Reviews (4)

not good
I have known something about Lie groups and Lie algebras (I have already read first 5 chapters of"Lie Groups, Lie Algebras, and Representations" by Brian C. Hall ) and wanted to combine it with the applications in physics. When I encounter this book, I looked at its content, I thought that I should read it to understand the relation between group theory and physics. But it disappointed me for the following reasons:
Superb book
This is an ultimate book for physics . Don't waste your time on
Covers a lot of ground, but not very well
At first glance, this book is accessible and well-written. This is an illusion. In this book, Jones tries to cover the theory of finite and continuous groups, representation theory, lie groups and algebras and applications to quantum mechanics, molecular vibrations, special relativity etc. In doing this, he tries not to confuse the reader with too many mathematical details, seeking instead introduce physical ideas quickly. This is in principle a sound idea, but Jones' implementation is abysmally poor. In particular, he often uses terms he does not define and abuses the notation he does define, even in theorems. (The fact that he doesn't prove many theorems makes it harder to work out the meanings of terms from context.) Even worse, there are often theorem-like statements in the text that are not even pointed to as such, but merely mentioned in passing. E.g. 'You don't need to know what a compact group is, just that the last equals sign is OK because the group is compact' (paraphrased) Many of his examples fail to illuminate the principles he is trying to explain and have the flavour of my students' homeworks when they have copied their answers from the back of the book. E.g. 'The answer is 2+1=3' (paraphased). All right, and whence the 2 and 1?Read more

Subjects:  1. Group Theory    2. Mathematical Physics    3. Science    4. Mathematics    5. Mathematics / Algebra / General    6. Theoretical methods   

Reviews (4)

Most gentle introduction
Stephanie Singer's book is a service to all students who wish to learn modern aspects of mechanics for the first time.

A nice introduction to modern methods
I think the previous review is a bit harsh, and that the book's intents are not what this reviewer expected. I don't think it was the author's intent to write a comprehensive treatise on the subject. The book simply aims at introducing undergraduate students to the use of symmetry in simplifying the analysis of classical mechanic problems, nothing more. If you want a comprehensive treatise, you probably want to read V.I. Arnols's "Mathematical methods in classical mechanics". If what you want is a simple introduction where all the steps are worked out in details, then this book is a good starting point, and I think this is what the author intended. At any rate, the cost ($$$) is quite reasonable.

Poorly written
This is one of the very few books which I returned for refund.Read more

Subjects:  1. Advanced    2. Analytic Mechanics (Mathematical Aspects)    3. Differential Geometry    4. General    5. Geometry - Differential    6. Geometry, Differential    7. Mathematical Physics    8. Mathematics    9. Mechanics - General    10. Mechanics, Analytic    11. Science    12. Science/Mathematics    13. Classical mechanics    14. Lie groups    15. Linear algebra    16. Mathematics / Group Theory    17. Theoretical methods    18. sympletic geometry   

Reviews (3)

A reprint at last!
A text truly deserving the designation "classic"; bravo to Springer for reprinting this book!This seminal text provides a clear exposition of the topic, along with numerous jumping-off points for exploring interesting outgrowths and tangents.A must-have text for anyone interested in the subject.

Great book
A "must read" for everybody who is interested in combinatorial aspects of algebra. You can read whole book or some chapters (free groups, free constructions, diagrams, 1-relator, ...). I don't think it's forabsolute beginners, but if you want, you understand it. It would be greatif this book were reprinted with some complements (which could be writtenby Ol'shanskii, Gersten, Sapir,Shupp, Stallings, Guba, S.Ivanov,Baumslag, Lysyonok ...)

A very good textbook
It's an absolute pity that this book is out of print, since it's one of the few good recent textbooks about combinatorial group theory. One can only hope it will be reprinted soon... ... Read more

Subjects:  1. Combinatorial group theory    2. Combinatorics    3. General    4. Group Theory    5. Mathematics    6. Medical    7. Psychiatry - General    8. 05E15    9. 20Exx    10. 20Fxx    11. 20J05    12. Combinatorics & graph theory    13. Groups & group theory    14. Linear algebra    15. Mathematics / Group Theory    16. combinatorial groups   

Subjects:  1. Algebra - General    2. Group Theory    3. Mathematics    4. Number Theory    5. Political Ideologies - General    6. Political Science    7. Politics/International Relations    8. Groups & group theory   

Subjects:  1. General    2. Group Theory    3. Mathematical recreations    4. Mathematics    5. Mathematics / Algebra / Abstract    6. Mathematics / Game Theory    7. Mathematics / Group Theory    8. Permutations    9. Science/Mathematics    10. Algebra - Abstract    11. Game Theory    12. Groups & group theory    13. Mathematics / General    14. Permutation groups    15. Puzzles   

