Handbook of Convex Geometry: A Comprehensive Survey of Convexity, Lattices, Crystallography, and Convex Functions by Boz

Introduction

The Handbook of Convex Geometry by Bozzano G. Luisa stands as a monumental resource in the field of mathematics, offering an exhaustive survey of convex geometry and its extensive branches. Published by North-Holland, this hardcover volume is an essential addition to the library of any serious student or researcher delving into the geometric and analytical aspects of convexity. For Indian readers and academics, this book bridges the gap between abstract mathematical theories and their practical applications in fields ranging from crystallography to computational geometry.

Book Overview

This volume, the second in a comprehensive series, presents a deep dive into the myriad facets of convex geometry. It systematically explores the geometry of numbers, lattice points, and the intricate problems of packing and covering with convex sets. The book also ventures into finite packing, tilings, valuations, and the fascinating intersection of convexity with differential geometry and crystallography. With its rigorous yet accessible approach, it serves as both a reference manual and a guide for advanced study.

Key Highlights

• Comprehensive Coverage: Offers a detailed survey of convex geometry, including lattice theory, packing problems, and convex functions.
• Interdisciplinary Connections: Explores the links between convex geometry and fields like crystallography, differential geometry, and number theory.
• Authoritative Content: Written by Bozzano G. Luisa, a respected figure in mathematical sciences, ensuring depth and accuracy.
• Hardbound Edition: A durable hardcover format suitable for long-term academic use and library collections.

Inside the Book

The Handbook of Convex Geometry is structured to guide readers from foundational concepts to advanced topics. Early chapters focus on the geometry of numbers, including reduction theory and the space of lattices, before moving to packing and covering problems in Euclidean and non-Euclidean spaces. Later sections delve into tilings, valuations, and the geometric properties of convex hypersurfaces. The book also covers convex functions, their differentiability, and inequalities, providing a holistic view of the subject.

Key Topics

• Geometry of numbers and lattice points
• Packing and covering with convex sets
• Finite packing and tilings
• Valuations and dissections
• Geometric crystallography
• Convexity and differential geometry
• Convex functions and inequalities
• Computational complexity of lattice point problems

Reader Benefits

This book empowers readers with a robust understanding of convex geometry, enabling them to tackle complex mathematical problems with confidence. It provides a structured pathway to grasp advanced concepts, making it ideal for self-study or as a companion to graduate courses. The inclusion of real-world applications, such as in crystallography and packing theory, enhances its practical value for Indian students pursuing careers in mathematics, physics, or engineering.

Learning Outcomes

By studying this handbook, readers will be able to analyze and solve problems related to lattice points, convex bodies, and packing configurations. They will gain proficiency in understanding the geometric properties of convex sets and their applications in number theory and geometry. Additionally, the book equips learners with the tools to explore advanced topics like valuations and differential geometry of convex hypersurfaces, fostering a deeper appreciation for mathematical symmetry and structure.

Who Should Read

• Graduate students and researchers in pure and applied mathematics
• Professionals working in geometry, number theory, or crystallography
• Academicians seeking a comprehensive reference on convex geometry
• Advanced undergraduates with a strong foundation in linear algebra and analysis

About the Author

Bozzano G. Luisa is a distinguished mathematician known for significant contributions to geometry and its applications. With a career spanning decades, the author has authored numerous works that have shaped modern mathematical thought. This handbook reflects a deep commitment to making complex geometric theories accessible and relevant to a broad academic audience.

About the Publisher

North-Holland, an imprint of Elsevier, is a renowned publisher of high-quality scientific and mathematical literature. With a legacy of publishing seminal works in mathematics, physics, and engineering, North-Holland ensures that each volume meets the highest standards of scholarly rigor. This handbook is a testament to their dedication to advancing mathematical knowledge worldwide.

Conclusion

The Handbook of Convex Geometry is an indispensable resource for anyone serious about mastering convex geometry and its applications. Whether you are a student preparing for advanced research or a professional seeking a reliable reference, this hardcover edition from Bookshops.in promises to be a valuable companion. Order your copy today and embark on a journey through the elegant world of convex shapes and structures.