Subjects:  1. Algebra - Linear    2. Geometry - Algebraic    3. Group Theory    4. Lie Groups    5. Lie algebras    6. Mathematics    7. Science/Mathematics    8. Topological Groups    9. BN-pairs    10. Coxeter groups    11. Groups & group theory    12. Linear algebra    13. Mathematics / Algebra / Linear    14. Mathematics / Group Theory    15. Mathematics-Group Theory    16. Tits systems    17. Weyl groups    18. root systems    19. semi-simple Lie algebras   

Reviews (1)

Extraordinarily Comprensive Review
This book has pretty much anything you could want about the theory of cyclotomic fields: Fermat's Last Theorem(See how it was done before Wiles!), an introduction to iwasawa theory, and a proof of Thaine's theorem for those of you who are interested in Mihailescu's proof of Catalan's conjecture. One thing though, this book is not really an introduction. If you're not familiar with Algebraic Number Theory and p-adic analysis, you will be completely lost in this book. It definitely doesn't hurt to know at least the major statements of Class Field Theory. Other than that, though, a truly great book! ... Read more

Subjects:  1. Algebraic Fields    2. Cyclotomy    3. Group Theory    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Theory Of Numbers    8. Algebraic number theory    9. Fields    10. Kreiskörper    11. Mathematics / Number Theory   

Subjects:  1. Algebra - General    2. Algebraic fields    3. Ideals (Algebra)    4. Mathematics    5. Number Theory    6. Rings    7. Rings (Algebra)    8. Science/Mathematics    9. Algebraic number theory    10. Fields & rings    11. Groups & group theory    12. Mathematics / Algebra / General    13. Mathematics / Number Theory    14. Mathematics | Pure Mathematics    15. Mathematics-Number Theory   

Subjects:  1. Algebra - General    2. General    3. Group Theory    4. Mathematics    5. Noncommutative rings    6. Rings    7. Science/Mathematics    8. Fields & rings    9. Mathematics / Algebra / General    10. Medical-General   

Subjects:  1. Applied    2. Group Theory    3. Mathematics    4. Science/Mathematics    5. Theory Of Groups    6. Bifurcation theory    7. Differential equations    8. Groups & group theory    9. Mathematics / Applied    10. Mathematics / Group Theory    11. Mathematics-Group Theory   

Subjects:  1. Chemistry - Physical & Theoretical    2. Engineering - Electrical & Electronic    3. Group Theory    4. Mathematics    5. Physics    6. Science    7. Science/Mathematics    8. Science / Physics   

Reviews (1)

Review of Knapp's "Lie groups: beyond an introduction."
The short version:this is a superbly written and conceived book;if I had to learn this material (the basic theory of Read more

Subjects:  1. Algebra - Linear    2. General    3. Group Theory    4. Lie Groups    5. Lie algebras    6. Mathematics    7. Representations of groups    8. Science/Mathematics    9. Algebra/Rings    10. Groups & Generalizations    11. Groups & group theory    12. Linear algebra    13. Math Physics    14. Mathematics / Group Theory    15. Mathematics for scientists & engineers    16. Representation/Lie Group    17. Theoretical methods   

Reviews (1)

great as references, and..
...even better when supplemented by other texts (be wary though, as the notation of Bourbaki is not universally accepted).
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Subjects:  1. General    2. Group Theory    3. Lie Groups    4. Mathematics    5. Science/Mathematics    6. Groups & group theory    7. Lie algebras    8. Linear algebra    9. Mathematics / Group Theory    10. fields of point distribution    11. invariant differential forms    12. invariant tensors   

Subjects:  1. Biography/Autobiography    2. Computer Books: General    3. Computers    4. General    5. Information Theory    6. Life Sciences - Botany    7. Mathematical models    8. Phyllotaxis    9. Physics    10. Plant Morphology    11. Plant morphogenesis    12. Science    13. Artificial intelligence    14. Computers / Information Theory    15. General Theory of Computing    16. Groups & group theory    17. Mathematical foundations    18. Medical-General    19. Science / Botany    20. Science-Physics   

Reviews (2)

A refreshingly clear introductory text on Lie groups
I rarely have time or feel strongly enough about a text to write a review. However, with Hall's book, I feel compelled. After struggling with the rather compact sixth chapter of Wulf Rossman's book on representations of Lie groups and algebras during a course on representation theory (the first five chapters were assumed), I turned to this one, and boy, am I ever glad I did. AT LAST, LIE GROUPS & ALGEBRAS I CAN UNDERSTAND!!
This book focuses on matrix Lie groups and Lie algebras, and their relations and representations.This makes things a bit simpler, and not much is lost, because most of the interesting Lie groups & algebras are (isomorphic to)groups & algebras of matrices.Read more

