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Topology for Computing 英文原版书籍详细信息
- ISBN：9780521836661
- 作者：暂无作者
- 出版社：暂无出版社
- 出版时间：2005-01
- 页数：243
- 价格：367.00
- 纸张：胶版纸
- 装帧：精装
- 开本：32开
- 语言：未知
- 丛书：暂无丛书
- TAG：暂无
- 豆瓣评分：暂无豆瓣评分
内容简介：
The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
书籍目录：
1. Introduction
Part I. Mathematics:
2. Spaces and filtrations
3. Group theory
4. Homology
5. Morse theory
6. New results
Part II. Algorithms:
7. The persistence algorithms
8. Topological simplification
9. The Morse-Smale algorithm
10. The linking number algorithm
Part III. Applications:
11. Software
12. Experiments
13. Applications.
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编辑推荐
The emerging field of computational topology utilizes theory
from topology and the power of computing to solve problems in
diverse fields. Recent applications include computer graphics,
computer-aided design (CAD), and structural biology, all of which
involve understanding the intrinsic shape of some real or abstract
space. A primary goal of this book is to present basic concepts
from topology and Morse theory to enable a non-specialist to grasp
and participate in current research in computational topology. The
author gives a self-contained presentation of the mathematical
concepts from a computer scientist's point of view, combining point
set topology, algebraic topology, group theory, differential
manifolds, and Morse theory. He also presents some recent advances
in the area, including topological persistence and hierarchical
Morse complexes. Throughout, the focus is on computational
challenges and on presenting algorithms and data structures when
appropriate.
? Presents classical topological subject of Morse theory in a
computer science context ? Material is widely used within
computation geometry and computer graphics
书籍介绍
The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
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