Reviews (2)

Abstract Algebra vol 2 by Spindler
Page 174 volume 2 the author did not follow completely the proof of Nagell theroem as in Algebraic Number Theory by Stewart & TallInstead Heintroduced the matrix [1 1, -2 0], We may name it here for short S, Theauthor claims that S**42k = [-1 -1, -1 -1] mod 3 which is wrong S**42k =+-[1 0, 1 0] 4|k or 2|k respectively and = +-S 4|k-1 or 2|k-1 respectivelyin both cases the first entery in the total matrix as S**(42k +13) * [0 1]would be -1 and destroy the logic of the author in his argument However itdeos not violate the theory for -1 in a field of chratersistic 3 need notbe -1 in the integral domain Z[sqrt(-7)] I do here thank Amazon.com for thechance to report that for neithe the author nor the editorial at thepublisher has an address to communicate with. Abdu Shokr35-17 Ditmarsblvd suite 202 NY NY 11105 August 3 2000

A thorough, accessible and indispensable resource on algebra
This two volume set is by far the most complete text on abstract algebra available.Rich in detail, a wealth of examples and clear yet concise explanations provide the reader an accesible source to deepen his understanding of abstract algebra.Spindler conveys his love of algebraand a desire to reveal its riches to the average student. If you'verelied on Hungerford's / Lang's Algebra or Warner's Modern Algebra, thistext is the last text you will need. ... Read more

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - General    4. Algebra, Abstract    5. Applied    6. Mathematics    7. Number Systems    8. Science/Mathematics    9. Fields & rings    10. Mathematics / Number Systems   

Subjects:  1. Advanced    2. Algebra - Abstract    3. Algebra, Abstract    4. Applied    5. Applied Sciences    6. Mathematics    7. Science    8. Science/Mathematics    9. Algebra    10. Business & Economics / Economic Development   

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   

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 (7)

one of the best books on abstract algebra
I like this book very much. Pure math, all the proofs are complete and relatively easy to follow. Solutions for the odd numbered problems are provided. If you like math and want to learn the fundamentals of abstract algebra then this book is exactly what you need. It's written in theorem-proof/corollary style. I think every undergraduate student of mathematics, physics or information sciences should be able to use this book.

too concise in some parts, good elsewhere
I picked this book up at my students' society used bookstore for $10, it turned out to be a pretty good bargain. However, there are some theorems where the authors say something is obvious & I didn't think so. It isn't very often though, the rest of the book is pretty good, and I was a bit surprised because I had only heard of the well-known authors like Gallian, Herstein, Lang, etc. It covers maybe 3 courses worth of material too, including groups, rings, fields, vector spaces & modules, Galois Theory (complete with every possible application!), and more advanced stuff like a separate chapter on modules (in addition to the section with vector spaces), tensor products and principal ideal domains. There are also complete solutions to the odd-numbered problems. This book is surprisingly good except in certain parts, I like it.

A must for every math library
Bhattacharya is very concise and readable for a very difficult subject, if you are new to abstract algebra.His proofs are complete and expert and his outline is great.Also his problems are useful ... Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Algebra, Abstract    4. Mathematics    5. Science/Mathematics    6. Fields & rings    7. Mathematics / Algebra / General   

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. Algebra    2. Algebra - Abstract    3. Algebra - General    4. Algebra, Abstract    5. Applied    6. Mathematics    7. Science/Mathematics    8. Applied mathematics    9. Lattice theory    10. Mathematics / Algebra / General   

Reviews (30)

useful text for an undergrad course
Hilariously, I found this book in a local library, in the section devoted to primary school and high school maths. I guess the "Algebra" in the title suggested this location to some librarian. Anyhow, not to worry. I informed the library and they will reshelve this book in a better place.
Excellent for an introductory abstract algebra book
This is a great book.It's introductory, appropriate for undergrads taking abstract algebra for the first time, but at the same time, it is also very comprehensive, useful for graduate students.Although it explains the material in great depth and at a relatively slow pace, it does so in a logically sound manner so that it can lead the reader to develop mathematical maturity.Like many more advanced books, it has good cross-references, helping people to develop connections between the different parts of the material, and allowing the reader to jump around once she has mastered the basics.
too wordy
This book is a standard one for graduate-level algebra courses.I practically wore mine out over a year-long course, and came to know it intimately.Dummit and Foote is a book that teaches via wordy explanations and lots of examples.Of course, examples are very important.However, the explanations are often muddled and not clear (e.g. see tensor products).They frequently relegate important theorems or definitions to the exercises, and the organization is poor.Consequently, it can be very hard to find things later when you might need them.Also, the bindings on this book frequently fail.My book fell apart very quickly, and I know other students who had the same problem.I recommend Rotman's Advanced Modern Algebra instead of Dummit and Foote. ... Read more

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

Reviews (1)

A Report on 25 Years of Development
This book represents the results of the last 25 years of study of polynomial Identities. The chapter heading of the book describe the major development areas:
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Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Algebra - Intermediate    4. Combinatorial analysis    5. Mathematics    6. PI-algebras    7. Polynomial rings    8. Science/Mathematics    9. Algebra   

Reviews (3)

GREAT!
Great indtroductory book, very user friendly.It explains and shows in an easy to understand and simple way....lots of examples and explanations. EASY AND ENJOYABLE READ.

