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中文题名:

 Nim游戏中的数学与课堂教学设计探索    

姓名:

 王姿婷    

保密级别:

 公开    

论文语种:

 中文    

学科代码:

 070101    

学科专业:

 数学与应用数学    

学生类型:

 学士    

学位:

 理学学士    

学位年度:

 2015    

学校:

 北京师范大学    

校区:

 北京校区培养    

学院:

 数学科学学院    

第一导师姓名:

 李建华    

第一导师单位:

 数学科学学院    

提交日期:

 2015-05-21    

答辩日期:

 2015-05-21    

外文题名:

 The exploration of the mathematical knowledge in Nim and the corresponding lesson plans    

中文关键词:

 Nim游戏 ; Nim型游戏 ; 制胜策略 ; 数学背景 ; 图论 ; 组合数学    

中文摘要:
Nim游戏是起源于几千年前的东方的一种双人决策游戏,其简单 的游戏规则背后却有着非常美妙的数学原理,以至于深受人们的追捧 以及数学家们的青睐。其经典的游戏形式发展至今,已衍生出多样的 游戏形式,并且在数学的多个学术领域(诸如图论、组合数学、集合 论、初等数论、近世代数等)有许多新的研究成果。本文首先对经典 Nim游戏形式、制胜策略等进行了由简入繁的梳理及系统整理;再抽 离其本质属性,归纳出Nim型游戏这一外延;继而在这个定义下给 出了多个衍生的Nim型游戏来进行具体的阐释;并试图在现代数学 的各个领域找出它们与Nim的联系,得到Nim在图论、集合论、组 合数学等方面的一些呈现形态;最后,借由这些梳理的结论,分析其 在数学教育上的价值并尝试给出一些教学案例。在这些工作中,读者 可以清晰感受到作为“游戏皇后”的Nim本身所具有的魅力与价值。
外文摘要:
Nim was originated from a duet decision games in the ancient eastern countries thousands of years ago. Behind its simple game rules is the amazing mathematical theory, which is why after all these years the game is still popular among people especially mathematical scientists. Many new game forms have derived from the classic one. Grounded on this situation, many research results have been achieved in several academic fields of mathematics, such as Graph Theory, Combinatorics, Set Theory, Elementary number theory and Modern algebra. This article aims to: Firstly reorganize classic Nim game forms and winning strategies in a simple-to-complex order; Secondly, define the Nim games according the analysis of previous materials; Thirdly, explain several derivative Nim games based on the previously-concluded definition and discover their relationship with the classic one; Fourthly, conclude the essence of Nim games from the perspectives of different modern mathematical studies, such as Graph Theory, Set Theory and Combinatorics; Finally, evaluate the Nim games in the education of mathematics and try to accordingly design some lesson plans. In the process, audience should be able to feel the charm and the value of the Nim games, 'the Queen of the games'.
参考文献总数:

 21    

插图总数:

 0    

插表总数:

 0    

馆藏号:

 本070101/15119    

开放日期:

 2016-05-31    

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