20世纪之数学

20世纪数学的重点从局部转移到整体，从低维转移到高维，从交换转移到非交换，以及从线性转移到非线性．几何学和代数学的对立统一依然存在，从哲学上反映了空间与时间之对立统一．与同调论、K-理论和李群有关的技巧和概念被广泛运用．在最近的20年间，量子场论和弦理论为数学注入新观念．理论物理学对数学的影响还将在21世纪延续下去．     

Special Article Mathematics in the 20th Century

A survey is given of several key themes that have characterisedmathematics in the 20th century. The impact of physics is alsodiscussed, and some speculations are made about possible developmentsin the 21st century. 2000 Mathematics Subject Classification00-02.     

二十世纪数学发展史的坐标——评李心灿教授编著的《当代数学大师》(修改版)

本文论述了数学著作《当代数学大师》出版的意义 .评价了 33位沃尔夫数学奖得主的光辉数学成就、学术思想、教育思想、治学态度和方法 ,因此 ,他们应成为广大读者特别是数学研究工作者、数学教师和数学爱好者的学习榜样 .     

中国现代数学家寿命分析

根据 2 1 2位中国现代数学家 (1 1 7位逝世 )的生存资料进行分析 ,得到如下结果 . 62位院士的期望寿命为 84.68岁 ,标准误差为 1 .96岁 ;1 5 0位非院士数学家的期望寿命为 79.2 6岁 ,标准误差为 1 .1 3岁 .院士和非院士数学家的寿命差异有显著性意义 (P =0 .0 5 ) .分别给出了院士和非院士数学家两个群体的寿命表 .结论 :中国现代数学家属于长寿之列 .脑部疾病、心脏疾病和癌症为数学家的主要死因 .     

Nonhomogeneity of the Measuring Channels in Technological Seismic Prospecting and Related Problems

A serious intrinsic contradiction in the MOCDP method related to a disastrous mistake in the technical realization of the synthesis of the method of multiple overlapping (MO) and the common-depth-point (CDP) method is discussed. Possible ways of partial removal of this contradiction are pointed out. Bibliography: 18 titles.     

The order of theorems in the teaching of Euclidean geometry: Learning from developments in textbooks in the early 20th Century

The question of the order of theorems in geometry teaching is very important and it was one of the central issues in the early 20^th Century in England Employing ideas from the methodological framework proposed by Schubring (1987), the order of theorems in the geometry textbooks written by Godfrey and Siddons is analysed within their pedagogy and social context. The main foci for this analysis areElementary Geometry (1903) andA Shorter Geometry (1912), which were widely used in secondary schools at that time. The theorems in these textbooks were arranged differently from those of Euclid'sElements Godfrey claimed the order was organised from an general educational point of view. InA Shorter Geometry, flexibility concerning the order of theorems was recognised as a revision fromElementary Geometry. The analysis presented in this paper provides us with information about teaching practice at that time, for example that teachers might still be bound by examinations after 1903, and helps us to understand important aspects of dealing on the order of theorems in geometry teaching.     

Seismic Prospecting by the Method of Reflected Waves from a Historical Standpoint

Relationship is established between some periods in the history of seismic prospecting and the changes in the understanding of its physical and geological foundations. Particular attention is given to the influence of the technological progress in seismic data processing on the change in the understanding of the structure and composition of a medium. Bibliography: 46 titles.     

