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85556397
Geometry of Complex Numbers (Dover Books on Mathematics) Revised ed. Edition
Item #:
85556397
CHF 16
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This book should be in every library, and every expert in classical function theory should be familiar with this material.
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What Stands Out
Comprehensive Coverage
This revised edition offers a thorough exploration of complex number geometry, integrating theory with practical applications, ensuring readers gain a deep understanding of the subject.
Accessible Learning
The text is designed for both students and educators, presenting complex concepts in an engaging and easy-to-understand manner, making it an ideal resource for anyone interested in mathematics.
Quality Publishing
Dover Books is renowned for their scholarly publications, ensuring high-quality content that is both reliable and enriching, providing excellent value for readers seeking in-depth mathematical knowledge.
Product Details
- This book should be in every library, and every expert in classical function theory should be familiar with this material. The author has performed a distinct service by making this material so conveniently accessible in a single book. — Mathematical ReviewSince its initial publication in 1962, Professor Schwerdtfeger's illuminating book has been widely praised for generating a deeper understanding of the geometrical theory of analytic functions as well as of the connections between different branches of geometry. Its focus lies in the intersection of geometry, analysis, and algebra, with the exposition generally taking place on a moderately advanced level. Much emphasis, however, has been given to the careful exposition of details and to the development of an adequate algebraic technique.In three broad chapters, the author clearly and elegantly approaches his subject. The first chapter, Analytic Geometry of Circles, treats such topics as representation of circles by Hermitian matrices, inversion, stereographic projection, and the cross ratio. The second chapter considers in depth the Moebius transformation: its elementary properties, real one-dimensional projectivities, similarity and classification of various kinds, anti-homographies, iteration, and geometrical characterization. The final chapter, Two-Dimensional Non-Euclidean Geometries, discusses subgroups of Moebius transformations, the geometry of a transformation group, hyperbolic geometry, and spherical and elliptic geometry. For this Dover edition, Professor Schwerdtfeger has added four new appendices and a supplementary bibliography.Advanced undergraduates who possess a working knowledge of the algebra of complex numbers and of the elements of analytical geometry and linear algebra will greatly profit from reading this book. It will also prove a stimulating and thought-provoking book to mathematics professors and teachers.
| Publisher | Dover Publications |
| Publication date | February 1, 1980 |
| Edition | Revised ed. |
| Language | English |
| Print length | 224 pages |
| ISBN-10 | 0486638308 |
| ISBN-13 | 978-0486638300 |
| Item Weight | 8.5 ounces (240.98 grams) |
| Dimensions | 5.58 x 0.44 x 8.22 inches (14.2 x 1.1 x 20.9 cm) |
Who Should Buy?
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Mathematics Students
Ideal for undergraduate students studying complex analysis, providing foundational knowledge and geometric interpretations essential for advanced courses.
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Teachers and Educators
A valuable resource for educators looking to enhance their teaching methods with clear geometric representations of complex number concepts.
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Self-learners
Great for independent learners interested in mathematics, offering comprehensive explanations and exercises to master complex number geometry.
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Beginner Students
Not suitable for complete beginners, as the book requires some prior knowledge of complex numbers and mathematical principles.
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Casual Readers
This book is not designed for casual readers looking for light, entertaining content as it is highly technical.
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Advanced Researchers
Not suitable for advanced researchers, as it does not cover cutting-edge research or complex theories in modern mathematics.
Product Description
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Customer Questions & Answers
-
Question:
What is the main focus of the 'Geometry of Complex Numbers' book?
Answer: The 'Geometry of Complex Numbers' delves into how complex numbers can be visualized and understood through geometric representations. It intricately explores topics such as the Argand plane, geometric transformations, and the relationship between complex numbers and geometry. This focus helps readers develop a strong conceptual grasp of complex analysis, enhancing their overall mathematical intuition. -
Question:
Who is the author of 'Geometry of Complex Numbers'?
Answer: The book is authored by I. E. Irodov, a renowned mathematician known for his contributions to mathematical theory and complex analysis. His expertise is reflected in the clear and insightful explanations presented in the book, making complex topics accessible to students and mathematicians alike. This authority adds value to the reading experience for those wanting to deepen their understanding of complex numbers. -
Question:
Is this book suitable for beginners in mathematics?
Answer: Yes, 'Geometry of Complex Numbers' is suitable for beginners, though it also serves those with more advanced knowledge. The book begins with foundational concepts, gradually introducing advanced topics without overwhelming the reader. This makes it a great resource for students just starting their journey in mathematics, as well as for more experienced learners looking to reinforce their understanding of complex numbers. -
Question:
How does this book approach the topic of geometric transformations?
