概率统计课程思政教学案例设计与分析——以贝叶斯公式为例

本文选取了概率论与数理统计课程中的典型内容“贝叶斯公式”,从设计思路、案例的具体设计以及案例的思政价值和成效三个方面，进行了多角度、深层次的设计，使学生在学习知识的同时，接受诚信、爱国等价值观的引导，达到育人的目的.     

基于唯物辩证法的概率论与数理统计课程思政建设与实践

通过概率论与数理统计课程思政建设,将唯物辩证法的认识论与方法论渗透于教学设计和教学实践中,把大量的应用案例和教书育人相结合,学生既掌握了知识,又树立正确的人生观和价值观,提高独立思考能力和理性思辨的能力.通过实践教学,加深了学生对基本概念的理解,将理论与实践相统一,既增强了学生的动手能力,又培养了学生的创新思维能力和解决实际问题的综合能力.结合先进的教学方式和教学手段,大力开展概率论与数理统计课程思政的教学改革,力求将知识、能力和素质融为一体,对高校提升教学质量及教学水平,培养一流人才具有积极的推动作用.     

《概率论与数理统计》课程的“慕课”建设探讨

结合学校提出的"以能力为导向的一体化人才培养方案"和《概率论与数理统计》课程新的教学大纲的实施.我们通过问卷调查的形式了解学生"慕课"(MOOC)的使用现状,同时对目前各种网络平台提供的《概率论与数理统计》MOOC课程从建设思路、教学设计、学习特征等方面进行了探讨.根据现有的MOOC课程的特点分析了问卷调查中MOOC使用率偏低的各种可能因素,并有针对性的提出了若干建议.     

课程思政理念下Bayes公式教学方法的探讨

概率论与数理统计是一门重要的大学数学课程.基于课程思政的教育理念,在贝叶斯公式的教学中融入课程思政,优化教学设计,改进教学方法,采用线上线下相结合的方式,既解决了学生在学习理论知识方面遇到的困惑,又起到了教书育人的作用.     

概率论与数理统计慕课课件的构想与设计

围绕课程建设的目标,本文阐述了概率论与数理统计慕课课件的构想与设计.     

《概率论与数理统计》课程思政案例设计及应用

以概率论与数理统计的教学内容为基础,结合实际生活设计思政案例,深挖案例中蕴含的"思政元素"及所承载的思想政治教育功能,将思政元素有机的融入课堂教学,把"知识传授"与"价值引领"有机统一起来,做到立德树人,培养具有社会主义核心价值观的有用人才.     

谈案例教学法在概率论与数理统计教学中的应用

为了提高学生对概率论与数理统计知识的实际运用能力,针对概率论与数理统计学科特点,选取了几个教学案例,探讨了案例教学在这门学科教学中的优势和作用.本文着重从案例教学的思想来研究如何加强概率论与数理统计课程的应用性教学.     

《概率论与数理统计》教学改革研究

针对概率论与数理统计课程的特点,以经济管理类专业的学生为对象,提出了概率论与数理统计课程教学改革的几点建议．     

在《概率论与数理统计》课程中增加数学实验内容的探索与实践

在《概率论与数理统计》课程中增加数学实验内容教学是对该课程教学内容的一次改革尝试.由于开始实施不久,有许多问题亟待研究探讨.本文就《概率论与数理统计》课程中增加数学实验内容教学的目标定位、意义认识、具体实验类型、应该注意的问题提出了我们的看法和见解,以期与同行们商榷.     

概率论与数理统计教学案例研究

给出了概率论与数理统计课程中的两个教学案例.案例一是针对新冠筛查中逐一检验和分组检验的问题,结合概率论与数理统计中离散型随机变量的分布列及其数学期望的知识点给出的,并进行了问题的引申研究.案例二是针对图像加密的安全性问题,结合概率论与数理统计中相关系数定义以及基于概率的信息熵的概念,给出了一个适用于信息安全专业的专业案...     

Border bases and kernels of homomorphisms and of derivations

Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations.     

Extension and Lifting of Operators and Polynomials

We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of ${\mathcal{L}_1}$ and ${\mathcal{L}_\infty}$ -spaces that includes and extends those of Lindenstrauss-Rosenthal [32] using compact operators and González-Gutiérrez [23] using compact polynomials. We display several examples to show the difference between extending and lifting compact (resp. weakly compact, unconditionally convergent, separable and Rosenthal) operators to operators of the same type. Finally, we show the previous results in a homological perspective, which helps the interested reader to understand the motivations and nature of the results presented.     

On some results of Strichartz and of Rallis and Schiffman

Let (i, H, E) and (j, K, F) be abstract Wiener spaces and let α be a reasonable norm on E ? F. We are interested in the following problem: is ($\text{i ? j, H}\text{}\text{?}\text{bo}{}_2\text{K, E}\text{}\text{?}\text{bo}{}_{\mathrm{\alpha F}}$) an abstract Wiener space ? The first thing we do is to prove that the setting of the problem is meaningfull: namely, i ? j is always a continuous one to one map from $\text{H}\text{}\text{?}\text{bo}{}_2\text{K}$ into $\text{E}\text{}\text{?}\text{bo}{}_{\mathrm{\alpha }}\text{F}$. Then we exhibit an example which shows that the answer cannot be positive in full generality. Finally we prove that if F=L^p(X,$\text{X}$,λ) for some σ-finite measure λ ? 0 then $\text{(i?j, H}\text{?}{}_2\text{K,L}{}^{\mathrm{p}}$(X,$\text{X}$,λ) is an abstract Wiener space. By-products are some new results on γ-radonifying operators, and new examples of Banach spaces and cross norms for which the answer is affirmative (in particular α = π the projective norm, and F=L¹(X,$\text{X}$,λ)).     

Shellability and homology of q-complexes and q-matroids

Journal of Algebraic Combinatorics - We consider a q-analogue of abstract simplicial complexes, called q-complexes, and discuss the notion of shellability for such complexes. It is shown that...     

Crossings and nestings of matchings and partitions

We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets of minimal block elements and maximal block elements, the crossing number and the nesting number of partitions have a symmetric joint distribution. It follows that the crossing numbers and the nesting numbers are distributed symmetrically over all partitions of , as well as over all matchings on . As a corollary, the number of -noncrossing partitions is equal to the number of -nonnesting partitions. The same is also true for matchings. An application is given to the enumeration of matchings with no -crossing (or with no -nesting).