课程简介：
数学实验是一门新型的数学课程，它主要的特点是让学生结合使用计算机解决实际问题的过程来学习数学的一些原理、思想和重要应用方法。课程特别注重发挥学生的主观能动性和培养学生的综合应用能力。
数学实验课程采取案例式教学法。
课程包含的数学知识和方法模块主要由三个部分的内容组成：数学软件学习，某些应用数学方法(主要是计算方法、优化方法等)，和某些新分支的知识介绍(这些分支的研究往往密切联系计算机的应用)。由于采取案例式的教学，每个案例通常都蕴涵了建模方法。
课程的学时为36－54，2/3为理论讲授，1/3为上机实验，另外需配约1/3的课外机时。
理论讲授的内容如下：
1)数学软件入门：介绍数学软件Mathematica的基本运算和绘图操作；介绍利用软件的程序编制；
2)数学方法的介绍：
（1）计算方法（方程求根的Newton方法,微分方程的Euler方法，预报－校正法，Runge-Kutte法；数值积分的梯形法和Simpsom），这部分内容相应的教学案例是“怎样计算π”、“导弹追踪问题”、“行星的轨道和位置” 、“教堂顶部曲面面积的计算方法”；
（2）某些离散问题的数学方法(差分方程问题，仿真方法，密码学等)，这部分内容相应的教学案例是“个人住房抵押贷款与其他金融问题“，“库存问题的仿真方法”，“Hill密码的加密、解密和破译”和“投入产出分析”等；
（3）优化方法和最优问题(线性规划，变分法)，这部分内容相应的教学案例是“合金工厂的生产规划”，“寻找最速降线”;
3）数学某些分支的简介（混沌，分形，金融数学），这部分内容相应的教学案例是 “ 从物种增长的Malthus模型到浑沌”，“浅谈分形”和“股票期权定价问题的Black－Scholes方程和二叉树方法”。
根据课时的情况上述内容可以作适当调整和选择。
Mathematics Experiment is a new style course of mathematics. Students will study some mathematical principles, theories and applied methods during the process of solving practical problems with help of computer. Great attention is paid to give full play of subjective initiative as well as the ability of comprehensive application.
The methodology of case study is preferred in this course.
This course is composed in three modules: (1)mathematics software, (2)basic methods of applied mathematics(numerical methods, optimization, etc.),(3)introduction of some new math branches closely related to computer application. Modeling is implicated in each case.
The teaching hours are about 36 to 54. 2/3 : lecturing; 1/3: experiment; 1/3 running computer after class.
The contents of lecturing as follows
1) Basic course of mathematics software including: Basic operations and graphical handling of mathematica, programming by means of software.
2) Introduction of math methods:
(1) Computational methods, such as Newton’s method of finding zeros ; Euler scheme, Predict- correct scheme and Runge-Kutta scheme to solve ODE; Trapezoidal formula and Simpson’s formula for numerical integration. The related cases are “How to calculate π”, “Missile tracing”, “Trajectory and position of a plane”, and “How to calculate the area of a church dom”.
(2) Methods in discrete mathematics, such as finite difference equation, simulation, coding, etc. The related cases are “Mortgage loan and other financial problems”, “Simulation of inventory problem”, “Adding cipher and extricating for Hill code”, and “Input-output analysis”.
(3) Optimization, such as linear programming, and variation method. The related cases are “Production plan for a factory”, and “Finding a fastest path of falling down”.
3) Brief introduction of some math branches, such as chaos, fractor, and financial math. The related cases are “From Malthus model to chaos, population growth”, “Fractor”, “Black-Scholes Equation and binomal tree method to study stock options”.
The above contents are just suggestion, they can be adjusted and partly chosen according to the real situation.
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