高等代数选讲课程中学生数学素质和数学能力的培养

探讨在高等代数选讲课程中,引导学生对经典的数学理论进行再发现的研究和探索,从而培养学生在代数方面的数学素养,提高学生的数学研究和创新能力。     

医学专业数学结构教学的重要性

现代医学从定性描述日趋定量化、精确化发展进程中 ,越来越需要广博的数学知识作基础。医学基础、临床医学和预防医学中已出现和正在出现的许多实际问题 ,越来越多的要数学去提供更多的工具和方法。临床工作者如何从大量的临床实践中获得精确的数学模型 ,从而对临床病例进行定量的描述 ,这就要求我们数学教育者如何更有效地提高数学教育质量。笔者从近十年的医学数学教学中发现“数学结构”教学对医学生数学教学尤为重要。一、所谓“数学结构”教学 ,是指在讲清基本的定义、概念、定律、定理、法则等一系列理论基础上 ,重点分析这些公式、定…     

数学解题方法探究

审题的重要性和内含,在数学解题过程中从审题角度对数学解题方法进行探究。     

数学实验课的实践与研究

介绍我院在数学课程建设和教学改革中开设数学实验课的认识和体会,提出数学实验的课程观和所遵循的原则,强调数学实验课必须有特色和实效性,并结合数学实验课的教学实例分析进行数学实验的方法,最后,提出数学实验课研究的问题和方向。     

数学在医学应用中存在的问题

数学在医学领域里的作用 ,不仅要求对医学问题要有深刻的认识 ,对数学本身要求也要有所发展。如对模型数学进行改造扩充 ,使之能适应于医学及其它生命学科应用的需要 ,这是解决许多生命学科问题的一个方向。在研究模糊数学的过程中应对生命现象的本质进行深入思考 ,从中得到有益的启示 ,同时也应充分利用现有的数学构架和其它数学分支取得的成果 ,丰富完善模糊数学 ,使之成为一门内涵广泛、严格意义上的独立数学学科分支 ,继而应用于医学和其它生命学科 ,促进生命学科的发展。     

从数学建模竞赛看医药高等数学教学改革

通过数学建模竞赛培养学生多方面能力,包括培养学生的想象力、洞察力、创造力、计算机应用能力、论写作能力、合作能力等,提出建模教学对医药高等数学教学改革的推进作用。     

医学化学中的数学问题

就医学化学以及化学研究中的一些数学问题,提出并加以讨论,希望引起中学和医学院校对化学中的数学问题的学习和教学予以重视。     

儿童数学学习不良的回顾和展望

数学学习不良日益成为学习不良研究的新热点,在总结近年来儿童数学学习不良研究成果的基础上,从数学学习不良的概念认识、诊断鉴定模型、认知特点等方面进行述评,最后根据已有研究成果对成人学习不良的研究提出未来研究要解决的问题。     

基因突变的元间数学描述

本文应用元间数学及作者新提出的元间数第二减法规则,描述并分析了有序的DNA大分子的四种结构性突变。元间数学量由秩和序两部分构成。元间数学量与DNA大分子一级结构序列成一一对应关系。用传统的申农定义的信息量来度量DNA包含的线性信息量,丢掉了一大部分信息。申农信息熵只考虑了元间数学量秩部分含有的由核苷酸数目决定的信息量,丢掉了元间序中含有的关于核苷酸排列顺序的信息量。元间数学能较完好地描述和分析有序的DNA大分子,且易于用计算机处理。     

