Integration of Ideological and Political Education into the Probability Theory and Mathematical Statistics Course:A Teaching Design Based on Estimation and Hypothesis Testing

With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.

Using Monte Carlo Simulation Technology to Improve Intuitive Effect of Teaching Probability and Mathematical Statistics Course

With the illustration of a specific problem, this paper demonstrates that using Monte Carlo Simulation technology will improve intuitive effect of teaching Probability and Mathematical Statistics course, and save instructors' effort as well.And it is estimated that Monte Carlo Simulation technology will be one of the major teaching methods for Probability and Mathematical Statistics course in the future.

Research on the Applications of Advanced Mathematics on Mathematical Modeling and the Inner Connections with Linear Algebra and Probability Statistics

In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical modeling and solving and model of evaluation and promotion of the two links, put forward the ＂bystander＂ and ＂the authorities＂ this two characters, and points out that excellent mathematical modeling participants should have ＂from a bystander to the authorities＂ and ＂from the authorities to return to bystanders＂ two-way role transformation ability. Great situation in mathematics teaching, by means of the mathematical modeling formed in the development of the teachers, as well as the teaching thought, teaching experience and achievements, the onward march of mathematical experiment should be faster than mathematical modeling. Our research provides the new paradigm for the math development which will be meaningful.

Past and Future of Mathematical Geology

This is a brief review of alternative methods of problem-solving in geoscience with emphasis on the role of mathematical geology. It is desirable to maintain a clear-cut distinction between reliable facts which can be stored in data banks and concepts that can be incorporated in the specifications of statistical models designed for specific purposes. If possible, subjective probabilities should be incorporated in hypotheses that are to be tested by statistical inference.

The Monty Hall Problem and beyond: Digital-Mathematical and Cognitive Analysis in Boole’s Algebra, Including an Extension and Generalization to Related Cases

The Monty Hall problem has received its fair share of attention in mathematics. Recently, an entire monograph has been devoted to its history. There has been a multiplicity of approaches to the problem. These approaches are not necessarily mutually exclusive. The design of the present paper is to add one more approach by analyzing the mathematical structure of the Monty Hall problem in digital terms. The structure of the problem is described as much as possible in the tradition and the spirit—and as much as possible by means of the algebraic conventions—of George Boole’s Investigation of the Laws of Thought (1854), the Magna Charta of the digital age, and of John Venn’s Symbolic Logic (second edition, 1894), which is squarely based on Boole’s Investigation and elucidates it in many ways. The focus is not only on the digital-mathematical structure itself but also on its relation to the presumed digital nature of cognition as expressed in rational thought and language. The digital approach is outlined in part 1. In part 2, the Monty Hall problem is analyzed digitally. To ensure the generality of the digital approach and demonstrate its reliability and productivity, the Monty Hall problem is extended and generalized in parts 3 and 4 to related cases in light of the axioms of probability theory. In the full mapping of the mathematical structure of the Monty Hall problem and any extensions thereof, a digital or non-quantitative skeleton is fleshed out by a quantitative component. The pertinent mathematical equations are developed and presented and illustrated by means of examples.

Statistical Theory of Turbulence by the Late Lamented Dr. Shunichi TsugéCase Study on Flow through a Grid in Wind Tunnel

This paper is concerned with statistical theory of turbulence by the late lamented Dr. Shunichi Tsugé.? The theory has been applied to the primary flow through a grid fixed vertically with respect to the horizontal axis of the wind tunnel.?The first analytical solution has been obtained and explained the well-known “the inverse-linear decay law” of the turbulent intensity.? It is believed that the present result is the first exact solution in the theory of turbulence.

SOME ISSUES OF TURBULENCE STATISTICS

The issue of dropping the random force f(i) and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random force f(i) should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However, f(i) is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time of f(i)), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly.

