You are here: Home / Shop / Product Detail Page |

## Springer Undergraduate Mathematics Series: Matrix Groups: An Introduction to Lie Group Theory (Softcover)"Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course." — From the back cover ## $27.99 |

### Need More Info?

Please contact us if you've got questions about this product.## Condition

**VERY GOOD:** The book is in very good condition, showing only slight signs of use and wear (namely, a mark along the outer page edge and slightly bent corners). The pages are clean of writing and the binding is tight. This book was printed on acid-free paper.

NOTE: British spelling.

## Description

From the back cover: “Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter.

“The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a Lie group and studies the associated notion of a homogeneous space using orbits of smooth actions.

“Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry.”

**BRIEF CONTENTS**

- Part I. Basic Ideas and Examples
- 1. Real and Complex Matrix Groups
- 2. Exponentials, Differential Equations and One-parameter Subgroups
- 3. Tangent Spaces and Lie Algebras
- 4. Algebras, Quaternions and Quaternionic Symplectic Groups
- 5. Clifford Algebras and Spinor Groups
- 6. Lorentz Groups
- Part II. Matrix Groups as Lie Groups
- 7. Lie Groups
- 8. Homogeneous Spaces
- 9. Connectivity of Matrix Groups
- Part III. Compact Connected Lie Groups and Their Classification
- 10. Maximal Tori in Compact Connected Lie Groups
- 11. Semi-simple Factorisation
- 12. Roots Systems, Weyl Groups and Dynkin Diagrams
- Hints and Solutions to Selected Exercises
- Bibliography
- Index

## Details

- SKU:
- 1786
- Subject:
- Mathematics
- Author:
- Baker, Andrew
- Publisher:
- Springer-Verlag
- Publish Date:
- 2007 (Fourth Printing)
- Format:
- Softcover
- Weight (pounds):
- 1.26
- Dimensions (W”xL”xH”):
- 6.7″x9.25″x0.8″
- ISBN-13:
- 9781852334703
- ISBN-10:
- 1852334703
- Grade Level:
- College, Graduate
- Series:
- Springer Undergraduate Mathematics Series (SUMS)

## Related Products

### Products related to "Springer Undergraduate Mathematics Series: Matrix Groups: An Introduction to Lie Group Theory (Softcover)"

- Views:

#### Undergraduate Texts in Mathematics: Groups and Symmetry (Hardback)

$35.15

"As prerequisites I assume a first course in linear algebra (including matrix multiplication and the representation of linear maps between Euclidean spaces by matrices, though not the abstract theory of vector spaces) plus familiarity with the basic properties of the real and complex numbers. It would be a pity to teach group theory without matrix groups available as a rich source of examples, especially since matrices are so heavily used in application." — Mark Anthony Armstrong, Author, in the Preface

#### Euclidean and Non-Euclidean Geometry: An Analytic Approach (Softcover)

$23.39

"This book gives a rigorous treatment of the fundamentals of plane geometry — Euclidean, spherical, elliptical, and hyperbolic — from an analytic point of view." — From the back cover

#### Discrete Mathematics and Its Applications: Handbook of Computational Group Theory (Hardback)

$79.99

"The origins of computational group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics." — From the back cover

#### Iterative Methods for Sparse Linear Systems, Second Edition (Softcover)

$73.95

"This book can be used to teach graduate-level courses on iterative methods for linear systems. Engineers and mathematicians will find its contents easily accessible, and practitioners and educators will value it as a helpful resource. The preface includes syllabi that can be used for either a semester- or quarter-length course in both mathematics and computer science." — From the back cover

#### Graduate Texts in Mathematics: Introduction to Cyclotomic Fields, Second Edition (Hardback)

$57.95

"

*Introduction to Cyclotomic Fields*is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory." — From the back cover#### An Introduction to Random Matrices (Hardback)

