怎样证明
How to prove it
Daniel J. Velleman · 初版 1994 年
78人推荐
104位读者提及
129次提及
为什么值得读
- 涵盖数学分析与证明书写的核心基础概念
- 教授严谨的结构化证明方法与逻辑推理
- 帮读者建立阅读进阶数学文献的信心
许多学生在初次修读以证明为主的数学课程时都会感到吃力。Velleman 这部成功教材的新版，将通过传授阅读和编写证明所需的技巧，帮助学生完成从求解问题到证明定理的过渡。全书从逻辑和集合论的基本概念讲起，让学生熟悉数学语言及其理解方式。这些概念被用作逐步剖析构建证明所用核心技术的基础。作者
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……微积分：《微积分辅导书》（The Calculus Tutoring Book）- Ash。大学阶段：3. 大学高阶数学准备：3a. 高阶数学通识准备：《如何学好数学专业》（How to Study as a Mathematics Major）- Alcock 3b. 证明书写：《怎样证明：一种结构化方法》（How to Prove It - A Structured Approach）- Velleman 或《证明之书》（Book of Proof，第二版）- Hammack（免费的！）4. 数学分析：4a. 分析学入门好书：《如何理解分析学》（How to Think About Analysis）- Alcock 4b. 《理解分析》（Understanding Analysis）……
…Calculus: The Calculus Tutoring Book - Ash. College: 3. Preparation for Collegel-level maths: 3a. General prep for high level maths: How to Study as a Mathematics Major - Alcock 3b. Proof writing: How to Prove It - A Structured Approach - Velleman OR Book of Proof (2nd ed) - Hammack (it's free!) 4. Mathematical Analysis: 4a. Good prep for Analysis: How to Think About Analysis - Alcock 4b. Understanding Analysis…
……我们的工作。要是你们班也应用思考常规（thinking routines），大家互相学习和理解起来就会容易得多。我推荐以下几本书：- 波利亚（Polya），《怎样解题》（How to Solve It）- 韦勒曼（Velleman），《怎样证明：一种结构化方法》（How to Prove It: A Structured Approach）- 里奇哈特（Ritchhart），《让思维可见》（Make Thinking Visible）。数学研究基本上就是一连串的等价变换和逻辑推理，从已知信息出发，最终推导出……
…our work. If your class also applies thinking routines, it’ll get even easier for everyone to learn and understand each other. I recommend the following books: - Polya, How to Solve It - Velleman, How to Prove It: A Structured Approach - Ritchhart: Make Thinking Visible Mathematical work is basically a series of equivalent transformations and logical reasonings, starting from the given informations to get where…
……思维。我随手列几个想到的。我真心觉得这些书能帮你打好数学思维的底子：Graham、Knuth、Patashnik 写的《具体数学》（Concrete Mathematics）；Spivak 的《微积分》（Calculus）；Velleman 的《怎样证明》（How to Prove It）；波利亚的《怎样解题》（How to Solve It）；E.T. Jaynes 的《概率论》（Probability Theory）；Lawvere 和 Schanuel 的《概念数学》（Conceptual Mathematics）。
…thinking. Here’s some off the top of my head. I really think these will help you build a good foundation for mathematical thinking. Concrete Mathematics by Graham, Knuth, Patashnik Spivak’s Calculus How to Prove It by Velleman Polya’s How to Solve It E.T. Jaynes’ Probability Theory Conceptual Mathematics by Lawvere and Schanuel
……把为真的命题连接成一张巨大的图（graph），并在可能的情况下通过推测来拓展这张图。有了这种直觉后，剩下的就是老老实实啃一本证明教材，比如 Velleman 的《怎样证明》（How to Prove It），直到你有信心去啃那些你真正感兴趣的内容。如果你没觉得自己像个一无所知的傻子，说明你还没够努力。感到困惑和自我怀疑，恰恰说明你终于……
…connect true statements together into a massive graph and extend that graph through speculation if possible. With that intuition it's simply a matter of slogging through a proof textbook like Velleman's "How to Prove It" until you have the confidence to work through the texts that truly interest you. If you don't feel like a clueless fool you're not trying hard enough. Confusion and self-doubt are sure signs you're finally…
嗯，要是你想找一本数学基础入门书（任何想深入钻研某一特定领域的人我都推荐看），Velleman 的《怎样证明》（How to Prove It）绝对是不二之选。它涵盖了数学分析和证明书写（或许更重要的是读懂证明）的基本概念，能为你后续阅读打下绝佳的基础……
Well, if you're looking for an introduction to the basics of mathematics (which I would recommend for anyone looking to delve deeper into any specific area), you can't really beat 'How to Prove It' by Velleman. It covers the fundamental concepts of mathematical analysis and proof-writing (and, perhaps more importantly, reading proofs) and will help give you a great grounding for further reading,…
要是有人对数学家的思考方式以及如何做证明感兴趣，市面上有很多有帮助的书。比如 Chartrand 等人写的《数学证明：通往高等数学的过渡》（Mathematical Proofs: A Transition to Advanced Mathematics）；Velleman 的《怎样证明：一种结构化方法》（How to Prove It: A Structured Approach）；Nancy Rodgers 的《学会推理：逻辑、集合与关系导论》（Learning to Reason: An Introduction to Logic, Sets, and Relations）。初等离散数学书也是了解证明和数学思维的绝佳入门读物：……
If anyone is interested in how mathematicians think and do proofs there are many helpful books. For example, Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand and others. How to Prove It: A Structured Approach by Velleman. Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers. Elementary Discrete Math books make for great intro to proofs and math thought:…