Intuitive Concepts in Elementary Topology (Dover Books on Mathematics) (Paperback)
暫譯: 初等拓撲學的直觀概念(Dover 數學叢書) (平裝)
B.H. Arnold
- 出版商: Dover Publications
- 出版日期: 2011-07-19
- 售價: $750
- 貴賓價: 9.5 折 $712
- 語言: 英文
- 頁數: 192
- 裝訂: Paperback
- ISBN: 0486481999
- ISBN-13: 9780486481999
-
相關分類:
數學
海外代購書籍(需單獨結帳)
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商品描述
Classroom-tested and much-cited, this concise text offers a valuable and instructive introduction for undergraduates to the basic concepts of topology. It takes an intuitive rather than an axiomatic viewpoint, and can serve as a supplement as well as a primary text.
A few selected topics allow students to acquire a feeling for the types of results and the methods of proof in mathematics, including mathematical induction. Subsequent problems deal with networks and maps, provide practice in recognizing topological equivalence of figures, examine a proof of the Jordan curve theorem for the special case of a polygon, and introduce set theory. The concluding chapters examine transformations, connectedness, compactness, and completeness. The text is well illustrated with figures and diagrams.
A few selected topics allow students to acquire a feeling for the types of results and the methods of proof in mathematics, including mathematical induction. Subsequent problems deal with networks and maps, provide practice in recognizing topological equivalence of figures, examine a proof of the Jordan curve theorem for the special case of a polygon, and introduce set theory. The concluding chapters examine transformations, connectedness, compactness, and completeness. The text is well illustrated with figures and diagrams.
商品描述(中文翻譯)
這本簡明著作經過課堂教學驗證,並廣受引用,為大學生提供了一份極具價值且富有啟發性的拓撲學基本概念入門讀物。本書採用直觀而非公理化的觀點,既可作為主要教材,也適合作為補充教材。
透過幾個精選主題,學生可以逐步熟悉數學中各類結果及證明方法,包括數學歸納法。後續章節討論網路與映射,讓學生練習辨識圖形之間的拓撲等價性;同時探討多邊形這個特殊情況下的 Jordan 曲線定理證明,並介紹集合論。最後幾章則探討變換、連通性、緊緻性與完備性。本書搭配豐富的圖形與示意圖,說明清晰易懂。
