Subjects:  1. Advanced    2. Algebra - Abstract    3. Calculus    4. Diophantine equations    5. Ergodic theory    6. Lie groups    7. Mathematics    8. Measure theory    9. Number theory    10. Science/Mathematics    11. Calculus & mathematical analysis    12. Mathematics / Algebra / Abstract   

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Boolean Algebra    4. Combinatorics    5. Discrete Mathematics    6. Lattice Theory    7. Mathematics    8. Science/Mathematics    9. Semimodular lattices    10. Mathematical logic    11. Mathematics / Combinatorics   

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

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - General    4. Mathematics    5. Rings    6. Science/Mathematics   

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Category Theory    4. Lattice Theory    5. Mathematics    6. Science/Mathematics    7. Linear algebra    8. Mathematics / Differential Equations   

Subjects:  1. Algebra - Abstract    2. Mathematics   

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra, Abstract    4. Computer Books: Languages    5. Computer Programming Languages    6. Computer-assisted instruction    7. Group Theory    8. ISETL (Computer program langua    9. ISETL (Computer program language)    10. Mathematics    11. Science/Mathematics    12. Mathematics / Group Theory   

Subjects:  1. Algebra - Abstract    2. Applied    3. Logic    4. Mathematics    5. Science/Mathematics    6. Algebra    7. Applied mathematics    8. Mathematics / Algebra / Abstract   

Reviews (1)

*The* reference for this stuff, but it's poorly indexed
This is *the* reference for symmetric functions and related topics.The second edition is greatly expanded, including (among other things) valuable material on Macdonald polynomials (though the author modestly does not refer to them by this term).The exposition is clean and to the point, as we have come to expect of Macdonald.The only defect of the book is that it can be hard to find things in it.The index is much too short, and much of the material is presented in long lists of disconnected "examples" that are very hard to search through quickly. ... Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Combinatorics    4. Group Theory    5. Mathematics    6. Science/Mathematics    7. Calculus & mathematical analysis    8. Combinatorics & graph theory    9. Groups & group theory    10. Mathematics / Combinatorics    11. Mathematics | Pure Mathematics   

Subjects:  1. Advanced    2. Algebra - Abstract    3. Business / Economics / Finance    4. Finance    5. Mathematical models    6. Mathematics    7. Rate of return    8. Science/Mathematics    9. Transaction costs    10. Finance & Accounting   

Subjects:  1. Algebra - Abstract    2. Applied    3. Functional Analysis    4. Functions, Special    5. Mathematical Analysis    6. Mathematics    7. Science/Mathematics    8. Theory Of Functions    9. Applied mathematics    10. Calculus & mathematical analysis    11. Mathematics / Applied    12. Mathematics | Applied Mathematics   

Subjects:  1. Algebra - Abstract    2. Algebra - Linear    3. Hopf algebras    4. Mathematics    5. Science/Mathematics    6. Fields & rings   

Reviews (5)

Shortest journey from group theory to Galois theory
This book provides the shortest journey from group theory to Galois theory (which determines when a polynomial equation can always be solved by means of an algebraic formula).Any topic in abstract algebra that isn't absolutely essential to this "trip" has been omitted from this book.Hence there's no coverage of ideals of rings, Euclidean domains, etc. The coverage of Galois theory is very rushed and proves only half of the theorem that is the book's ultimate goal; namely, that a polynomial equation can be solved by means of an algebraic formula if and only if the equation's Galois group is solvable.Some of the important proofs later in the book are sketchy.
Excellent text for a first course
I taught out of the hardcover version of this book at SUNY College at Oneonta many moons ago.It was a course for first-semester sophomore mathematics majors.The goal of the book is to develop the subject matter that is needed to prove that the fifth degree polynomial is not solvable by radicals, i.e. there is no analogy to the Quadratic Formula for the quintic.(There is for the cubic and the quartic.)We had a good time because the course was focused on this one goal and the class knew exacly where we were headed.We got there, too.It was very easy to teach from this book and students rated it very highly.The students that I taught had Calculus I and II and a Foundations course as freshmen.The prior exposure to logic, sets and methods of proof (development of the integers) was very helpful, as was the maturity gained from the calculus (although the subject matter of Calculus was not necessary).I supplemented by rigorously developing the rational numbers, saving the reals for the Intro to Analysis course that followed this one.I am now a biostatistician outside of academia, but I hope that professors who are now teaching Abstract (Modern) Algebra will consider using this text in paperback form.

