组合数学在数学竞赛中的应用
组合数学在数学竞赛中的应用(论文10000字)
摘要：数学竞赛，作为发掘数学人才的一种手段，在中学和大学越来越受到师生的喜欢。在内容上，数学竞赛中的组合数学大致可以分成两大类，组合设计问题和组合计数问题，我们在这里主要研究组合计数问题。组合数学的知识基础是加法原理和乘法原理；常用的组合数学方法有抽屉原理、容斥原理、排列组合和递推关系等等。
本文主要对组合数学的历史背景以及发展过程进行解说，通过几类数学竞赛中常见的组合数学问题进行解析研究，主要包括排列组合、抽屉原理、容斥原理、递推原理以及其他典型方法，并在排列组合中应用组合数学中的计数方法解决安卓手机九宫格解锁问题。
关键词：抽屉原理，容斥原理，排列组合，递推关系
Application Of Combinatorial Mathematics In Mathematics Competition
Abstract：Mathematics competition, as a mean of exploring mathematics talents, is more and more popular in teachers and students in middle schools and colleges. In the content, the mathematical contest in the combinatorial mathematics can be divided into two categories, the combinatorial design problems and combinatorial counting problems. We are here mainly to study combinatorial counting problems. The knowledge base of combinatorial mathematics are the addition principle and the multiplication principle, The common methods used in Combinatorial Mathematics are the principle of drawer, the principle of inclusion and exclusion, the permutation and combination, the recurrence relation and so on.
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This paper mainly explains the historical background and development process of the combination of mathematics through analyzing and studying the common mathematical problems in several kinds of mathematical competitions , mainly including the arrangement and combination, the drawer principle, the principle of inclusion and exclusion, the recurrence principle and other typical methods, and uses the counting method in combinatorial mathematics to solve the mobile phone Android 3 3 Grids unlocking problems in permutations and combinations.
Key words： Drawer principle, inclusion-exclusion principle, permutations and combinations，recurrence relation
目 录
1.引言 1
2.组合数学与数学竞赛的简介 1
2.1 组合数学 1
2.2 数学竞赛 2
3.学习组合数学的方法 2
4.组合数学的几种数学方法在数学竞赛中的应用 3
4.1 排列组合 3 [版权所有：http://DOC163.com]
4.2 抽屉原理 6
4.3 容斥原理 8
4.4 递推关系 9
参考文献 14
致谢 15
附录 16