A Topological Aperitif

Stephen Huggett, David Jordan

166 pages, parution le 01/05/2001

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Résumé

This is a book of elementary geometric topology, in which geometry, frequently illustrated, guides calculation. The book starts with a wealth of examples, often subtle, of how to be mathematically certain whether two objects are the same from the point of view of topology. After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. Even in the simplest case, of spherical polyhedra, there are good questions to be asked. More refined tools are developed in a chapter on winding number, and an appendix gives a glimpse of knot theory.
There are many examples and exercises making this a useful textbook for a first undergraduate course in topology. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity will be able to enjoy the book. As well as arousing curiosity, the book gives a firm geometrical foundation for further study.

Contents

1 Homeomorphic Sets
2 Topological Properties
3 Equivalent Subsets
4 Surfaces and Spaces
5 Polyhedra
6 Winding Number
A Continuity
B Knots
C History
D Solutions
Bibliography
Index

L'auteur - David Jordan

David Jordan founded Object Identity, Inc. in 2001 to provide JDO consulting services. He became interested in the integration of object type systems and databases while earning his M.S. in Computer Science in the early 1980s. At Bell Labs in 1985, he initiated the development of the first C++ object database. He has developed a variety of applications using C++ object models on top of network, relational, and object database systems. Bell Labs appointed him a Distinguished Member of Technical Staff in 1990 for his contributions in object and database technologies.

The Object Data Management Group (ODMG) asked him to serve as their C++ editor in 1993. He served in that role until 2000 and was appointed their Java editor in 1998. He coedited four books published by the ODMG. David served as a C++ Report columnist describing the ODMG standard from 1994 to 1996, at which point he stopped to write his first book, C++ Object Databases.

David started using Java in late 1995. Upon his selection as ODMG's Java editor, he became a columnist for Java Report, initially covering ODMG and then JDO. David was part of the small group that initiated JSR-12, and he became one of the initial members of the JDO expert group. The JDO specification has a special acknowledgment of David's contributions to the JDO standard. When the JDOcentral.com community web site was formed, David was selected to serve as its moderator. David can be reached at david.jordan@objectidentity.com

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Stephen Huggett, David Jordan
Parution	01/05/2001
Nb. de pages	166
Format	17 x 23,5
Couverture	Broché
Poids	302g
Intérieur	Noir et Blanc
EAN13	9781852333775
ISBN13	978-1-85233-377-5