国内最为知名的数学科普书恐怕是Richard Courant的《什么是数学》(What is Mathematics),但其四五百页的厚度和大量的公式估计会吓到一片。再比如说胡作玄老先生的《数学是什么》,页数也是将近四百页。
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在库兰特(Richard(]ourant)与罗宾斯(HerbeIt Robbins)合著的《数学是什么》(What Is Mathematics)一书中就有一个基本证明。它利用了波尔查诺定理。
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什么是数学 对思想和方法的基本研究 what is mathematics 但如果你改变主意,你知道这里是生病 but if you change your mind you know that ill be here ..
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How students perceive "What is mathematics?" directly affected how they learn mathematics and how they solve mathematics problems.
学生对“数学是什么”的认知直接影响他们学习数学和解数学题的方式。
Milnor says that what he loves most about mathematics is “a feeling of miracles.
米尔诺尔说数学让他最喜爱的地方是那种“奇迹的感觉”。
The aim is to discover not what pupils know but how well they can manipulate what they have learned in reading, mathematics and science.
考察的目的主要是发现学生的知识面以及他们对已学到的阅读素养、数学素养和科学素养。
"I thought that what is the end would destroy him would be the mathematics examination.
VOA: special.2009.01.03
What mathematicians are doing is using their mind to think about these Platonic ideas of mathematics.
数学家所做的就是用他们的心灵,来思考那些数学的柏拉图理念
So, what we're dealing here with is a situation where the ancient Greeks were very much into mathematics as a way of explaining the world and explaining music in particular And they thought these ratios were primary.
那么,我们现在要潜心琢磨,古希腊人热衷于,用数学来解释世界,尤其是音乐的这种情形,他们认为这些比例才是基础
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