课程代码

045101341

课程名称

数学建模与实验

英文名称

Mathematical Modeling 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。

教学内容与学时分配

第一章：绪论 3学时

本章介绍什么是数学建模，以及数学建模的意义，强调数学建模方法对国家建设和经济发展的重要作用；其次介绍基本的建模过程和数学建模的分类；最后了解在国内外的建模比赛情况，以及数学建模这门课程的章节划分和考核情况。

第二章：规划模型 3学时

首先，简单地介绍了一般优化问题的建模方法；然后从不同角度介绍了优化问题的分类，包括线性规划和非线性规划等；其中，详细介绍了整数规划、多目标问题的规划模型。其次，分别讲述了如何对线性建模和非线性建模进行建模，并举例说明。最后，介绍了动态规划的建模过程以及举例示范如何对动态规划问题进行建模。

第三章：图论模型 3学时

首先，简单地介绍图的定义，以及高性能网络中地内联网络的逻辑图；其次，详细地分别介绍了在图论模型中几种最典型的代表性问题的建模方法，包括最短路径问题、旅行商问题、最大最小流问题、图匹配问题、基于树问题、图填色问题、项目调度问题和社交网络问题。

第四章：概率模型 3学时

首先，对什么是概率模型进行介绍，包括离散的概率模型和连续的概率模型，分别举例说明了这两种概率模型的建模过程；然后介绍了概率模型的仿真方法，包括蒙特卡洛仿真和排队系统；然后，介绍了概率随机系统，从实验设计到实验结果具体地阐述了马尔可夫过程和系统置信度；最后，概率决策的建模方法分别在决策树、博弈理论、条件概率、模糊系统四个问题上展示建模的方法及过程。

第五章：差分模型和动态模型 3学时

介绍了差分模型的建模过程和基本类型。差分方程可以描述离散时间段上的客观对象的动态变化过程，差分模型是对现实世界中随时间变化的动态过程建立的模型。通过实例介绍了现有的基本类型：线性常系数差分方程组和非线性差分方程组。

第六章：数据统计模型 3学时

本章从描述性统计、回归分析、相关分析、因子分析、正交实验设计、集群和分类、假设检验七个方面对数据统计模型进行介绍。首先，对数据统计的描述方法进行了介绍；其次，在统计建模中，回归分析被用来分析变量之间的关系，简单的介绍了线性回归、多项式回归、分段式回归、逻辑回归、非线性回归的数学模型。然后，在相关性分析中，描述了现象之间的相关性以及相关系数的定义等；因子分析作为另外一种统计方法，举例说明因子分析的过程。还介绍了正交实验设计的设计过程。集群也是一种统计模型，并且介绍了集群模型的分类，以及典型的集群算法k-means算法，一些典型的分类算法也被简单的介绍；最后讲述了假设检验这种推理统计过程，并举例说明。

第七章： 神经网络和进化算法 3学时

本章首先介绍了人工智能的来源以及定义；其次介绍了神经网络和进化计算的区别与联系；并介绍了神经网络和进化计算中典型的算法流程。

复习课 3学时

复习所学过的重点知识，介绍考试相关须知内容。

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：

平时作业和课堂表现：20%上机实验及报告：30%课程设计：50%

教材及参考书

《Mathematical Modeling: 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] A First 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

Course Code

145153

Course Title

Mathematical Modeling

Course Category

Specialty Basic Courses

Course Nature

Compulsory Course

Class Hours

The third term

Credits

Computer Science and Engineering

Semester

Computer science and technology, Network engineering, Information security

Institute

English

ProgramOriented

Linear algebra, probability statistics, mathematical analysis, C language, discrete mathematics, etc.

Teaching Language

English

Prerequisites

Linear algebra, probability statistics, mathematical analysis, C language, discrete mathematics, etc.

 Student Outcomes

 (Special Training Ability)

 This course has the following contributions for students to meet the following graduation requirements:

 1. Engineering knowledge: master basic theoretical knowledge of mathematics and related fields, and lay a solid theoretical foundation for solving complex computer engineering problems.

 2. Problem analysis: be able to analyze, identify and express complex computer engineering problems by applying basic mathematical knowledge and basic computer professional knowledge.

 3. Design/develop solutions: master the basic professional research skills and basic practical skills which are necessary for designing solutions to complex computer-related engineering problems (including designing systems, units (parts) or processes to meet specific requirements).

 4. Research: master the basic methods and theories (literature, data sorting and analysis) for the research of complex engineering problems related to computers based on scientific principles and using scientific methods; master the skills of modeling, analyzing and testing computer science and technology related complex engineering problems based on scientific principles and using scientific methods; master the skills of modeling, analyzing and testing computer related complex engineering problems based on scientific principles and scientific methods.

 5. Use of modern tools: be able to develop, select and use appropriate technology, resources, modern engineering tools, and information technology tools for complex computer-related engineering problems, including prediction and simulation of complex engineering problems, and be able to understand their limitations.

