Elements of Topology: Theory and Practice
暫譯: 拓撲學要素：理論與實踐

Krantz, Steven G.

Elements of Topology: Theory and Practice
  • 出版商: CRC
  • 出版日期: 2026-04-30
  • 售價: $4,280
  • 貴賓價: 9.5 折 $4,066
  • 語言: 英文
  • 頁數: 226
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1041216831
  • ISBN-13: 9781041216834
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This book is an ambitious but optimistic treatment of the subject of topology. Not only does Elements of Topology: Theory and Practice, Second Edition treat the standard basic material on point-set topology, but it also gives an introduction to algebraic topology, a treatment of manifolds, a discussion of function spaces, and some ideas of knot theory. Even the exciting new topic of the Jones polynomial is covered. After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory.

Topic coverage has been reduced in this second edition, and exercise sets have been added at the end of each section. The book as a whole--and the first two chapters in particular-- offer many examples. Solutions to selected exercises are included at the end.

Today's students need a text that speaks to them in their own language, and at a pace with which they are comfortable. That is the goal of this edition. Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond.

商品描述(中文翻譯)

這本書是一部雄心勃勃但充滿樂觀的拓撲學主題探討。《拓撲學要素：理論與實踐，第二版》不僅涵蓋了點集拓撲的標準基本材料，還介紹了代數拓撲、流形的處理、函數空間的討論以及一些結理論的概念。甚至連令人興奮的喬恩斯多項式（Jones polynomial）這一新主題也有涉及。在討論拓撲學的關鍵概念後，作者進一步探討了代數拓撲和流形理論的更高級主題。

在這第二版中，主題的涵蓋範圍有所縮減，並在每個章節的末尾新增了練習題集。整本書，尤其是前兩章，提供了許多範例。選定練習題的解答也包含在書末。

當今的學生需要一本能用他們自己的語言與他們對話的教材，並以他們感到舒適的速度進行學習。這是本版的目標。這本書以新穎且易於理解的方式探討這一古老的主題，提供了拓撲學概念的優秀表述。它為進一步的數學學習奠定了基礎，包括實分析、抽象代數等領域。

作者簡介

Steven G. Krantz is a professor at Washington University in St. Louis where he teaches mathematics. He has previously taught at UCLA, Princeton University, and Penn State University. He earned his PhD from Princeton University in 1974. Prof. Krantz has directed 20 PhD students and 8 master's-degree students, and he published over 130 books and over 300 scholarly articles. He is the holder of the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Prize, and he is a fellow of the American Mathematical Society.

作者簡介(中文翻譯)

史蒂芬·G·克蘭茨是聖路易斯華盛頓大學的數學教授。他曾在加州大學洛杉磯分校、普林斯頓大學和賓州州立大學任教。他於1974年在普林斯頓大學獲得博士學位。克蘭茨教授指導了20位博士生和8位碩士生，並出版了超過130本書籍和300篇學術文章。他是喬文內獎、貝肯巴赫書籍獎和肯珀獎的得主，並且是美國數學學會的會士。

類似商品