Topology: A Geometric Approach (Oxford Graduate Texts in Mathematics)
暫譯: 拓撲學:幾何方法(牛津研究生數學系列)

Terry Lawson

  • 出版商: Oxford University
  • 出版日期: 2006-08-24
  • 售價: $1,180
  • 貴賓價: 9.8$1,156
  • 語言: 英文
  • 頁數: 408
  • 裝訂: Paperback
  • ISBN: 0199202486
  • ISBN-13: 9780199202485
  • 下單後立即進貨 (約5~7天)

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Description

This new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style that encourages the student to be an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one-semester or two-quarter course, and Part II (which is problem based) allows the book to be used for a year-long course which supports a variety of syllabuses.

The over 750 exercises range from simple checks of omitted details in arguments, to reinforce the material and increase student involvement, to the development of substantial theorems that have been broken into many steps. The style encourages an active student role. Solutions to selected exercises are included as an appendix, with solutions to all exercises available to the instructor on a companion website.

 

 

Table of Contents

Part I: A Geometric Introduction to Topology
1. Basic point set topology
2. The classification of surfaces
3. The fundamental group and its applications
Part II: Covering Spaces, CW Complexes and Homology
4. Covering spaces
5. CW complexes
6. Homology
Selected solutions
References
Index

商品描述(中文翻譯)

**描述**

這本新出版的平裝本拓撲學入門書籍強調幾何方法,並專注於表面。其主要特點是擁有大量的練習題和專案,這促進了一種教學風格,鼓勵學生積極參與課堂。書中涵蓋了不同層次的廣泛材料,支持各種學生的靈活使用。第一部分適合一學期或兩個學季的課程,而第二部分(以問題為基礎)則允許本書用於支持各種課程大綱的為期一年的課程。

超過750道練習題的範圍從簡單的檢查論證中遺漏的細節,到加強材料和增加學生參與度,再到發展被分解為多個步驟的實質性定理。這種風格鼓勵學生積極參與。選定練習題的解答作為附錄包含在內,所有練習題的解答可在伴隨網站上供教師使用。

**目錄**

**第一部分:拓撲學的幾何介紹**

1. 基本點集拓撲
2. 表面的分類
3. 基本群及其應用

**第二部分:覆蓋空間、CW 複合體與同調**

4. 覆蓋空間
5. CW 複合體
6. 同調
7. 選定解答
8. 參考文獻
9. 索引

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