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185792014
Linear Algebra Through Geometry (Undergraduate Texts in Mathematics)
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Item #:
185792014
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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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What Stands Out
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.
Product Details
| 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 |
Who Should Buy?
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Undergraduate Students
Ideal for undergraduate students seeking to understand linear algebra through a geometric perspective and visual methods.
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Educators and Instructors
Useful for teachers who want to present linear algebra concepts in a more intuitive and visually engaging way.
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Mathematics Enthusiasts
Great for those with a passion for mathematics looking to explore linear algebra concepts through geometric interpretations.
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Advanced Researchers
Not suitable for experienced mathematicians or researchers seeking deep theoretical insights without a geometric approach.
Product Description
Linear Algebra Through Geometry (Undergraduate Texts in Mathematics)
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Customer Questions & Answers
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Question:
What is the main focus of the book 'Linear Algebra Through Geometry'?
Answer: The main focus of 'Linear Algebra Through Geometry' is to connect linear algebra concepts with geometric intuition. It emphasizes visual understanding through geometric interpretations of vector spaces, transformations, and other linear structures. This approach aids students in grasping complex abstract concepts by presenting them in a more tangible form. For instance, understanding eigenvectors can be made clearer by visualizing them as directions in which transformations stretch or compress space. -
Question:
Who is the intended audience for 'Linear Algebra Through Geometry'?
Answer: 'Linear Algebra Through Geometry' is designed for undergraduate students, particularly those studying mathematics, engineering, or physics. It's ideal for those who seek to deepen their grasp of linear algebra concepts through a geometric lens. Instructors may also find this book beneficial for guiding their teaching process, offering clear diagrams and examples that promote better comprehension among students struggling with abstract mathematical ideas. -
Question:
Does the book include exercises and solutions?
Answer: Yes, 'Linear Algebra Through Geometry' includes a variety of exercises and, in many editions, provides solutions or hints for selected problems. This feature is crucial for self-study, allowing students to apply concepts learned in each chapter. By working through these exercises, readers can solidify their understanding of key principles and develop problem-solving skills important in both academic and practical applications, such as data science and computer graphics. -
Question:
Is prior knowledge of linear algebra required to understand this book?
Answer: No prior knowledge of linear algebra is strictly required, as 'Linear Algebra Through Geometry' begins with foundational concepts and builds up to more advanced topics. This incremental approach makes it accessible for beginners while still offering depth for more advanced readers. For example, individuals new to the subject can start with basic vector operations and gradually advance to complex topics like transformations while supported by geometric illustrations. -
Question:
What are the unique features of 'Linear Algebra Through Geometry'?
Answer: Unique features of 'Linear Algebra Through Geometry' include its strong emphasis on geometric interpretations, rich illustrations, and a focus on applications that show how linear algebra is utilized in various fields. The visuals aid in contextualizing abstract ideas, like span and linear independence, making them easier to grasp. Such features make the book particularly effective for visual learners and those interested in the real-world applications of mathematics. -
Question:
How does this book differ from traditional linear algebra texts?
Answer: 'Linear Algebra Through Geometry' differentiates itself from traditional texts by prioritizing geometric reasoning over purely algebraic manipulations. While conventional texts may focus extensively on computations, this book integrates visual aspects to enhance understanding and insight into linear algebra concepts. For students, this approach can transform their learning experience, allowing them to see the 'big picture' in applications ranging from engineering to computer science. -
Question:
Can 'Linear Algebra Through Geometry' be used for self-study?
Answer: Absolutely, 'Linear Algebra Through Geometry' is well-suited for self-study due to its clear explanations, structured progression of topics, and engaging exercises. Students studying independently can effectively learn at their own pace, utilizing the book's geometric perspectives for enhanced understanding. Additionally, the diverse problem sets allow learners to test comprehension and apply concepts, making it an excellent resource for those preparing for exams or seeking to strengthen their mathematical foundation. -
Question:
What mathematical prerequisites are helpful for reading this book?
Answer: While a specific prerequisite knowledge is not mandatory, a basic understanding of high school algebra and geometry will support readers in grasping the concepts presented in 'Linear Algebra Through Geometry.' Familiarity with functions, graphs, and basic mathematical reasoning will enhance comprehension of the visual approaches used in the text. Students with a solid foundation in these areas are likely to find the transition into linear algebra concepts smoother and more intuitive. -
Question:
Are there any accompanying online resources for this book?
Answer: Some editions of 'Linear Algebra Through Geometry' may come with accompanying online resources, such as supplementary materials, additional exercises, or solution manuals. These resources can provide invaluable support to both students and instructors, offering further practice and insights into methods discussed in the book. Users are encouraged to check the publisher's website or educational platforms for any relevant online content that can complement their learning experience. -
Question:
Where can I buy 'Linear Algebra Through Geometry' in The Bahamas?
Answer: You can buy 'Linear Algebra Through Geometry' in The Bahamas on Ubuy. Ubuy provides a convenient online shopping experience, allowing you to browse various editions of the book, compare options, and select the one that best suits your needs. Their platform offers a user-friendly interface and reliable service to help you obtain this valuable resource for your studies.
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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Pros
- 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.
Cons
- Criticisms regarding organization and coherence of certain chapters.
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Features & Benefits
- 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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