Green's Function in Some Contributions of 19th Century Mathematicians

Many questions in mathematical physics lead to a solution in terms of a harmonic function in a closed region with given continuous boundary values. This problem is known as Dirichlet's problem, whose solution is based on an existence principle—the so-called Dirichlet's principle. However, in the second half of the 19th century many mathematicians doubted the validity of Dirichlet's principle. They used direct methods in order to overcome the difficulties arising from this principle and also to find an explicit solution of the Dirichlet problem at issue. Many years before, one of these methods had been developed by Green in 1828, which consists in finding a function—called a Green's function—satisfying certain conditions and appearing in the analytical expression of the solution of the given Dirichlet problem. Helmholtz, Riemann, Lipschitz, Carl and Franz Neumann, and Betti deduced functions similar to Green's function in order to solve problems in acoustics, electrodynamics, magnetism, theory of heat, and elasticity. Copyright 2001 Academic Press.Molte questioni fisico matematiche conducono a una soluzione in termini di una funzione armonica in una regione chiusa con dati valori continui al contorno. Questo problema è noto come problema di Dirichlet, la cui soluzione si basa su un principio di esistenza, il cosiddetto principio di Dirichlet. Tuttavia, nella seconda metà del diciannovesimo secolo, molti matematici cominciarono a mettere in dubbio la validità del principio di Dirichlet. Sia per superare le difficoltà sorte da tale principio, sia per trovare una soluzione esplicita del problema di Dirichlet dato, essi presero ad adoperare metodi diretti. Molti anni prima, uno di questi metodi era stato sviluppato da Green nel 1828 e consiste nel trovare una funzione, detta funzione di Green, che soddisfa certe condizioni e mediante la quale si rappresenta analiticamente la soluzione del problema di Dirichlet in questione. Helmholtz, Riemann, Lipschitz, Carl e Franz Neumann, e Betti dedussero delle funzioni simili alla funzione di Green allo scopo di risolvere problemi di acustica, elettrodinamica, magnetismo, teoria del calore ed elasticità. Copyright 2001 Academic Press.Nombreuses questions de physique mathématique mènent à une solution en termes d'une fonction harmonique dans une région fermée avec des valeurs continus donnés sur la frontière. Ce problème est connu comme problème de Dirichlet, la solution duquel est fondée sur un principe d'existence, le principe de Dirichlet. Cependant dans la seconde moitié du dix-neuvième siècle plusieurs mathématiciens mirent en doute la validité du principe de Dirichlet. Alors ils employèrent des méthodes directes soit pour surmonter le difficultés nées de ce principe, soit pour déduire une solution explicite du problème de Dirichlet en question. Avant plusieurs annèes une de ces méthodes a été développée par Green en 1828 et consiste à trouver une fonction, dite fonction de Green, qui satisfait certaines conditions et moyennant laquelle on représente analytiquement la solution du problème de Dirichlet donné. Helmholtz, Riemann, Lipschitz, Carl et Franz Neumann, et Betti déduisirent des fonctions semblables à la fonction de Green pour résoudre de problèmes d'acoustique, électrodynamique, magnétisme, théorie de la chaleur et élasticité. Copyright 2001 Academic Press.MSC 1991 subject classifications: 01A55, 31-03.     

19世纪上半叶的无穷级数敛散性判别法

对19世纪上半叶欧洲数学家在正项级数敛散性判别方面的工作作了考察和分析.     

A Few Words to the 20^th Birthday of ATA

Our Journal ATA was found in the Winter of 1984 at the beautiful coastal city Dalian, China, the Editors in chief were Professor C.K.Chui (abroad), and the late Professor M.D.Cheng (domestic). 20 years, it seems to be short, however, the Journal has developed quickly and changed a lot.     

Karamata functions and differential equations: Achievements from the 20th century

This paper presents the major achievements of the 20th century regarding Karamata functions and the theory of differential equations, made mostly by V. Mari?, M. Tomi?, E. Omey, J.L. Geluk. The connection between these notions was first noticed by V.G. Avakumovi? (1910–1990). Slowly and regularly varying functions were introduced by J. Karamata (1902–1967). A group of mathematicians from the Karamata School of classical mathematical analysis were pioneers in research on these functions and their role in the theory of differential equations. Special attentions is given to the study of the Thomas–Fermi, Emden–Fowler and Friedmann equations, as well as the classical second order linear differential equations.     

Remarks on the relations between the Italian and American schools of algebraic geometry in the first decades of the 20th century

In this paper we give an overview of the interactions between Italian and American algebraic geometers during the first decades of the 20th century. We focus on three mathematicians—Julian L. Coolidge, Solomon Lefschetz, and Oscar Zariski—whose relations with the Italian school were quite intense. More generally, we discuss the importance of this influence in the development of algebraic geometry in the first half of the 20th century.     

The Rise and Fall of Science Education: A Content Analysis of Science in Elementary Reading Textbooks of the 19th Century

In the 19th century the textbook dominated the curriculum and methods of instruction. The most important textbook was the textbook of reading known as the reader. In the early 1800s science was not established as a separate primary grade subject. The science students encountered in these reading textbooks may have been their only formal science education. This study used content analysis to determine the type of science and the quantity of science in popular U.S. readers of the 19th century. The percent of science rose in the middle of the century and declined at the end. This decline may have been due to the desire to make the study of reading literary based. The percentage of science that was biological increased throughout the century, and the percentage of Earth science declined.