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   

Reviews (1)

Be prepared
This monograph gives an excellent introduction to a very abtruse and difficult subject. Readers familiar with the K-theory of operators due to Brown-Douglas-Fillmore and the Kadison-Ringrose theory of operator algebras should have ample background to read this book. These background works are very advanced mathematical subjects and so this book should be viewed as one written for specialists only.KK-theory can be thought of in some sense as a unification of K-homology and K-cohomology. This takes place via the KK bivariant groups of the mathematician G.G. Kasparov. Ordinary K-theory has its origins of course in the theory of elliptic operators via the work of M.Atiyah and I.Singer on index theory. The authors of this book however do not motivate their book at all with any history or with any discussion of elliptic operators but instead proceed from a purely algebraic/axiomatic point of view. This approach is well suited to mathematicians coming to the subject for the first time since no doubt they are familiar with the BDF theory if they are choosing to learn KK-theory. However, KK-theory is now finding applications in physics, such as superstring and dual theories, and physicists would not in general be familiar with the BDF/Kadison-Ringrose works. For physicists then this book might be very difficult to follow. That being said this is an interesting subject, and the authors do a good job for those who are prepared. The product on KK groups that Kasparov constructed can be used to obtain all the usual products in topological K-theory, such as the cap, cup, and slant products. Reading the book will also prepare one for the fascinating area of non-commutative geometry ala Alain Connes. ... Read more

Subjects:  1. Algebra    2. Algebra - Linear    3. General    4. KK-theory    5. Mathematics    6. Science/Mathematics    7. Mathematics / Algebra / General   

Reviews (30)

CAUTION: No answers or solutions provided!
I learn mathematics by solving problems (including proving theorems etc). The author states it clearly in the introduction: No answers or solutions are provided for the exercises in the book (apart from the solved examples) and the solutions manual is available ONLY to course instructors that use the book in their course; the solutions manual is NOT available to individual readers for self study. I say, buy at your own risk.

A great book, innovative!!
I love the style of the author a lot. But if you are looking for some more comprehensive and less abstract but more applied oriented book, go for Hubbard's. Also if you want to just master the TECHNIQUES of Linear Algebra, try Harold Edwards' Linear Algebra--This is a very standard classic type of book written by a great mathematician.

this book is short and skips a lot in proving step.little annoying to proof all the omitting by prof.Axler
I read all this book at 4week.proving all the omitted proof process professor Axler did.At first it was fun but when I wanted to read a little faster it was a little bit obstacle also a lottle bit annoying.
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Subjects:  1. Algebra - Linear    2. Algebras, Linear    3. Linear Algebra    4. Mathematics    5. Science/Mathematics    6. Mathematics / Algebra / Linear   

Reviews (2)

Not what i'd hoped for
This book gives you the theorems, with examples of how to use the theorems.However i was disappointed because i was hoping to that it would make linear algebra clearer for me.Specifically, i was hoping for proof's of the theorems, which this book doesn't contain.It is a good reference book to look things up in, but not a book for obtaining a deeper understanding.

Great study guide / reference book!
I really, really don't like learning mathematics, but unfortunately some maths is required by my university's computer science course.Read more

Subjects:  1. Algebra - Linear    2. Linear Algebra    3. Mathematics    4. Study Guides    5. Mathematics / Algebra / General    6. Mathematics and Science   

Subjects:  1. Computer Books: General    2. Computer Graphics - Design    3. Computer Graphics - General    4. Computers    5. Computers - Other Applications    6. Quaternions    7. Computers / Computer Graphics / Design    8. Linear algebra   

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. Algebra - Linear    2. Algebras    3. Banach algebras    4. Differential Equations    5. Mathematics    6. Probability & Statistics - General    7. Science/Mathematics    8. Functional analysis    9. Linear algebra    10. Mathematics / Differential Equations   

