实数与超实数

本文对实数如何扩充到超实数作了探讨，并证明了超实数的5个重要性质。     

0—1数列与超限组合

本文给出了0-1数列若干性质.设a,c分别表示自然数集和实数集的基数,我们有下列结果:(1)C_a~a=c,(2)C_a~0+C_a~1+C_a~2+…+C_a~n+…+C_a~a=2~a     

Triangular numbers

The triangular numbers, which are numbers associated with certain arrays of dots, were known to the ancient Greeks and viewed by them with reverence. Though possessing a simple definition, they are astonishingly rich in properties of various kinds, ranging from simple relationships between them and the square numbers to very complex relationships involving partitions, modular forms, etc. ?? topics which belong to advanced mathematics. They also possess many pretty combinatorial properties. In this expository article we survey a few of these properties.     

数字的警示

素有“万物之灵”之称的人类，凭借自己的聪明才智和勤劳的双手，利用地球上的资源，为自己创造了一个个高度发达的物质文明。高楼大厦随处可见，如网的交通线在地球上延伸，一个个工业区在不同地方勾勒出人类的文明与进步，超市中的商品琳琅满目……当人类在充分享受物质文明的同时，接踵而来的环境危机也在为人类敲响警钟，让人类痛心疾首。让我们一同走进一组组令人触目惊心的数字。     

From natural numbers to numbers and curves in nature - II

In this second part of the article we discuss how simple growth models based on Fibbonachi numbers, golden section, logarithmic spirals, etc. can explain frequently occuring numbers and curves in living objects. Such mathematical modelling techniques are becoming quite popular in the study of pattern formation in nature.     

从Fibonacci数的恒等变换到Lucas数的同余式

研究了Fibonacci数的和式∑a b=nUa^mUb^m/a!b!,得出了一些关于Fibonacci数与Lucas数的恒等变换和一些有趣的Lucas数的同余式。     

Are numbers logographs?

Researchers generally assume that logographs such as numerals form a homogeneous set. This paper presents a study whose results challenge that assumption. Using a visual search task, it is shown that native Chinese speakers, who can read and speak English, process strings of Chinese numerals differently from the way they process strings of Western numerals. The different pattern of results found with these two sets of numerals also contrasts with the pattern typically found when native English speakers process Western numerals. An explanation of this result is proposed based on the notion that visual search functions can be the outcome of the combined effect of different basic search procedures.     

关于酉完全数

证明了酉完全数都不是幂数.     

数形结合引入数列极限概念

本文就高等数学教学中怎样运用数形结合思想突破数列极限概念这个教材难点提 出了几点设想．     

Afterword: embracing numbers?

ABSTRACT

While the use of numbers in governance has a long history, the kinds of numbers we now produce enable a range of new possibilities for monitoring, regulation and policy decision-making. Global policy actors are now calling for a steep increase in investment in education data. The growing trust in numbers has been critiqued by education policy scholars and social scientists, who have pointed to the reductionist nature of numbers and the dangerous decontextualisation of information which are leading to detrimental policies. The entry of big data poses even more complex epistemological and ontological challenges, many of which we do not fully understand as yet. This paper acknowledges these challenges, and at the same time speculates that big data might afford unique possibilities for new relational theories that may lead to better policy decision-making.     

利用函数思想 巧解数列问题

利用函数思想,给出了求递推数列通项及进行不等式证明的一种简便方法.     

几个有关Euler数的恒等式

利用生成函数法研究了正割函数与欧拉数的关系,得到了几个关于欧拉数的有趣的恒等式.