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Jingdong book

用数学的语言看世界

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用数学的语言看世界

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美国加州理工学院理论物理研究所所长,日本东京大学Kavli数学物理学联合宇宙研究机构研究主任大栗博司教授

日本数学启蒙名作

让喜欢数学的人更喜欢数学

让恐惧、厌恶数学的人开始喜欢数学

日本神户大学文理综合素养课程选定数学读物

日本《每日新闻》《钻石周刊》推荐图书

突破传统数学教育教学顺序、方式/以“语言思维”讲解数学核心概念、原理/回归“基本原理”重新认识数学本质


Content Description

用数学的语言看世界为知名理论物理学家大栗博司先生写给女儿的数学启蒙书,书中以用“数学语言”解读自然为线索,突破传统数学教育的顺序和教学方式,用历史事件、生动故事以及比喻直接讲解数学核心概念的原理与相关体系,并且讲解了把数学作为一门“语言”、用数学探索自然不可见结构的思维方式,是重新认识和理解数学的科普佳作。

Author Description

大栗博司,美国加州理工学院理论物理讲席教授,理论物理研究所(burkeinstitute.caltech.edu)所长,日本东京大学Kavli数学物理学联合宇宙研究机构(KavliIPMU)研究主任。东京大学理学博士,发现了量子场论与超弦理论的深层数学构造,其研究曾获得美国数学学会大奖(2008年)、德国洪堡研究奖(2009年)、日本仁科纪念奖(2009年)、日本数学学会詹姆斯?西蒙斯奖(2012年),《超弦理论:探究时间、空间及宇宙的本原》获得2014年日本第30届日本讲谈社科学出版奖。著有前沿物理科普三部曲《引力是什么》《强力与弱力》《超弦理论》,数学入门科普《用数学的语言看世界》等。

Catalogue

第1章 从不确定的信息中作出判断1

序 欧 杰 辛普森审判与德肖维茨教授的辩护主张1

1.先来掷骰子3

2.赌博中的不败之法4

3.条件概率与贝叶斯定理8

4.乳腺癌检查是否没有意义?10

5.用数学来“学习经验”13

6.核电站重大事故再次发生的概率15

7.欧?杰?辛普森真的杀害了妻子吗?18

第2章 回归基本原理21

序创新与创造的必要条件21

1.加法、乘法与运算三定律22

2.减法与0的发现25

3.(.1)×(.1) 为何等于1 ? 29

4.分数与无限分割32

5.假分数→带分数→连分数33

6.用连分数制作历法35

7.过去不被认可的无理数37

8.二次方程的华丽历史43

第3章 大数字并不恐怖49

序最初的原子弹爆炸实验与“费米问题”49

1.大气中的二氧化碳究竟增加了多少51

1.1人类消耗了多少能量51

1.2人类排放了多少二氧化碳52

2.遇到大数字不必慌张53

3.让天文学家寿命倍增的秘密武器56

4.复利最大化的存款方法59

5.让银行存款翻倍需要多少年61

6.用对数透视自然法则64

第4章 不可思议的素数69

序纯粹数学的精华69

1.埃拉托斯特尼筛法与素数的发现72

2.素数有无穷个74

3.素数的分布存在规律77

4.用素数判定“帕斯卡三角形”79

5.通过费马检测就是素数?82

6.保护通信秘密的“公钥密码”85

7.公钥密码的钥匙,欧拉定理87

8.信用卡卡号SSL传输的原理90

第5章 无限世界与不完备性定理97

序欢迎来到加州旅馆!97

11=0.99999...让人难以接受?107

2.阿喀琉斯永远追不上乌龟?110

3.“我正在说谎”112

4.“不在场证明”与“反证法”114

5.哥德尔不完备性定理115

第6章 测量宇宙的形状121

序古希腊人如何测量地球周长?121

1.基础中的基础,三角形的性质125

1.1证明三角形内角和为180°127

1.2让人终生难忘的“勾股定理”证明130

2.笛卡儿坐标与划时代的创想134

3.六维、九维、十维138

4.欧几里得公理不成立的世界140

5.唯独平行公理不成立的世界142

6.不用外部观测即可得知形状的“神奇定理”145

7.画一个边长为100亿光年的三角形148

第7章 微分源于积分153

序来自阿基米德的书信153

1.为何先从积分开始?155

2.面积究竟如何计算156

3.任何形状都OK,阿基米德的夹逼定理158

4.积分究竟计算什么160

5.积分与函数164

6.飞矢不动?167

7.微分是积分的逆运算169

8.指数函数的微分与积分171

第8章 真实存在的“假想数字”175

序假想的朋友,假想的数字175

1.平方为负的奇怪数字176

2.从一维的实数到二维的复数179

3.复数的乘法运算“旋转与伸长”185

4.从加法导出的加法定理189

5.用方程解决几何问题191

6.三角函数、指数函数与欧拉公式195

第9章 测量“难”与“美”201

序伽罗瓦,20年的生涯与不灭功绩201

1.图形的对称性是什么206

2.“群”的发现210

3.二次方程求根公式的秘密214

4.三次方程为何可解218

5.方程可解是什么意思224

6.五次方程与正二十面体227

7.伽罗瓦最后的书信229

8.方程的“难度”与图形的“美”230

9.拥有第二个灵魂233

后记237


Book Abstract

《用数学的语言看世界》:
古希腊人之所以无法观测到地球公转引起的视差,是因为恒星实在太遥远。例如把太阳看作一颗直径为1厘米的弹珠,那么我们所在的地球就只有0.1厘米,比一粒沙子还小。沙子在距离弹珠1米外的位置绕一圈,这就是地球的公转运动。此时,到最接近地球的恒星比邻星的距离相当于比东京到名古屋的距离还远300千米。然而,地球公转引起的视差只有0.76秒≈0.0002度。因此,按照古希腊的技术无法测量到恒星并不奇怪。因为没有发现上述依据,而且存在例如“既然地球在运动,为什么我们感受不到呢”的直观反论,所以在当时地心说是天文学的主流学说。也许当时的希腊人选择地心说是出于宗教原因,不过他们也有根据科学依据作出了判断。
古埃及和古巴比伦时期积累了很多有关数与图形的知识,希腊人将其发展成了一门称作数学的学问。在人类历史中,这是一件划时代的大事件,甚至可以称为奇迹。希腊人试图使用几何学去研究地球、月球、太阳以及行星的位置与运动。接下来我们试着追寻几何学从古希腊到现代的发展过程,同时思考关于宇宙形状的问题。
……

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