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Topology for computing /

Zomorodian, Afra J., (1974-)

Topology for computing /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	514
書名/作者:	Topology for computing // Afra J. Zomorodian.
作者:	Zomorodian, Afra J.,
面頁冊數:	1 online resource (xiii, 243 pages) : : digital, PDF file(s).
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Topology.
標題:	Topology - Data processing.
ISBN:	9780511546945 (ebook)
內容註:	Introduction -- Mathematics -- Spaces and filtrations -- Group theory -- Homology -- Morse theory -- New results -- Algorithms -- The persistence algorithms -- Topological simplification -- The Morse-Smale complex algorithm -- The linking number algorithm -- Applications -- Software -- Experiments -- Applications.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1017/CBO9780511546945

Topology for computing /
Zomorodian, Afra J.,1974-

Topology for computing /Afra J. Zomorodian. - 1 online resource (xiii, 243 pages) :digital, PDF file(s). - Cambridge monographs on applied and computational mathematics ;16. - Cambridge monographs on applied and computational mathematics ;14..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Introduction -- Mathematics -- Spaces and filtrations -- Group theory -- Homology -- Morse theory -- New results -- Algorithms -- The persistence algorithms -- Topological simplification -- The Morse-Smale complex algorithm -- The linking number algorithm -- Applications -- Software -- Experiments -- Applications.

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.

ISBN: 9780511546945 (ebook)Subjects--Topical Terms:

405711
Topology.

LC Class. No.: QA611 / .Z65 2005

Dewey Class. No.: 514

Topology for computing /
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490 1 $a Cambridge monographs on applied and computational mathematics ; $v 16
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Introduction -- Mathematics -- Spaces and filtrations -- Group theory -- Homology -- Morse theory -- New results -- Algorithms -- The persistence algorithms -- Topological simplification -- The Morse-Smale complex algorithm -- The linking number algorithm -- Applications -- Software -- Experiments -- Applications.
520 $a 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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856 4 0 $u http://dx.doi.org/10.1017/CBO9780511546945

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