Subjects:  1. Algebra - Linear    2. Geometry - Algebraic    3. Group Theory    4. Mathematical Analysis    5. Mathematics    6. Microcomputer Programming    7. Sociology    8. Mathematics / Group Theory   

Subjects:  1. Applied    2. Differential Equations    3. Global analysis (Mathematics)    4. Global differential geometry    5. Hamiltonian systems    6. Lie groups    7. Mathematical Physics    8. Mathematics    9. Science    10. Science/Mathematics    11. Analytic topology    12. Mathematics / Group Theory   

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

Subjects:  1. Advanced    2. Geometric group theory    3. Group Theory    4. Hyperbolic groups    5. Mathematics    6. Science/Mathematics    7. Groups & group theory   

Subjects:  1. Group Theory    2. Mathematics    3. Problems, exercises, etc    4. Groups & group theory    5. Mathematics / General   

Reviews (5)

Well done explanations of basic group theory
The study of abstract algebra begins with the study of groups and that starts with the basics of mathematical proof, sets and binary operations. This book begins with those basics and then steps through the fundamental concepts of group theory. The chapters on groups are:
A very fine introduction
I'm learning group theory in order to use it in physics. I found this book very good for a first introduction to the subject. It starts with pretty simple stuff and then proceeds with more serious matters. I find the example very clear, and I especially appreciate that full solutions to the exercises are provided, so that you can check your own findings. There are a few easy to amend typos, and I think the demonstration on page 46, theorem 20, part (2) is false. Finding another demo was a good exercise ! A pleasant surprise
Many books on algebra lose sight of the basic underlying ideas when the author gets caught up in the formalism. Formalism is good but, as Bourbaki has demonstrated, it isn't always the best thing for teaching newcomers.Read more

Subjects:  1. Algebra - General    2. Group Theory    3. Mathematics    4. Science/Mathematics    5. Set Theory   

Reviews (1)

A Fine Synthesis of Combinatorics, Geometry, and Algebra
With his usual lucidity, Fulton brings together the surprisingly wide area of mathematics concerned with Young tableaux.These are combinatorial patterns which index basis vectors of group representations (either of the symmetric group or the general linear group).These vectors can be seen as Plucker coordinate functions on non-linear representations, namely homogeneous spaces (Grassmannians and flag varieties).Thus, Young tableaux form an invaluable tool to examine these representations and varieties in concrete detail.Fulton also gives a good exposition of the combinatorial operations on tableaux which reflect the crystal basis structure from quantum GL(n), though Fulton does not explicitly discuss quantum groups.Other good expositions of these topics, from a more algebraic and combinatorial point of view, are Sagan's newly revised "The Symmetric Group", and Stanley's "Enumerative Combinatorics", Vol 2. ... Read more

Subjects:  1. Algebra - General    2. Geometry - General    3. Group Theory    4. Mathematics    5. Science/Mathematics    6. Young tableaux    7. Combinatorics & graph theory    8. Mathematics / Algebra / General   

Subjects:  1. Algebra - General    2. Algebraic Geometry    3. General    4. Geometry - Algebraic    5. Group Theory    6. Mathematics    7. Number Theory    8. Rational points (Geometry)    9. Science/Mathematics    10. Theory Of Numbers    11. Torsion theory (Algebra)    12. Geometry    13. Mathematics / Number Theory   

Subjects:  1. Graphic Methods    2. Mathematics    3. Science/Mathematics    4. Combinatorics & graph theory    5. Groups & group theory    6. Mathematics / Graphic Methods    7. Mathematics | Pure Mathematics   

Reviews (2)

The Perfect Supplement to RJ ZIMMER!
As I read this masterpiece of 20th century mathematics, I couldn't help thinking of its relation to the book that defines modern group theory, RJ Zimmer's Ergodic Theory and Semisimple Groups.Coincidence?I think not.Robert Zimmer's book is simply the best there is, and Margoulis' brilliant work is an excellent supplement to that standard mathematical text.As the great Swiss mathematician Armand Borel once said, "Margoulis' masterpiece, while inferior to some of my own work, is an excellent supplement to Zimmer's classic.Zimmer's book is the standard to which all mathematicians should aspire (along with myself, bien sur).Other than my own work, Margoulis' comes as close as possible to reaching that standard."

The Perfect Supplement to RJ ZIMMER!
As I read this masterpiece of 20th century mathematics, I couldn't help thinking of its relation to the book that defines modern group theory, RJ Zimmer's Ergodic Theory and Semisimple Groups. Coincidence? I think not. Robert Zimmer's book is simply the best there is, and Margoulis' brilliant work is an excellent supplement to that standard mathematical text. As the great Swiss mathematician Armand Borel once said, "Margoulis' masterpiece, while inferior to some of my own work, is an excellent supplement to Zimmer's classic. Zimmer's book is the standard to which all mathematicians should aspire (along with myself, bien sur). Other than my own work, Margoulis' comes as close as possible to reaching that standard." ... Read more

Subjects:  1. Algebra - Linear    2. Group Theory    3. Lattice theory    4. Lie Groups    5. Mathematics    6. Science/Mathematics    7. Semisimple Lie groups   