Roots (as in square roots)
This charming little introit to abstract algebra is keyed on a theme of the algebraic equation, and the discovery of the insolubility of the quintic. This includes the history and final plight of the circle-squarers, and some of the history of Galois and Abel, working heroically and heuristically in the early nineteenth century without the recent easier access to the subject now available.

Subjects:  1. Algebra - Abstract    2. Mathematics   

Subjects:  1. Algebra - Abstract    2. Mathematics   

Subjects:  1. Algebra - Abstract    2. Differential Equations    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Calculus & mathematical analysis   

Reviews (1)

Very well written and motivates the subject well.
Physicists view vertex algebras in many different ways, depending on their area of research. Some have used them without calling them as such, such as those dealing with the quantum operator equations of motion in the Heisenberg picture for potentials of higher order than quadratic. Researchers in string theory will view them in the context of two-dimensional conformal field theory, and in the use of the ubiquitous Virasoro algebra. Those in quantum field theory/elementary particle physics come across them in the context of the operator product expansion.
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Subjects:  1. Algebra - Abstract    2. Algebra - Linear    3. Curves, Algebraic    4. Mathematics    5. Science/Mathematics    6. Vertex operator algebras   

Reviews (1)

A good new graduate text in abstract algebra
The student who wishes to understand module theory needs to have an understanding of the several results from lattice theory . This well-written text seeks to bring together all of the results that can be brought to bear on this subject into one self contained text that includes, not only the necessary basics of lattice theory, but detailed proofs of all the results in a manner that makes the subject approachable. Beginning with a basic definition of a lattice and its well known properties,the textmoves on to materials on lattice theory from recent texts on module theory. Several new concepts by the authorsuch as fully invariant extending lattices are interspersed throughout the text. In addition to a useful index and a comprehensive list of references, more than fifty pages are devoted to solutions to a comprehensive list of exercises(forty in the first chapter and about a dozen in each of the others). This text seems to fill a gap. It is readable and well done. ... Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Algebraic Fields    4. General    5. Group Theory    6. Lattice Theory    7. Logic    8. Mathematics    9. Modules (Algebra)    10. Science/Mathematics    11. Groups & group theory    12. Mathematics / Algebra / General    13. Mathematics / Logic    14. Medical-General   

Subjects:  1. Algebra - Abstract    2. Applied    3. Computer Science    4. Discrete Mathematics (Computer Science)    5. Lattice Theory    6. Logic    7. Logic Design    8. Mathematics    9. Science/Mathematics    10. Boolean Algebras    11. Computers / Computer Science    12. Lattice Equations    13. Lattice Functions    14. Mathematical logic   

Reviews (1)

The latest developments!
Students and researchers can find here the material which lies at the foundation of the subject, and read about the latest and most exciting developments in this wonderful book.-- Material which would otherwise be difficult to extract from the diverse journal literature in math and in physics. The bibliography and the index are both great as well. The treatment of the material in the book aims at students interested in operator algebras, mathematical physics, [especially statistical mechanics and conformal field theory], and low dimensional topology. The book starts with a very nice treatment of the basics in operator algebras, K-theory, and it then moves on to the applications: eg., the Ising model, subfactors and bimodels, the Jones index [for subfactors] and its applications, topological quantum field theory, and more. ... Read more

Subjects:  1. Algebra - Linear    2. Mathematical Physics    3. Mathematics    4. Operator algebras    5. Quantum groups    6. Science    7. Science/Mathematics    8. Symmetry (Physics)    9. Category theory    10. Fields & rings    11. Functional analysis    12. Mathematics / Algebra / Abstract    13. Mathematics | Applied Mathematics    14. Relativistic quantum mechanics & quantum field theory    15. Statistical physics   

Subjects:  1. Algebra - Abstract    2. Unassigned Title    3. Algebra