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书名:《尘封的经典――初等数学经典文献选读.第2卷》 英文书名:Dusty classlcs:selected reading of elementary mathematical literature(vol.II)
丛书系列: 数学专业英语系列 图书编号:∑206
作者:[美]迪克森著 出版社:哈尔滨工业大学出版社
ISBN:978-7-5603-3619-0 开本:787mm×960mm 1/16
版次:2012年7月第1版 2012年7月第1次印刷 印张:19.5  字数:210千字千字
定价:38.00元 页数:300

 

【内容提要】

本书包含“复数”“方程根的初等理论”“尺规作图”“三次和四次方程的解法及判别式”等共十章内容,适用于专业学生使用,也可作为数学爱好者的读物.

 



  

PREFACE


The theory of equations is not only a necessity in the subsequent mathematical courses and their applicationsbut furnishes an illuminating sequel to geometryalgebra and analytic geometry. Moreoverit develops anew and in greater detail various fundamental ideas of calculus for the simplebut importantcase of polynomials. The theory of equations therefore affords a useful supplement to differential calculus whether taken subsequently or simultaneously.

It was to meet the numerous needs of the student in regard to his earlier and future mathematical courses that the present book was planned with great care and after wide consultation. It differs essentially from the author's Elementary Theory of Equations both in regard to omissions and additions and since it is addressed to younger students and may be used parallel with a course in differential calculus. Simpler and more detailed proofs are now employed. The exercises are simpler more numerous of greater variety and involve more practical applications.

This book throws important light on various elementary topics. For examplean alert student of geometry who has learned how to bisect any angle is apt to ask if every angle can be trisected with ruler and compasses and if not why not. After learning how to construct regular polygons of 34568 and 10 sideshe will be inquisitive about the missing ones of 7 and 9 sides. The teacher will be in a comfortable position if he knows the facts and what is involved in the simplest discussion to date of these questionsas given in Chapter . Other chapters throw needed light on various topics of algebra. In particularthe theory of graphs is presented in Chapter  in a more scientific and practical manner than was possible in algebra and analytic geometry.

There is developed a method of computing a real root of an equation with minimum labor and with certainty as to the accuracy of all the decimals obtained. We first find by Horner's method successive transformed equations whose number is half of the desired number of significant figures of the root. The final equation is reduced to a linear equation by applying to the constant term the correction computed from the omitted terms of the second and higher degreesand the work is completed by abridged division. The method combines speed with control of accuracy.

Newton's methodwhich is presented from both the graphical and the numerical standpoints has the advantage of being applicable also to equations which are not algebraic it is applied in detail to various such equations.

In order to locate or isolate the real roots of an equation we may employ a graph provided it be constructed scientificallyor the theorems of DescartesSturm and Budan which are usually neither statednor provedcorrectly.

The long chapter on determinants is independent of the earlier chapters. The theory of a general system of linear equations is here presented also from the standpoint of matrices.

For valuable suggestions made after reading the preliminary manuscript of this bookthe author is greatly indebted to Professor Bussey of the University of MinnesotaProfessor Roever of Washington UniversityProfessor Kempner of the University of Illinoisand Professor Young of the University of Chicago. The revised manuscript was much improved after it was read critically by Professor Curtiss of NorthwesternUniversity. The author's thanks are due also to Professor Dresden of the University of Wisconsin for various useful suggestions on the proof-sheets.

 

CHICAGO 1921

 


  【目  录】

  第一章      1

  第二章  方程根的初等理论  18

  第三章  尺规作图  50

  第四章  三次和四次方程的解法及其判别式  78 

  第五章  方程的图  95

  第六章  实方程的实根分离  124

  第七章  数字方程的解法  151

  第八章  行列式和线性方程组  176

  第九章  对称函数  221

  第十章  消元、结式及判别式  245

      代数基本定理  265

      271

  编辑手记  289

 


  【编辑手记】

本书是上世纪初的一本经典西方数学名著,它很早就被引入到中国大学的课堂中,因当时西风正健.梁漱溟之父梁济是晚清眼光突出,不为时俗所困之人.他在甲午战争之前,已决心研习西学.18925月,他在《论读书次第缓急》中说,西学在当时“为清流所鄙,正人所斥”.可是,“洋务西学新出各书,深切时事,断不可以不看,盖天下无久而不变之局.我只为求实事,不能避世人讥讪也.

