数学王子——高斯

高斯是近代数学伟大的奠基人之一 ,被人们誉为“数学王子” .他与阿基米德、牛顿一起被称为历史上最伟大的三位数学家 .高斯出生在一个贫苦的家庭里 ,祖父是农民 ,父亲做短工 .“穷人的孩子早当家” ,高斯从小爱动脑筋 ,如果承认历史上有神童 ,那么 ,高斯就是其中之一 .传说有一次 ,他父亲计算账目 ,小高斯在旁边好奇地看着 ,等父亲好不容易算完后 ,想不到小高斯说 :“爸爸 ,你算错了 ,应该是……” .经过核对 ,果然是小高斯正确 .高斯的父亲又惊又喜 ,本来不想送他上学 ,考虑到他出奇的聪明好学 ,于是在他 7岁的时候送他进了小学 .小高斯经…     

朝气蓬勃的南开大学数学科学学院

数学是一个奥妙有趣的世界。有人说,“数学是科学的女王”有人说,“数学是通向科学大门的钥匙”。21世纪是信息的时代,没有相当数学素养的人才不能算是合格的人才。数学大师陈省身在十五年前就说过,“希望21世纪看见中国成为数学大国”。最近陈先生又寄语青少年数学爱好者:“数学使问题简单化,科学简单化。”     

数学的历史发展

数学本身是不断丰富 ,不断发展的 ,数学的内涵随着时代的变化而变化 ,给数学下一个一劳永逸的定义是不可能的。公元前 6世纪以前 ,数学主要是关于“数”的研究。这一时期在古埃及、巴比伦、印度与中国等地区发展起来的数学 ,主要是计数、初等算术与算法 ,几何学则可看作是应用算术。从公元前 6世纪开始 ,古希腊数学的兴起 ,突出了对“形”的研究。数学于是成为关于数与形的研究 ,从那时起直到 1 7世纪 ,数学的对象没有本质的变化。公元前 4世纪的希腊哲学家亚里士多德将数学定义为 :“数学是量的科学”。其中“量”的涵义是模糊的 ,显然不能…     

与青年学生们谈谈学习数学

众所周知 ,数学是一门非常古老而又时时焕发出青春的学科 .曾经有一位数学家说过 :“数学是科学的女王 ,数学也是科学的仆人 .”这句话中的‘女王’与‘仆人’尊卑悬珠 ,但却表达了同一个意思 ,即 ,数学是科学中非常重要、不可缺少的工具 .由于这个原因 ,数学才在科学中享有极为崇高的地位 .近一百多年来 ,数学一方面向着高度抽象化发展 ,形成了多种深奥的数学理论 ,创造出许多复杂而美妙的方法 ,另一方面又不断向人们的物质生产与日常生活等方面渗透 ,使得从事文化工作的人们 ,不论其工作性质如何 ,都必须学习一些有关的数学知识 .据笔者的…     

聚焦“高斯函数”的交汇性

十八世纪,函数f（x）=[x]被“数学王子”高斯采用,因此得名为高斯函数．“高斯函数”,又叫“取整函数”,其定义简洁、内涵丰富、应用灵活,与数论、组合数学息息相关,在离散数学、计算机算法分析、微积分、竞赛数学等领域得到广泛应用．     

数学王子与数学创造性思维的培养

数学创造性思维就是解决数学问题的全过程中 ,在了解现成结论的同时 ,又设法突破现成结论 ,去努力发现新的知识 .作为学生 ,如何努力培养自己的数学创造性思维 ?我们的学生有这种潜能吗 ?教育家奥托曾说过 :“我们所有的人 ,都有惊人的创造力 .”如何将这种潜能转化为现实的能力 ,关键在于培育和教育 .本文试图从数学王子———高斯的成功之路来探讨数学创造性思维的培养 ,以期有更多的创造性人才出现 .1　专心求学 ,营造创新环境有人问高斯 :“你为什么在科学上有那么多发现 ?”高斯回答 :“假如别人和我一样专心和持久地思考数学真理 ,他…     

对于讲授最简方程的两点说明

根据中学教学数学大纲(草案)的规定,在初中二年级第一学期应该讲最简单的方程(按即指一元一次方程),兹对此提出两点说明供教师们参考.1.教学大纲(草案)的代数部分说明中指出:“要在学生已知的算术运算性质的基础上来作解方程演算(按即解方程)”.又在大纲(草案)的单元纲目中指出:“根据算术四则运算的定义与性质解最简单的方程,……”.所谓算术四则的定义,即加法定     

古典算术问题解题策略探析

1 引言 “术”的辞典学意义是指技艺、方法,算术意指计算的方法.在我国古代,算是一种竹制的计算器具,算术是指操作这种计算器具的技术.古典算术问题便是以“术”或“术日”给出解题策略.     

