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Matrix Groups for Undergraduates (Student Mathematical Library,)
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17 of 18 people found the following review helpful
on February 15, 2008
Format: PaperbackVerified Purchase
This book is a great introduction to matrix groups and related ideas. The author explains the basic ideas in a clear, concise, and precise way. Although there are many excellent texts on matrix groups and more abstract properties of groups, this book provides the most accessible introduction to the subject that I have found. The book is short and easy to read through, compact, and economically priced. I strongly recommend reading this book before attempting to delve into more advanced texts.

The clear and unified treatment of the real, complex, and quaternion groups is *very* nice. Overall, the writing style is so lucid, it is the kind of book where you feel that the writer is teaching you personally, rather than lecturing to an empty hall.

Because the book provides such an excellent introduction to the subject, I give it the full 5 stars. The book has a few typos and gaps, but most are pretty obvious. I hope that the author will expand on this book in a future edition, perhaps including a chapter on basic group theory. When you finish reading the book, your only complaint will be that it isn't longer! Given the excellent exposition, I will be on the lookout for any future texts from this author.
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8 of 9 people found the following review helpful
on November 15, 2010
Format: PaperbackVerified Purchase
It's true as the other reviewers have said: this is an exceptionally good introduction to Lie groups and Lie algebras via matrix groups. It's also suitable for self-study provided you have the required math background. Although it's very much in the definition-theorem-proof mode, there's plenty of insightful and well-written exposition motivating the formal development.

My only complaint is that there are no solutions to any exercises and even worse, the proofs of a number of propositions are left to the reader. This detracts from the value of the book for self-study, but not too much because on balance, in my view, the sheer excellence of the presentation pretty much makes up for that all too common "sin of omission".

The book is extremely concise: only about 137 small pages excluding exercises (no solutions) and back matter. To illustrate: in the chapter (pp. 5-20), one rapidly covers fields and skew-fields (pp. 7-8), quaternions (pp 8-9); the real, complex and quaternion skew-field inclusions (p. 10); matrices as linear transformations (pp. 15-16); general linear groups (pp. 17-18); and finally, change of basis via conjugation (pp. 18-20). In its entirety, the book covers, in the same no-nonsense way: Ch 1. Matrices, Ch. 2 All matrix groups are real matrix groups, Ch. 3 The orthogonal groups, Ch 4. The topology of matrix groups, Ch 5. Lie algebras, Ch 6. Matrix exponentiation, Ch. 7 Matrix groups as manifolds, Ch 8. The Lie bracket, Ch 9. Maximal tori. And, as another reviewer pointed out, the author's AMS website has a free download, Ch 10. Roots, and an errata sheet.

The pace might seem daunting for a first introduction, especially for self-study, but the exposition is so crystal clear that I could hardly put the book down (and I am not a mathematics major, just someone interested in learning the mathematics required for modern physics).

Autodidacts should especially note that it is essential that you have the prerequisites as stated in the introduction on p 7. To wit: multivariable calculus & basic analysis; abstract algebra (groups, subgroups, quotient groups, fields, morphisms, conjugation) and standard linear algebra including linear transformations and relation to matrices, eigenvalues/eigenvectors. You also need to be confident in your abstract mathematical skills; proofs are clear but they're generally quite abstract and concise; there's no hand-holding in that area.

If you're ready for the fast lane, fasten your seat belt and enjoy the ride!
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6 of 7 people found the following review helpful
on October 1, 2011
Format: PaperbackVerified Purchase
This book gathers the important properties of matrix groups and shows where the studies of these groups tend to. Indeed, the great thing about such groups is that they are :
a.) groups
b.) topological groups
c.) smooth manifolds (for most of them)
And usually in literature, you don't find these properties treated in the same book. That would be the original thing about this one.

It's clearly undergraduate level, but well explained. The only regret if I may say, is that many proofs are left as exercise, and I know it must be a size problem with the editor, but it's always better to have an "adult" view on the proofs instead of doing them on our own (that's why we have exercises, to use the theorems and properties).
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2 of 3 people found the following review helpful
on September 30, 2010
Format: Paperback
This is a great little book. It introduces all the major ideas of Lie group theory while keeping everything very accessible. Everything is presented in terms of matrix groups instead of abstract Lie groups so it avoids any big machinery and approaches the material in a very hands-on way.

The book is ideal for advanced undergrads or beginning graduate students wanting to understand the main topics and ideas of Lie groups from a down-to-earth perspective. It would also be good as a companion text for someone reading an abstract Lie group book.

I used the book to teach a seminar course for math-grad-school-bound juniors and seniors at a big state university. It was very successful with the students able to read, follow and present the material from the book to their peers in the seminar.

I understand the author has written an additional chapter of the book covering root systems which is available for free at the AMS webpage for the book, which can be found by googling "Tapp matrix groups." That site also keeps a running log of typos in the book.
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0 of 3 people found the following review helpful
on June 27, 2011
Format: PaperbackVerified Purchase
Il libro che ho comprato mi piace ed è utile per i miei studi.
El libro que he comprado me gusta y es útil para mis estudios.
I like the book I bought; it is useful for my studies.
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1 of 5 people found the following review helpful
on December 4, 2011
Format: PaperbackVerified Purchase
The book is free online and with much better reproduction of the photographs in the figures. Otherwise, the book is as the other readers have indicated.
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