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Matrix Groups for Undergraduates: Second Edition
 
Kristopher Tapp Saint Joseph’s University, Philadelphia, PA
Matrix Groups for Undergraduates
Softcover ISBN:  978-1-4704-2722-1
Product Code:  STML/79
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2938-6
Product Code:  STML/79.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-1-4704-2722-1
eBook: ISBN:  978-1-4704-2938-6
Product Code:  STML/79.B
List Price: $108.00 $83.50
Matrix Groups for Undergraduates
Click above image for expanded view
Matrix Groups for Undergraduates: Second Edition
Kristopher Tapp Saint Joseph’s University, Philadelphia, PA
Softcover ISBN:  978-1-4704-2722-1
Product Code:  STML/79
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2938-6
Product Code:  STML/79.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-1-4704-2722-1
eBook ISBN:  978-1-4704-2938-6
Product Code:  STML/79.B
List Price: $108.00 $83.50
  • Book Details
     
     
    Student Mathematical Library
    Volume: 792016; 239 pp
    MSC: Primary 20; Secondary 22

    Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent 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 the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots.

    This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.

    From reviews of the First Edition:

    This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. ... The book combines an intuitive style of writing with rigorous definitions and proofs, giving examples from fields of mathematics, physics, and other sciences where matrices are successfully applied. The book will surely be interesting and helpful for students in algebra and their teachers.

    European Mathematical Society Newsletters

    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.

    MathSciNet (or Mathematical Reviews)

    Readership

    Undergraduate and graduate students and research mathematicians interested in teaching and learning Lie groups, in particular, classical Lie groups.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Why study matrix groups?
    • Chapter 2. Matrices
    • Chapter 3. All matrix groups are real matrix groups
    • Chapter 4. The orthogonal groups
    • Chapter 5. The topology of matrix groups
    • Chapter 6. Lie algebras
    • Chapter 7. Matrix exponentiation
    • Chapter 8. Matrix groups are manifolds
    • Chapter 9. The Lie bracket
    • Chapter 10. Maximal tori
    • Chapter 11. Homogeneous manifolds
    • Chapter 12. Roots
  • Reviews
     
     
    • This book offers a very nice introduction to the theory of matrix groups and their Lie algebras. The background is kept to a minimum, only basics of calculus, linear algebra and group theory are assumed, while background on topology (of subsets of Euclidean space) is developed in the text. While the text gives complete and exact proofs, it is easy to read, appeals to intuition, and contains many pictures and helpful exercises.

      A. Cap, Monatshefte für Mathematik
    • [T]he second edition is an expanded and improved version of the original. It can be strongly recommended for an undergraduate course in Lie groups, or as complementary reading for a course in group theory. Prerequisites are basic: knowledge of algebra, geometry, and analysis at an undergraduate level. Hence the book is suitable for a wide audience of readers who are meeting applications of group theory in other areas of mathematics and physics, or even further afield.

      Alla S. Detinko, Mathematical Reviews
    • The author gives an inspiring presentation of the topics presented in this book.

      Erich W. Ellers, Zentralblatt Math
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 792016; 239 pp
MSC: Primary 20; Secondary 22

Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent 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 the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots.

This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.

From reviews of the First Edition:

This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. ... The book combines an intuitive style of writing with rigorous definitions and proofs, giving examples from fields of mathematics, physics, and other sciences where matrices are successfully applied. The book will surely be interesting and helpful for students in algebra and their teachers.

European Mathematical Society Newsletters

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.

MathSciNet (or Mathematical Reviews)

Readership

Undergraduate and graduate students and research mathematicians interested in teaching and learning Lie groups, in particular, classical Lie groups.

  • Chapters
  • Chapter 1. Why study matrix groups?
  • Chapter 2. Matrices
  • Chapter 3. All matrix groups are real matrix groups
  • Chapter 4. The orthogonal groups
  • Chapter 5. The topology of matrix groups
  • Chapter 6. Lie algebras
  • Chapter 7. Matrix exponentiation
  • Chapter 8. Matrix groups are manifolds
  • Chapter 9. The Lie bracket
  • Chapter 10. Maximal tori
  • Chapter 11. Homogeneous manifolds
  • Chapter 12. Roots
  • This book offers a very nice introduction to the theory of matrix groups and their Lie algebras. The background is kept to a minimum, only basics of calculus, linear algebra and group theory are assumed, while background on topology (of subsets of Euclidean space) is developed in the text. While the text gives complete and exact proofs, it is easy to read, appeals to intuition, and contains many pictures and helpful exercises.

    A. Cap, Monatshefte für Mathematik
  • [T]he second edition is an expanded and improved version of the original. It can be strongly recommended for an undergraduate course in Lie groups, or as complementary reading for a course in group theory. Prerequisites are basic: knowledge of algebra, geometry, and analysis at an undergraduate level. Hence the book is suitable for a wide audience of readers who are meeting applications of group theory in other areas of mathematics and physics, or even further afield.

    Alla S. Detinko, Mathematical Reviews
  • The author gives an inspiring presentation of the topics presented in this book.

    Erich W. Ellers, Zentralblatt Math
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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