当时有许多有识之士都认识到向西方学习的必要性,大量国外最新著作被引入到中国,同时许多国学大家也开始反省国学之局限.1904年王国维在《论新学语之输入》中比较中西思想的特性时指出:

我国人之特质,实际的也,通俗的也;西洋人之特质,思辨的也,科学的也,长于抽象而精于分类,对世界一切有形无形之事物,无往而不用综括(generalization)及分析(specification)之二法……吾国人之所长,宁在于实践之方面,而于理论之方面则以具体的知识为满足,至分类之事,则除迫于实际之需要外,殆不欲穷究之也……及至近代还有人在剖析中国文化在理性方向的不足.余英时在《从价值系统看中国文化的现代意义》(中国台北时报出版公司,1992年版.p68-89)中指出:

大体而言,中国思想确是比较实际的,贴切于人生的,有内在系统而无外在系统的.抽象化,理论化,逻辑化的思考方式不是中国的特色,也不受重视……由此可见,中国之所以发展不出科学是具有文化背景的……西方科学的突飞猛进虽是近两三百年的事,可是它的源头却必须上溯至希腊时代.

这是一本美国数学家写的方程论著作.

其实早期的美国数学水平并不高,甚至可以说低得可怜.1700年之前,美国只产生了一篇数学硕士论文,它的题目是“圆面积可求吗?”当然作者给出了肯定的结论.这就是1693年美国哈佛大学的数学水平.

真正使美国成为世界数学中心的是一次谁也不曾预测到的千年不遇的事件.第二次世界大战的爆发,使得一大批德国数学家移民到了美国,特别是犹太数学家.如果不是希尔伯特考虑到年事已高,故土难离而留在哥廷根的话,哥廷根学派就全部到了美国.今天普林斯顿就是这样成名的.

有人曾不无悲观地说:“我们生活在一个没有价值观的时代,失去事物对错与东西好坏的鉴别与鉴赏能力.

现在数学教材太多了,但唯其精品缺失.这时我们不禁会将目光回溯到民国初期,西南联大时期,看一看那时的大学生都读些什么数学书.中国的数论及代数传统始于杨武之先生(杨武之在中国的名声现在大多是靠其子杨振宁得来,40以后看子敬父)而杨武之学成于美国芝加哥大学,其导师正是本书作者,大名鼎鼎的迪克森(L.E.Dickson).

王萼芳、石生明、王杰三位教授在为段学复院士所写的传略中这样写道:

段学复在清华的四年中先后听过熊庆来、郑桐荪、杨武之、赵访熊、曾远荣等教授的课.这些老师各有特点,使段学复在分析、代数、几何诸方面都得以打下了坚实的基础.相比之下,他学习杨武之先生的课比较多,杨讲课用的教材主要是他自己的博士导师迪克森的著作.这对段学复以后主要从事代数学方面的研究是很有影响的.

中国社科院进行的《全国国民阅读调查》表明,近几年中国人年平均阅读书籍都不到一本.越来越多的杂志主打轻阅读浅阅读,我们已没有耐心去阅读专业书籍,用完整的理论框架去分析世界,所以有人提出:肤浅也是生产力!

数学书向来是肤浅的死敌,以深刻、艰深为美,所以和者寡是预科之中的,但我们就是要逆潮流而动.随后,我们工作室还会推出迪克森的另一部名作,《数论史》洋洋三大卷.只不过鉴于其内容的专业程度较高,所以我们将其译成了中文.

翻译是个吃力的活,英译中,中译英都挺难.有人还举了几个例子,例如“折腾”一词,很难在现有英文词汇中找到贴切的译法,后来干脆创造了“Zhe teng”这一新词;类似的还有近年流行的“忽悠”译成hu you.

鉴于翻译的困难和现在普遍英文水平的提高,所以保持原汁原味也比现在有些自编的双语教材强百倍,因为它毕竟出自大家之手.

 

 

刘培杰

2012.6.20于哈工大

 


   
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