离散数学教学大纲Discrete Mathematics Subject Syllabus，课程信息SubjectInformation课程编号：开课学期：63100213020Subject IDSemester课程分类：所属课群：专业教育PA专业基础MFCategorySection课程学分：总学时/周：348/12Credit PointsTotal Hours/Weeks理论学时：实验学时：480LECT. HoursEXP. HoursPBL学时：实践学时/周：00PBL HoursPRAC. Hours/Weeks东北大学悉尼智能科技学院开课学院：Sydney Smart适用专业：计算机科学与技术CSTCollegeTechnology CollegeStreamNortheasternUniversity课程模式：课程属性：选修Elective自建NEUPatternMode赵媛中方课程协调人：成绩记载方式：百分制MarksNEU CoordinatorZhao YuanResult Type先修课程：高等数学建模（一）Advancedmathematicalmodeling（1),Requisites高等数学建模（二）Advancedmathematicalmodeling（2）英文参考教材无NoneENTextbooks中文参考教材王新心等，《离散数学》，东北大学出版社，2011年，第一版CN Textbooks教学资源：https://www.mhhe.com/rosenResources课程负责人(撰写人)：提交日期：赵媛4/10/2023Subject DirectorSubmitted Date任课教师(含负责人)赵媛Taught by审核人：批准人：韩鹏史闻博Checked byApproved by批准日期：4/10/2023Approved Date1 / 10
1 / 10 离散数学 教学大纲 Discrete Mathematics Subject Syllabus 一、课程信息 Subject Information 课程编号: Subject ID 3100213020 开课学期: Semester 6 课程分类: Category 专业教育 PA 所属课群: Section 专业基础 MF 课程学分: Credit Points 3 总学时/周: Total Hours/Weeks 48/12 理论学时: LECT. Hours 48 实验学时: EXP. Hours 0 PBL 学时: PBL Hours 0 实践学时/周: PRAC. Hours/Weeks 0 开课学院: College 东北大学 悉尼智能科技学院 Sydney Smart Technology College Northeastern University 适用专业: Stream 计算机科学与技术 CST 课程属性: Pattern 选修 Elective 课程模式: Mode 自建 NEU 中方课程协调人: NEU Coordinator 赵媛 Zhao Yuan 成绩记载方式: Result Type 百分制 Marks 先修课程: Requisites 高等数学建模（一）Advanced mathematical modeling (1), 高等数学建模（二）Advanced mathematical modeling (2) 英文参考教材: EN Textbooks 无 None 中文参考教材: CN Textbooks 王新心等，《离散数学》，东北大学出版社，2011 年，第一版 教学资源: Resources https://www.mhhe.com/rosen 课程负责人(撰写人): Subject Director 赵媛 提交日期: Submitted Date 4/10/2023 任课教师(含负责人): Taught by 赵媛 审核人: Checked by 韩鹏 批准人: Approved by 史闻博 批准日期: Approved Date 4/10/2023
二、教学目标SubjectLearningObjectives（(SLOs）注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject离散数学是研究计算机科学的基本数学工具。离散数学具有概念较多、理论性较强、应用性较广的特点。主要包括集合论、代数系统、图论、数理逻辑四方面内容。通过本门课程学习培养学生概括及逻辑推理的能力，使用所学知识分析和解决实际问题的能力，为学习后续课程打下良好的基础。培养学生具备一定的科学思维、科学精神和科学素质，树立科学思想以及正确的世界观和方法论。Discretemathematics is abasic mathematical tool forthe study of整体目标：computer science. Discrete Mathematics has many characteristics,Overall Objectivestrong theoretical and wide applicability.It mainly includes fouraspects: set theory, algebra system, graph theory and mathematicallogic.This course cultivates students'ability of generalization andlogical reasoning,as well astheirabilitytoanalyze and solvepracticalproblems with what they have learned, thus laying a good foundationfor subsequent courses. Train students to have certain scientificthinking, scientific spirit and scientific quality,establish scientificthought and correct world outlook and methodology.掌握离散数学的基本概念和基本原理。1-1Master the basic concepts and principles of discretemathematics初步掌握处理离散结构所必须的描述工具和方法，为学习后续课程打下基础。