关于开设数学建模课程的必要性探究

本文从现行高等数学教育存在的问题出发,阐述了数学建模教育的特点及优势,将数学建模思想和方法融入数学课程教学,通过案例、数学实验及应用计算机求解模型等方面论证,提出开设数学建模课程是高职教育数学教改的一个重要举措。     

计算机模拟建模

通过在数学建模教学实践中编写的两个典型案例的建模和利用MATLAB软件求解，具体展示了对连续系统计算机模拟的建模步骤和方法。     

数学建模融入财经类大学数学教学的理论与实践

本文首先论述了数学建模融入大学数学教学的内容、模式、意义、目的、必要性与可能性，然后举例说明设计并作了具体的实践的具有财经类院校特点的教学单元、案例、章节。     

如何从数学建模的角度加强数学教学

数学建模与数学教学有着相互制约、相互促进的关系。数学教学是数学建模的基础,是数学建模的初始阶段,数学建模促进了数学教学观念、教学方法的改革。从数学建模的角度加强数学教学,创造数学教学的新局面。     

高职高专数学建模方法的策略研究

高职高专数学建模课程开设的目的是培养学生的科学计算能力和数学知识应用能力,让学生真正掌握用数学知识和技能来解决实际问题的能力.在高职高专中开展数学建模教学,对于激发学生的学习积极性也有积极作用,还能提升学生综合素养.本文对于高职高专数学教学现状进行剖析,结合数学建模课程教学作用,分析高职高专数学建模教学对策.     

高职数学案例教学法初探

打破传统"灌输式"固定教学模式,数学案例教学法以培养学生实际能力为核心,提倡教师引导学生运用所学数学知识解决实际的生活问题,是值得深入研究并应用的新型教育教学方法。通过文献法、实验法,结合高职数学的特点,对数学案例教学概念、高职数学的现状,以及数学案例教学在高职教学中的积极作用加以阐述。研究和论证数学案例与高职数学教育的关系,并分析和探讨在我国高职数学教育中实施数学案例教学的实用途径。     

数学建模融入传统经济数学基础课教学的障碍和对策

数学建模竞赛有助于推动经济数学基础课的教学改革。将数学建模的思想和方法融入到传统经济数学基础课教学中来，有利于提高学生应用数学的能力。但将数学建模思想和方法融入到传统经济数学基础课教学中去面临诸多障碍，对此进行分析并提出相应的对策，可以促使这项工作更好地开展下去。     

将数学建模教学贯穿大学生培养全过程

全国大学生数学建模竞赛已开展了十二届，参赛学校和队数逐年大幅度增加，目前面临的一个关键问题是许多学校片面追求竞赛的获奖情况，而忽视了数学建模教学的重要性，没能将竞赛与大学生培养全过程结合起来。近年来，浙江大学在数学建模教学上进行了大胆改革和尝试，以数学建模竞赛为载体，培养大学生的素质和能力，在国内、美国大学生数学建模竞赛中取得了非常优异成绩，文章从六方面陈述浙江大学数学建模教学改革的经验。     

将数学建模融入高等数学教学提高学生的创新能力

本文结合作者在高等数学教学改革中的经验体会,对数学建模在数学中的地位和作用以及在高等数学教学中渗透数学建模的途径做了探讨。     

数学建模思想融入高等数学教学的研究与探讨

数学建模是培养学生创新性应用能力的重要途径。本文通过分析了目前高等数学教学现状和存在的问题,提出了高等数学教学中渗透数学建模思想的的重要作用以及方法。     

"Mathematics made no contribution to the public weal": why Jean Fernel (1497-1558) became a physician

This paper offers a caution that emphasis upon the importance of mathematics in recent historiography is in danger of obscuring the historical fact that, for the most part, mathematics was not seen as important in the pre-modern period. The paper proceeds by following a single case study, and in so doing offers the first account of the mathematical writings of Jean Fernel (1497-1558), better known as a leading medical innovator of the 16th century. After establishing Fernel's early commitment to mathematics, and attempt to forge a career as a cosmographer, it goes on to explain his abandonment of mathematics for a career in medicine. The 'mathematization of the world picture' is usually explained in terms of the perceived usefulness of mathematics, but Fernel's case shows that for many pre-modern thinkers, mathematics was not regarded as a useful pursuit. The paper should serve as a reminder, therefore, that the take-up of mathematics by natural philosophers was by no means inevitable, but had to be carefully managed by early modern mathematical practitioners. The case of Fernel indicates that perhaps he was not the only would-be mathematical practitioner to abandon mathematics in favor of a calling that was more appreciated by contemporaries.     

