A Short Course in Computational Geometry and Topology

A Short Course in Computational Geometry and Topology presents core concepts from these mathematical fields through lectures originally delivered at a summer school. The text covers fundamental geometric and topological ideas while maintaining focus on computational aspects and algorithmic implementations. The book progresses from basic geometric constructions to advanced topological concepts, including Voronoi diagrams, Delaunay triangulations, and persistence theory. Examples and exercises complement the theoretical material throughout the chapters, providing practical applications and opportunities for hands-on learning. The content bridges pure mathematics with computer science applications, particularly in areas like data analysis and visualization. Graphics and illustrations support the mathematical concepts, making abstract ideas more concrete. This work demonstrates the deep connections between computational methods and classical mathematical theory. The text serves as both an introduction for students and a reference for researchers working at the intersection of geometry, topology, and algorithms.

This book has limited online reviews to analyze. The only public ratings found are on Goodreads, where it has a 4.50/5 rating but with just 2 ratings and no written reviews. Given the specialized academic nature of this text and lack of public reviews, a fair summary of reader sentiment cannot be generated. The book focuses on computational geometry and topology at an advanced graduate level, which inherently limits its audience and public discussion. To maintain accuracy and avoid speculation, this summary acknowledges the insufficient data for a meaningful review analysis. Goodreads: 4.50/5 (2 ratings, 0 reviews) Amazon: No reviews Google Books: No reviews

Computational Geometry: Algorithms and Applications by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars This text covers fundamental geometric algorithms with applications in areas like computer graphics and robotics.

Computational Topology: An Introduction by Herbert Edelsbrunner The book presents topological concepts through a computational lens with focus on persistent homology and applications in data analysis.

Discrete and Computational Geometry by Satyan L. Devadoss, Joseph O'Rourke The work connects discrete geometry with computational methods through geometric algorithms and data structures.

Elements of Mathematical Theory of Computation by Zohar Manna This text bridges mathematical foundations with computational methods through rigorous treatment of algorithms and computation theory.

Computational Topology in Image Context by Nicolas Passat and Yukiko Kenmochi The book explores topology algorithms with specific applications to image processing and computer vision.

🔷 Herbert Edelsbrunner is considered a pioneer in computational geometry and won the prestigious Alan T. Waterman Award in 1991 for his groundbreaking work in the field. 🔷 The book introduces persistent homology, a revolutionary mathematical method that helps analyze the shape and structure of data by tracking how topological features persist across different scales. 🔷 Computational geometry has essential applications in modern technology, from computer graphics and robot motion planning to molecular modeling and geographic information systems. 🔷 The author holds over 30 patents and is a member of multiple academies of science, including the German Academy of Sciences Leopoldina and the American Academy of Arts and Sciences. 🔷 The mathematical concepts covered in the book are fundamental to understanding modern data science techniques, particularly in the analysis of high-dimensional data sets and pattern recognition.