1-2Tomaster the description tools and methods of dealing withdiscrete structure, and lay the foundation for learning thefollow-up courses（1）专业目标：培养学生抽象思维、提高概括及逻辑推理的能力Professional Ability1-3Cultivate students' abstract thinking, improve the ability ofgeneralizationand logical reasoning使学生具有良好的开拓专业理论的素质，及使用所学知识分析和解决实际问题的能力。1-4To enable students to have a good quality of developingprofessional theory, and the ability to use the knowledge toanalyze and solve practical problems.理解离散数学知识对于刻画工程实践问题的重要意义。2-1Understand the significant meanings of the discretemathematicsindepictingthepractical engineeringproblems.（2）德育目标：认知大国工匠精神的内涵及时代意义，增强专业认同感、民Essential Quality族责任感。2-2Understand the connotation and significance of the craftsmanspirit of a great country and enhance our professional identityand senseofnational responsibility2 /10
2 / 10 二、教学目标 Subject Learning Objectives (SLOs) 注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数 Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject. 整体目标: Overall Objective 离散数学是研究计算机科学的基本数学工具。离散数学具有概念较 多、理论性较强、应用性较广的特点。主要包括集合论、代数系统、 图论、数理逻辑四方面内容。通过本门课程学习培养学生概括及逻 辑推理的能力，使用所学知识分析和解决实际问题的能力，为学习 后续课程打下良好的基础。培养学生具备一定的科学思维、科学精 神和科学素质，树立科学思想以及正确的世界观和方法论。 Discrete mathematics is a basic mathematical tool for the study of computer science. Discrete Mathematics has many characteristics, strong theoretical and wide applicability. It mainly includes four aspects: set theory, algebra system, graph theory and mathematical logic. This course cultivates students' ability of generalization and logical reasoning, as well as their ability to analyze and solve practical problems with what they have learned, thus laying a good foundation for subsequent courses. Train students to have certain scientific thinking, scientific spirit and scientific quality, establish scientific thought and correct world outlook and methodology. （1）专业目标: Professional Ability 1-1 掌握离散数学的基本概念和基本原理。 Master the basic concepts and principles of discrete mathematics. 1-2 初步掌握处理离散结构所必须的描述工具和方法，为学习后 续课程打下基础。 To master the description tools and methods of dealing with discrete structure, and lay the foundation for learning the follow-up courses. 1-3 培养学生抽象思维、提高概括及逻辑推理的能力 Cultivate students' abstract thinking, improve the ability of generalization and logical reasoning 1-4 使学生具有良好的开拓专业理论的素质，及使用所学知识分 析和解决实际问题的能力。 To enable students to have a good quality of developing professional theory, and the ability to use the knowledge to analyze and solve practical problems. （2）德育目标: Essential Quality 2-1 理解离散数学知识对于刻画工程实践问题的重要意义。 Understand the significant meanings of the discrete mathematics in depicting the practical engineering problems. 2-2 认知大国工匠精神的内涵及时代意义，增强专业认同感、民 族责任感。 Understand the connotation and significance of the craftsman spirit of a great country and enhance our professional identity and sense of national responsibility