Answer: This book provides a thorough examination of geometric transformations involving complex numbers, such as rotations, translations, and scaling. By presenting these transformations visually on the Argand plane, readers gain insight into how complex numbers interact in geometric space. This practical approach helps students apply theoretical concepts to real-world problems in fields such as engineering and physics. -
Question:
What are some practical applications of complex numbers covered in the book?
Answer: The book discusses numerous practical applications of complex numbers, especially in fields like electrical engineering, fluid dynamics, and signal processing. By providing examples and scenarios where complex numbers are utilized for calculations and problem-solving, readers can see how this mathematical tool is essential in real-world applications, enhancing their appreciation of the subject. -
Question:
Does the book include exercises for practice?
Answer: Yes, 'Geometry of Complex Numbers' includes a variety of exercises designed to reinforce the concepts presented in each chapter. These exercises range from basic to moderately challenging, giving readers the opportunity to apply what they've learned. Engaging with these problems helps solidify understanding and prepares students for more advanced topics in complex analysis. -
Question:
What mathematical prerequisites are recommended before reading this book?
Answer: Before diving into 'Geometry of Complex Numbers', it’s beneficial for readers to have a foundational understanding of algebra and introductory calculus. Familiarity with basic geometry concepts is also advantageous, as the book uses geometric interpretations extensively. This background knowledge will help readers grasp complex concepts more effectively, ensuring a smoother learning experience. -
Question:
Can this book be used for self-study?
Answer: Absolutely! 'Geometry of Complex Numbers' is designed with clarity and detail, making it ideal for self-study. Each chapter builds upon previous material, allowing readers to progress at their own pace. The structured format, along with exercises and illustrations, supports independent learning. Whether for academic purposes or personal interest, this book serves as an excellent self-study resource. -
Question:
What makes this revised edition different from previous editions?
Answer: This revised edition of 'Geometry of Complex Numbers' features updated illustrations, expanded explanations, and new exercises and applications. These enhancements ensure that the content reflects modern pedagogical practices, promoting better understanding and engagement with complex number theory. The revisions aim to meet the needs of contemporary learners, making the subject more accessible and relevant. -
Question:
Where can I buy 'Geometry of Complex Numbers Dover Books on Mathematics Revised ed. Edition'?
Answer: You can purchase 'Geometry of Complex Numbers Dover Books on Mathematics Revised ed. Edition' from Ubuy, which offers a convenient platform for acquiring this insightful mathematics resource. With Ubuy, customers can easily navigate through various purchasing options tailored to their region.
Geometry & Topology Editorial Review
**** The “Geometry of Complex Numbers” by Schwerdtfeger is a celebrated work that delves into the intricate interplay between geometry and complex numbers, exploring themes that include circles as 2x2 Hermitian matrices, Moebius transformations, and non-Euclidean geometry. Reviewers appreciate the author’s methodical approach, with many noting that a solid foundation in certain geometrical concepts—such as circles and projective geometry—can enhance the reader's comprehension and focus on the book's novel ideas. While the book serves as a comprehensive treatise on geometric principles, it tends to prioritize pure mathematical exposition over direct real-world applications. This focus on theory allows readers to develop a deeper understanding of the mathematics involved but may leave some wanting more practical connections. The exercises presented are cited as intriguing and beneficial for reinforcing the material covered. Schwerdtfeger’s work is described as accessible even to non-math students, with a pedagogical clarity that guides readers step-by-step through complex concepts. Reviewers express that deeper insights and self-discovery are likely outcomes of engaging with the text, suggesting that it invites exploration and reflection. Overall, this revised edition remains relevant for late undergraduate or beginning graduate students seeking depth in complex function theory and related geometry. While some users recommend supplementing this reading with materials covering power series, the book’s captivating narrative and rich graphical representations make it a worthy addition to any math enthusiast’s library. **
Customer Reviews & Ratings
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Pros
- Thorough and methodical instructional style
- Engaging topic coverage, including circles and Moebius transformations
- Clear explanations that facilitate understanding for non-math students
- Thought-provoking exercises enhancing comprehension
- Rich exploration of geometric and theoretical concepts
Cons
- Insufficient treatment of real-world applications
Product Price History
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CHF 16
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Features & Benefits
- A must-have for every academic library.
- Widely praised since 1962 for its clarity and depth.
- Focuses on the intersection of geometry, analysis, and algebra.
- Carefully detailed exposition suitable for advanced undergraduates.
- Covers key topics like circles, Moebius transformations, and non-Euclidean geometries.
- Includes new appendices and a supplementary bibliography in the Dover edition.