Subjects:  1. Advanced    2. Homotopy theory    3. Mathematics    4. Science/Mathematics    5. Steenrod algebra    6. Topology - General    7. Geometry - Algebraic    8. Algebraic Topology    9. Category Theory    10. Associative rings    11. Associative algebras   

Subjects:  1. Advanced    2. Automorphic forms    3. Complex manifolds    4. Functions Of Complex Variables    5. Geometry - Algebraic    6. Mathematics    7. Reference    8. Shafarevich maps   

Reviews (3)

dense and uninviting
This is a typical mathematical monograph
There is a lot here for such a short book
This book is a pretty good introduction to the theory of Lie algebras and their representations, and its importance cannot be overstated, due to the myriads of applications of Lie algebras to physics, engineering, and computer graphics. The subject can be abstract, and may at first seem to have minimal applicability to beginners, but after one gets accustomed to thinking in terms of the representations of Lie algebras, the resulting matrix operations seem perfectly natural (and this is usually the approach taken by physicists). The book is aimed at an audience of mathematicians, and there is a lot of material covered, in spite of the size of the book. Readers who desire an historical approach should probably supplement their reading with other sources. Readers are expected to have a strong background in linear and abstract algebra, and the book as a textbook is geared toward graduate students in mathematics. Only semisimple Lie algebras over algebraically closed fields are considered, so readers interested in Lie algebras over prime characteristic or infinite-dimensional Lie algebras (such as arise in high energy physics), will have to look elsewhere. Physicists can profit from the reading of this book but close attention to detail will be required. Excellent Introduction to Lie Algebras
Humphreys' book on Lie algebras is rightly considered the standard text.Very thorough, covering the essential classical algebras, basic results on nilpotent and solvable Lie algebras, classification, etc. up to andincluding representations.Don't let the relatively small number of pagesfool you; the book is quite dense, and so even covering the first 30 pagesis a nice accomplishment for a student.Small caveat, the notation mightbe a bit confusing until you get used to it, but this is a common problemdue to having both a Lie and a matrix product floating around, and is not afault of the text.There is also a nice selection of exercises, between 5and 10 per section.Read more

Subjects:  1. Algebra - Abstract    2. Calculus    3. Group Theory    4. Lie algebras    5. Mathematics    6. Representations of algebras    7. Representations of groups    8. Science/Mathematics    9. Algebras    10. Darstellung (Math.)    11. Lie    12. Liesche Algebra    13. Linear algebra    14. Mathematics / Group Theory   

Subjects:  1. Algebra    2. Algebra - General    3. General    4. Group Theory    5. Mathematics    6. Probability & Statistics - General    7. Science/Mathematics    8. Mathematics / Algebra / General    9. Mathematics / Statistics    10. Mathematics-Group Theory    11. Medical-General    12. actions    13. groups    14. linear maps    15. modules    16. ring fields   

Subjects:  1. Complexes    2. General    3. Geometry - Algebraic    4. Homology Theory    5. Homotopy Theory    6. Mathematics    7. Model categories (Mathematics)    8. Science/Mathematics    9. Algebraic topology    10. Fields & rings    11. Groups & group theory   

Reviews (1)

Excellent, concise introduction
Peter J. Cameron's "Introduction to Algebra" is exactly that, an introduction to algebra and a good one at that.I must confess that before reading this book had a very limited knowledge of abstract algebra however with a little bit of time and effort I am now quite comfertable with the subject thanks to this book.Read more

Subjects:  1. Algebra - Abstract    2. Algebra - Elementary    3. Algebra, Abstract    4. Mathematics    5. Science/Mathematics    6. Fields & rings    7. Groups & group theory    8. Mathematics / Algebra / Abstract    9. Mathematics | Pure Mathematics   

Reviews (1)

A joyful, illuminating book
Although I've taught quantum mechanics many times, I am learning a great deal from this splendid book.I much admire the care and consideration Singer has devoted to helping readers comprehend and enjoy fascinating, fundamental material.I hope she writes more such exceptional, mind-opening books! Dudley Herschbach, Prof. of Chemistry Harvard & Prof. of Physics, Texas A & M Univ. ... Read more

Subjects:  1. Atoms    2. Group Theory    3. Hydrogen    4. Mathematical Physics    5. Mathematics    6. Quantum Theory    7. Science/Mathematics    8. Atomic & molecular physics    9. Mathematics / Group Theory    10. Quantum physics (quantum mechanics)   

Subjects:  1. Compact groups    2. Finite groups    3. Group Theory    4. Mathematics    5. Representations of groups    6. Science/Mathematics    7. Theory Of Groups    8. Calculus & mathematical analysis    9. Groups & group theory   