Subjects:  1. Differential Equations - Partial Differential Equations    2. Differential equations    3. Differential equations, Partia    4. Differential equations, Partial    5. Lie groups    6. Mathematics    7. Numerical solutions    8. Science/Mathematics    9. Groups & group theory    10. Science / Mathematical Physics   

Subjects:  1. Adeles    2. Automorphic forms    3. Group Theory    4. Linear algebraic groups    5. Mathematics    6. Representations of groups    7. Science/Mathematics    8. Groups & group theory    9. Linear algebra    10. Mathematics / Group Theory   

Reviews (1)

Decent at best.
The book is decent.But is not a great text book.It's highlihgted formulas, etc... are very helpful, but it doesn't seem to explain a lot of things in a way to make them easily understandable.I have used manydifferent math books, and I would not use this one unless you are teaachingextremely bright students. ... Read more

Subjects:  1. Algebra    2. Algebra - College    3. Group Theory    4. Mathematics    5. Science/Mathematics    6. Trigonometry    7. Euclidean geometry    8. Groups & group theory   

Reviews (1)

Good Introduction to the zoo of Hyperbolic Geometry
This book is intended to introduce readers toHyperbolic Geometry in 3dimensions.The book covers from a review of hyperbolicsurfaces to theclassification program of 3-manifold initiated by Thurston. ... Read more

Subjects:  1. Geometry    2. Geometry - Algebraic    3. Geometry, Hyperbolic    4. Group Theory    5. Kleinian groups    6. Mathematical Analysis    7. Mathematics    8. Science/Mathematics    9. Theory Of Functions    10. Three-manifolds (Topology)    11. Topology - General    12. Algebraic topology    13. Complex analysis    14. Mathematics / Geometry / Algebraic    15. Mathematics | Computational Mathematics   

Subjects:  1. Algebra - Linear    2. Group Theory    3. Linear algebraic groups    4. Mathematics    5. Science/Mathematics    6. Theory Of Groups    7. Groups & group theory    8. Mathematics / Algebra / Linear    9. Mathematics / Group Theory    10. Mathematics-Group Theory   

Reviews (4)

Great mathematics and graphics
The mathematician Felix Klein(1849-1925) made some great discoveries that can now be well understood by using computer graphics.Felix Klein is known for his work in non-euclidean geometry and for his work on the connections between geometry and group theory.
How mathematics can be used to create physical beauty
As a long-time reviewer of mathematics books, there was a time when I grew very bored with books written for the general mathematical audience. For years, it seemed mandatory that all contain a section on basic fractals and the Mandelbrot and Julia sets. It was not that the topics were not interesting, I found them fascinating, it was just that the explanations were all so similar that it became tedious to read them. Therefore, when I looked at the coverage of this book, I felt a pang of negative nostalgia, thinking that what I would find would be a repeat of what I had read so many times. Discrete groups made easy
[this review shall replace the already existing one]Read more

Subjects:  1. 1849-1925    2. Algebra - General    3. Discrete Mathematics    4. Fractals    5. Group Theory    6. Klein, Felix,    7. Mathematics    8. Science/Mathematics    9. Theory Of Groups    10. Algebra    11. Computing and Information Technology    12. Geometry    13. Mathematics / Applied   

Subjects:  1. Algebra - Linear    2. Group Theory    3. International Relations - Arms Control    4. Mathematics    5. Political Science    6. Politics/International Relations    7. Safety    8. Algebraic topology    9. Groups & group theory   

Reviews (2)

typical math text
Sadly, this book does not live up to its Comprehensive, well organized, very applicable
The book may be considered an update of Weyl's classicfrom 1946 "The classical groups, their invariants andrepresentations". Naturally the theory has developedimmensly since then and a new comprehensive presentation has been urgently overdue.Goodman and Wallach are not only among the most qualified to write this next "classic" on the subject, they alsoput a phantastic effort into making it comprehensive, readable, and pleasant to use. I found it easy to find needed resultsand concrete formulae on decompositions of tensors andharmonics, duailty groups and centralizer algebras, mulitiplicity formulae, branching laws, etc.. The results aresystematically organized - almost in an "encyclopedial" style.The book also contains rather modern results, such as, for example, new proofs of the Kostant Rallis Theorem or therelationsbetween invariant theory and the Jones knot polynomial. Read more

Subjects:  1. Control Theory    2. Mathematics    3. Partial Differential Equations    4. Probability & Statistics - General    5. Science/Mathematics    6. Groups & group theory    7. Mathematics / Algebra / General   

Subjects:  1. Algebra - General    2. Group Theory    3. Mathematics    4. Permutation groups    5. Science/Mathematics    6. Groups & group theory    7. Mathematics / Algebra / General   

Subjects:  1. Advanced    2. Automorphic forms    3. General    4. Group Theory    5. Mathematics    6. Representations of groups    7. Science    8. Science/Mathematics    9. Trace formulas    10. Unitary groups    11. Calculus of variations    12. Groups & group theory    13. Mathematics / Advanced    14. Mathematics / Group Theory    15. Mathematics-Advanced