主编推荐语
菲尔兹奖得主作品，教你数学思维方式，启示你如何抽象思考。
内容简介
The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?")
目录
- COPYRIGHT
- Preface
- List of diagrams
- Chapter 1 Models
- How to throw a stone
- What is a mathematical model?
- Rolling a pair of dice
- Predicting population growth
- The behaviour of gases
- Modelling brains and computers
- Colouring maps and drawing up timetables
- Various meanings of the word 'abstract'
- Chapter 2 Numbers and abstraction
- The abstract method
- Chess without the pieces
- The natural numbers
- Zero
- Negative numbers and fractions
- Real and complex numbers
- A first look at infinity
- Raising numbers to negative and fractional powers
- Chapter 3 Proofs
- The irrationality of the square root of two
- The irrationality of the golden ratio
- Regions of a circle
- Pythagoras' theorem
- Tiling a square grid with the corners removed
- Three obvious-seeming statements that need proofs
- Chapter 4 Limits and infinity
- 1. The square root of 2 is about 1.41421356
- 2. We reached a speed of 40 m.p.h. just as we passed that lamp-post
- 3. The area of a circle of radius r is πr2
- Chapter 5 Dimension
- How to define high-dimensional space
- Can four-dimensional space be visualized?
- What is the point of higher-dimensional geometry?
- Fractional dimension
- Chapter 6 Geometry
- Euclidean geometry
- The parallel postulate
- Spherical geometry
- Hyperbolic geometry
- How can space be curved?
- Manifolds
- Chapter 7 Estimates and approximations
- A simple sequence not given by a simple formula
- Ways of approximating
- All you need to know about logarithms, square roots etc.
- The prime number theorem
- Sorting algorithms
- Chapter 8 Some frequently asked questions
- 1. Is it true that mathematicians are past it by the time they are 30?
- 2. Why are there so few women mathematicians?
- 3. Do mathematics and music go together?
- 4. Why do so many people positively dislike mathematics?
- 5. Do mathematicians use computers in their work?
- 6. How is research in mathematics possible?
- 7. Are famous mathematical problems ever solved by amateurs?
- 8. Why do mathematicians refer to some theorems and proofs as beautiful?
- Further reading
- Index
评分及书评
- 给这本书评了5.0很棒的一本数学科普书
有的好书并不是告诉了你什么箴言道理，而是她激起了你对某一方面知识探索的兴趣甚或是激情。而这本书，毫无疑义的属于这类好书中的佼佼者。尽管我们从小到大学了不少年的数学，从小学学的基本运算到大学学的微积分、概率论、线性方程等高等数学，学的东西是不少，但是真的学进去的人怕是不多。以我为例，我大学之前的数学还是很不错的，可那会儿我就是理解了老师讲的各种数学公式和定理，然后再去做题，从来没有去深想过这些定理背后的意义，只是知其然而不知其所以然，导致了我日后上大学还是这种学习方法，数学成绩也就一落千丈。而且当你不理解数学各个分支的底层逻辑的话，你学的那些公式定理很快就会被通通忘记，遇到一些困难的问题时你跟没怎么学过数学的人也没有本质上的区别，都是两眼一抓瞎，这样的学习数学并没有什么重大的意义。而这本书并没有教你什么公理公式定理，他更多的教你的是数学的底层逻辑，一种数学思维，当你理解了这些，数学可以帮助你在各个方面都建立起一个相当扎实的看待世界的底层逻辑。
给这本书评了5.0深入浅出讲述数学的本质。
给这本书评了4.0很好的科普读物很好的科普读物，不需要专业知识，没有负担地提高对数学的认识。
- 查看全部5条书评
出版方
牛津大学出版社
牛津大学出版社隶属牛津大学，以环球出版为志业，弘扬牛津大学卓于研究、博于学术、笃于教育的优良传统。 牛津大学出版社成立于1478年，是世界上历史最悠久的大学出版社之一，现也是世界上最大的大学出版社，雇员6000余名，遍布全球50多个国家。每年出版物超过6000种。除了出版发行最优质的教材以外，牛津大学出版社还力求创新，通过不断引进先进的教学法和积极发展电子出版来引领教育。 牛津在北京、上海、广州及成都的代表机构是牛津大学出版社的重要成员，在教科书、词典、学术合作出版方面成绩斐然。牛津以专业积极的姿态，积极引进先进的教育资源和教育方法来协助中国大陆英语教育市场的发展，关注教师职业发展与需求，引领行业创新与进步。