数学中的思维方法

简述数学学习中常用的10种思维方法,为学生提高学习数学的效率,促进“数学大脑”的形成给予了新的启示。     

Mathematical modeling of drug dissolution

The dissolution of a drug administered in the solid state is a pre-requisite for efficient subsequent transport within the human body. This is because only dissolved drug molecules/ions/atoms are able to diffuse, e.g. through living tissue. Thus, generally major barriers, including the mucosa of the gastro intestinal tract, can only be crossed after dissolution. Consequently, the process of dissolution is of fundamental importance for the bioavailability and, hence, therapeutic efficacy of various pharmaco-treatments. Poor aqueous solubility and/or very low dissolution rates potentially lead to insufficient availability at the site of action and, hence, failure of the treatment in vivo, despite a potentially ideal chemical structure of the drug to interact with its target site. Different physical phenomena are involved in the process of drug dissolution in an aqueous body fluid, namely the wetting of the particle's surface, breakdown of solid state bonds, solvation, diffusion through the liquid unstirred boundary layer surrounding the particle as well as convection in the surrounding bulk fluid. Appropriate mathematical equations can be used to quantify these mass transport steps, and more or less complex theories can be developed to describe the resulting drug dissolution kinetics. This article gives an overview on the current state of the art of modeling drug dissolution and points out the assumptions the different theories are based on. Various practical examples are given in order to illustrate the benefits of such models. This review is not restricted to mathematical theories considering drugs exhibiting poor aqueous solubility and/or low dissolution rates, but also addresses models quantifying drug release from controlled release dosage forms, in which the process of drug dissolution plays a major role.     

Mathematical modeling of drug delivery

Due to the significant advances in information technology mathematical modeling of drug delivery is a field of steadily increasing academic and industrial importance with an enormous future potential. The in silico optimization of novel drug delivery systems can be expected to significantly increase in accuracy and easiness of application. Analogous to other scientific disciplines, computer simulations are likely to become an integral part of future research and development in pharmaceutical technology. Mathematical programs can be expected to be routinely used to help optimizing the design of novel dosage forms. Good estimates for the required composition, geometry, dimensions and preparation procedure of various types of delivery systems will be available, taking into account the desired administration route, drug dose and release profile. Thus, the number of required experimental studies during product development can be significantly reduced, saving time and reducing costs. In addition, the quantitative analysis of the physical, chemical and potentially biological phenomena, which are involved in the control of drug release, offers another fundamental advantage: The underlying drug release mechanisms can be elucidated, which is not only of academic interest, but a pre-requisite for an efficient improvement of the safety of the pharmaco-treatments and for effective trouble-shooting during production. This article gives an overview on the current state of the art of mathematical modeling of drug delivery, including empirical/semi-empirical and mechanistic realistic models. Analytical as well as numerical solutions are described and various practical examples are given. One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design parameters of the dosage form on the resulting drug concentration time profiles at the site of action and the pharmacodynamic effects will become predictable.     

数学应用三题

题 1　设计制剂无菌操作窗 ,使上部为半圆形 ,下部为矩阵 ,周长 2 m ,如达透光面积最大 ,问弧半径、矩形高取何值 ?解 :　设弧半径为 R,矩形高为 h,底为 2 R,建立方程组 :面积 A=12 πR2 2 R　　　　　　　　　　　　　 ( 1)周长 S=2 R 2 h πR=2　　　　　　　　　　　 ( 2 )解此方程组 :h=12 ( 2 - 2 R-πR) ( 3 )将 ( 3 )代入 ( 1) ,得 :A =12 πR2 R( 2 - 2 R-πR) =12 πR2 2 R- 2 R2 -πR2=2 R- 2 R2 -πR2 ( 4 )A对 R求导得 :A R=2 - 4 R-πR ( 5 )令 A R=0 ,得R( 4 π) =2　　R=24 π=0 .2 8( m) ( 6)将 R=…     

Mathematical representations of cancer chemotherapy effects

Predictive models have been developed to simulate cancer cell populations under treatment with cytotoxic drugs, with both direct-acting and cell cycle specific drugs being considered. Models of cell growth kinetics have been combined with simple pharmacokinetic models to complete the cell-drug interaction system. The models depend on knowing the distribution of generation time in the cell population, the cell-drug interaction, and the local concentration of the drug at the effective site. All of the quantities can be obtained, in principle, from separate experiments and combined to form a model describing several aspects of the cell-drug response system.     

《医药数理统计方法》教学体会

以作者的教学体会,论述在教学中采用数理统计与专业知识相结合、试验设计为导向的教学方法,培养学生的统计思维和试验设计能力。