDaniel, and John J. Alexander 0-471-62978-2
* Basic Inorganic Chemistry, 3/E, by F. Albert Cotton, Paul Gaus, and Geoffrey Wilkinson 0-471-50532-3

Customer Reviews:

clear, concise book.......2003-10-09

this small book on symmetry and group theory is easy to understand and packed with examples. it is a small book (only about 300 pages) but everything in it is relevant and to the point. the writing is easy to grasp and the back includes character tables for all the common symmetry groups. buy it!

A Group Theory book that allows students to learn.......2000-10-27

The strength of this book is its many examples. Carter takes the concepts and applies them to simple inorganic or organic compounds. Very helpful to students. The end of chapter problems are nice as well. A great text and one that I would recommend to students as well as faculty.

A much needed breath of fresh air!.......1998-07-29

This is a text set apart from the pack. It clearly states what other books attempt to describe. There need to be more texts on the market like this. Dr. Carter has taken a subject that has historically been elusive, and presented it in a comprehensive, READABLE volume. This text is helping me through my thesis in chemistry. It is highly practical, easily read, and heavily referenced, all of the qualities, I believe, that make up an excellent text! Excellent work!

Group Theory and Its Application to Physical Problems (Dover Books on Physics and Chemistry)

Average customer rating:

Not the very best choice.
the language of theoretical physics
great book for beginners
Good book
A good reference

Group Theory and Its Application to Physical Problems (Dover Books on Physics and Chemistry)
Morton Hamermesh
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486661814

Book Description

One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems. "Well-organized, well-written and very clear throughout." — Mathematical Reviews. 71 illustrations.

Customer Reviews:

Not the very best choice........2007-08-09

It's a fine text, but Tinkham is probably the best route for the (particularly solid state) physicist.

the language of theoretical physics.......2003-01-06

When I first encountered this book I was an undergrad, a junior. I flipped through the pages and could barely read the English portions, not to mention the proofs and examples. I must say that it's a tough book for a beginner; MH quickly runs through group theory in the beginning (pay attention: there are some important sentences in there that pop up later when you least expect them to) and then goes into rather a lengthy description of symmetry (point) groups, fit for a chemist or crystallographer more than a theoretical physicist.

After those two chapters come perhaps the most important chapters in the book: the ones on group representation theory. There is a long chapter on theory, and then a great short one on applications of GR that's extremely helpful in understanding what you've just read. After that MH gets into Kronecker products and Clebsch-Gordon coefficients as well as other operations with GR, and has another neat chapter afterwards on physical applications. He speak about the symmetric group in great length, and then about continuous groups, another extremely important chapter. The rest of the book uses the core of what you've just learned to help you understand linear groups in Hilbert space, and applications to sub-atomic physics.

Here's what you need to do to consume this book successfully:

1) Don't wait for MH to give you an example. Make them up as you go along! And make sure you fully understand each and every little statement he makes: there's no extravagant sentences here, all are vitally important and he will make use of every statement at least once to prove another point.

2) If you haven't had quantum mechanics yet, hold off on the last half of the book until you have! MH assumes this knowledge, but you can get away with your ignorance for the first part of the book, up until chapter six (and then you can skip around a little bit).

3) Know the fundamentals of group theory before you begin. It's true that MH doesn't assume this knowledge, but I assure it's vital for ease of reading. There are enough new concepts to absorb with out making your brain less permeable by not having group theory under your belt.

