Mathematica软件在数学教学中的应用探索

Mathematica软件是专门进行数学类计算的软件,其主要功能是符号运算功能和绘图功能.在高等数学的教学过程中引入Mathematica软件,有利于增强教学内容的直观性,激发学生学习数学的兴趣,提高解决实际问题的能力.     

财经院校《高等数学》结合Mathematica软件教学探讨

Mathemadca软件有强大的数学计算功能和绘图功能,财经院校学生学习《高等数学》的理论知识和计算存在着困难．可在教学过程中结合使用Mathematica软件。通过这种直观、生动的教学手段,可以丰富教学内容,激发学生学习兴趣,还能培养学生的动手能力,从而真正达到提高教学质量的目的。     

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计算思维和翻转课堂在Java 教学中的研究和应用

《Java 程序设计》作为高校计算机专业程序设计课程中的一门核心专业课,具有概念多、知识点抽象、难理解的 特点,许多学生学完此门课程后,不具备真正的编程思想。因此,本文以六盘水师范学院计算机科学与技术系的学生为研究对 象,分别采用普通的课堂教学模式和基于计算思维和翻转课堂的教学模式进行比较。研究表明:在《Java 程序设计》教学中融入 计算思维和翻转课堂,可以帮助学生理解抽象的知识点,充分调动学生学习的积极性,提高学生的动手实践能力,并逐步培养 学生利用算法求解问题的思路和编程思想,为今后从事编程工作打下夯实的基础。     

Teaching Computational Economics in an Applied Economics Program

Effective teaching of computational methods to economists in an introductory graduate-level course requires difficult choices regarding the material to be covered, the level at which the material will be covered, and the role of assigned exercises, laboratory sessions, and required readings. In this paper, I discuss the goals that I set and the pedagogical choices that I make in teaching computational methods to doctoral students in economics in a quarter-length course. The discussion is based on 15 years of teaching computational methods to students with a broad range of research interests and professional objectives. I also discuss some of the pedagogical obstacles that I often face when teaching the course and how I address them. I hope that the discussion will provide a useful starting point for instructors wishing to develop computational methods courses in other economics graduate programs.     

Learning physics with a computer algebra system

Abstract   To become proficient problem-solvers, physics students need to form a coherent and flexible understanding of problem situations with which they are confronted. Still, many students have only a limited representation of the problems on which they are working. Therefore, an instructional approach was devised to promote students' understanding of these problems and to support them in forming associations between problem features and solution methods. The approach was based on using the computer algebra software Mathematica as a tool for problem solving and visualisation. An electrostatics course module was implemented based on this instructional approach, and this module was compared with a usual paper-and-pencil based one. Learning outcomes for both courses were not significantly different. The experimental course was found to impose a high cognitive load on the students. Based on the outcomes, proposals are made for ways in which the course could be improved.     

Programming Languages in Economics

Young economists sometimes ask which computer programming languages they should learn. This paper answers that question by suggesting that they begin with a high level language like GAUSS, GAMS, Mathematica, Maple or MATLAB depending on their field of specialization in economics. Then they should work down to one of the low level languages such as Fortran, Basic, C, C++ or Java depending on the planned areas of application. Finally, they should proceed to the languages which are used to develop graphical interfaces and internet applications, viz. Visual Basic, C, C++ or Java.     

Computer vision and Mathematica

Computer vision algorithms are strongly based on advanced mathematical methods. Tools to efficiently develop new methods are increasingly based on computer algebra systems, such as Matlab, Maple and Mathematica. For rapid prototyping both symbolic as numerical capability is required. However, the application to large datasets such as images has always been frustated by the expensive use of memory or long computing times. Today such programs have improved substantially in numerical data handling, making them an ideal tool for rapid prototyping in computer vision. This paper gives a short variety of examples of the use of Mathematica in computer vision research.     

Computational Economics: Help for the Underestimated Undergraduate

Our concern in this paper is that the capability of economics undergraduates is substantially underestimated in the design of the present college curriculum and that our students are insufficiently challenged and motivated. Students enter our classrooms with substantial previous knowledge about computers and computation and we are not taking full advantage of this opportunity. We suggest a set of examples from computational economics which are challenging enough to motivate students and simple enough that they can master them within a few hours. By encouraging the students to modify the models in directions of their own interest, avenues for creative endeavor are opened which deeply involve the students in their own education.     

