证明之书
Book of Proof
Richard Hammack · 初版 2009 年
54人推荐
66位读者提及
86次提及
为什么值得读
- 有效锻炼数学证明思维并规范大脑逻辑
- 网上提供免费PDF版本供学习者阅读
- 适合作为大学高阶数学与分析课程的先修准备
本书是对数学语言和标准证明方法的入门介绍。它是从学生大学一年级通常接触的计算类课程（如 calculus 或 differential equations）迈向更抽象视角的桥梁。它为 topology、analysis 和 abstract algebra 等更偏重理论的课程奠定了基础。
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……大学水平数学的准备工作：3a. 高阶数学的通用准备：《How to Study as a Mathematics Major》- Alcock 3b. 证明写作：《How to Prove It - A Structured Approach》- Velleman 或者《Book of Proof》（第2版）- Hammack（这本书是免费的！）4. 数学分析：4a. 分析学的良好准备：《How to Think About Analysis》- Alcock 4b. 《Understanding Analysis》（第2版）- Abbott 或者《Yet Another Introduction……
…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 (2nd ed) - Abbott OR Yet Another Introduction…
……章节，把解答做一遍，要是还是搞不懂就到处问问。坚持和形成日常习惯是这里的关键。书的话，我喜欢 Stewart 的《Calculus》、Lay 的《Linear Algebra》和 Hammack 的《Book of Proof》。物理方面，我不知道你的背景如何。Giancoli 是一本挺受欢迎的本科大一教材，而 Griffith 的电动力学（electrodynamics）则更进阶一些。
…chapter, work through the solutions, and ask around if you still can't figure it out. Persistance and routine are key here. As for books, I like Stewart's Calculus, Lay's Linear Algebra, and Hammack's Book of Proof. For physics, I don't know what your background is. Giancoli is a popular undergrad freshman year book, where as griffith's electrodynamics is a bit more advanced.
……让我会心一笑。我随着深入钻研数据科学，正好在重新学数学，这时机简直太完美了。等我啃完我的数学证明书（Richard Hammack 的《Book of Proof》，我向想入门数学的人推荐这本书 https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472...），就去看这个系列。
…brings a smile to my face. I just happen to be relearning math right now as I dive deeper into data science and this is perfect timing. Going to watch this series once I get through my math proofs book ("Book of Proof" by Richard Hammack which I recommend to people getting into math https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472...).
……关于算法和数据结构），并通过刷完 Bryant 和 O'Hallaron 的《Computer Systems: A Programmer's Perspective》来学习底层细节。你可以从 Hammack 的《Book of Proof》（网上免费获取）学习证明。从那之后，你可以去 Coursera 上看斯坦福和/或普林斯顿的算法和数据结构课程。以上内容相当于一个扎实的 CS 辅修了。从……
…on algorithms and data structures), and learn lower level details by working your way through Bryant and O'Halloron's Computer Systems: A Programmer's Perspective. You can learn proofs from Hammack's Book of Proof, freely available online. From there, you can learn algorithms and data structures from Stanford and/or Princeton's courses on Coursera. The above would be the equivalent of a strong CS minor. From…
……他们的定义，要检查它们在某个运算下是否构成半群就很简单了：我们只需检查结合性。要掌握这些东西，我推荐以下书籍： Richard Hammack 的《Book of Proof》（行业工具） Kuldeep Singh 的《Linear Algebra》（严谨的教程：结合了教科书的严谨性和教程的易用性） Dos Reis 的《Abstract Algebra》（严谨……
…me their definition, it'd be trivial to check if they form a semigroup under a certain operation: we'll just check it for associativity. To get a hang of this stuff I recommend the following books: Book of Proof by Richard Hammack (tools of the trade) Linear Algebra by Kuldeep Singh (rigorous tutorial: combines the rigor of a textbook and the ease of use of tutorial) Abstract Algebra by the Dos Reis (rigorous…
最初让我变成好奇之人的是《Surely You're Joking, Mr. Feynman!》和《Gödel, Escher, Bach》。然后是《Book of Proof》和《Forallx: an introduction to formal logic》帮我培养了对数学的兴趣。但真正算得上审美裂变的是《The UNIX Programming Environment》和《The TeXbook》。
What initially turned me into a curious person were Surely You Are Joking Mr Feynman & Godel, Escher, Bach. Then Book of Proof & Forallx: an introduction to formal logic helped me develop an interest in mathematics. But what was really a kind of aesthetic crack was The UNIX Programming Environment and The TeXbook.