Near-field artifact reduction in planar coded aperture imaging

Coded apertures for imaging problems are typically based on arrays having perfect cross-correlation properties. These arrays, however, guarantee a perfect point-spread function in far-field applications only. When these arrays are used in the near-field, artifacts arise. We present a mathematical derivation capable of predicting the shape of such artifacts. The theory shows that methods used in the past to compensate for the effects of background nonuniformities in far-field problems are also effective in reducing near-field artifacts. The case study of a nuclear medicine problem is presented to show good agreement of simulation and experimental results with mathematical predictions.     

Validation of atmospheric sounders by correlative measurements

A linear mathematical model for the statistical estimate of the bias and noise of satellite sounders and a case study are presented. The model provides the tool for proper comparison of actual performance of the remote sensing system while in orbit to correlative data sets. The model accounts for: (i) noncoincidence in time and space of satellite and validating systems sampling; (ii) different characteristics of the validated and validating systems, e.g., different vertical resolutions and noise levels. In the case study the model is applied to validation of temperature profile retrievals using radiosondes for the reference.     

PROJECT CRASHING WITH VARIATIONS IN REWARD AND PENALTY FUNCTIONS: SOME MATHEMATICAL PROGRAMMING FORMULATIONS

In this paper some mathematical programming formulations for project crashing in the presence of rewards for timely project completion and penalties for delay are proposed. Three different combinations of reward and penalty structures are considered. A case study with a piecewise linear penalty for delay and a fixed reward for timely completion is presented     

Spectral analysis using Fourier Transform techniques

The present study is intended as a guide for those who wish to undertake spectral analyses using Discrete Fast Fourier Transforms. Points of particular difficulty in using Fourier Transforms are derived in some detail. Experimental results are offered to illustrate the mathematical derivations. Finally the case of a signal with discontinuities along the time-axis is discussed.     

A novel bi-level hierarchy towards available-to-promise in mixed-model assembly line sequencing problems

This article addresses advanced available-to-promise (AATP) in mixed-model assembly line sequencing problems. In the developed framework, customers are prioritized with respect to 11 defined criteria using the technique for order of preference by similarity to ideal solution (TOPSIS) method, and order quantities are calculated using a nonlinear mathematical program. Next, a mixed binary nonlinear mathematical program is developed to determine the optimum sequence of the optimized order quantities to minimize the total lateness. Since the proposed models are intractable, a hybrid genetic algorithm–simulated annealing method is also developed. Finally, an industrial case study is reported, the results of which validate the developed AATP framework.     

An overview of quantitative risk measures for loss of life and economic damage

A comprehensive overview of methods to quantify and limit risks arising from different sources is still missing in literature. Therefore, a study of risk literature was carried out by the authors. This article summarises about 25 quantitative risk measures. A risk measure is defined as a mathematical function of the probability of an event and the consequences of that event. The article focuses mainly on risk measures for loss of life (individual and societal risk) and economic risk, concentrating on risk measurement experiences in The Netherlands. Other types of consequences and some international practices are also considered. For every risk measure the most important characteristics are given: the mathematical formulation, the field of application and the standard set in this field. Some of the measures have been used in a case study to calculate the flood risks for an area in The Netherlands.     

Existence and uniqueness of the traveling front in premixed combustion of porous media

We study a mathematical model of combustion processes in an inert porous media filled with a combustible gaseous mixture. We focus on the phenomenon of a combustion wave driven by a local pressure elevation. In this article, we are concerned with subsonic pressure-driven flames and with the case of a quadratic dependence of the friction force on the velocity of the gaseous mixture. After a suitable non-dimensionalization, the resulting mathematical model includes three nonlinear ordinary differential equations (ODEs). The system contains an unknown parameter V that represents the traveling wave speed. The existence of the traveling wave is proven in this study. It means that the parameter V can be chosen so that the corresponding phase trajectory satisfies the boundary conditions. Moreover, under reasonable assumptions about the monotonicity of the flame front, we prove the uniqueness of the pressure-driven wave.     

Selective withdrawal from an intake channel connected to a reservoir

This paper investigates selective withdrawal from an intake channel connected to a two-layer stratified reservoir using a line sink located at the downstream end of the intake channel. Such a withdrawal scenario is commonly observed at intake channels, skimming operations, and pump intake bays. This study formulates mathematical expressions for such a withdrawal scenario in order to extend our knowledge and to develop a mathematically simpler method in the case where a solution already exists. An expression to compute the incipient Froude number was developed considering the effect of a boundary. Expressions were developed to obtain discharge ratios for the scenarios when the line sink is located at the channel bottom and far away from the channel bottom. When the interface is located below the channel bottom and only at the reservoir, the intake channel itself behaves as a rectangular orifice, and an expression to compute the incipient Froude number for such a case was developed. The mathematical results were compared to the results obtained from a computational fluid dynamics solver and other relevant published studies.