课程教学目标与毕业要求的对应关系MatrixofGA&SLOs毕业要求GA指标点GAIndex教学目标SLOs2、问题分析：能够应用数学、自然科学和工程科学的基本指标点2-1：能够应用数学、自然科学和原理、方法和手段，识别、工程科学的基本原理、方法和手段，分1-1,1-2,1-3,表达、并通过文献研究分析析、识别、表达本专业相关的复杂工程1-4, 2-1复杂工程问题，以获得有效问题。结论。3、设计/开发解决方案：能够设计针对复杂工程问题的解决方案，设计满足特定需指标点3-1：能够设计针对本专业相关复求的系统、单元或流程，并杂工程问题的解决方案，能够设计和开1-3，1-4，2-1、能够在设计环节中体现创新发实现特定功能、满足特定需求的计算2-2意识，考虑社会、健康、安机、软件或网络系统。全、法律、文化以及环境等因素。4、研究：能够基于科学原理并采用科学方法对复杂工程指标点4-1：能够基于科学原理并采用科问题进行研究，包括设计实1-3,1-4, 2-1,学方法，在本专业相关理论指导下对复验、分析与解释数据、并通2-2杂工程问题设计实验进行研究。过信息综合得到合理有效的结论。9、个人与团队：能够在多学指标点9-1：能够认识团队协作的重要科背景下的团队中承担个性，具有强烈的团队协作意识和能力、1-4,2-1,2-2体、团队成员以及负责人的卓越的组织管理能力、较强的表达能力角色。和人际交往能力。10、沟通：能够就本专业复杂工程问题与业界同行及社会公众进行有效沟通和交指标点10-1：能够就计算机领域相关复流，包括撰写报告和设计文杂工程问题与业界同行及社会公众进行1-4,2-1,2-2稿、陈述发言、清晰表达或有效沟通和交流，能够通过口头或书面回应指令。具备一定的国际方式实现有效表达。视野，能够在跨文化背景下进行沟通和交流。三、教学内容Content(Topics)注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减Note:Filled in both CN and EN,extend or reducebased on the actual numbers of knowledge unit(1)理论教学Lecture3/10
3 / 10 课程教学目标与毕业要求的对应关系 Matrix of GA & SLOs 毕业要求 GA 指标点 GA Index 教学目标 SLOs 2、问题分析：能够应用数学、 自然科学和工程科学的基本 原理、方法和手段，识别、 表达、并通过文献研究分析 复杂工程问题，以获得有效 结论。 指标点 2-1：能够应用数学、自然科学和 工程科学的基本原理、方法和手段，分 析、识别、表达本专业相关的复杂工程 问题。 1-1，1-2，1-3， 1-4，2-1 3、设计/开发解决方案：能 够设计针对复杂工程问题的 解决方案，设计满足特定需 求的系统、单元或流程，并 能够在设计环节中体现创新 意识，考虑社会、健康、安 全、法律、文化以及环境等 因素。 指标点 3-1：能够设计针对本专业相关复 杂工程问题的解决方案，能够设计和开 发实现特定功能、满足特定需求的计算 机、软件或网络系统。 1-3，1-4，2-1、 2-2 4、研究：能够基于科学原理 并采用科学方法对复杂工程 问题进行研究，包括设计实 验、分析与解释数据、并通 过信息综合得到合理有效的 结论。 指标点 4-1：能够基于科学原理并采用科 学方法，在本专业相关理论指导下对复 杂工程问题设计实验进行研究。 1-3，1-4，2-1， 2-2 9、个人与团队：能够在多学 科背景下的团队中承担个 体、团队成员以及负责人的 角色。 指标点 9-1：能够认识团队协作的重要 性，具有强烈的团队协作意识和能力、 卓越的组织管理能力、较强的表达能力 和人际交往能力。 1-4，2-1，2-2 10、沟通：能够就本专业复 杂工程问题与业界同行及社 会公众进行有效沟通和交 流，包括撰写报告和设计文 稿、陈述发言、清晰表达或 回应指令。具备一定的国际 视野，能够在跨文化背景下 进行沟通和交流。 指标点 10-1：能够就计算机领域相关复 杂工程问题与业界同行及社会公众进行 有效沟通和交流，能够通过口头或书面 方式实现有效表达。 1-4，2-1，2-2 三、教学内容 Content (Topics) 注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减 Note: Filled in both CN and EN, extend or reduce based on the actual numbers of knowledge unit (1) 理论教学 Lecture
知识单元序号支撑教学目标：11-1,1-2,1-4,2-1Knowledge Unit No.SLOs Supported知识单元名称集合论SetTheoryUnit Title集合的基本概念和运算：集合的概念及其表示、集合的基本运算、包含排斥原理Basic concepts and operations of set: concept and representation of set,basic operations of set, inclusion exclusion principle二元关系：序偶与笛卡尔乘积、关系及关系表示、关系的性质、复知识点：合关系和逆关系、关系的闭包运算、等价关系与等价类、序关系Knowledge DeliveryBinary relations: product of order pairs and Descartes, relations andtheir representations, properties of relations, composite relations andinverse relations, closure operations of relations, equivalence relationsandequivalenceclasses,andorderrelations集合的定义与表示方法，序偶与笛卡尔积，复合关系和逆关系了解：The definition and representation of set, ordered pairRecognizeand Cartesian product, composite relation and inverserelation包含排斥定理，关系的性质，等价关系与等价类，偏序关系理解：学习目标：Inclusion exclusion theorem, properties of relation,UnderstandLearning Objectivesequivalencerelationandequivalenceclass,partial orderrelation集合的基本运算，关系矩阵与关系图的表示方法，闭包的求法，哈斯图表示方法掌握：The basic operation of set, the representation ofrelationMastermatrix and graph, the solution of closure and therepresentation of Hass diagram理解离散数学知识对于刻画工程实践问题的重要意义。