高考中的数学文化

高考中的数学文化
作 者: 齐龙新
出版社: 电子工业出版社
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作者简介

  齐龙新,北京市数学特级教师,山东省教学能手,山东省新课程研修团队专家,山东省基础教育教师培训专家,山东省优质课一等奖、教育部一师一优课一等奖获得者,现为北京市育英学校经济学实验班班主任。作者致力于“新数学自学辅导教学法”的实践与研究,所编自学教材曾获得山东省优秀课程资源一等奖,在日常教学实践中也取得了非常显著的教学效果。其微信个人公众号“龙新数学(zxfd66)”曾经获得2016年数学文化杂志社主办的携手北大数学文化节公众号评选全国第二名。“把数学教得通俗易懂,让学生学得幸福有趣”是作者一以贯之的精致追求,其教学风格独特,教法细腻、技巧纯熟,教学成绩突出,与学生之间亦师亦友,深得学生的喜爱。作者教学之余写出了数十篇教育教学论文,撰写了《初高中数学衔接教材》等多部教研论著。

内容简介

教育部考试中心以正式文件明确提出在高考数学考题中要体现数学文化,这是一个明显的信号:要求学生加强对数学文化知识的学习,自觉地、有针对性地重视对数学文化修养的提升。本书创新性地从“以数化人”与“人数学化”两个角度来谈数学文化,对数学文化在数学历史、数学精神、数学应用、数学之美、数学语言、交汇拓展、数学游戏等各个主题上都作出了全面透彻的剖析和论述。除此之外,作者还结合历年高考数学试题进行具体的案例分析,以此让高考生能够精准消化吸收高考中的各种数学文化知识。对高中生而言,这是一部让他们明确数学文化“是什么”“怎么考”“怎么练”,为备考数学文化提供清晰学习方向的宝书;对数学教学工作者或研究者而言,这是一部系统揭示命制背景、展示解题过程、凸显数学文化价值的宝贵内参书;对于广大的数学文化爱好者而言,这又是一部让人崇尚真理,净化心灵,提升文化修养和文化品格的数学美书。

图书目录

第一章

数学文化总论

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第一节

什么是数学文化

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第二节

数学文化的四个层面

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一、知识系统

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二、工具系统

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三、价值系统

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四、史实系统

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第三节

数学文化的人本特性

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一、精神特性

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二、物质特性

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三、行为特性

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四、审美特性

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第二章

数学历史

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第一节

数学名著

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一、《九章算术》

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二、《数书九章》

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三、《算数书》

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第二节

数学故事

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一、毕达哥拉斯的故事

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二、高斯的故事

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三、哥德巴赫的故事

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第三节

数学名题

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一、米勒问题

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二、斐波那契数列

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三、阿基米德穷竭法

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四、柯西不等式

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五、角谷猜想

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六、阿波罗尼奥斯圆

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七、回文数

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八、勾股数

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九、平均数

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十、皮克定理

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十一、数字黑洞

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十二、伯努利不等式

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十三、正整数方幂和

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十四、切比雪夫多项式

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十五、马尔科夫定理

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十六、四色问题

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十七、莱布尼茨三角形

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十八、黄金分割比

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第三章

数学精神

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第一节

理性求真

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第二节

创新意识

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第四章

数学应用

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第一节

营销决策类

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第二节

金融经济类

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第三节

环境保护类

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第四节

建设工程类

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第五节

交通运输类

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第六节

概率统计类

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第七节

日常民生类

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第五章

数学之美

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第一节

和谐美

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一、结构形式的和谐统一

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二、项、项数、次数的和谐统一

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三、转换的和谐统一

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第二节

简洁美

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第三节

对称美

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第四节

奇异美

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一、解法多样的奇异美

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二、解法之巧的奇异美

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第六章

数学语言

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第七章

交汇拓展

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第八章

数学游戏

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附录一

本书习题参考答案

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附录二

高考数学文化最新动态

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参考文献

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