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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)
《轉向證明：高等數學入門》將撰寫證明描述為一個創造性的過程。在撰寫數學證明之前，有許多工作需要進行。書中充分討論了如何理解證明的「基本要素」：思考過程、草稿工作以及解決問題的方法。讀者將學習如何不僅撰寫數學，還能進行數學運算。接著，他們將學會如何有效地傳達數學。
本書強調創造力、直覺和正確的數學表述，為學生準備超越微積分序列的課程。作者鼓勵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「數學應該和不應該」來實現的，這些內容以引人注目的「文本框」形式呈現在書中。最終結果使讀者能夠充分理解證明的基本原則。
特色：
- 本書針對過渡課程，幫助學生準備進入分析課程
- 促進創造力、直覺和準確的表述
- 證明的語言在前兩章中建立，涵蓋邏輯和集合論
- 包含有關基數和初步拓撲的章節
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)
尼爾·R·尼克爾森博士是北中學院的數學副教授。他擁有愛荷華大學的數學博士學位，專攻結理論。他的研究興趣始終是本科生能夠接觸的主題；與學生合作進行原創研究是他專業發展的基本目標。2015年，他獲得北中學院的克拉倫斯·F·迪辛格初級教學獎。他擔任北中學院的NCAA教職員運動代表。