Overall, this book is good for physicists who want to become more adept in the language of theoretical physics (especially quantum mechanics and quantum field theory). I recommend it; but I also recommend you keep at least three other texts on hand that have their own way of explaining the things MH tries to explain. It is a good idea to do that in any independent learning venture, anyway.

great book for beginners.......2001-02-22

At the time I ran into this book I was doing research on martensitic transformations in metals. For that, as an engineer, I needed lots of information on point groups. The first chapter of the book contains the basics of group theory and teaches the totally ignorant all he has to know about the subject. The second chapter immediately deals with the point groups as one encounters them in crystallography. Very comprehensive and usefull information. Then the formal theory on groups is treated and general theorems are derived. For an average engineer without too much mathematical background this may be a bit too much, but the chapter is well written and provides usefull information that is used in chapter 4 to derive the irreducible representations and character tables for the point groups discussed in chapter 2. After that, I did not need the book anymore besides the short treatement of translation groups at the end of the book. I definately recommend te book for anyone who has to deal with point groups and wants to know more than just the basics.

Good book.......1999-10-19

A great book for a beginner. I recomend i

A good reference.......1998-08-24

This is one of those books that appear just before their subject matter becomes a fashion. The most famous example is Courant-Hilbert "Methods of Mathematical Physics", which contained the mathematics of quantum mechanics as if the authors had guessed what the future had in store. Hamermesh taught group theory for physicists just before SU(3), quarks, etc, dominated particle physics. Everybody learned groups from "Hamermesh". Now time passed, more specialized books appeared, physicists learned more mathematics... What of Hamermesh? Well, I always thought it was rather boring, a collection of methods with very little motivation. If one compares it with a modern book such as Inui, Tanabe, Onodera, one sees the difference: much more physical context. Hamermesh has, notwithstanding, done his job.

Average customer rating:

A very good book
An Excellent Book on Group Theory for Chemistry
Eminently readable introduction to point groups
Looks hard as a rock, tastes smooth and easy going down!

Group Theory and Chemistry
David M. Bishop
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486673553

Book Description

Concise, self-contained introduction to group theory and its applications to chemical problems. Symmetry, symmetry operations, point groups, matrices, matrix representations, equivalent and reducible representations, irreducible representations and character tables, representations and quantum mechanics, molecular vibrations, molecular orbital theory, hybrid orbitals, and transition metal chemistry. Advanced-undergraduate/graduate level. 1973 edition.

Customer Reviews:

A very good book.......2007-08-16

I really wish I had this book when it first came out!
The table on page 46 is of great use.
The coverage in the books goes well with my own experience and Cottom's book on Inorganic Chemistry.
My one very basic bone to pick is from my long ( 40 or more years) work involving group theory. Neither Cartan groups or Coxeter are mentioned or their relationship to these point groups. The Federov space groups used in crystallography are also ignored. The result is to make western Chemistry students second class in world education( ignorant of basics in the Mathematics of groups). I can't blame this on Bishop as he is only following Dr. Cotton's lead. I read a recent cosmology book in which a very well educated American physics Ph.D. shows a basic ignorance of Federov space groups. None of the editors caught it and it is in print ...
Russians everywhere must be laughing.
I think that we have to integrate the mathematical approach to group theory
with the Chemical-Physical approach, so that instead of rote use of
formulas, understanding is involved.

An Excellent Book on Group Theory for Chemistry.......2007-08-06

This book presents the theory in a straightforward way. Nevertheless, it is far from being superficial. It covers the basics about symmetry operations, point groups, matrices, matrix representations, equivalent and reducible representations, irreducible representations and character tables. Then, it connects the theory with quantum mechanics and molecular vibrations. For me, the ratio satisfaction/price of this book is very high.

Eminently readable introduction to point groups.......2000-06-18

Bishop's book is intended for students in the fields of physical chemistry and chemical physics, and limits its scope to subjects of interest to these people. Hard core physicists may want to turn to some other text for this reason, but the ease of presentation should still make the book attractive to them. It more or less only covers finite point groups, but the full rotation group is also discussed (superficially, not to scare away the mathematically disinclined). The book is eminently readable, and explains the uses of group theory within chemistry in a lucid and actually enjoyable way. The text is self-contained, and is suitable for private study. Vibrational spectroscopy, hybridization and symmetrization of wave functions in quantum chemistry are among the applications covered.