Incomplete nonextensive statistics and the zeroth law of thermodynamics

On the basis of the entropy of incomplete statistics （IS） and the joint probability factorization condition, two controversial problems existing in IS are investigated： one is what expression of the internal energy is reasonable for a composite system and the other is whether the traditional zeroth law of thermodynamics is suitable for IS. Some new equivalent expressions of the internal energy of a composite system are derived through accurate mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it cannot be proven theoretically. Finally, it is pointed out that the generalized zeroth law of thermodynamics for incomplete nonextensive statistics is unnecessary and the nonextensive assumptions for the composite internal energy will lead to mathematical contradiction.

统计活动过程视角下小学“统计与概率”教材内容的分析与比较——以“苏教版”“北师版”为例

以“统计活动过程”视角为理论基础,从统计活动过程的各环节要素对苏教版和北师版小学数学教材中“统计与概率”内容进行分析和比较.研究发现:两版教材在统计活动过程的各环节上有所侧重,整体上各具风格;两版教材均直接突出对统计基础知识的重视,并间接蕴涵着对数据意识的培养.对教材使用的启示有:以“统计活动视角”为基础,注重对教材进行创生;将活动视角与统计教学间的“冲突”化为提升素养的机会;进而在统计活动中促进批判性思维的发展.对教材编写或修订提供启发:从学科角度厘清“统计”与“概率”的本质关系,整体把握统计活动的全过程,给予学生更多获取直接经验的机会.

工程教育认证下“概率论与数理统计”教学改革

“概率论与数理统计”是理工和经管类各专业的数学基础课程,课程中的方法在解决实际问题时应用广泛。但是该课程理论性强、学习难度大,课程教学中通常存在课时少、实践少、学用分离等教学痛点,不符合工程教育认证理念。分析了防灾科技学院地质工程专业工程教育认证对“概率论与数理统计”课程的要求,以及大学传统的数学课堂教学存在的问题,结合地质工程专业发展规划和应用型人才培养目标,探讨如何进行数学类课程的教学改革,以达到工程教育认证标准。

概率论与数理统计课程情境化教学模式探索与实践

概率论与数理统计是高校理工专业的核心基础课程,开展概率论与数理统计情境化教学模式探索与实践能够显著提升教学质量。该文首先从课程属性、智慧教学环境、教学理念等视角分析开展情境化教学模式的必要性,进而从情境案例准备、学习情境设定、自主探究学习、智能系统辅助和数据分析与评估等五个环节探讨情境化教学模式设计问题。最后,以条件概率为例,研究情境化教学模式的实施过程。情境化教学模式还可以向其他公共基础课程与专业课程推广应用,能够在学生创新实践能力培养方面发挥重要作用。

“少教多学”理念下国家级一流课程概率论与数理统计本校化混合式教学实践研究

“少教多学”倡导“先学后教,以学定教”,体现以学生为中心的现代教育理念。在该理念的指导下,引入国家级一流线上课程概率论与数理统计资源,并进行适合该校学生特点的本校化课程改造使之可以更好地服务于课程教学。基于BOPPPS的混合式教学设计和实施,有效地提高该课程的过关率和学生的学习能力,促进学生思维的发展。

新文科背景下面向财经类高校的“概率论与数理统计”课程建设与实践——以贵州财经大学为例

根据“新文科”建设的核心要义,分析了财经类高校在探索“概率论与数理统计”课程建设的现状与困境。重点以贵州财经大学为例,探讨了“概率论与数理统计”的课程建设与实践。以超星信息技术平台为依托,深入贯彻基于学习成果为导向的教学理念,以学科竞赛为抓手,着力提升人才培养质量为目标,按照一流课程建设要求,融入课程思政,助推统计学一流专业和一流学科建设。

