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Review
From the reviews of the first edition: MATHEMATICAL REVIEWS "This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited background…The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate students…To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory." "This book is an introduction to Lie group theory with focus on the matrix case. … This book can be recommended to students, making Lie group theory more accessible to them." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003)
Product Description
This book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility.
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First Sentence
Throughout, k will denote a (commutative) field. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Throughout, k will denote a (commutative) field. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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2 reviews
9 of 9 people found the following review helpful
Find a better introduction
28 Dec 2009
Format:Paperback|Amazon Verified Purchase
It's about time that some decent attention is being given to matrix groups and Lie theory. I like the range of this book. However, there are better introductions. The main problem with this book is that its prerequisites are extremely unclear and its content is somewhat uneven. For example, it's hardly an undergraduate introduction if it needs a strong foundation in topology and a first reading doesn't seem to really require that or even some of the other concepts introduced. Sometimes when a concept is introduced, a theorem is stated or snatches of theory are brought in, the reader is left hanging without a more thorough contextual explanation or even a proof. For example, it's annoying to see a theorem stated and unproven without further comment and without any reference. The text might even be a little overwhelming for a first year graduate student. It would be difficult to teach a cogent and logically laid out course using the text. There are better introductory texts available now which are far more accessible to the intended audience. The author might want to do a little rewriting using Occam's Razor because it has the potential to be a more thorough intro than that available elsewhere.
On the plus side (more for the SUMS series than for any one book), having answers to the exercises helps the student immeasurably. In my opinion, any math text that has no answers to the exercises belongs to the last century and is either a reflection on the author's lack of industry or a basic fear that students would find little need to attend classes. But at this level of subject, we all know that attendance is directly proportional to the quality of the lecturer, not the quality of the text.
On the plus side (more for the SUMS series than for any one book), having answers to the exercises helps the student immeasurably. In my opinion, any math text that has no answers to the exercises belongs to the last century and is either a reflection on the author's lack of industry or a basic fear that students would find little need to attend classes. But at this level of subject, we all know that attendance is directly proportional to the quality of the lecturer, not the quality of the text.
7 of 30 people found the following review helpful
worst binding quality I've ever seen
29 Mar 2008
Format:Paperback
I've been been reading it for only half an hour so I can't say much about the content of this book,however one thing is clear this book's life is going to be very very very short,in fact I don't think that tomorrow will be in one piece,I'm very disappointed to say the least,I don't understand how springer can produce such a poor quality book
now I could try to glue it wich is a mess or collect the pages as they fall apart and staple them,unfortunately I have to say that this is not a very rare case, cause many Springer paperbacks suffer from similar lack of binding quality
now I could try to glue it wich is a mess or collect the pages as they fall apart and staple them,unfortunately I have to say that this is not a very rare case, cause many Springer paperbacks suffer from similar lack of binding quality
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