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Beginning Topology

ISBN-10: 0821847961
ISBN-13: 9780821847961
Edition: 2009
Authors: Sue E. Goodman
List price: $66.00
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Description: Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is  More...

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Book details

List price: $66.00
Copyright year: 2009
Publisher: American Mathematical Society
Publication date: 2/19/2009
Binding: Hardcover
Pages: 236
Size: 6.50" wide x 9.25" long x 0.50" tall
Weight: 0.946
Language: English

Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes. The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while illustrating the need for rigor. Most of the material in this and the next two chapters is essential for the remainder of the book. One can then choose from chapters on map coloring, vector fields on surfaces, the fundamental group, and knot theory. A solid foundation in calculus is necessary, with some differential equations and basic group theory helpful in a couple of chapters. Topics are chosen to appeal to a wide variety of students: primarily upper-level math majors, but also a few freshmen and sophomores as well as graduate students from physics, economics, and computer science. All students will benefit from seeing the interaction of topology with other fields of mathematics and science; some will be motivated to continue with a more in-depth, rigorous study of topology.

Introduction to point set topology Surfaces
The Euler characteristic
Maps and graphs Vector fields on surfaces
The fundamental group
Introduction to knots
Bibliography and reading list
Index

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