Lie algebra demystified
A practical introduction to an esoteric topic which frightens many physics students.
An excellent practical guide
This short book covers an important aspect that has been neglected by most textbooks on Lie algebras written for physicists, namely providing a comprehensible introduction for undergraduates based on detailed examples, computations and precise motivations, without having to develop the formal theory. This is not a textbook on Lie algebras in the usual sense, but a practical guide whose intention is to provide a solid comprehension of the main facts on (finite dimensional) Lie algebras used in physics. This justifies the choice of the objects analyzed, the compact real form su(N) of the Lie algebras sl(N,C), which constitute an essential tool in the study of the interacting boson model and nuclear rotational states. The topics covered by this book are quite modest (there are no general proofs and no development of classical problems like the classification of simple Lie algebras), and focuses on a detailed comment on the properties of simple algebras using mainly three Lie algebras, su(2),su(3) and su(4), before ennouncing the general case in the last chapter. However, this should not be understated, specially because the book explains carefully the usual notations (which change in the literature from author to author) and tries to clarify the reasons that justify the study of the formal theory. Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Geometry - General    4. Group Theory    5. Mathematical Physics    6. Mathematics    7. Science/Mathematics    8. Algebra    9. Lie algebra    10. Lie algebras    11. Mathematics / Algebra / General    12. Mathematics-Geometry - General    13. Nonassociative rings    14. Representation theory    15. Science-Mathematical Physics   

Subjects:  1. Algebra - Abstract    2. Mathematics    3. Science/Mathematics    4. Algebraic geometry    5. Mathematics / Algebra / Abstract   

Reviews (4)

A Fine Intro to Modern Algebra
A very readable first text on modern algebra!This book does a great job to ease the reader into the subject.Durbin keeps it in mind that students often struggle with reading and writing proofs at this level, and accomadates starting off with detailed proofs in the beginning and backs off as he moves on through the text.Those who want a more rigorous treatment may want to read Herstein.Over all, it's a fine introductory text.

Too vague with many errors in later chapters/sections
This book covers many of foundations of abstract algebra including groups, rings, homomorphisms, isomorphisms, Sylow's theorem, Galois theory, etc. While most of the sections are fairly well-worded, most of the text is vague and the more challenging problems are given without too much training on them in the section's text. Good Exposition, Poor Problems
This is a nice book overall.Clear exposition, good examples, and not too thick.I personally found the problems lacking in motivation and scandalously simple, which made it difficult for me to complete my homework sets (if you ain't learning nothin', it ain't worth doin').Read more

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - Elementary    4. Algebra - General    5. Algebra, Abstract    6. Mathematics    7. Science/Mathematics   

Reviews (2)

Great for beginners in the subject
This book is wonderful for beginners in K-theory of operator algebras because it also covers some fundamentals from other subjects that are needed. The proofs are always very clear. The best of it are theexcercises! Very many details of K-theory and its applications become clearwhen you do the excercises.

Great introduction to the subjects!
This book is a rarity in mathematics - a technical book on a difficult subject that remains entirely readable, even to non-specialists. Rather than the usual 300 pages of dense text and inscrutable proofs, the authorgives examples, straightforward proofs, and a writing style that borders onthe (gasp!) conversational. Highly recommended, especially fornon-mathematicians needing to learn K-theory. :) ... Read more

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - Linear    4. C*-algebras    5. English as a Second Language    6. Foreign Language Study    7. K-theory    8. Language    9. Mathematics    10. Research    11. Science/Mathematics    12. Algebraic topology    13. English    14. Groups & group theory    15. Mathematics / Research    16. Mathematics | Pure Mathematics   

Subjects:  1. Advanced    2. Algebra - Abstract    3. Algebra - General    4. Applied    5. General    6. Mathematics    7. Science    8. Science/Mathematics    9. Differential equations    10. Mathematics / Applied   

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Subjects:  1. Algebra - Abstract    2. Algebra, Abstract    3. Mathematics    4. Algebra   

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Galois theory    4. Mathematics    5. Science/Mathematics    6. Fields & rings    7. Mathematics / Algebra / General   

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - General    4. Applied    5. Finite fields (Algebra)    6. Mathematics    7. Science/Mathematics    8. Algebraic number theory    9. Mathematics / Algebra / General   

Subjects:  1. Algebra - Abstract    2. Algebra, Abstract    3. Mathematics    4. Science/Mathematics    5. Algebra   

Subjects:  1. Algebra - Abstract    2. Mathematics   

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Applied    4. Mathematics    5. Sociology    6. Algebraic number theory