关于一次同余方程组的历史研究【论文

X X 师 范 大 学

本科毕业论文（设计）

题目：关于一次同余方程组的历史研究

学 院：初等教育学院 学生姓名： 学 号：

专 业：小学教育专业 年 级：2009级 完成日期： 指导教师：

一次同余方程组的历史研究

摘要：一次同余方程组从古到今，从小学到大学的数学教学中都有涉及。一次

同余方程组是同余问题之一，它具有很强的应用价值。本课题基于对中国剩余定理、秦九韶的大衍求一术和欧拉解法理解和对比，从中发现它们的局限性，进而介绍解一次同余方程组的新方法，使学生能系统全面的掌握一次同余方程组。同时希望通过本课的研究能够展现数学的文化价值，为学生展现数学的文化内涵，也提醒教师们在教学时应有意识的向学生渗透一些与课程有关的数学史，激发学生的学习兴趣，扩宽学生的思维。

关键字：一次同余方程组；中国剩余定理；大衍求一术；欧拉

Historical Research on the System of Linear Congruence

Equations

Abstract: a Congruence Equations since ancient times, ranging from primary

school to university mathematics teaching in. A congruence equation group is a congruence problem, it has very strong application value. The subject of the Chinese remainder theorem, Qin Jiushao's big Yan Shu and Euler method based on a understanding and comparison, find their limitations from, and then introduces the solution of system of Linear Congruence Equations, so that the students can systematically grasp a congruence equations. At the same time, hope that through the study of this class to show the value of mathematics culture, mathematics for the students to show the cultural connotation, but also to remind the teachers in teaching should have the awareness of the infiltration to the students and curriculum history of mathematics related, stimulate students interest in learning, broaden the students' thinking.

Keywords: Linear Congruence Equations; Chinese remainder theorem; Dayan a

Shu; Euler