 6. Individual and team: cultivate certain teamwork ability.

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

Course Objectives

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

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

 (2) through the mathematical model and the mathematical modeling case study, students' ability of applied mathematics knowledge to solve practical problems for further improvement.

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

(4) learn to write scientific papers.

Course Description

 This course is an interdisciplinary subject that studies how to combine mathematical methods and computer knowledge to solve practical problems. It is an important means and approach to solve practical problems by applying mathematics. It is also a bridge connecting mathematics, computer and practical engineering applications. This course mainly introduces the overview of mathematical modeling, elementary model, probability and statistics model, graph theory and decision theory model, computer classical algorithm and other basic modeling methods and solving techniques, through the introduction of specific examples to enable students to master the basic ideas, methods and types of mathematical modeling. Through the study of the concepts and characteristics of mathematical models and the introduction of the application examples of mathematical models, students are trained to apply mathematical knowledge and computer technology to solve practical problems.

Teaching Content and Class Hours Distribution

 Chapter 1: introduction  3 credit hours

 This chapter introduces what is mathematical modeling, and the significance of mathematical modeling; Secondly, the basic modeling process and the classification of mathematical modeling are introduced. Finally, the situation of modeling competitions at home and abroad is introduced, as well as the chapter division and assessment of mathematical modeling.

 Chapter 2: planning model  3 credit hours

 Firstly, the modeling method of general optimization problem is briefly introduced. Then the classification of optimization problems is introduced from different angles, including linear programming and nonlinear programming. Among them, the programming models of integer programming and multi-objective problem are introduced in detail. Secondly, how to model linear modeling and nonlinear modeling are discussed respectively, and some examples are given. Finally, the modeling process of dynamic programming is introduced and an example is given to demonstrate how to model dynamic programming problems.

 Chapter 3: graph theory model   3 credit hours

 Firstly, the definition of the graph and the logic graph of the inlining network in the high-performance network are briefly introduced. Secondly, several modeling methods of the most typical representative problems in graph theory model are introduced in detail, including shortest path problem, travel salesman problem, maximum and minimum flow problem, graph matching problem, tree-based problem, graph coloring problem, project scheduling problem and social network problem.

 Chapter 4: probability model  3 credit hours

 Firstly, what is a probability model is introduced, including discrete probability model and continuous probability model, respectively illustrating the modeling process of these two probability models. Then the simulation method of probability model is introduced, including monte carlo simulation and queuing system. Then, the probabilistic stochastic system is introduced, and the markov process and system confidence are described from experimental design to experimental results. Finally, the modeling method of probabilistic decision shows the modeling method and process of decision tree, game theory, conditional probability and fuzzy system respectively.

 Chapter 5: difference model and dynamic model   3 credit hours

 The modeling process and basic types of difference models are introduced.

 The difference equation can describe the dynamic change process of the objective object in the discrete time period. The existing basic types, linear constant coefficient difference equations and nonlinear difference equations, are introduced by examples.

 Chapter 6: data statistical model  3 credit hours

 This chapter introduces the data statistical model from seven aspects: descriptive statistics, regression analysis, correlation analysis, factor analysis, orthogonal experimental design, clustering and classification, and hypothesis testing. Firstly, the description method of data statistics is introduced. Secondly, in statistical modeling, regression analysis is used to analyze the relationship between variables. Mathematical models of linear regression, polynomial regression, piecewise regression, logistic regression and nonlinear regression are simply introduced. Then, in the correlation analysis, the correlation between phenomena and the definition of correlation coefficient are described. Factor analysis, as another statistical method, illustrates the process of factor analysis with examples. The design process of orthogonal experimental design is also introduced. Cluster is also a kind of statistical model. It also introduces the classification of cluster model and the k-means algorithm of typical clustering algorithm. Some typical classification algorithms are also simply introduced. Finally, this paper describes the inference statistical process of hypothesis testing and gives an example.

 Chapter 7: neural network and evolutionary algorithm  3 credit hours

 This chapter first introduces the source and definition of artificial intelligence; Secondly, the difference and relation between neural network and evolutionary computation are introduced. The typical algorithm flow in neural network and evolutionary computation is also introduced.

 Recitation  3 credit hours

Review the key knowledge learned, introduce the examination related instructions

 Teaching Method

The course teaching is implemented by classroom teaching, extracurricular homework, comprehensive discussion and computer experiment.

Examination Method

 This course pays attention to process evaluation, achievement ratio for: regular assignments and class performance: 20%

 computer experiments and reports: 30%

course report : 50%

Teaching Materials and Reference Books

 Mathematical Modeling: Fourth Edition, Mark m. Meerschaert, Mathematical industry press;

 Reference:

 [1] mathematical model, edited by jiang qiyuan, higher education press

 [2] economic mathematical model, edited by hong yi et al., south China university of technology press

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

Prepared by Whom and When

Wei-Neng Chen, 2019.4.10

课程代码

045101341

课程名称

数学建模与实验

英文名称

Mathematical Modeling 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：

平时作业和课堂表现：20%上机实验及报告：30%课程设计：50%

教材及参考书

《Mathematical Modeling: 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] A First 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

Course Code

145153

Course Title

Mathematical Modeling

Course Category

Specialty Basic Courses

Course Nature

Compulsory Course

Class Hours

The third term

Credits

Computer Science and Engineering

Semester

Computer science and technology, Network engineering, Information security

Institute

English

ProgramOriented

Linear algebra, probability statistics, mathematical analysis, C language, discrete mathematics, etc.

