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Matrix Groups for Undergraduates (Student Mathematical Library,) [Paperback]

Kristopher Tapp
4.3 out of 5 stars  See all reviews (6 customer reviews)

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Book Description

June 13, 2005 0821837850 978-0821837856
Matrix groups are a beautiful subject and are central to many fields in mathematics and physics. They touch upon an enormous spectrum within the mathematical arena. This textbook brings them into the undergraduate curriculum. It is excellent for a one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori. The volume is suitable for graduate students and researchers interested in group theory.

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Matrix Groups for Undergraduates (Student Mathematical Library,) + Matrix Groups: An Introduction to Lie Group Theory
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Editorial Reviews


"this is an excellent, well-written textbook which is strongly recommended to a wide audience of readers interested in mathematics and its applications. The book is suitable for a one-semester undergraduate lecture course in matrix groups, and would also be useful supplementary reading for more general group theory courses." ---- Mathematical Reviews

Product Details

  • Series: Student Mathematical Library
  • Paperback: 166 pages
  • Publisher: American Mathematical Society (June 13, 2005)
  • Language: English
  • ISBN-10: 0821837850
  • ISBN-13: 978-0821837856
  • Product Dimensions: 5.5 x 8.3 inches
  • Shipping Weight: 8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #544,892 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
17 of 18 people found the following review helpful
5.0 out of 5 stars A Real Gem for Learning the Subject February 14, 2008
Format:Paperback|Verified 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
Format:Paperback|Verified 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.
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6 of 7 people found the following review helpful
5.0 out of 5 stars Great book on matrix groups September 30, 2011
By Pedro
Format:Paperback|Verified 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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