对数学本质特征的若干认识

什么是数学 ?这是任何一个数学教育工作者都应认真思考的问题 .只有对数学的本质特征有比较清晰的认识 ,才能在数学教育研究中把握正确的方向 .1　数学 ,其英文是ｍａｔｈｅｍａｔｉｃｓ,这是一个复数名词 ,“数学曾经是四门学科 :算术、几何、天文学和音乐 ,处于一种比语法、修辞和辩证法这三门学科更高的地位 .”[1 ] 自古以来 ,多数人把数学看成是一种知识体系 ,是经过严密的逻辑推理而形成的系统化的理论知识总和 ,它既反映了人们对“现实世界的空间形式和数量关系”的认识 ,又反映了人们对“可能的量的关系和形式”的认识 .数学既可以…     

高斯奖——纪念"数学王子"

高斯(1777年—1855年),是德国著名数学家.他是近代数学奠基者之一,有"数学王子"之称,和牛顿、阿基米德一起,被誉为"世界三大数学家".     

Ky Fan (1914�C2010), he spent every waking moment thinking about mathematics

This survey article on Dr. Ky Fan summarizes his versatile achievements and fundamental contributions in the fields of topological groups, nonlinear and convex analysis, operator theory, linear algebra and matrix theory, mathematical programming, and approximation theory, etc., and as well reveals Fan’s exemplary mathematical formation opening up the beauty of pure mathematics, with natural conditions, concise statements and elegant proofs. This article contains a brief biography of Dr. Fan and epitomizes his life. He was not only a great mathematician, but also a very serious teacher known to be extremely strict to his students. He loved his motherland and made generous donations for promoting mathematical development in China. He devoted his life to mathematics, continued his research and published papers till 85 years old.     

Contributions of Lo Yang to Value Distribution Theory

Professor Lo Yang is a world famous mathematician of our country. He made a lot of outstanding achievements in the value distribution theory of function theory, which are highly rated and widely quoted by domestic and foreign scholars. He also did a lot of work to develop Chinese mathematics. It can be said that Professor Yang is one of the mathematicians who made main influences on the mathematical development in modern China. This paper briefly introduces Professor Yang’s life, mainly discusses his academic achievement and influence, and briefly describes his contributions to the Chinese mathematics community.     

Pure mathematics applied in early twentieth-century America: The case of T.H. Gronwall,consulting mathematician

Thomas Hakon Gronwall (1877–1932) was a Swedish-American mathematician with a broad range of interests in mathematical analysis, physics, and engineering. Though he was primarly known for his results in pure mathematics, his career as a “consulting mathematician” in America from 1912 to his death in 1932 provides a backdrop against which one can discuss contemporary issues involved in the increasing application of mathematics to engineering, industrial, and scientific problems. This paper attempts a summary of his major mathematical contributions to industrial, governmental, and academic institutions while relating his often difficult life during these years.     

Peirce's place in mathematics

This article compares treatments of the infinite, of continuity and definitions of real numbers produced by the German mathematician Georg Cantor and Richard Dedekind in the late 19th century with similar interests developed at virtually the same time by the American mathematician/philosopher C. S. Peirce. Peirce was led, not by the internal concerns of mathematics which had motivated Cantor and Dedekind, but by research he undertook in logic, to investigate orders of infinite sets (multitudes, in his terminology), and to introduce the related concept of infinitesimals. His arguments in support of the mathematical and logical validity of infinitesimals (which were rejected by such eminent mathematicians as Cantor, Peano, and Russell at the turn of the century) are considered. Attention is also given to the connections between Peirce's mathematics, his philosophy, and especially his interest in continuity as it was related to his Pragmatism.     