Looks hard as a rock, tastes smooth and easy going down!.......1997-08-20

Ever wonder how to simplify those hard to solve quatum mechanics chemistry problems, well I just don't have the anwer. I can, however, say that this fantastic book does a great job of explaining such a hard subject and,as an added bonus as the end, give you a fresh new hope of being able to solve such problems using group theory. First chemistry book I couldn't put down

Primer for Point and Space Groups (Undergraduate Texts in Contemporary Physics)

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Primer for Point and Space Groups (Undergraduate Texts in Contemporary Physics)
Richard L. Liboff
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387402489

Book Description

Written in the spirit of Liboff’s acclaimed text on quantum mechanics, Primer for Point and Space Groups is an ideal introductory text for undergraduates in physics, engineering, materials science, chemistry. With its shrewd selection and arrangement of examples, the book traces at every turn the physical implications of abstract concepts. The book will therefore provide a solid background for those students who expect to use group theory in nuclear and particle physics and other specific applications. Among the many introductions to group theory currently available, few are as closely attuned to the needs of the applied scientist without compromise to the logic and lucidity of the presentation.

Here are some of the applications covered in Liboff’s Primer for Point and Space Groups:

Applications to Quantum Mechanics:

- Irreducible representations and degeneracy

- Full rotation group; SU(2) group; angular momentum

- Symmetry group and the wavefunction

- Young diagrams and the wavefunction

- Degenerate perturbation theory

- Great Orthogonality Theorem

Applications to Solid-State Physics:

- Translation and Crystallographic Point Groups

- Holohedral groups

- Bloch waves and space groups

- Bravais lattice

- Energy -band eigenenergies

- Seitz operator, (Translation and Rotation)

- Glide-plane and screw operators

- Diamond structure

- Group of {bf k} and Star of $bf k $.

- Space group of {bf k}

- Time reversal and Space inversion effects on the

- wavefunction and eigenenergies

- Symmorphic group

- Factor Group theorem

Applications to Material Media:

- Splitting of electron levels in crystals with symmetry

- Correlation diagrams

- Neumann's Principle

- Polarizability

- Piezoelectric effect

- Classification of magnetic crystals

- Black and white groups

Molecular Symmetry and Group Theory : A Programmed Introduction to Chemical Applications, 2nd Edition

Average customer rating:

Best in its field
Pretty good reference and quick read
Great for beginners
Exam tomorrow, and still in confusion with group theory...?

Molecular Symmetry and Group Theory : A Programmed Introduction to Chemical Applications, 2nd Edition
Alan Vincent
Manufacturer: Wiley
ProductGroup: Book
Binding: Paperback

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ASIN: 0471489395

Book Description

This substantially revised and expanded new edition of the bestselling textbook, addresses the difficulties that can arise with the mathematics that underpins the study of symmetry, and acknowledges that group theory can be a complex concept for students to grasp.

Written in a clear, concise manner, the author introduces a series of programmes that help students learn at their own pace and enable to them understand the subject fully. Readers are taken through a series of carefully constructed exercises, designed to simplify the mathematics and give them a full understanding of how this relates to the chemistry.

This second edition contains a new chapter on the projection operator method. This is used to calculate the form of the normal modes of vibration of a molecule and the normalised wave functions of hybrid orbitals or molecular orbitals.

The features of this book include:

A concise, gentle introduction to symmetry and group theory
Takes a programmed learning approach
New material on projection operators, and the calcultaion of normal modes of vibration and normalised wave functions of orbitals

This book is suitable for all students of chemistry taking a first course in symmetry and group theory.

