A Transition to Proof: An Introduction to Advanced Mathematics

Nicholson, Neil R.

A Transition to Proof: An Introduction to Advanced Mathematics
  • 出版商: CRC
  • 出版日期: 2023-01-21
  • 售價: $2,180
  • 貴賓價: 9.5 折 $2,071
  • 語言: 英文
  • 頁數: 464
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 1032475722
  • ISBN-13: 9781032475721

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商品描述

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively.

 

The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do's and don'ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof.

 

Features:

 

 

 

 

 

 

 

 

 

 

 

 

 

  • The text is aimed at transition courses preparing students to take analysis
  • Promotes creativity, intuition, and accuracy in exposition
  • The language of proof is established in the first two chapters, which cover logic and set theory
  • Includes chapters on cardinality and introductory topology

 

商品描述(中文翻譯)

《證明的轉變：高等數學導論》描述了證明的撰寫過程，強調證明是一個創造性的過程。在撰寫證明之前，需要進行大量的思考和解決問題的方法討論，包括思考過程、草稿和解決問題的方法。讀者不僅學會如何撰寫數學，還學會如何進行數學。然後，他們將學會有效地傳達數學。

本書強調創造力、直覺和正確的數學表達，為學生在微積分課程之外的課程做好準備。作者敦促讀者努力定義自己的數學聲音。這是通過風格提示和嚴格的“數學要做”和“數學不要做”來實現的，這些提示以引人注目的“文本框”形式呈現在整本書中。最終的結果使讀者能夠充分理解證明的基礎。

特點：
- 本書針對過渡課程，為學生準備進入分析學課程。
- 促進創造力、直覺和準確的表達。
- 前兩章建立了證明的語言，包括邏輯和集合論。
- 包括關於基數和入門拓撲學的章節。

作者簡介

Dr. Neil R. Nicholson is Associate Professor of Mathematics at North Central College. He holds a Ph.D. in Mathematics from The University of Iowa, specializing in knot theory. His research interests have consistently been topics accessible to undergraduates; collaborating with them on original research is a fundamental goal of his professional development. In 2015, he earned the Clarence F. Dissinger Award for Junior Faculty Teaching at North Central College. He serves as the Faculty Athletic Representative to the NCAA for North Central College.

作者簡介(中文翻譯)

「Dr. Neil R. Nicholson」是北中央學院的數學副教授。他擁有愛荷華大學的數學博士學位，專攻結繩理論。他的研究興趣一直都是對本科生易於理解的主題；與他們合作進行原創研究是他專業發展的基本目標。2015年，他在北中央學院獲得了Clarence F. Dissinger優秀青年教師教學獎。他還擔任北中央學院的全國大學體育協會（NCAA）教職員代表。

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