Real Analysis: A Long-Form Mathematics Textbook

Cummings, Jay

  • 出版商: Independently Published
  • 出版日期: 2019-07-15
  • 售價: $1,140
  • 貴賓價: 9.5$1,083
  • 語言: 英文
  • 頁數: 446
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 1077254547
  • ISBN-13: 9781077254541
  • 立即出貨 (庫存 < 3)

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商品描述

This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own. Examples often drive the narrative and challenge the intuition of the reader. The text also aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and includes interesting historical notes, periodic attempts at humor, and occasional diversions into other interesting areas of mathematics. The text covers the real numbers, cardinality, sequences, series, the topology of the reals, continuity, differentiation, integration, and sequences and series of functions. Each chapter ends with exercises, and nearly all include some open questions. The first appendix contains a construction the reals, and the second is a collection of additional peculiar and pathological examples from analysis. The author believes most textbooks are extremely overpriced and endeavors to help change this.Hints and solutions to select exercises can be found at LongFormMath.com.

商品描述(中文翻譯)

這本教科書是為學生設計的。與典型的定義-定理-證明-重複的風格不同,這本教材包含更多的評論、動機和解釋。證明並不簡潔,而是以理解為目標,而非經濟性。此外,許多證明前都有“草稿”或證明草圖,以便給學生提供整體觀點,並解釋他們如何自己想出這個證明。例子通常推動敘述並挑戰讀者的直覺。本教材還旨在使思想可見,並包含200多個插圖。文字輕鬆,包含有趣的歷史注解,定期嘗試幽默,並偶爾涉及其他有趣的數學領域。本教材涵蓋了實數、基數、序列、級數、實數的拓撲、連續性、微分、積分,以及函數的序列和級數。每章結束時都有練習題,幾乎所有章節都包含一些開放性問題。第一個附錄包含了實數的構造,第二個附錄是一個從分析學中收集的其他特殊和病態例子的集合。作者認為大多數教科書價格過高,並努力改變這一狀況。部分練習的提示和解答可在LongFormMath.com上找到。