$53.95

"The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic, and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even to the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences who have mastered probability theory at the graduate level, but who have not necessarily been exposed to advanced notions of functional analysis, algebra, or geometry." — From the back cover

#### Polyhedra (Softcover)

$45.99

"Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics and group theory." — From the back cover

#### Undergraduate Texts in Mathematics: Linearity, Symmetry, and Prediction in the Hydrogen Atom (Hardback)

$41.79

"This user-friendly exposition, driven by numerous examples and exercises, requires a solid background in calculus and familiarity with either linear algebra or advanced quantum mechanics. ... [It] will benefit students in mathematics, physics and chemistry, as well as a literate general readership." — From the back cover

#### Student Mathematical Library, Volume 46: Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them (Softcover)

$39.59

"The assumed background is the standard calculus sequence, some linear algebra, and rudiments of ODE and real analysis. All notions are introduced and discussed, and virtually all results proved, based on this background." — From the back cover

#### Complex Functions: An Algebraic and Geometric Viewpoint (Softcover)

$38.65

"This book is based on lectures given to advance undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread application throughout mathematics." — From the back cover

#### Quantum Computer Science: An Introduction (Hardback)

$34.95

"In the 1990s it was realized that quantum physics has some spectacular applications in computer science. This book is a concise introduction to quantum computation, developing the basic elements of this new branch of computational theory without assuming any background in physics." — From the back cover

#### Lecture Notes in Mathematics #1915: Laplacian Eigenvectors of Graphs: Perron-Frobenius and Faber-Krahn Type Theorems (Softcover)

$31.99

"The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ('nodal domains'), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology." — From the back cover

#### Linear Differential Equations and Group Theory from Riemann to Poincaré, Second Edition (Softcover)

$29.95

"The book contains an amazing wealth of material relating to the algebra, geometry, and analysis of the nineteenth century.... Written with accurate historical perspective and clear exposition, this book is truly hard to put down." — Zentralblatt für Mathematik (review of the first edition, taken from the back cover)

#### Springer Undergraduate Mathematics Series: Elementary Differential Geometry (Softcover)

$27.99

"This book will prove an invaluable resource to all those taking a first course in differential geometry, for their lectures, and for all others interested in the subject." — From the back cover

#### Springer Undergraduate Mathematics Series: Topics in Group Theory (Softcover)

$27.99

"The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed to support a reader engaged in a first serious group theory course, or a mathematically mature reader approaching the subject for the first time, this book reviews the essentials." — From the back cover

#### An Introduction to Tensors and Group Theory for Physicists (Hardback)

$27.95

This book "provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics." — From the back cover

#### Mathematical World, Volume 18: Portraits of the Earth: A Mathematician Looks at Maps (Softcover)

$26.15

"This book would make an excellent text for a basic undergraduate mathematics or geography course and would be especially appealing to the teacher who is interested in exciting visual applications in the classroom. It would also serve nicely as supplementary reading for a course in calculus, linear algebra, or differential geometry. Prerequisites include a strong grasp of trigonometry and basic calculus." — From the back cover

#### Computer Graphics and Geometric Modeling: Mathematics (Hardback)

$12.49

"In addition to its use as a companion volume to computer graphics or geometric modeling courses, this volume would also make a good mathematics reference book, in particular for practitioners in the field of geometric modeling. Furthermore, because of its broad coverage and emphasis on explanation it could even be used as text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential and algebraic)." — From the back cover

#### Perturbation Techniques in Mathematics, Engineering & Physics (Softcover)

$3.89

"An introduction to a variety of perturbation techniques for ordinary differential equations, this work outlines applications through specific examples. Mathematicians, engineers, and applied scientists will find its exposition entirely accessible." — From the back cover

#### Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians (Hardback)

$279.95

From the Preface: “This book is a classical and detailed introduction to advanced analytical mechanics (AM), with special emphasis on its basic principles and equations of motion, as they apply to the most general constrained mechanical systems with a finite number of degrees of freedom..."