Subjects:  1. Algebra - Linear    2. Geometry - General    3. Geometry, Differential    4. Lie groups    5. Mathematics    6. Science/Mathematics    7. Analytic geometry    8. Groups & group theory   

Subjects:  1. Algebra - Linear    2. Computer Books: General    3. Computer Science    4. Computers    5. Mathematical Analysis    6. Mathematics    7. Number Theory    8. Mathematics / Number Theory   

Subjects:  1. Algebra - Linear    2. Mathematical Analysis    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Character    7. Ergodic    8. Lattice    9. LocalGlobal    10. Mathematics / Number Theory   

Subjects:  1. Advanced    2. Applied    3. Control Theory    4. Differentiable Dynamical Systems    5. Differentiable dynamical syste    6. Differential Equations    7. Engineering - General    8. Mathematics    9. Matrices    10. Science/Mathematics    11. Stability    12. Linear programming    13. Mathematics / Algebra / Linear    14. Mathematics / Matrices    15. Mathematics-Applied    16. Technology-Engineering - General    17. control engineering    18. matrix computations    19. stability of dynamical systems   

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

Reviews (2)

Time of No Reply
A month after I placed my order, it still hadn't arrived.Via email, I contacted the seller, who never bothered to reply.Caveat emptor!

Theory heavy
I used this textbook as part of my linear algebra course at university.The positive aspects about this book is that it is well-written and the concepts are nicely presented.The practice problems at the end of each section are also quite helpful.Read more

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

Reviews (5)

Good service
Buying from Aamazon.com directly instead of from its markplace is a pleasent experience. It is safe and faster delivery. Highly recommend.

Solid and understandable guide to matrix algebra
I am a PhD level graduate student who has never had a matrix algebra course.I got this book to help with a Linear Models course I am currently taking.The book is very helpful, and provides a solid background in the first few chapters before building on them for more complex results.Definitely a good reference to have nearby.

Its a good tool book
This is a pretty good tool book for a statistician but it still has some samll problems, (1) the first few chapters, author should give more examples to describe concepts. (2) author can use more clear or simple way to describe many basic concepts but he does not do it! (if you have taken Linear Algebra from math, you will understand what I mean). Overall, this is a pretty good bookfor beginners. ... Read more

Subjects:  1. Algebra - General    2. Algebra - Linear    3. Algebras, Linear    4. Linear Algebra    5. Linear models (Statistics)    6. Mathematics    7. Matrices    8. Multivariate Analysis    9. Probability & Statistics - General    10. Science/Mathematics    11. Algebra    12. Mathematics / Statistics    13. Matrix Algebra    14. Probability & statistics   

Subjects:  1. Algebra - Linear    2. Calculus    3. Geometry - General    4. Mathematical Physics    5. Mathematics    6. Science    7. Science/Mathematics    8. Topology - General    9. Mathematics for scientists & engineers    10. Vector & tensor analysis   

Reviews (6)

Used for Self Study
I used this book for an independent study of linear algebra in undergrad.I'd had no prior exposure to the field, but had taken very good real analysis and abstract algebra courses prior.My self-study was quite effective, which is a testament to the book, since it was essentially the only material I had.(There were a few typos I remember seeing, as well as some unclear formulas/notation here and there, hence the four stars, but nothing serious).

Beautiful Work
I used this book for a first course in linear algebra at Ohio State University and I could not have been more satisfied.It is a challenging book to use, but very rewarding for those who put the time into it.

