中心极限定理在统计数学中拥有广泛应用,它揭示了一组相互独立的随机变量X_1,X_2,…,X_n的和的标准化变量总是服从正态分布.历史上第一个中心极限定理De.Movire-Laplace定理是由De.Movire首先发现,1773年用其估计大量抛掷硬币时正面出...中心极限定理在统计数学中拥有广泛应用,它揭示了一组相互独立的随机变量X_1,X_2,…,X_n的和的标准化变量总是服从正态分布.历史上第一个中心极限定理De.Movire-Laplace定理是由De.Movire首先发现,1773年用其估计大量抛掷硬币时正面出现次数的分布.1812年由Laplace在《Théorie Analytique des Probabilités》一书中再次提及.那之后,中心极限定理又经过了一定的推广和发展,先后出现了Lindeberg-Levy定理,Lindeberg-Feller定理,将独立随机变量组的规律推向了更统一的理论中.在现在一般概率论与数理统计教材中,省略了这三个定理的证明,这是因为严格的分析证明需要利用一些非初等的内容.文章将利用Riemann-Stieltjes积分以及积分变换,给出Lindeberg-Levy定理和Lindeberg-Feller定理的严格论证,同时这个论证也从理论上解释为何大量统计结果中正态分布总是频频出现的原因.展开更多
教育数字化的概念自提出以来就是教学改革的热点话题。在此,我们围绕北京化工大学“立德树人”的教育理念,结合大学工科专业的需求和数学基础课程的特色,以《复变函数与积分变换》数学课程为例,在数智赋能数学类基础课的教学内容、教学...教育数字化的概念自提出以来就是教学改革的热点话题。在此,我们围绕北京化工大学“立德树人”的教育理念,结合大学工科专业的需求和数学基础课程的特色,以《复变函数与积分变换》数学课程为例,在数智赋能数学类基础课的教学内容、教学模式和教学评价上进行探索与实践,通过数字化教学内容实现课程内容优化、知识图谱构建和课程思政融合,通过数字化教学模式达到课前深度参与、课堂高频互动、课后精准反馈的良性循环,通过数字化课程考核进行伴随式评估、阶段化考核和全方位考评,以此让学生深刻体会到《复变函数与积分变换》等数学课程在工科专业中解决问题的思想,从而改善教学效率与学习效果,达到课程育人目标。It has been a hot topic since the concept of digitalization in education was proposed;focusing on the talent training goal of Beijing University of Chemical Technology, combined with the characteristics of basic mathematics courses, we take the course of “complex variable functions and integral transformations” as an example to explore and practice the teaching content, teaching mode and teaching evaluation of the basic courses of mathematics empowered by digital intelligence. Through digital teaching content, the optimization of course content, the construction of a knowledge graph, and the integration of course ideology and politics are realized, and the virtuous circle of deep participation before class, high-frequency interaction in the classroom, and accurate feedback after class is achieved through the digital teaching mode, and the accompanying assessment, staged assessment, and all-round evaluation are carried out through digital course assessment, so as to enhance students’ cognition and interest in basic mathematics courses such as “complex variable function and integral transformation”, improve teaching efficiency and learning effect, so as to achieve the goal of curriculum education.展开更多
文摘中心极限定理在统计数学中拥有广泛应用,它揭示了一组相互独立的随机变量X_1,X_2,…,X_n的和的标准化变量总是服从正态分布.历史上第一个中心极限定理De.Movire-Laplace定理是由De.Movire首先发现,1773年用其估计大量抛掷硬币时正面出现次数的分布.1812年由Laplace在《Théorie Analytique des Probabilités》一书中再次提及.那之后,中心极限定理又经过了一定的推广和发展,先后出现了Lindeberg-Levy定理,Lindeberg-Feller定理,将独立随机变量组的规律推向了更统一的理论中.在现在一般概率论与数理统计教材中,省略了这三个定理的证明,这是因为严格的分析证明需要利用一些非初等的内容.文章将利用Riemann-Stieltjes积分以及积分变换,给出Lindeberg-Levy定理和Lindeberg-Feller定理的严格论证,同时这个论证也从理论上解释为何大量统计结果中正态分布总是频频出现的原因.
文摘教育数字化的概念自提出以来就是教学改革的热点话题。在此,我们围绕北京化工大学“立德树人”的教育理念,结合大学工科专业的需求和数学基础课程的特色,以《复变函数与积分变换》数学课程为例,在数智赋能数学类基础课的教学内容、教学模式和教学评价上进行探索与实践,通过数字化教学内容实现课程内容优化、知识图谱构建和课程思政融合,通过数字化教学模式达到课前深度参与、课堂高频互动、课后精准反馈的良性循环,通过数字化课程考核进行伴随式评估、阶段化考核和全方位考评,以此让学生深刻体会到《复变函数与积分变换》等数学课程在工科专业中解决问题的思想,从而改善教学效率与学习效果,达到课程育人目标。It has been a hot topic since the concept of digitalization in education was proposed;focusing on the talent training goal of Beijing University of Chemical Technology, combined with the characteristics of basic mathematics courses, we take the course of “complex variable functions and integral transformations” as an example to explore and practice the teaching content, teaching mode and teaching evaluation of the basic courses of mathematics empowered by digital intelligence. Through digital teaching content, the optimization of course content, the construction of a knowledge graph, and the integration of course ideology and politics are realized, and the virtuous circle of deep participation before class, high-frequency interaction in the classroom, and accurate feedback after class is achieved through the digital teaching mode, and the accompanying assessment, staged assessment, and all-round evaluation are carried out through digital course assessment, so as to enhance students’ cognition and interest in basic mathematics courses such as “complex variable function and integral transformation”, improve teaching efficiency and learning effect, so as to achieve the goal of curriculum education.
