新工科背景下线性代数课程教学改革与实践

在新工科背景下探讨线性代数课程教学内容、教学模式和考核方式改革,通过优化知识体系、建设丰富的网络资源和课程思政内容、构建多元化教学模式、采取多元化评价方式等,充分发挥学生的主体作用,强化线性代数知识的应用,培养学生的数学素养、实践能力和创新能力,切实提高线性代数课程教学效果和人才培养成效．     

线性代数课程思政教学案例的设计与实践

在线性代数课程中进行课程思政教学案例的设计,应以课程内容为源头,综合运用学习的课堂、文化的课堂、实践的课堂.在学习的课堂,通过深入挖掘知识点,帮助学生理解线性代数知识体系中蕴含的马克思主义哲学观;在文化的课堂,通过数学史料的讲解,帮助学生树立文化自信,激发爱国情怀;在实践的课堂,通过应用实例的分析和实践,激励学生学以致用,报效祖国.     

线性代数课程思政设计及实践

以价值引领为导向,探讨了在线性代数课程中将专业教育与思政教育有机融合的多种设计思路,并通过具体案例介绍了将抽象数学概念与生动生活语言相结合的实施方式,以期在线性代数课程思政中润物细无声式地实现立德树人的目标.     

基于线性代数的浸入式课程思政教学实践

本文研究如何在线性代数课程中贯彻课程思政的教学要求.     

线性代数课程实践教学网络平台的研究和探索

本文针对借助Blackboard平台,从用实际问题驱动线性代数课程教学,介绍与线性代数课程内容相关的数学软件(MATLAB数学软件),增加线性代数课程在实际问题中应用的内容等方面,探讨线性代数课程实践教学网络平台问题.     

数学基础课程图论的课程思政探索与实践

全面推进课程思政建设是落实立德树人根本任务的战略举措,新时代的大学教育更加注重专业教育和拔尖创新人才的培养,更加凸显课程思政的重要性.作为一门专业基础课程,图论具有重要的理论研究价值和广阔的应用价值.以研究生图论课程为例,介绍了如何将思政元素引入课堂教学,培养学生数学核心素养的探索与实践的能力.     

基于CDIO理念的线性代数课程教学改革

CDIO是当前高等工程教育的一种新型教育模式,对工程教育的基础课程教学具有同样的指导意义.本文针对工科线性代数课程的特点和教学现状,提出了基于CDIO理念的线性代数课程教学改革,立足于调动学生主动学习的积极性,对教学模式、教学方法与手段、实验教学、考核方式等方面进行探索,指出了主动式学习方式对提高教学质量和教学效果的重要作用.     

在高中数学教学中实践课程思政的策略研究

立德树人是中国特色社会主义教育事业的根本任务,也是教师在教育教学中的重要责任.在数学课堂上,教师要引入思政元素,加强课程思政教育,本文先分析挖掘数学课程思政素材的原则,介绍实施数学课程思政教育的路径和手段,并借助几个典型案例,对如何在高中数学教学中实践课程思政进行研究.     

数学模型“课程思政”的思考与教学实践

"课程思政"是将思政融入教学的全过程,实现全员、全程、全方位育人.本文对数学模型实践课程教学中渗透"课程思政"的必要性和实践路径进行了探索与研究.以传染病模型为例,从课题背景的引入到数学模型的建立,再到获得预防与控制传染病的基本手段,最后到传染病模型的应用,多角度、多方位的进行课程思政.意在不仅使学生掌握专业知识,而且要引导学生树立正确的价值观,更要激发学生的爱国热情与勇于探索的精神.     

创新型人才培养目标下高校公共数学类课程教学创新实践——以宁夏大学公共基础课线性代数为例

创新型人才符合我国新时期社会发展的需求,同时也是高校人才培养的重要目标,在互联网+教育背景下,线性代数课程教学以学生发展为中心,教师为主导,通过“引导”“互动”“管理”三位一体,开展线上+线下混合式课程教学创新改革,提高线性代数课程教学质量.通过近三年的教学改革创新实践,结果表明,学生的创新思维,创新能力有了明显改善,这为后续深化课程建设,提升人才培养质量,积累了教学实践经验,具有一定示范和借鉴作用.     

Affine-inscribed and affine-circumscribed polygons and polytopes

Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are proved by topological methods. In particular, it is proved that for every interior point O of a convex compact set in ℝ³, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon. It is also proved that every compact convex set in ℝ³ (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram P and contained in a cylinder with directrix P. Bibliography: 29 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 286–298. Translated by B. M. Bekker.     

Partitions and pairwise sums and products

A seven cell partition of N is constructed with the property that no infinite set has all of its pairwise sums and products in any one cell. A related Ramsey Theory question is shown to have different answers for two and three cell partitions.     

Linear birth and death models and associated Laguerre and Meixner polynomials

We study birth and death processes with linear rates λ_n = n + α + c + 1, μ_{n + 1} = n + c, n 0 and μ₀ is either zero or c. The spectral measures of both processes are found using generating functions and the integral transforms of Laplace and Stieltjes. The corresponding orthogonal polynomials generalize Laguerre polynomials and the choice μ₀ = c generates the associated Laguerre polynomials of Askey and Wimp. We investigate the orthogonal polynomials in both cases and give alternate proofs of some of the results of Askey and Wimp on the associated Laguerre polynomials. We also identify the spectra of the associated Charlier and Meixner polynomials as zeros of certain transcendental equations.     

Distributive and Multiplication Modules and Rings

We study rings in which every ideal is a finitely generated multiplication right ideal.     

Beliefs and beyond: affect and the teaching and learning of mathematics

The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education.     

Ritz and harmonic Ritz values and the convergence of FOM and GMRES

The Ritz and harmonic Ritz values are approximate eigenvalues, which can be computed cheaply within the FOM and GMRES Krylov subspace iterative methods for solving non‐symmetric linear systems. They are also the zeros of the residual polynomials of FOM and GMRES, respectively. In this paper we show that the Walker–Zhou interpretation of GMRES enables us to formulate the relation between the harmonic Ritz values and GMRES in the same way as the relation between the Ritz values and FOM. We present an upper bound for the norm of the difference between the matrices from which the Ritz and harmonic Ritz values are computed. The differences between the Ritz and harmonic Ritz values enable us to describe the breakdown of FOM and stagnation of GMRES. Copyright © 1999 John Wiley & Sons, Ltd.