OK, but could be better.
The book sometimes eliminates using some symbols when the meaning is clear from the context; this is OK only if you either have prior understanding of the material presented or easy access to an expert. ... Read more

Subjects:  1. Algebra - Linear    2. Algebras, Linear    3. Linear Algebra    4. Mathematics    5. Science/Mathematics    6. Algebra    7. Lineare Algebra    8. Mathematics / Algebra / Linear   

Subjects:  1. Algebra - Linear    2. Algebras, Linear    3. Geometry, Analytic    4. Linear operators    5. Mathematics    6. Science/Mathematics    7. Study and teaching    8. Linear algebra   

Reviews (2)

Excellent
Topos theory now has applications in fields such as music theory, quantum gravity, artificial intelligence, and computer science. It has been viewed by some as being excessively abstract and difficult to learn, and this is certainly true if one attempts to learn it from the research literature. The use of this book to learn topos theory certainly puts this view to rest, as the authors have given the readers an introduction to topos theory that is crystal clear and nicely motivated from an historical point of view. Indeed the prologue to the book gives the reader a deep appreciation of the origins of the subject, and could even serve as an introduction to a class on algebraic geometry.
Clear explicit descriptions
This book is written in the best Mac Lane style, very clear and very well organized. It also benefits from Moerdijk's extensive work organizing the theory of Grothendieck toposes by elementary means. The reader should havebasic graduate knowledge of algebra and topology. The book is long becauseit gives very explicit descriptions of many advanced topics--you can learna great deal from this book that, before it was published, you could onlylearn by knowing researchers in the field. ... Read more

Subjects:  1. Algebra - General    2. Algebra - Linear    3. Algebraic Topology    4. Logic    5. Mathematics    6. Science/Mathematics    7. Toposes    8. Geometry    9. Mathematical logic    10. Mathematics / Algebra / General    11. Mathematics / Algebra / Linear    12. Mathematics-Logic    13. Topology   

Reviews (3)

Long Live the Homoligarchy!
This is by far the most accessible and well-written Homological Algebra book I've dealt with.I'm an analyst at heart, so the subject does not in any way come easy to me.However, the exposition in this book greatly shortened the learning curve, and Dr. Weibel provided a plethora of understandable examples and accessible exercises, all of which greatly aided my understanding of the subject.

Deeeep!
Now Homological Algebra is not a simple subject that can be picked up with only a minimal background.The subject is deep and permeates many different braches of mathematics.If you are thinking of buying this text, then I have two suggestions.First, just buy it.For the price, you will not find another book that is as up to date or as rich in content.Second, ask yourself you are ready for this text?What I would do is use Amazon's "Search Inside" in order to check out the first two or three pages of chapter one.If you feel at home with the material presented there, then just buy it.You will not be upset.Well, you may get upset-this book covers a lot of material and at times can be rather overwhelming.Let me stress that the level of comfort with the preliminary material is analogous to a tenured professors level of comfort with, say, Calculus.That is, very comfortable.With respect to the actual text, I am hard pressed to find any negative words.Weibel has set the modern standard and this text is fast becoming the standard from which all other texts will have to model themselves after.The material is presented in small palatable chunks that can be consumed at any time.Just make sure you have a new pencil and couple notebooks handy when you read this text.

Great homological algebra book!
This book was absolutely priceless for me while I was doing my qualifying exams and dissertation. Excellently written, with modern notation and applications and a clearly-exposited writing style. I wish all "hard" math books were written like this. Thanks Prof. Weibel ... Read more

Subjects:  1. Algebra - General    2. General    3. Mathematics    4. Science    5. Science/Mathematics    6. Linear algebra    7. Mathematics / Algebra / General   

Reviews (1)

A very recommanded book on the subject
This book is an introduction to the subject of Lie groups and Lie algebras. This is a general overview on the subject for students with no background on the subject. There are almost no proofs and this is not a text book. Nevertheless for the mature reader (say someone toward the end of his graduate studies) this is an amazing general introduction. It is clear that a lot of effort was used in order to give the reader as much knowledge as possible with minimal technical details as possible. Intuitive arguments are used when ever possible and motivation is there all along the way. The writing is very elegant and it is clear that the writers are masters in their field. So, if you want an overview on the subject and you do not need to go into technical details look no further then this book. ... Read more

Subjects:  1. Algebra - General    2. Algebra - Linear    3. Lie algebras    4. Lie groups    5. Mathematics    6. Science/Mathematics    7. Linear algebra    8. Mathematics / Algebra / General