德育目标Understand the significant meanings of the discrete mathematics inMoral Objectivesdepicting the practical engineering problems.集合的基本运算；The basic operation of set,包含排斥定理；Inclusion exclusion theorem;关系的性质：重点：Properties of relation;Key Points等价类；Equivalence class;闭包的求法；The solution of closure;哈斯图。4 / 10
4 / 10 知识单元序号: Knowledge Unit No. 1 支撑教学目标: SLOs Supported 1-1,1-2,1-4,2-1 知识单元名称 Unit Title 集合论 Set Theory 知识点: Knowledge Delivery 集合的基本概念和运算：集合的概念及其表示、集合的基本运算、 包含排斥原理 Basic concepts and operations of set: concept and representation of set, basic operations of set, inclusion exclusion principle 二元关系：序偶与笛卡尔乘积、关系及关系表示、关系的性质、复 合关系和逆关系、关系的闭包运算、等价关系与等价类、序关系 Binary relations: product of order pairs and Descartes, relations and their representations, properties of relations, composite relations and inverse relations, closure operations of relations, equivalence relations and equivalence classes, and order relations 学习目标: Learning Objectives 了解: Recognize 集合的定义与表示方法，序偶与笛卡尔积，复合关系 和逆关系 The definition and representation of set, ordered pair and Cartesian product, composite relation and inverse relation 理解: Understand 包含排斥定理，关系的性质，等价关系与等价类，偏 序关系 Inclusion exclusion theorem, properties of relation, equivalence relation and equivalence class, partial order relation 掌握: Master 集合的基本运算，关系矩阵与关系图的表示方法，闭 包的求法，哈斯图表示方法 The basic operation of set, the representation of relation matrix and graph, the solution of closure and the representation of Hass diagram 德育目标 Moral Objectives 理解离散数学知识对于刻画工程实践问题的重要意义。 Understand the significant meanings of the discrete mathematics in depicting the practical engineering problems. 重点: Key Points 集合的基本运算； The basic operation of set; 包含排斥定理； Inclusion exclusion theorem; 关系的性质； Properties of relation; 等价类； Equivalence class; 闭包的求法； The solution of closure; 哈斯图
Hass diagram包含排斥定理；Inclusion exclusion theorem;关系矩阵与关系图的表示方法：难点：The representation of relation matrix and relation graph,Focal points闭包的求法；The solution of closure;哈斯图。Hass diagram知识单元序号支撑教学目标21-1,1-2,1-3,2-1Knowledge Unit No.SLOs Supported知识单元名称代数系统AlgebraicSystemUnit Title代数系统的一般概念和性质：二元运算及性质、二元运算的特殊元素、代数系统、代数系统的同态与同构General concepts and properties of algebraic systems:binaryoperations and properties,special elements of binary operations,algebraic systems,homomorphism and Isomorphismof algebraic知识点：systemsKnowledge Delivery几个典型的代数系统：半群、群、子群、循环群和置换群、陪集与拉格朗日定理、环与域Several typical algebraic systems: semigroup,group,subgroup,cyclicgroup and permutation group, coset and Lagrange theorem, ring andfield二元运算及性质，代数系统，代数系统的同态与同构各种典型代数系统在构成上的差异了解：Binary operation and properties, algebraic system,Recognizehomomorphism and Isomorphism of algebraic system,differences in composition of various typical algebraicsystems学习目标：二元运算的特殊元素，群及子群的概念及其基本性Learning Objectives质，元素的阶，拉格朗日定理理解：Special elements of binary operation, concepts andUnderstandbasic properties of groups and subgroups, order ofelements,Lagrange theorem半群的证明，不同代数系统的判定，陪集的求法掌握：Theproofof semigroup,thedeterminationofdifferentMasteralgebraic systems, and the solution of coset理解离散数学知识对于刻画工程实践问题的重要意义。