文档介绍：毕业设计(论文)
数学归纳法及其在中学数学中的应用
Mathematical Induction and the Application in Middle School
学院:理学院
专业: 数学教育
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二〇一二年六月
摘要
数学归纳法是一种非常重要的数学方法,它不仅对我们中学数学的学习有着很大的帮助,而且在高等数学的学习及研究中也是一种重要的方法,数学归纳法对公式的正确性检验中也有着很大的应用。数学归纳法是将无限化为有限的桥梁,主要探讨关于自然数集的有关命题或者恒等式,数学归纳法在中学数学中的整除问题,恒等式证明,公理证明,排列和组合,几何领域等都有着广泛的应用,这里我们主要结合初中教材来详细列举数学归纳法在中学数学中的应用,要准确的运用数学归纳法,首先必须准确的理解其意义以及熟练的掌握解题步骤,而在三个步骤中运用归纳假设尤为关键,运用归纳假设推出猜想最为重要。最后我们在通过用数学归纳法证明简单恒等式的过程中,可以更加深刻理解和掌握“归纳——猜想——证明”这一探索发现的思维方法。
关键词:归纳法; 数学归纳法; 中学数学; 证明
ABSTRACT
Mathematical induction is a very important mathematical methods, it is not only to our middle school mathematics learning have great help, but also in higher mathematics after the study and research is also an important way. Mathematical induction to the correctness of the formulas of the inspection of the application of also has the very big. Mathematical induction into the limited is infinite bridge, mainly discusses the relevant proposition about natural number set or identities, Mathematical induction has wide application in middle school mathematics,such as ,the problem of division,the proof of identity,the proof of axiom,permutations binations, we bination junior middle school teaching material to a detailed list mathematical induction in the middle school mathematics application .To the application of mathematical induction skilled, we must first accurately understand its significance and skilled The master problem-solving steps, and in three steps into the use of assumptions is particularly critical, the use of assumptions summarized introduced guess the most important. In the end we proved that by using a simple mathematical induction identities in the process, can more deeply understand and master, "summed up - guess - prove" this discovery to explore ways of thinking.
Key words: induction; mathematical induction; middle school mathematics; proof
目录
绪论 1
问题的提出与课题意义 1
问题的提出 1
课题的研究意义 1
1. 数学归纳法概述 2
数学归纳法