What Is Mathematics?

R·柯朗（Richard Courant）是20世纪杰出的数学家，哥廷根学派重要成员。他生前是纽约大学数学系和数学科学研究院的主任，该研究院后被重命名为柯朗数学科学研究院。他写的书《数学物理方程》为每一个物理学家所熟知；而他的《微积分学》已被认为是近代写得最好的该学科的代表作。H·罗宾（Herbert Robbins）是新泽西拉特杰斯大学的数理统计教授。I·斯图尔特（Ian Stewart）是沃里克大学的数学教授，并且是《自然界中的数和上帝玩色子游戏吗》一书的作者；他还在《科学美国人》杂志上主编《数学娱乐》专栏；他因使科学为大众理解的杰出贡献而在1995年获得了皇家协会的米凯勒法拉第奖章。

出版者:Oxford University Press

作者:Richard Courant

页数:592

出版时间:1996-7-18

价格:GBP 11.99

装帧:Paperback

isbn号码:9780195105193

图书标签:数学Mathematics科普思维英文原版Math方法论英文

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For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.

读后感

中国的数学教材写得差的缘由是那些学者和教授并没有真的理解他所写的东西，一句话，他们理解的不透彻，所以写不出这样的书，这不是卖弄写书技巧这种小聪明的问题。 我在看前面的部分时就发觉这书好，及至看到原书第40页关于哥德巴赫猜想的叙述时作者一针见血直达本质的话一下子...  

我觉得副标题非常的贴切。 初等数学的脉络讲解的非常清晰，对解决问题的思想方法分析的简洁、深刻。我以为能把事情用简单的方式叙述出来都是要么非常花费功夫，要么就是领域中的大师——正如《Programming Pearls》和《 The C Programming Language》，薄薄一本书，值得翻来覆...  

关于评价，我选了“推荐”。我说我是来提供事实和灵感的。这本书上有一页是介绍数学归纳法的，如果你学过高中数学，就知道这方法在求通项公式时非常好用。但前提是你的数学归纳法的格式必须符合要求。在这本书中呢，关于数学归纳法，这位哥廷根人讲了一大堆纯学术意义上的关于...  

http://books.google.com/books?id=_kYBqLc5QoQC&printsec=frontcover&dq=What+is+Mathematics&ei=8ZtTSL7bHp_otQODrsTNCw&sig=k7DQzxSHVRMP02ZCYTU-NrhuB8E 大家试试。  

特别有爱 特别立志 非专业观点！ 主旨是攒德行~ 专业中类似科普的著作，我就当高精尖，带回来报答从小到大的数学老师们了~  

用户评价

我实话实说我没读完，我智商不够

2.2/2.4/3.1/4.6/7.7 精彩

再次读了一二六八章，带着比几年前更强烈的好奇，希望把自己对数学的机械理解统统推倒重建。我对微积分和infinity着迷，因为我相信眼前transient的万物都是一种illusion。我想借助数学去去重新理解space-time，进一步敞开无尽的想象去理解眼前的世界是——它积分的结果，要探清它的面目需对其微分再微分。借助infinity的思考方式，重新理解了无理数，极限，连续，微分、积分、自然对数缘所从来，处处都是哲学之美，上帝创世的永恒旋律????

从数论，到射影几何、非欧几何，到拓扑学的心里路程依次是：“啊这个竞赛学过，好怀念”，“数学好有趣，好厉害，教练我要学数学！”，“等等，这是什么鬼，为什么我什么都看不懂”，“呵呵，我觉得我还是比较适合上文科”。。

i love mathematics