Triangulations: Structures for Algorithms and Applications

Book Details:

• Book Title: Triangulations: From Geometry to Applications

• Author: Jesus A. De Loera

• Publisher: Springer

• Language: English

• Edition: First Edition

• ISBN: 9783642129704

• Pages: 535

• Cover: Hardcover

• Dimensions: 10.6 x 8.0 x 1.1 inches

About the Book:

Triangulations: From Geometry to Applications by Jesus A. De Loera is a comprehensive and insightful exploration of the mathematical theory of triangulations and their practical applications in various fields, including geometry, computer science, combinatorics, and optimization. The book highlights how triangulations are an essential tool for decomposing regions of space into smaller, manageable parts, enabling efficient volume computations, meshing, and even surface reconstruction.

This work provides a detailed treatment of the theory of regular subdivisions, secondary polytopes, flips, and their interactions. Through clear and numerous illustrations, the author takes readers on a journey from basic concepts to advanced computational problems, such as counting triangulations or finding optimal triangulations based on different criteria.

The book emphasizes the use of the geometric structure of triangulation spaces to solve computational problems and establish connections to a wide range of applications in algebra, computer science, and optimization. De Loera’s writing is thorough and engaging, offering readers valuable insight into both elementary principles and cutting-edge research. With exercises and over 500 illustrations, this book serves as a critical resource for students, researchers, and professionals working in the areas of discrete mathematics, geometry, and optimization.

This book is ideal for graduate students and researchers who want a comprehensive and detailed understanding of triangulations and their many applications in modern mathematics and computer science.