楼上其他人已经给出了不少极好的推荐，那我来推一本稍微冷门点的：《数学基础》（Foundations of Mathematics）https://www.amazon.com/Foundations-Mathematics-Ian-Stewart/d... 这本书旨在帮助大家实现转变：从按套路算法做数学，过渡到基于逻辑去写证明，并且……
Others here have offered some great suggestions already, so I will offer one a little off the beaten path: Foundations of Mathematics https://www.amazon.com/Foundations-Mathematics-Ian-Stewart/d... This book is meant to help one transition from performing math in an algorithmic manner to generating proofs based on logic and also…
……能把这么硬核的一门学科讲得让人觉得“这绝对是本好书”？不是，难道大家平时学数学都不止读一本教材的吗？！ > ……为了让大家体验一下大学风格的数学 我刚开始读 Ian Stewart 和 David Tall 写的《数学基础》（The Foundations of Mathematics）。目前感觉真的相当不错。
…through such a tough subject that it has to be a good book? I mean, do people normaly study from more than one text?! > ...to give people a flavour of university style mathematics I've just started The Foundations of Mathematics by Ian Stewart & David Tall. So far it's really promising.
看完了所有评论，我也来分享一下我的选择：1. Stewart 和 Tall 写的《The foundations of mathematics》 2. Arthur Engel 写的《Problem Solving Strategies》 3. Rotman 写的《Journey into Mathematics》 4. Knuth 等人写的《Concrete Mathematics》
After reading all the comments I am sharing my choices 1. The foundations of mathematics by Stewart and Tall 2. Problem Solving Strategies by Arthur Engels 3. Journey into Mathematics by Rotman 4. Concrete Mathematics by Knuth et al.
Ian Stewart 写的《数学基础》（The Foundations of Mathematics）。我倒不会说它教给我的知识最多，倒不如说它帮我推开了一扇大门，让我在此之后能学懂更多的东西。
The Foundations of Mathematics - Ian Stewart. I wouldn't say it taught me the most, but more like it opened the door so I could learn the most out of everything after it.
……我给很多背景各不相同的朋友和家人都买过这书（从数学专业研究生到高中毕业四十年没碰过数学的人都有）。另外还有 Baylis 和 Haggarty 写的《Alice and Numberland》，以及 Stewart 和 Tall 写的《数学基础》（The Foundations of Mathematics）。这两本的深度都介于高中和大学水平之间，衔接过渡做得非常好。
…I've bought it for friends and family with a wide range of maths backgrounds (graduate mathematicians to not-since-school-forty-years-ago). Also "Alice and Numberland", Baylis and Haggarty; and "The Foundations of Mathematics", Stewart and Tall. These are both pitched somewhere between high school and university level and bridge the gap well.
我建议先去读读 Stewart 和 Tall 写的《数学基础》（The Foundations of Mathematics）：https://global.oup.com/ukhe/product/the-foundations-of-mathe... 读了之后你就会心里有数，知道哪些内容你能看懂，哪些你基本跟不上节奏。在此基础上，……
I would suggest to start with reading The Foundations of Mathematics by Stewart and Tall: https://global.oup.com/ukhe/product/the-foundations-of-mathe... This will give you an understanding of which topics make sense to you and which you can barely follow. From that,…
楼上其他人已经给出了不少极好的推荐，那我来推一本稍微冷门点的：《数学基础》（Foundations of Mathematics）https://www.amazon.com/Foundations-Mathematics-Ian-Stewart/d... 这本书旨在帮助大家实现转变：从按套路算法做数学，过渡到基于逻辑去写证明，并且……
Others here have offered some great suggestions already, so I will offer one a little off the beaten path: Foundations of Mathematics https://www.amazon.com/Foundations-Mathematics-Ian-Stewart/d... This book is meant to help one transition from performing math in an algorithmic manner to generating proofs based on logic and also…
……能把这么硬核的一门学科讲得让人觉得“这绝对是本好书”？不是，难道大家平时学数学都不止读一本教材的吗？！ > ……为了让大家体验一下大学风格的数学 我刚开始读 Ian Stewart 和 David Tall 写的《数学基础》（The Foundations of Mathematics）。目前感觉真的相当不错。
…through such a tough subject that it has to be a good book? I mean, do people normaly study from more than one text?! > ...to give people a flavour of university style mathematics I've just started The Foundations of Mathematics by Ian Stewart & David Tall. So far it's really promising.
看完了所有评论，我也来分享一下我的选择：1. Stewart 和 Tall 写的《The foundations of mathematics》 2. Arthur Engel 写的《Problem Solving Strategies》 3. Rotman 写的《Journey into Mathematics》 4. Knuth 等人写的《Concrete Mathematics》
After reading all the comments I am sharing my choices 1. The foundations of mathematics by Stewart and Tall 2. Problem Solving Strategies by Arthur Engels 3. Journey into Mathematics by Rotman 4. Concrete Mathematics by Knuth et al.
Ian Stewart 写的《数学基础》（The Foundations of Mathematics）。我倒不会说它教给我的知识最多，倒不如说它帮我推开了一扇大门，让我在此之后能学懂更多的东西。
The Foundations of Mathematics - Ian Stewart. I wouldn't say it taught me the most, but more like it opened the door so I could learn the most out of everything after it.
……我给很多背景各不相同的朋友和家人都买过这书（从数学专业研究生到高中毕业四十年没碰过数学的人都有）。另外还有 Baylis 和 Haggarty 写的《Alice and Numberland》，以及 Stewart 和 Tall 写的《数学基础》（The Foundations of Mathematics）。这两本的深度都介于高中和大学水平之间，衔接过渡做得非常好。
…I've bought it for friends and family with a wide range of maths backgrounds (graduate mathematicians to not-since-school-forty-years-ago). Also "Alice and Numberland", Baylis and Haggarty; and "The Foundations of Mathematics", Stewart and Tall. These are both pitched somewhere between high school and university level and bridge the gap well.
我建议先去读读 Stewart 和 Tall 写的《数学基础》（The Foundations of Mathematics）：https://global.oup.com/ukhe/product/the-foundations-of-mathe... 读了之后你就会心里有数，知道哪些内容你能看懂，哪些你基本跟不上节奏。在此基础上，……
I would suggest to start with reading The Foundations of Mathematics by Stewart and Tall: https://global.oup.com/ukhe/product/the-foundations-of-mathe... This will give you an understanding of which topics make sense to you and which you can barely follow. From that,…