英文原版 Elementary Point-Set Topology 初等点集拓扑向高等数学的过渡 Andre L. Yandl英文版进口英语原版书籍

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作者André L. Yandl and Adam Bowers

出版社Dover Publications

ISBN9780486803494

出版时间2016-05

装帧平装

定价248元

货号YB-86728

上书时间2024-06-29

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商品描述: 内容摘要
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