花园幽径句解码效果与反应时的关联性研究

该文以126名中国大学生为测试样本,并采用非独立t检验为计算方法,讨论英语花园幽径句解码效果与解码反应时之间的关联性。花园幽径句是能引发行进错位的局部歧义句,大学生在歧义消解过程中易产生认知困惑。在其他条件不变的情况下,先后两次的语言实验将单样本花园幽径句的反应时从5s延长至10s,并进行了相应的t值计算。S1实验中,测定5s反应时和10s反应时的非独立t检验值为3.71,大于理论临界值并具有显著性差异。在S2-S100的实验中,分析发现材料的选择对实验结果有影响。总体而言,英语花园幽径句解码效果与解码反应时之间具有一定关联性,阅读时间的延长可以在一定程度上帮助学生更好地消解局部歧义。     

用Mathematica构建L-P算法

本文以单自由度系统的Duffmg方程为例,应用Mathematica构建非线性振动L-P法的符号运算,推导摄动公式,既方便又准确.此法可以方便地推广应用于构建和实现单自由度其他振动系统或多自由度非线性振动系统L-P方法.     

Mathematica在信息安全类课程实验教学中的应用

在信息安全类课程的实验教学中利用Mathematica应用程序来演示整数乘法群逆元的性质、扩展欧几里得算法、模冥周期性等教学内容,通过这些可视化的实验程序来帮助学生学习和理解信息安全领域涉及到的抽象的数学基础知识,对提高教学质量起到了事半功倍的效果。     

The high-energy physicistʼs guide to MathLink

MathLink is Wolfram Research?s protocol for communicating with the Mathematica Kernel and is used extensively in their own Notebook Frontends. The Mathematica Book insinuates that linking C programs with MathLink is straightforward but in practice there are quite a number of stumbling blocks, in particular in cross-language and cross-platform usage. This write-up tries to clarify the main issues and hopefully makes it easier for software authors to set up Mathematica interfacing in a portable way.     

质点法机器证明视角下的近世几何研究

优化并发展了质点法机器证明算法的核心程序,用Mathematica创建了新的几何定理证明器。拓展了机器证明的研究范畴,首次实现了近世几何的机器证明,且可读性令人满意。在该证明器的帮助下,发现了一些新的近世几何性质,深化了近世几何的研究成果,并对已有的近世几何研究成果提出一些意见。     

基于计算思维的大学计算机教学改革与实践

现在的大学计算机基础教学,应该训练和提高当今大学生的计算思维和计算文化素养。本文分析了目前大学 计算机教学中存在的问题和面临的困难,提出了提高学生计算思维能力的大学计算机教学改革和实践措施。     

基于Python程序设计的生物信息学人才培养模式探析

生物信息学是当今自然科学重要前沿领域之一。随着基因测序技术的进步,大量生物数据需要计算机来处理和分析,对生物信息学人才的要求越来越高。“大学计算机基础”作为大学新生的必修课程,其教学目标之一就是让学生具备基本的信息处理能力——不仅要学会计算机,还要掌握利用计算机来解决实际问题,特别是解决专业问题,这对学生的编程能力提出了一定要求。而Python程序设计语言因学习入门难度低,是一非常适合低年级及非计算机专业大学生学习的编程语言,通过学习编程能培养学生的计算思维和提高解决问题的能力。在生物专业的“大学计算机基础”课程中加入Python程序设计内容,对生物信息学人才的培养具有很强的现实意义。     

A Mathematica interface for FormCalc-generated code

This note describes a Mathematica interface for Fortran code generated by FormCalc. The interfacing code is set up automatically so that only minuscule changes in the driver files are required. The interface makes a function to compute the cross-section or decay rate available in Mathematica. This function depends on the model parameters chosen for interfacing in the Fortran code.     

Analytica – An Experiment in Combining Theorem Proving and Symbolic Computation

Analytica is an automatic theorem prover for theorems in elementary analysis. The prover is written in the Mathematica language and runs in the Mathematica environment. The goal of the project is to use a powerful symbolic computation system to prove theorems that are beyond the scope of previous automatic theorem provers. The theorem prover is also able to deduce the correctness of certain simplification steps that would otherwise not be performed. We describe the structure of Analytica and explain the main techniques that it uses to construct proofs. Analytica has been able to prove several nontrivial theorems. In this paper, we show how it can prove a series of lemmas that lead to the Bernstein approximation theorem.     

计算思维在计算机应用型人才培养中的应用探索

在计算机专业教学过程中,如何培养学生计算思维能力的问题是当前计算机教育中的热点课题。结合培养计算机应用型人才的需要,提出并践行基于计算思维的探究式教学模式,包括课程教学改革、上机实践、评价机制等方面的教学改革。经过两年多的实践证明,该模式有助于强化培养计算机专业学生的计算思维能力和专业实践能力,为高等学校培养应用型人才开展教学改革提供了新的思路。