Real Analysis: With Proof Strategies

Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student's preparation and the mathematical skills that are required to be successful in such a course.

Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies offered in this textbook will be appreciated by all readers.

Features

• Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis
• Suitable for junior or senior undergraduates majoring in mathematics.

通常，大學生認為實分析是數學專業中最困難的課程之一。這種觀點的主要原因有兩個：學生必須理解新的抽象概念，並學習以前所未有的嚴謹性和證明水平處理這些概念。實分析教師面臨的一個關鍵挑戰是找到一種方法來彌補學生的準備和在這門課程中取得成功所需的數學技能之間的差距。

《實分析：證明策略》提供了解決「彌補差距問題」的方法。這本書不僅介紹了實分析的基本定理，還向讀者展示了如何構建和產生這些定理的證明。這本教科書提供的細節、嚴謹性和證明策略將受到所有讀者的讚賞。

特點：

- 明確向讀者展示如何構建和產生實分析基本定理的證明
- 適合主修數學的大三或大四本科生使用。

Daniel W. Cunningham is a Professor of Mathematics at SUNY Buffalo State, a campus of the State University of New York. He was born and raised in Southern California and holds a Ph.D. in mathematics from the University of California at Los Angeles (UCLA). He is also a member of the Association for Symbolic Logic, the American Mathematical Society, and the Mathematical Association of America.

Cunningham is the author of multiple books. Before arriving at Buffalo State, Professor Cunningham worked as a software engineer in the aerospace industry

Daniel W. Cunningham 是紐約州立大學水牛城州立學院（SUNY Buffalo State）的數學教授。他在南加州出生和長大，並在加州大學洛杉磯分校（UCLA）獲得數學博士學位。他還是符號邏輯學協會、美國數學學會和美國數學協會的成員。

Cunningham 是多本書的作者。在來到水牛城州立學院之前，Cunningham 在航空航天工業擔任軟體工程師。