Subjects:  1. Algebra - General    2. Algebra - Linear    3. Group Theory    4. Lie algebras    5. Lie groups    6. Mathematics    7. Matrices    8. Representations of algebras    9. Representations of groups    10. Science/Mathematics    11. Linear algebra    12. Mathematics / Algebra / Linear    13. Mathematics / Group Theory    14. Mathematics-Matrices   

Subjects:  1. General    2. General Topology    3. Group Theory    4. Harmonic Analysis    5. Infinity    6. Mathematics    7. Science    8. Science/Mathematics    9. Symmetric spaces    10. Fourier analysis   

Subjects:  1. Group Theory    2. Mathematics    3. Science/Mathematics    4. Theory Of Groups    5. Algebra    6. Groups & group theory    7. Mathematics / Algebra / General    8. Mathematics / Group Theory    9. Symmetry   

Subjects:  1. Group Theory    2. Mathematics    3. Modules (Algebra)    4. Number Theory    5. Rings    6. Rings (Algebra)    7. Science/Mathematics    8. Theory Of Numbers    9. Fields & rings    10. Mathematics / Algebra / General    11. Mathematics / Number Theory   

Reviews (4)

the language of theoretical physics
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. great book for beginners
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
A great book for a beginner. I recomend i ... Read more

Subjects:  1. Group Theory    2. Mathematics    3. Physics    4. Science/Mathematics    5. Groups & group theory    6. Science / Physics   

Reviews (2)

the best math textbook I've ever had
This book was the foundational textbook for a 100-level class in symmetry at my university. I recommend it highly to anyone who wants to get a better feel for what mathematicians actually do and think about and work with. Folks who never got into the higher math classes often have a different idea of what mathematics is all about than mathematicians. At the level of introductory algebra and geometry and even some calculus, math education often seems to be mainly about memorizing formulas and recognizing in which situations to apply them. That's an important thing to learn, but it is not useful for imparting an idea and a feel of the field of mathematics as a whole. Farmer's book brings home the understanding that mathematics is, at its heart, about patterns and that mathematics is not so much about memorization and application as it is about discovery.
An excellent primer on abstract algebra
Groups are the first structures encountered in abstract algebra and form the foundation for most of the others. Fortunately, they are also the easiest to physically represent, so in some sense they are the most concrete. In this book, groups are introduced as the motions and structures of geometric figures, so the presentation is largely by diagram rather than formula. Very little previous knowledge of mathematics is required and after reading the book, you will have a solid understanding of what a group is. Read more

Subjects:  1. Group theory    2. Logic    3. Mathematics    4. Pattern perception    5. Science/Mathematics    6. Symmetry (Physics)    7. Theory Of Groups    8. Groups & group theory   

Subjects:  1. Calculus    2. Functional Analysis    3. Functions of real variables    4. Group Theory    5. Integrals, Generalized    6. Mathematics    7. Measure theory    8. Science/Mathematics    9. Topology    10. Calculus & mathematical analysis    11. Mathematics / Differential Equations   

Subjects:  1. Algebraic Fields    2. Class field theory    3. Group Theory    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Abelian closure    8. Algebraic number theory    9. Mathematics / Number Theory    10. idele groups    11. number fields    12. reciprocity laws   

Subjects:  1. Applied    2. Group Theory    3. Mathematics    4. Science/Mathematics    5. Algebra    6. Mathematics / Algebra / General   

Reviews (9)

the source!
This is modern Galois Theory, straight from the horse's mouth! Galois Theory is taught today using field extensions rather than by actually solving polynomials, students also learn to view a field extension as a vector space over the smaller field; both of these things were pioneered by Artin. The book also has short, clear proofs of all the main theorems. The only problem is that there are no problems to work on, so I have to say this is only a good reference for Galois Theory.

Succinct exposition of modern Galois theory by a pioneer.
Emil Artin's short book gets a mention in most texts on just enjoy
during reading this cute booklet, you can surely hear the gentle talk of an old math maven.(from the publishing date, the auther was 44 but that's my impression.) with a cup of coffee, stretch those edgy wrinkles of your brain. ... Read more

Subjects:  1. Algebra - General    2. Galois theory    3. Group Theory    4. Mathematics    5. Science/Mathematics    6. Fields & rings    7. Mathematics / General    8. Theory of art   

Reviews (1)

Excellent introduction.
This book is an excellent introduction to the use of group theory in physics, especially in crystallography, special relativity and particle physics. Perhaps most importantly, Sternberg includes a highly accessible introduction to representation theory near the beginning of the book. All together, this book is an excellent place to get started in learning to use groups and representations in physics. ... Read more

Subjects:  1. Algebra - General    2. Mathematics    3. Physics    4. Science    5. Science/Mathematics    6. Groups & group theory    7. Groups (Mathematics)    8. Mathematics / Algebra / General