Algorithmic topology and classification of three-dimensional manifolds

Algorithmic topology and classification of three-dimensional manifolds

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LF/754738414/R
Russian
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The book "Algorithmic topology and classification of three-dimensional manifolds", created by the team of authors, is a unique and in-depth study in the field of modern geometry and topology. This work is intended for those who seek to understand the complex structures of three-dimensional manifolds and to master modern methods of their classification, combining theoretical foundations and practical algorithms. The focus of the book is not only abstract mathematical concepts. but also specific algorithms, Allows for research, Recognize and classify three-dimensional spaces , which makes it especially relevant for specialists in the field of topology , Mathematical Modeling and Computer Geometry . "Algorithmic topology and classification of three-dimensional manifolds" is not just a collection of theoretical calculations. This is a practical guide that reveals to the reader the modern methods and algorithms used in the study of complex topological structures. The authors, who have extensive experience in the field of mathematical logic, computational topology and algorithmic methods, offer the reader to go from basic concepts to complex techniques used in modern research. Particular attention is paid to the issues of automatic recognition and classification of three-dimensional varieties, which makes the book a valuable resource for those who are engaged in software solutions development or explore new approaches in topological analysis. This book is ideal for senior students, graduate students and professionals involved in mathematics, computer graphics, robotics or artificial intelligence . It will be interesting for those who are looking not only for theoretical knowledge, but also practical tools for solving complex problems in the field of three-dimensional topology. Readers interested in algorithms, automation and computer modeling of spatial structures will find in it valuable ideas and methods that can be applied in scientific research or in the development of new technologies. The topics raised in the book cover a wide range of issues from the foundations of topological theory and the classification of varieties to modern algorithms that allow these processes to be automated. A special place is occupied by the discussion of algorithms for the recognition and isomorphism of three-dimensional manifolds, which makes the book not only a theoretical work, but also a practical tool for developing software solutions. The authors analyze in detail complex concepts, such as the decomposition of manifolds, Hausdorff's theory, as well as modern methods based on computational topology and geometry. The style of the author(s) is a combination of strict scientific accuracy and accessible presentation, which makes complex topics understandable even for those who are just beginning to get acquainted with topology. Their approach is not only an explanation of the theory, but also a demonstration of practical methods, which makes the book a valuable tool for independent study and research. In general, “Algorithmic Topology and Classification of 3D Varieties” is a book that can become a desktop guide for those who want to not only understand what 3D varieties are, but also learn to recognize and classify them with the help of modern algorithms. If you are looking for a book that combines mathematics, computer science and practical application, then this work is exactly what you need. It is ideal for those who value an interdisciplinary approach and are committed to mastering best practices in topology and computational geometry. In a world where three-dimensional structures play a key role in modeling, robotics, computer graphics and even in the biological sciences, this book opens new horizons for research and practical application. “Algorithmic topology and classification of three-dimensional varieties” is not just a textbook, but a guide to the exciting world of modern mathematical technologies, which will surely interest everyone who is looking for new ideas and solutions in the field of topology.
LF/754738414/R

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Algorithmic topology and classification of three-dimensional manifolds

The book "Algorithmic topology and classification of three-dimensional manifolds", created by the team of authors, is a unique and in-depth study in the field o...

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