Customer Reviews:

Best in its field.......2007-02-13

I bought this book because it is advised from one of my classmates of Transition metal chemistry.
If you need to learn molecular symmetry, this book is very good. It teachs in a logical order. The only not good part may be its size. I prefer bigger books so you can easily bend. So you should be polite to this book when reading.
It is also expensive for its size but if you need to learn the molecular symmetry and/or group theory, this book is strongly recommended :)
I hope this review helps.
Happy wishes

Pretty good reference and quick read.......2006-03-28

The text does a good job of covering the subject material. It is not so advanced as to be difficult to master symmetry, matrices, and applications to vibrational spectra. The book is designed as a programme. The reader follows along and is interrupted to test his/her ability. After successful mastering of topics, the reader goes on, but if the reader does not answer the practice questions well enough, there is a guide to do more review. This is a great intro text for undergraduates, or as a reference for graduate students studying in the Inorganic field.
The text also uses great examples and has good step by step instructions. The reader can get up to speed on most of the subject material within one weekend. It is also not necessary to read the book cover to cover to get useful learning out of the text. It has a good ability to modulate the different aspects of the different subjects. Overall, worth the money.

Great for beginners.......2000-05-25

If you don't have the math background it often takes to penetrate Cotton, this book could be the answer. For learning the quick and dirty basics of the use of group theory for molecules, this is the book. The only problems are its sparseness and the high price for a 156 page book. Excellent for self-teaching, though.

Exam tomorrow, and still in confusion with group theory...?.......1999-09-26

Cotton's(or Bishop's or like that...) book on group theory is too wonderful for me to grade. But, you may agree with me, in that it really takes times! You must read those books to understand the internal structure of group theory, but if you have exam tomorrow, Vincent's will be an emergency measure. Just follow him about 5 hours. Then you can solve some crucial spectroscopy problems, make MO's, and so third. But don't forget to check the books of details. This book is just for an emergency measure. But truly great enough for that.

Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften)

Average customer rating:

The book on lattice

Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften)
John Horton Conway , and Neil J. A. Sloane
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387985859

Book Description

The third edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the previous edition, the third edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. Of special interest to the third edtion is a brief report on some recent developments in the field and an updated and enlarged Supplementary Bibliography with over 800 items.

Customer Reviews:

The book on lattice.......2001-09-10

This book is devoted to the subject of lattice packings. It is an outstanding book with all pages interesting. It acts as a reference on the subjects of lattices. What you will find:
--Sphere packings, ie the problem of packing spheres in order to maximize density.
--The problem of Kissin numbers: maximize the number of adjacent sphere to a given sphere in a lattice
--Code, design, and Groups
--Error correcting codes
--Leech lattice
--Integral quadratic forms
--Voronoi cell
--many, many other subjects
What you WON'T find in this book:
--The study of Delaunay cells (or holes, L-polytopes) is quite limited
--The study of continuous families of lattice is not done, you won't find the Voronoi memoires here
--There is just one page on computational aspects of lattice

Book Description

A unique, much-needed introduction to molecular symmetry and group theory Elements of Molecular Symmetry takes the topic of group theory a step further than most books, presenting a quantum chemistry treatment useful for computational, quantum, physical, and inorganic chemists alike. Clearly explaining how general groups and group algebra describe molecules, Yngve Öhrn first develops the theory, then provides coverage not only for point groups, but also permutation groups, space groups, and Lie groups. With over three decades of teaching experience, Dr. Öhrn brings to the discussion unprecedented depth and clarity, incorporating rigorous topics at a level accessible to anyone with basic knowledge of calculus and algebra. This unique and timely book:
* Extends coverage to molecular orbital theory,
* Utilizes powerful examples to illustrate basic concepts
* Contains introductory material on space groups and continuous groups, including point-group character tables
* Provides a solid background for exploring the theoretical literature

Customer Reviews:

Super Book!.......2000-04-22

Ohrn is one of today's most respectable ab initio quantum chemists. In his newest book he precisely directs the reader from the rigorous mathematics of groups and group algebras to the application of simplifying problems in quantum chemistry. This book contains much more mathematics than any other book on this subject and is a must for anyone who cares to know the nuts and bolts of group theory as applied to chemistry. I highly recommend Yngve's book and know that most practitioners of quantum chemistry will benefit much more from this text than from any other watered-down and inadequate text on the subject such as that written by Cotton.

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