共查询到19条相似文献,搜索用时 140 毫秒
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本文讨论了在矩阵习题课教学中要加强:利用多项式除法求证逆矩阵;利用初等变换解矩阵方程;利用矩阵的特征值证明正定矩阵等问题,以便加深学生对矩阵知识的理解. 相似文献
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本文在正定二次型的基础上定义了半正定二次型,并给出了半正定二次型的一些性质及其证明,最后用半正定二次型的有关知识解决了一类初等数学问题——不等式证明。 相似文献
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研究矩阵方程AXAT BYBT=C的广义正定解。利用广义奇异值分解给出该矩阵方程有解的充要条件及解的通式。 相似文献
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本文主要是利用正定矩阵的概念、相关性质以及有关结论给出了一类2n阶实对称矩阵为正定矩阵的充分必要条件,并给出了详细的证明过程。 相似文献
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利用广义奇异值分解和广义逆给出了矩阵方程AXAT+BYBT=C有对称半正定解的充要条件及解的表达式. 相似文献
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冯棉 《华东师范大学学报(哲学社会科学版)》2002,34(4):30-36
数学哲学中的直觉主义学派高度重视直觉和个人的创造性思维在科学实践中的作用,这具有积极的意义,它对排中律和间接证明方法有效性的质疑,揭示了经典逻辑只具有相对的真理性;它所倡导的构造性和能行性的研究方法,促进了人工智能和计算机科学的发展。但是,对直觉功能的过分夸大则并不足取。 相似文献
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李红 《重庆职业技术学院学报》2006,15(2):153-154
本论文介绍了公式蕴含的几种证法:真值表法、等价演算法、直接证法、间接证法等,灵活应用公式蕴含的证明方法,有利于逻辑推理的顺利进行。 相似文献
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Savas Basturk 《Educational studies》2010,36(3):283-298
The aim of this study is to investigate students’ conceptions about proof in mathematics and mathematics teaching. A five‐point Likert‐type questionnaire was administered in order to gather data. The sample of the study included 33 first‐year secondary school mathematics students (at the same time student teachers). The data collected were analysed and interpreted using the methods of qualitative and quantitative analysis. The results have revealed that the students think that mathematical proof has an important place in mathematics and mathematics education. The students’ studying methods for exams based on imitative reasoning which can be described as a type of reasoning built on copying proof, for example, by looking at a textbook or course notes proof or through remembering a proof algorithm. Moreover, they addressed to the differences between mathematics taught in high school and university as the main cause of their difficulties in proof and proving. 相似文献
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Juan Pablo Mejia-Ramos Evan Fuller Keith Weber Kathryn Rhoads Aron Samkoff 《Educational Studies in Mathematics》2012,79(1):3-18
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research
on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper,
we address these issues by presenting a multidimensional model for assessing proof comprehension in undergraduate mathematics.
Building on Yang and Lin’s (Educational Studies in Mathematics 67:59–76, 2008) model of reading comprehension of proofs in high school geometry, we contend that in undergraduate mathematics a proof is
not only understood in terms of the meaning, logical status, and logical chaining of its statements but also in terms of the
proof’s high-level ideas, its main components or modules, the methods it employs, and how it relates to specific examples.
We illustrate how each of these types of understanding can be assessed in the context of a proof in number theory. 相似文献
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证明不等式是高等数学学习中的一个重点和难点,通过解答考研数学中出现的不等式试题,对一些常用的不等式证明方法进行总结。 相似文献
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Shailesh A. Shirali 《Resonance》1996,1(3):78-95
Euclid’s elegant proof that there are infinitely many prime numbers is well known. Elder proved the same result, in fact a stronger one, byanalytical methods. This article gives an exposition of Euler’s proof introducing the necessary concepts along the way. 相似文献
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利用协变微分及反对称性证明了Bianchi恒等式,并加以应用.改进了部分学者的证明方法,为初学者提供了通俗易懂的证明思路与应用技巧. 相似文献