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给孩子的数学三书 原来数学可以这样学:马先生谈算学 数学趣味 数学的园地(套装全三册)刘薰宇

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给孩子的数学三书 原来数学可以这样学:马先生谈算学 数学趣味 数学的园地(套装全三册)刘薰宇

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★1、双色印刷

①印刷更精美

②学习不枯燥

③增加学习兴趣

★2、开本增大

①字大行疏

②保护视力

③舒适的阅读体验

★3、图文并茂

①直观清晰

②便于思考

③运算便捷


Content Description

《马先生谈算学》是著名数学教育家刘薰宇写给中小学生的数学科普经典。本书以第三人称——“马先生”的口吻进行书写,主要围绕如何用图解法求解一些算术四则问题,收集了100多道题目加以解释,充分体现了作者对数学严谨的态度。

《数学趣味》是著名数学教育家刘薰宇写给中小学生的数学科普经典。本书中所收录的都是作者从日常生活中随处拾来的数学文章。贴近人们日常生活的枯燥、繁难、令人头痛的数学题材和算法经过作者巧妙地书写,都变成趣味丰富、令人爱读的文字了。

《数学的园地》是著名数学教育家刘薰宇写给中小学生的数学科普经典。本书比较系统地说明了函数、连续、诱导函数、微分、积分和总集等概念及它们的运算法的基本原理。抽象、枯燥的高等数学内容,经过作者巧妙的手法写出来,只要学过初等代数和几何的人,就会很轻松、毫不费力读完并掌握,所以该书完全可以作为中小学生必备的重要自学书籍。


Author Description

刘薰宇(1896—1967),我国现代数学家、数学教育家、出版家,受过法国数学教育的熏陶。曾任多所大学和中学数学教师或校长,担任过人民教育出版社副总编辑,审定过我国中小学数学教材,出版了中小学数学教科书和科普读物,发表了大量数学教育方面的论文,筹备出版了《中学生》《新青年》等青少年期刊。他的论著对杨振宁、谷超豪、丰子恺等都有着深远的影响。


Comments

有一位刘薰宇先生,他是位数学家,写过许多通俗易懂和极其有趣的数学方面的文章。我记得,我读了他写的关于一个智力测验的文章,才知道排列和奇偶排列这些极为重要的数学概念。

——杨振宁1983年和香港中学生的谈话



Catalogue

马先生谈算学

一、他是这样开场的

二、怎样具体地表出数量以及两个数量间的关系

三、解答如何产生——交差原理

四、就讲和差算罢

五、“追赶上前”的话

六、时钟的两只针

七、流水行舟

八、年龄的关系

九、多多少少

十、鸟兽同笼问题

十一、分工合作

十二、归一法的问题

十三、截长补短

十四、还原算

十五、五个指头四个叉

十六、排方阵

十七、全部通过

十八、七零八落

十九、韩信点兵

二十、话说分数

二十一、三态之一——几分之几

二十二、三态之二——求偏

二十三、三态之三——求全

二十四、显出原形

二十五、从比到比例

二十六、这要算不可能了

二十七、大半不可能的复比例

二十八、物物交换

二十九、按比分配

三十、结束的一课

数学趣味

一、数学是什么

二、数学所给与人们的

三、数的启示

四、从数学问题说到我们的思想

五、恨点不到头

六、堆罗汉

七、八仙过海

八、棕榄谜

九、韩信点兵

十、王老头子的汤圆

十一、假使我们有十二根手指

数学的园地

一、开场话

二、第一步

三、速度

四、函数和变数

五、无限小的变数——诱导函数

六、诱导函数的几何的表示法

七、无限小的量

八、二次诱导函数——加速度——高次诱导函数

九、局部诱导函数和全部的变化

十、积分学

十一、面积的计算

十二、微分方程式

十三、数学究竟是什么

十四、总集论

附录:中国数学发展简史


Book Abstract

解答如何产生——交差原理

“昨天讲的最后三个例子,你们总没有忘掉吧!——若是这样健忘,那就连吃饭、走路都学不会了。”马先生一走进门,还没立定,笑嬉嬉地这样开场。大家自然只是报以微笑。马先生于是口若悬河地开始这一课的讲演。

昨天的最后三个例子,图上都是一条直线,各条直线都表出了两个量所保有的一定关系。从直线上的任意一点,往横看又往下看,马上就知道了,合于某种条件的甲量在不同的时间,乙量是怎样。如图7,合于每小时走二里这条件,4小时便走了8里,5小时便走了10里。

这种图,对于我们当然很有用。比如说,你有个弟弟,每小时可走六里路,他离开你出门去了。你若照样画一张图,他离开你后,你坐在屋里,只要看看表,他走了多久,再看看图,就可以知道他离你有多远了。倘若你还清楚这条路沿途的地名,你当然可以知道他已到了什么地方,还要多长时间才能到达目的地。倘若他走后,你突然想起什么事,须得关照他,正好有长途电话可用,只要沿途有地点可以和他通电话,你岂不是很容易找到打电话的时间和通话的地点吗?

这是一件很巧妙的事,已落了中国旧小说无巧不成书的老套。古往今来,有几个人碰巧会遇见这样的事?这有什么用场呢?你也许要这样找茬儿。然而这只是一个用来打比方的例子,照这样推想,我们一定能够绘制出一幅地球和月亮运行的图吧。从这上面,岂不是在屋里就可以看出什么时候地球和月亮的相互位置吗?这岂不是有了孟子所说的“天之高也,星辰之远也,苟求其故,千岁之日至,可坐而致也”那副神气吗?算学的野心,就是想把宇宙间的一切法则,统括在几个式子或几张图上。

按现在说,这似乎是犯了夸大狂的说法,姑且丢开,转到本题。算术上计算一道题,除了混合比例那一类以外,总只有一个解答,这解答靠昨天所讲过的那种图,可以得出来吗?

当然可以,我们不是能够由图上看出来,张老大得九块钱的时候,宋阿二得的是六块钱吗?

不过,这种办法对于这样简单的题目虽是可以得出来,遇见较复杂的题目,就很不便当了。比如,将题目改成这样:

张老大、宋阿二分十五块钱,怎样分法,张老大比宋阿二多得三块?

当然我们可以这样老老实实地去把解法找出来:张老大拿十五块的时候,宋阿二一块都拿不到,相差的是十五块。张老大拿十四块的时候,宋阿二可得一块,相差的是十三块……这样一直看到张老大拿九块,宋阿二得六块,相差正好是三块,这便是答案。

这样的做法,就是对于这个很简单的题目,也需做到六次,才能得出答案。较复杂的题目,或是题上数目较大的,那就不胜其烦了。

而且,这样的做法,实在和买彩票差不多。从张老大拿十五块,宋阿二得不着,相差十五块,不对题;马上就跳到张老大拿十四块,宋阿二得一块,相差十三块,实在太胆大。为什么不看一看,张老大拿十四块九角,十四块八角……乃至于十四块九角九分九九九……的时候怎样呢?

喔!若是这样,那还了得!从十五到九中间有无限的数,要依次看去,人寿几何?而且比十五稍稍小一点儿的数,谁看见过它的面孔是圆的还是方的?

老老实实的办法,就不是办法!人是有理性的动物,变戏法要变得省力气、有把握,才会得到看客的赞赏呀!你们读过《伊索寓言》吧?里面不是说人学的猪叫比真的猪叫,更叫人满意吗?

所以算术上的解法必须更巧妙一些。

这样,就来讲交差原理。


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