Subjects:  1. Algebra    2. Galois theory    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Fields & rings    7. Groups & group theory   

Reviews (4)

Great book, but not perfect or ideal for every purpose
This is a solid introduction to the foundations (and not just the basics) of differential geometry. The author is rather laconic, and the book requires one to work through it, rather than read it. It presupposes firm grasp of point-set topology, including paracompactness and normality. The basics (Inverse and Implicit Function Theorems, Frobenius Theorem, orientation, and rudiments of de Rham cohomology) are covered in about 100 pages (Chapters 1, 2, and 4). This is not really suitable for an undergraduate course in differential geometry, but is great for a graduate course.
Don'twaste your money
This review refers only to the book printing quality not to the contents.
Good, as long as you have enough background
I read this book at the very beginning of my studying in differential geometry and was striked. The definitions and methods used in this book seemed totally incomprehensible to me. However, after some development in this field, I found that this book is very concise. It is a very good surey on differential geometry but not a good book to start with. Definitions are given from the most "down to bottom" one. It is a very good attitude, yet, if you do not have much background in differential geometry, this book may takes you several days in order to understand the concept of tensor and exterior algebra. ... Read more

Subjects:  1. Algebra - Linear    2. Algebraic Topology    3. Differentiable manifolds    4. Geometry - General    5. Group Theory    6. Lie Groups    7. Mathematics    8. Science/Mathematics    9. Differenzierbare Mannigfaltigkeit    10. Groups    11. Lie    12. Liesche Gruppe    13. Linear algebra    14. Manifolds    15. Mathematics / Algebra / Linear    16. Mathematics / Geometry / General    17. Mathematics-Geometry - General    18. Mathematics-Group Theory   

Subjects:  1. Discrete groups    2. Geometry    3. Geometry - General    4. Geometry, Hyperbolic    5. Group Theory    6. Isometrics (Mathematics)    7. Mathematics    8. Mobius transformations    9. Science/Mathematics    10. Theory Of Groups    11. Groups    12. Groups & group theory    13. Mathematics / Group Theory   

Subjects:  1. Algebra - General    2. Algebra - Linear    3. Group Theory    4. History & Philosophy    5. Mathematics    6. Science/Mathematics    7. Algebra    8. Mathematics / History   

Reviews (3)

Right On!
I had some previous exposure to Group Theory, but then my thesis (in Computer Science) actually needed Group Theory, so I was forced to dig deeper and get some real understanding. This book was more than adequate, and the price was just unbeatable. If you actually need explicit algorithmic details (for implementation), check out "Fundamental Algorithms for Permutation Groups" from Greg Butler as well.

NOT SO EASY
On the strength of the previos review from France, I bought this book in the hope of a nice intro to group theory. Imagine my consternation when I read the preface in which it was clearly stated that the book specificallycovers FINITE group theory and presupposes that the reader has had prior,elementary course in group theory.If you don't know group theory already,start with some other book, then try this one.

A complete book by John S. Rose
This book is very complete: it is intended as a guide about group theory for the beginners who want to study it seriously. Exercises are excellent. Moreover it contains a chapter which hasn't been published before (abouttransfer and splitting theorems). ... Read more

Subjects:  1. Group Theory    2. Mathematics    3. Science/Mathematics    4. Groups & group theory    5. Mathematics / General   

Reviews (1)

This book fulfils a great lack
Application of symmetries and Lie groups to differential equations (primarily PDE's) is a hot issue in contemporary Mathematics and Physics. Unfortunately, only few textbooks are available on this area. Read more

Subjects:  1. Algebra - Linear    2. Differential Equations    3. Group Theory    4. Lie Groups    5. Mathematics    6. Science/Mathematics    7. Groups & group theory    8. Mathematics / Differential Equations    9. Mathematics / Mathematical Analysis    10. Mathematics-Algebra - Linear    11. Mathematics-Group Theory   

Reviews (1)

Good Introduction to Central Simple Algebras
This is a very nice introduction to the theory of semisimple modules and rings, central simple algebras, and the Brauer group. It starts off with some review of basic concepts such as modules, tensor products, and field extensions - much of which is in the exercises. Indeed, a lot of the material is developed in the exercises so it is very useful to go through them. Most of the exercises aren't exceedingly difficult either, and hints are provided for the more tricky ones.Read more

Subjects:  1. Algebra - General    2. Algebras    3. General    4. Group Theory    5. Mathematics    6. Noncommutative algebras    7. Science/Mathematics    8. Algebra    9. Groups & group theory    10. Mathematics / Algebra / General    11. Mathematics / Group Theory    12. Mathematics-Algebra - General