Computational Topology: An Introduction by Herbert Edelsbrunner (PDF)

Description

Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

User’s Reviews

Editorial Reviews: Review This book is a very welcome, untraditional, thorough and well-organized introduction to a young and quickly developing discipline on the crossroads between mathematics, computer science, and engineering. –DMV Newsletter

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐An excellent and practical textbook on Topology.

⭐This is good for a cursory overview, but you’ll need to supplement it with another topology book if you want detailed exposition of theory.

⭐New as advertised

⭐A must have if you are new to the field of computational topology.It caters both to mathematicians and engineers.I would recommend it to all people interested.

⭐Horrible. The English is a nightmare. Explanations are poor and notation sucks.If you want a good intro to topology (which is what half this book is) get anything out there, except for the Dover versions. And if you want the real deal in computational topology get a book in computational homology

⭐This book is good for the topic, but if you are not familiar with topology to begin with, I would recommend an additional text. This book’s section on topology is terse.

⭐Everything is great with with the condition of the book and the delivery.

⭐Edelsbrunner und Harer legen hier das Standardwerk für Computational Topology vor. Das Buch setzt eigentlich kaum Grundlagen jenseits der Grundvorlesungen in einem guten Informatik/Mathematik-Studium voraus. Nach einem kurzen Abstecher in die Gebiete der Graphentheorie gibt es dann eine kurze, präzise Einführung in die algebraische Topologie. Darauf aufbauend werden dann etwas Morse-Theorie sowie (schlussendlich) die persistente Homologie eingeführt. Für die persistente Homologie werden einige Erweiterungen sowie Anwendungen vorgestellt.Für jemanden, der Interesse an diesem Gebiet hat, würde ich den Kauf ohne Zweifel empfehlen. Gegebenenfalls könnte der Kauf von Allen Hatchers “Algebraic Topology” oder Glen E. Bredons “Topology and Geometry” den Einstieg in die algebraische Topologie erleichtern.

⭐

⭐Libro muy ameno, de lectura fácil. Es una buena primera aproximación al campo. Además, frogzilla es muy mona.

⭐

⭐This textbook is extremely good, a must for everyone who wants to study computational topology. It is pretty clear and full of exercise.

⭐Not an original copy. It is just a Xerox or Printout.

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