Elementary Point-Set Topology: A Transition to Advanced Mathematics (Aurora: Dover Modern Math Originals) - Softcover

Yandl, Andre L.; Bowers, Adam

Softcover

ISBN 10: 048680349X ISBN 13: 9780486803494

Publisher: Dover Publications, 2016

Synopsis

In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses.
Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations.
"This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America

About this title

About the Author

André L. Yandl is Professor Emeritus of Mathematics at Seattle University.
Adam Bowers is a Lecturer in Mathematics at the University of California, San Diego.

From the Back Cover

In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses.
Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations.
Dover (2016) Aurora Modern Math Original.
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www.doverpublications.com

Edition details

• Publisher: Dover Publications
• Publication date: 2016
• Language: English
• ISBN 10: 048680349X
• ISBN 13: 9780486803494
• Binding: Paperback
• Edition number: 1
• Number of pages: 256