如何像数学家一样思考
How to think like a mathematician
Kevin Houston · 初版 2009 年
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为什么值得读
- 涵盖集合、极限与可数性等证明基础概念
- 提供易于消化的全景式数学思维引导
- 帮学生在正式接触高级分析或代数前做好过渡
这套丰富的技巧和方法可以帮助新生轻松适应本科数学的学习，为他们开启定义、定理和证明的大门。
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How to think like a mathematician
Kevin Houston · 初版 2009 年
这套丰富的技巧和方法可以帮助新生轻松适应本科数学的学习，为他们开启定义、定理和证明的大门。
正在加载完整评论……
……定理/公理、集合论、epsilon-delta/连续性/极限/可微性、自然数/有理数/实数/可数性等，然后再去上你的第一门基于证明的线性代数或数学分析序列课程：- Kevin Houston 的《How to Think Like a Mathematician》- Keith Devlin 的《Intro Mathematical Thinking》- Lara Alcock 的《How to Study as a Mathematics Major》（出于某种原因，她/牛津大学出版社有两本内容看似完全相同的书，冠以 Math Major 和……
…theorems/axioms, set theory, epsilon/delta/continuity/limits/differentiability, natural/rationals/reals/countability etc before heading into your first proof based LA or analysis sequence: - Kevin Houston "How to Think Like a Mathematician" - Keith Devlin "Intro Mathematical Thinking" - "How to Study as a Mathematics Major" Lara Alcock (for some reason, she/Oxford Press has 2 books with seemingly identical content under Math Major and…
除了上面提到的，我还想加几本：Kevin Houston 的《How to Think Like a Mathematician》（开课前必读的绝佳好书）Solow 的《How to Read and Do Proofs》Solow 的《The Keys to Advanced Mathematics: Recurrent Themes in Abstract Reasoning》Spivak 的《Calculus》（其实……
To the above I would add: How to Think Like a Mathematician - Kevin Houston (an excellent book to read before starting) How to Read and Do Proofs - Solow The Keys to Advanced Mathematics: Recurrent Themes in Abstract Reasoning - Solow Calculus - Spivak (Actually…
……它涵盖的主题除了算术和简单的逻辑之外，啥都不用。话虽如此，它并不是一本好的通识数学书（它被设计成了一本计算机科学的书）。能帮到你的一本书是——《How to think like a Mathematician》：http://www.amazon.ca/How-Think-Like-Mathematician-Undergradu...
…of the topics it covers use nothing more than arithmetic and simple logic. That said it is not a good general mathematics book (it is designed as a Computer Science book). A book that will help you - How to think like a Mathematician: http://www.amazon.ca/How-Think-Like-Mathematician-Undergradu...
……（许多/大部分）讲义和学生笔记都挂出来了：http://www.maths.cam.ac.uk/studentreps/res/notes.html 还有学习指南：http://www.maths.cam.ac.uk/undergrad/studyskills/text.pdf - 关于如何像数学家一样思考的书：Keith Devlin、Kolmogorov/Alexandrov 等人写的两本 Dover 出版社的书，以及 Houston 的书：http://www.amazon.com/How-Think-Like-Mathematician-Undergrad... 还有 http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199...…
…(many/most) of lecture notes and student notes up: http://www.maths.cam.ac.uk/studentreps/res/notes.html as well as study guides: http://www.maths.cam.ac.uk/undergrad/studyskills/text.pdf - books about how to think like a mathematician: Keith Devlin, Kolmogorov/Alexandrov et al did 2 Dover books, and Houston: http://www.amazon.com/How-Think-Like-Mathematician-Undergrad... and http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199...…
你对数学的哪个领域感兴趣？还是说你想要一个通俗易懂的全科入门？如果是这样的话，我推荐 Kevin Houston 的《How to Think Like a Mathematician》。
What field of mathematics interests you? Or you want some digestable intro to all of them? In that case I would recommend Kevin Houston "How to Think Like a Mathematician".
书单：https://www.topicsinmaths.co.uk/cgi-bin/sews.py?SuggestedRea... 如果只推荐一本，那是 Kevin Houston 的《How to Think Like a Mathematician》。第二个推荐：Tom Körner 的《A Companion to Analysis》。但这很大程度上取决于你想看关于数学的书（科普），还是数学本身的书（专业）。听起来你更想要后者……
A list: https://www.topicsinmaths.co.uk/cgi-bin/sews.py?SuggestedRea... For a single suggestion, "How to Think Like a Mathematician" by Kevin Houston. A second suggestion: "A Companion to Analysis" by Tom Körner. But it depends a lot on whether you want books about math, or books of math. It sounds like you want the latter ...…