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Numéro d'article:
185792014
Linear Algebra Through Geometry (Undergraduate Texts in Mathematics)
Numéro d'article:
185792014
XOF 46665
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Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry.
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rapide
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Ce qui se démarque
Geometric Insights
This text emphasizes geometric interpretations of linear algebra concepts, facilitating deeper understanding and appreciation of the subject matter, making it ideal for visual learners.
Comprehensive Coverage
The second edition offers updated and expanded content, addressing a wide range of topics and applications, ensuring a well-rounded education in linear algebra for undergraduate students.
Clear Explanations
With accessible language and illustrative examples, this book breaks down complex theories into digestible concepts, helping students grasp challenging material more effectively and confidently.
Détails du produit
- Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms. The final chapter treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only prerequisite for reading this book (with the exception of one section on systems of differential equations) are high school geometry, algebra, and introductory trigonometry.
| Publisher | Springer |
| Publication date | November 25, 1991 |
| Edition | 2nd |
| Language | English |
| Print length | 320 pages |
| ISBN-10 | 0387975861 |
| ISBN-13 | 978-0387975863 |
| Item Weight | 1.4 pounds (640 grams) |
| Dimensions | 6.4 x 1.1 x 9.4 inches (16.3 x 2.8 x 23.9 cm) |
| Part of series | Undergraduate Texts in Mathematics |
À qui est-ce destiné ?
-
Undergraduate Students
Ideal for undergraduate students seeking to understand linear algebra through a geometric perspective and visual methods.
-
Educators and Instructors
Useful for teachers who want to present linear algebra concepts in a more intuitive and visually engaging way.
-
Mathematics Enthusiasts
Great for those with a passion for mathematics looking to explore linear algebra concepts through geometric interpretations.
-
Advanced Researchers
Not suitable for experienced mathematicians or researchers seeking deep theoretical insights without a geometric approach.
DESCRIPTION DU PRODUIT
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Questions et réponses des clients
-
question:
What prior knowledge is required to read this book?
répondre: The only prerequisites are high school geometry, algebra, and introductory trigonometry. -
question:
What topics are covered in the book?
répondre: Topics include vectors, linear transformations, matrices, dot products, eigenvalues, and applications in differential systems. -
question:
Is this book suitable for beginners?
répondre: Yes, it is designed for undergraduates and is approachable with basic math skills.
Linear Editorial Review
**Editorial Review of "Linear Algebra Through Geometry, 2nd Edition"** The "Linear Algebra Through Geometry" textbook, authored by Banchoff and Wermer, presents a unique approach to understanding linear algebra through a geometric lens. Reviewers have praised the text for its innovative progression from simpler to more complex concepts, which is beneficial for beginners. The methodical introduction of elementary concepts, building through various dimensions from R^1 to R^n and beyond, is highlighted as a strong educational strategy. Many users found the book to be crystal clear in its exposition, skillfully connecting geometric insights with algebraic principles. The text's ability to elucidate the significance of eigenvalues and eigenvectors while maintaining intuition is particularly noted, making it suitable for both scientists and budding mathematicians. The clarity of writing is frequently lauded, providing a sense of accessibility for learners. However, the book is not without its criticisms. Some readers have voiced concerns about the organization and motivation behind certain sections, asserting that the order of topics could be improved. In particular, the chapter dedicated to "Conic Sections" has generated mixed reviews; while some see it as an important application of eigenvalue theory, others feel it lacks coherence and relevance to its title. The lack of solutions or partial answers for exercises has also been remarked upon, with some recommending the book as a supplementary resource rather than a standalone text. In summary, "Linear Algebra Through Geometry" appears to have garnered positive reception among those with a foundational understanding of the subject. For self-learners and those willing to engage with its material, the book is seen as a valuable resource, although its structural issues might present challenges for some readers. **
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Avantages
- Presents linear algebra concepts through a geometric approach.
- Clear and accessible writing style.
- Gradual introduction of complex ideas, beneficial for beginners.
- Good insights into the significance of topics like eigenvalues and eigenvectors.
- Suitable for both scientists and mathematical novices.
Les inconvénients
- Criticisms regarding organization and coherence of certain chapters.
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XOF 46665
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Caractéristiques et avantages
- Learn linear algebra through the lens of Euclidean geometry.
- Understand vectors, linear transformations, and matrices in a familiar context.
- Explore advanced topics like dot products, determinants, and eigenvalues.
- Delve into n-dimensional Euclidean space and finite-dimensional vector spaces.
- Perfect for those with basic knowledge of high school geometry and algebra.
- Applications include differential systems and curvature of surfaces.
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