基于“三全育人”理念的概率论与数理统计课程思政教学探索与实践

课程思政是实现有效育人的重要教学方式。根据当前概率论与数理统计课程思政的现状,并基于概率论与数理统计课程教学内容,从融入时机、思政元素类型两方面阐述课程思政教学的做法,挖掘案例中蕴含的“思政元素”及所承载的思想政治教育功能,以润物无声的方式将思政元素融入课堂教学,促成知识传授、思政教育、价值引领三者有机统一,做到全员、全程、全方位育人,以此实现概率论与数理统计课程立德树人的目标。

概率统计“3542”课程思政教学模式的研究与实践

以专业人才培养目标为依据,根据教育部颁布的《高等学校课程思政建设指导纲要》,结合概率统计课程的特点,通过明确教学目标,优化教学内容,实施教学过程,设计教学评价,探索并构建了3维度教学目标,5方面教学内容,4环节教学过程,2方面教学评价的“3542”立体化课程思政闭环教学模式,在实践中获得了良好的教学效果。

基于层次分析法的课堂教学质量评价体系研究——以概率论与数理统计课程为例

课堂教学质量评价体系作为整个教学过程中的关键环节具有重要的地位,传统的课堂教学质量评价模式单一、评价标准固定,在一定程度上很难反映当前课堂教学效果。基于此,文章以概率论与数理统计课程为例,从学生的视角出发,提出了准则层和指标层的影响因素,构建课堂教学质量评价指标体系,并利用层次分析法研究各影响因素的权重系数。实例分析进一步验证了模型的可行性、科学性,为课堂教学质量评价研究提供了新方法。

智慧教学模式赋能概率论与数理统计教学改革

在“互联网+”背景下,一些学者将MOOC融合SPOC进行翻转课堂和混合教学以提升教学质量。为充分发挥MOOC+SPOC的优势,培养新时代大学生应具备的数学能力,结合概率论与数理统计课程培养方案,提出基于MOOC+SPOC+雨课堂直播的融合式智慧教学模式。以“中心极限定理”知识单元为例介绍融合式智慧教学模式下具体教学设计和实施过程。结果表明,雨课堂直播教学与MOOC+SPOC融合的智慧教学模式提高学生学习兴趣,体现以学生为中心的教学思想。

基于学生需求的概率论与数理统计教学策略优化

基于学生需求视角的概率论和数理统计更加关注学生在课堂教学中的表现和收获,同时对教学目标、知识呈现形式、教学辅助资源等都提出了更高的要求,旨在帮助学生理解复杂深奥的数学知识,并掌握学习要点,充分激发其学习兴趣。基于此,本文对高等院校概率论与数理统计课程的教学现状展开分析,针对存在的问题提出了相应的应对策略。

基于课程思政理念的概率论与数理统计案例设计

课程思政理念与概率论与数理统计课程进行有机结合,并基于对课程思政的理解,从政治认同、国家意识、文化自信、公民人格、人文精神、科学精神和职业素养7个方面进行案例设计.课程思政的融入,将学生的平均成绩提高4.6分,并且得到超过80%的学生认可.课程思政案例的设计,拓宽学生的知识储备,激发学生的学习兴趣,同时促进学生思想政治素质的提升,进而达成课程育人的成效.

文化视角下的直觉教学:概率论与数理统计课程的教学创新研究

本文探讨了在概率论与数理统计课程中融合中国传统文化元素的创新教学方法,旨在推动教学创新并深化学生对课程内容的理解。针对传统教学方法过于侧重于理论知识传授的局限,研究提出通过引入中国古典哲学思想和文化元素,如《道德经》和《易经》的故事,帮助学生在文化和哲学的层面上建立起对概率论概念的直觉理解。通过具体案例分析和创新教学方法的应用,展示了如何有效地结合传统文化理念和概率论教学,不仅丰富了教学内容,还激发了学生的学习兴趣,提高了他们解决实际问题的能力。研究还讨论了这种跨学科教学策略实施过程中的挑战,并提出了未来发展方向,强调该教学模式对于培养学生的数学技能以及增进对本土文化的理解和尊重具有重要意义,为学生的全面发展提供了支持。