课程代码

045101341

课程名称

数学建模与实验

英文名称

MathematicalModeling and Experiment

课程类别

专业基础课

课程性质

必修

学时

总学时：40   实验学时：16     

学分

2

开课学期

第3学期

开课单位

计算机科学与工程学院

适用专业

计算机科学与技术

授课语言

英语

先修课程

数学分析、离散数学、线性代数与解析几何、高级程序语言设计、

课程对毕业要求的支撑

本课程对学生达到如下毕业要求有如下贡献：

1.工程知识：掌握数学及相关领域的基础理论知识，并为解决计算机复杂工程问题奠定扎实的理论基础。

2.问题分析：能够应用数学基础知识以及计算机专业基础知识进行计算机复杂工程问题分析、识别、表达的能力。

3.设计/开发解决方案：掌握设计针对复杂计算机相关工程问题的解决方案（包括设计满足特定需求的系统、单元（部件）或工艺流程等）所必须的专业基本研究技能和基本实践技能。

4.研究：掌握基于科学原理并采用科学方法对与计算机相关复杂工程问题进行研究的基本方法和基本理论（文献、数据整理和分析）；掌握基于科学原理并采用科学方法对与计算机相关复杂工程问题进行研究计算机科学与技术问题建模、分析测试技能；掌握基于科学原理并采用科学方法对与计算机相关复杂工程问题进行研究网络工程问题建模、分析测试技能。

5.使用现代工具：能够针对与计算机相关复杂工程问题，开发、选择与使用恰当的技术、资源、现代工程工具和信息技术工具，包括对复杂工程问题的预测与模拟，并能够理解其局限性。

6.个人和团队：培养一定的团队协作能力。

7.沟通：培养专业信息交流与沟通的技能(报告撰写，设计文档，陈述发言，表达及回应指令)

课程目标

完成课程后，学生将具备以下能力：

（1）掌握如何将实际问题转化为数学问题，进而将数学问题的解转化为实际问题的解。

（2）通过学习数学模型以及数学建模案例，学生应用数学知识解决实际问题的能力得到进一步提升。

（3）熟练掌握一门及以上运算软件，如Matlab或Lingo等。

（4）具备运用英语撰写数学建模报告的能力。

课程简介

本课程是研究如何将数学方法和计算机知识结合起来用于解决实际问题的一门交叉学科，是应用数学解决实际问题的重要手段和途径，是连接数学、计算机、与实际工程应用的桥梁。本课程主要介绍数学建模的概述、概率统计模型、图论与决策论模型、计算机经典算法等基本建模方法及求解技术。通过数学模型有关的概念、特征的学习和数学模型应用实例的介绍，培养学生应用数学知识、计算机技术解决实际问题的能力。

实验教学（包括上机学时、实验学时、实践学时）

实验1数学规划模型实验 2学时

实验目的：学习使用Matlab或Lingo软件解决数学规划问题，并分析模型结果及参数的敏感性，提交相应的实验报告。

实验2图论模型实验 2学时

实验目的：针对给定的实际工程问题，建立图论模型，并在计算机上实现算法求解，提交相应的实验报告。

实验3概率模型实验 2学时

实验目的：针对给定的实际工程问题，建立概率模型，并在计算机上实现算法求解，提交相应的实验报告。

实验4差分与动态模型实验  2学时

实验目的：针对给定的实际工程问题，建立差分或动态模型，并在计算机上实现算法求解，提交相应的实验报告。

实验5数据统计模型实验  2学时

实验目的：掌握Matlab或R语言中对常用数据统计方法的调用，对给定的实际工程问题，能选择合适的统计模型并运用计算机对相关数据进行统计分析，提交相应的实验报告。

实验6神经网络与进化计算方法实验  2学时

掌握运用计算机编写或调用神经网络和进化计算算法的方法，针对给定的问题，能利用计算机实现神经网络或进化算法进行求解，提交相应的实验报告。

实验7数学建模综合大实验  4学时

从给定的今年MCM国际数学建模竞赛中的样题或自命题库中，选择1道大题，综合运用数学建模方法进行求解，完成完整的数学建模报告作为课程设计。

教学方法

课程教学以课堂教学、课外作业、综合讨论、上机实验等共同实施

考核方式

本课程注重过程考核，成绩比例为：

课堂表现：10%  作业、上机实验及报告：20%

课程设计：30%  期末考（开卷）:40%

教材及参考书

《MathematicalModeling: Fourth Edition》,Mark M. Meerschaert,机械工业出版社；

参考书：

[1]《数学模型》，姜启源主编，高等教育出版社

[2]《经济数学模型》，洪毅等主编，华南理工大学出版社

[3] AFirst Course in Mathematical Modeling, Frank R. Giordano等编著

制定人及制定时间

陈伟能，2019年4月10日

CourseCode

145153

CourseTitle

Mathematical Modeling

CourseCategory

SpecialtyBasic Courses

CourseNature

CompulsoryCourse

ClassHours

The thirdterm

Credits

ComputerScience and Engineering

Semester

Computerscience and technology, Network engineering, Information security

Institute

English

ProgramOriented

Linearalgebra, probability statistics, mathematical analysis, Clanguage, discrete mathematics, etc.