Teaching Language

English

Prerequisites

Linear algebra, probability statistics, mathematical analysis, C language, discrete mathematics, etc.

 Student Outcomes

 (Special Training Ability)

 This course has the following contributions for students to meet the following graduation requirements:

 1. Engineering knowledge: master basic theoretical knowledge of mathematics and related fields, and lay a solid theoretical foundation for solving complex computer engineering problems.

 2. Problem analysis: be able to analyze, identify and express complex computer engineering problems by applying basic mathematical knowledge and basic computer professional knowledge.

 3. Design/develop solutions: master the basic professional research skills and basic practical skills which are necessary for designing solutions to complex computer-related engineering problems (including designing systems, units (parts) or processes to meet specific requirements).

 4. Research: master the basic methods and theories (literature, data sorting and analysis) for the research of complex engineering problems related to computers based on scientific principles and using scientific methods; master the skills of modeling, analyzing and testing computer science and technology related complex engineering problems based on scientific principles and using scientific methods; master the skills of modeling, analyzing and testing computer related complex engineering problems based on scientific principles and scientific methods.

 5. Use of modern tools: be able to develop, select and use appropriate technology, resources, modern engineering tools, and information technology tools for complex computer-related engineering problems, including prediction and simulation of complex engineering problems, and be able to understand their limitations.

 6. Individual and team: cultivate certain teamwork ability.

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

Course Objectives

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

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

 (2) through the mathematical model and the mathematical modeling case study, students' ability of applied mathematics knowledge to solve practical problems for further improvement.

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

(4) learn to write scientific papers.

Course Description

 This course is an interdisciplinary subject that studies how to combine mathematical methods and computer knowledge to solve practical problems. It is an important means and approach to solve practical problems by applying mathematics. It is also a bridge connecting mathematics, computer and practical engineering applications. This course mainly introduces the overview of mathematical modeling, elementary model, probability and statistics model, graph theory and decision theory model, computer classical algorithm and other basic modeling methods and solving techniques, through the introduction of specific examples to enable students to master the basic ideas, methods and types of mathematical modeling. Through the study of the concepts and characteristics of mathematical models and the introduction of the application examples of mathematical models, students are trained to apply mathematical knowledge and computer technology to solve practical problems.

 Experimental Teaching

 Experiment 1: mathematical programming model experiment  2 credit hours

 Experimental objective: learn how to use Matlab or Lingo software to solve mathematical programming problems, analyze the sensitivity of model results and parameters, and submit corresponding experimental reports.

 Experiment 2 : diagram theory model experiment  2 credit hours

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

 Experiment 3: probabilistic model experiment  2 credit hours

 Experimental objective: establish a probabilistic model for a given practical engineering problem, implement algorithm solution on a computer, and submit the corresponding experimental report.

 Experiment 4 : differential and dynamic model experiment  2 credit hours

 Experimental objective: for a given practical engineering problem, the differential or dynamic model is established, and the algorithm is solved on the computer, and the corresponding experimental report is submitted.

 Experiment 5: data statistics model experiment  2 credit hours

 Experimental objective: master Matlab or R language to the commonly used data statistics method, for a given practical engineering problems, can choose the appropriate statistical model and use the computer to statistical analysis of the relevant data, submit the corresponding experimental report.

 Experiment 6: neural network and evolutionary computing method experiment   2 credit hours

 Experimental objective: master the method of using computer to write or call neural network and evolutionary computing algorithm, aiming at a given problem, can use computer to realize neural network or evolutionary algorithm to solve, submit the corresponding experimental report.

 Experiment 7: mathematical modeling comprehensive university experiment  4 credit hours

Experimental objective: from the sample questions or self-styled question bank in this year's MCM international mathematical modeling contest, choose one big question, solve the problem comprehensively with mathematical modeling method, and complete the complete mathematical modeling report as the course design.

Teaching Method

The course teaching is implemented by classroom teaching, extracurricular homework, comprehensive discussion and computer experiment.

Examination Method

 This course pays attention to process evaluation, achievement ratio for: regular assignments and class performance: 20%

 computer experiments and reports: 30%

course report : 50%

Teaching Materials and Reference Books

 Mathematical Modeling: Fourth Edition, Mark m. Meerschaert, Mathematical industry press;

 Reference:

 [1] mathematical model, edited by jiang qiyuan, higher education press

 [2] economic mathematical model, edited by hong yi et al., south China university of technology press

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

Prepared by Whom and When

Wei-Neng Chen, 2019.4.10