John von Neumann, the Mathematician

Imagine a poll to choose the best-known mathematician of the twentieth century. No doubt the winner would be John von Neumann. Reasons are seen, for instance, in the title of the excellent biography [M] by Macrae: John von Neumann. The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More. Indeed, he was a fundamental figure not only in designing modern computers but also in defining their place in society and envisioning their potential. His minimax theorem, the first theorem of game theory, and later his equilibrium model of economy, essentially inaugurated the new science of mathematical economics. He played an important role in the development of the atomic bomb. However, behind all these, he was a brilliant mathematician. My goal here is to concentrate on his development and achievements as a mathematician and the evolution of his mathematical interests.     

The state-of-art in mathematical creativity

Creativity is a topic which is often neglected within mathematics teaching. Usually teachers think that it is logic that is needed in mathematics in the first place, and that creativity is not important and learning mathematics. On the other hand, if we consider a mathematician who develops new results in mathematics. we cannot overlook his/her use of the creative potential. Thus, the main questions are as follows: What methods could be used to foster mathematical creativity within school situations? What scientific knowledge, i.e. research results, do we have on the meaning of mathematical creativity?     

Beyond mathematical content knowledge: A mathematician's knowledge needed for teaching an inquiry-oriented differential equations course

In this research report we examine knowledge other than content knowledge needed by a mathematician in his first use of an inquiry-oriented curriculum for teaching an undergraduate course in differential equations. Collaboratively, the mathematician and two mathematics education researchers identified the challenges faced by the mathematician as he began to adopt reform-minded teaching practices. Our analysis reveals that responding to those challenges entailed formulating and addressing particular instructional goals, previously unfamiliar to the instructor. From a cognitive analytical perspective, we argue that the instructor's knowledge — or lack of knowledge — influenced his ability to set and accomplish his instructional goals as he planned for, reflected on, and enacted instruction. By studying the teaching practices of a professional mathematician, we identify forms of knowledge apart from mathematical content knowledge that are essential to reform-oriented teaching, and we highlight how knowledge acquired through more traditional instructional practices may fail to support research-based forms of student-centered teaching.     

Die Habilitation von John von Neumann an der Friedrich-Wilhelms-Universität in Berlin: Urteile über einen ungarisch-jüdischen Mathematiker in Deutschland im Jahr 1927

The mathematician John von Neumann was born in Hungary but principally received his scientific education and socialization in the German science system. He received his Habilitation from the Friedrich-Wilhelms–Universität in Berlin in 1927, where he lectured as a Privatdozent until his emigration to the USA. This article aims at making a contribution to this early part of Neumann’s scientific biography by analyzing in detail the procedure that led to his Habilitation as well as the beginnings of Neumann’s research on functional analysis. An analysis of the relevant sources shows that in Berlin in the year 1927 Neumann was not yet regarded as the outstanding mathematical genius of the 20th century. Furthermore it will be seen that Neumann had great difficulties in developing the fundamental concepts for his path breaking work in spectral theory and only managed to do so with the support of the Berlin mathematician Erhard Schmidt.     

“Knowledge gained by experience”: Olaus Henrici—engineer,geometer and maker of mathematical models

The German mathematician Olaus Henrici,¹ who was born in Denmark in 1840, studied engineering and mathematics in Germany before making his career in London. Initially, and for only a short time, he worked in an engineering business. He subsequently took on academic positions, first at University College London and then, from 1884, at the newly formed Central Institution (later Central Technical College) where he established a Laboratory of Mechanics. While at University College he became an active promoter of pure geometry and a producer of models of surfaces. In this paper I explore the geometrical side of Henrici's work, setting it into the context of his career and arguing that his interdisciplinary background was a key factor in his success as a creator of models.     

J. Howard Redfield 1879–1944

During much of his life J. Howard Redfield earned his living as an engineer but his main interests lay elsewhere. He performed and wrote music and was a gifted linguist, familiar with almost all European languages, as well as with some African and Asian tongues. In middle age he turned his attention towards combinatorial mathematics but it was not until many years after his death that the mathematical world realized that he had obtained significant results.