TeachingLanguage

English

Prerequisites

Linearalgebra, probability statistics, mathematical analysis, Clanguage, discrete mathematics, etc.

Student Outcomes

(Special Training Ability)

This course has the followingcontributions for students to meet the following graduationrequirements:

1. Engineering knowledge:master basic theoretical knowledge of mathematics and relatedfields, and lay a solid theoretical foundation for solving complexcomputer engineering problems.

2. Problem analysis: be ableto analyze, identify and express complex computer engineeringproblems by applying basic mathematical knowledge and basiccomputer professional knowledge.

3. Design/develop solutions:master the basic professional research skills and basic practicalskills which are necessary for designing solutions to complexcomputer-related engineering problems (including designingsystems, units (parts) or processes to meet specificrequirements).

4. Research: master the basicmethods and theories (literature, data sorting and analysis) forthe research of complex engineering problems related to computersbased on scientific principles and using scientific methods;master the skills of modeling, analyzing and testing computerscience and technology related complex engineering problems basedon scientific principles and using scientific methods; master theskills of modeling, analyzing and testing computer related complexengineering problems based on scientific principles and scientificmethods.

5. Use of modern tools: beable to develop, select and use appropriate technology, resources,modern engineering tools, and information technology tools forcomplex computer-related engineering problems, includingprediction and simulation of complex engineering problems, and beable to understand their limitations.

6. Individual and team:cultivate certain teamwork ability.

7.Communication: cultivate professional information exchange andcommunication skills (report writing, document design, statementand speech, expression and instruction response)

CourseObjectives

After finishing the course,students will have the following abilities:

(1) to master how to practicalproblems into math problems, and then the solution of mathematicalproblems can be converted into solution of practical problems.

(2) through the mathematicalmodel and the mathematical modeling case study, students' abilityof applied mathematics knowledge to solve practical problems forfurther improvement.

(3) master a foreign and abovecalculation software, such as Matlab or Lingo.

(4)learn to write scientific papers.

CourseDescription

This course is aninterdisciplinary subject that studies how to combine mathematicalmethods and computer knowledge to solve practical problems. It isan important means and approach to solve practical problems byapplying mathematics. It is also a bridge connecting mathematics,computer and practical engineering applications. This coursemainly introduces the overview of mathematical modeling,elementary model, probability and statistics model, graph theoryand decision theory model, computer classical algorithm and otherbasic modeling methods and solving techniques, through theintroduction of specific examples to enable students to master thebasic ideas, methods and types of mathematical modeling. Throughthe study of the concepts and characteristics of mathematicalmodels and the introduction of the application examples ofmathematical models, students are trained to apply mathematicalknowledge and computer technology to solve practical problems.

ExperimentalTeaching

Experiment 1: mathematicalprogramming model experiment  2 credit hours

Experimental objective: learnhow to use Matlab or Lingo software to solve mathematicalprogramming problems, analyze the sensitivity of model results andparameters, and submit corresponding experimental reports.

Experiment 2 : diagram theorymodel experiment  2 credit hours

Experimental objective: set upa graph theory model for a given practical engineering problem,and solve the algorithm on a computer, and submit thecorresponding experimental report.

Experiment 3: probabilisticmodel experiment  2 credit hours

Experimental objective:establish a probabilistic model for a given practical engineeringproblem, implement algorithm solution on a computer, and submitthe corresponding experimental report.

Experiment 4 : differentialand dynamic model experiment  2 credit hours

Experimental objective: for agiven practical engineering problem, the differential or dynamicmodel is established, and the algorithm is solved on the computer,and the corresponding experimental report is submitted.

Experiment 5: data statisticsmodel experiment  2 credit hours

Experimental objective: masterMatlab or R language to the commonly used data statistics method,for a given practical engineering problems, can choose theappropriate statistical model and use the computer to statisticalanalysis of the relevant data, submit the correspondingexperimental report.

Experiment 6: neural networkand evolutionary computing method experiment   2 credit hours

Experimental objective: masterthe method of using computer to write or call neural network andevolutionary computing algorithm, aiming at a given problem, canuse computer to realize neural network or evolutionary algorithmto solve, submit the corresponding experimental report.

Experiment 7: mathematicalmodeling comprehensive university experiment  4 credit hours

Experimentalobjective: from the sample questions or self-styled question bankin this year's MCM international mathematical modeling contest,choose one big question, solve the problem comprehensively withmathematical modeling method, and complete the completemathematical modeling report as the course design.

TeachingMethod

Thecourse teaching is implemented by classroom teaching,extracurricular homework, comprehensive discussion and computerexperiment.

ExaminationMethod

This course pays attention toprocess evaluation, achievement ratio for:

Class performance: 10%

Assignments, experiments andreports: 20%

Course report : 30%

Final Exam (Open Book): 40%

TeachingMaterials and Reference Books

Mathematical Modeling: FourthEdition, Mark m. Meerschaert, Mathematical industry press;

Reference:

[1] mathematical model, editedby jiang qiyuan, higher education press

[2] economic mathematicalmodel, edited by hong yi et al., south China university oftechnology press

[3]A First Course in Mathematical Modeling, Frank r. Giordano et al

Preparedby Whom and When

Wei-NengChen, 2019.4.10