德育目标Moral ObjectivesUnderstand the significant meanings of the discrete mathematics in5/10
5 / 10 Hass diagram. 难点: Focal points 包含排斥定理； Inclusion exclusion theorem; 关系矩阵与关系图的表示方法； The representation of relation matrix and relation graph; 闭包的求法； The solution of closure; 哈斯图。 Hass diagram. 知识单元序号: Knowledge Unit No. 2 支撑教学目标: SLOs Supported 1-1,1-2,1-3,2-1 知识单元名称 Unit Title 代数系统 Algebraic System 知识点: Knowledge Delivery 代数系统的一般概念和性质：二元运算及性质、二元运算的特殊元 素、代数系统、代数系统的同态与同构 General concepts and properties of algebraic systems: binary operations and properties, special elements of binary operations, algebraic systems, homomorphism and Isomorphism of algebraic systems 几个典型的代数系统：半群、群、子群、循环群和置换群、陪集与 拉格朗日定理、环与域 Several typical algebraic systems: semigroup, group, subgroup, cyclic group and permutation group, coset and Lagrange theorem, ring and field 学习目标: Learning Objectives 了解: Recognize 二元运算及性质，代数系统，代数系统的同态与同构， 各种典型代数系统在构成上的差异 Binary operation and properties, algebraic system, homomorphism and Isomorphism of algebraic system, differences in composition of various typical algebraic systems 理解: Understand 二元运算的特殊元素，群及子群的概念及其基本性 质，元素的阶，拉格朗日定理 Special elements of binary operation, concepts and basic properties of groups and subgroups, order of elements, Lagrange theorem 掌握: Master 半群的证明，不同代数系统的判定，陪集的求法 The proof of semigroup, the determination of different algebraic systems, and the solution of coset 德育目标 Moral Objectives 理解离散数学知识对于刻画工程实践问题的重要意义。 Understand the significant meanings of the discrete mathematics in
depictingthepractical engineeringproblems二元运算的特殊元素；Special elements of binary operation;半群的证明：The proof of semigroup,群的一般概念；Thegeneral conceptofgroup;重点：群的基本性质；Key PointsThe basic properties of groups;元素的阶；The order of elements;陪集的求法；The solution of coset;拉格朗日定理。Lagrange theorem群的概念及其基本性质：The concept of group and its basic properties,难点：元素的阶；Focal pointsThe order of elements;整环与域的判定。The determination of integral ring and field。知识单元序号：支撑教学目标31-1,1-2,1-4,2-2Knowledge Unit No.SLOs Supported知识单元名称图论GraphTheoryUnit Title图的一般概念与性质：图的基本概念、图的连通性、赋权图的最短路径、图的矩阵表示General concepts and properties of graph: basic concepts of graph,知识点：connectivity of graph, shortest path of weighted graph, matrixKnowledge Deliveryrepresentation of graph几种特殊的图：欧拉图、哈密尔顿图、二部图、平面图、树Several special graphs: Euler graph, Hamiltonian graph, bipartitegraph, planar graph, tree图论的教学内容及其在计算机领域中的应用，简单图的主要特征，图的连通，点割集与边割集，图的同构，二部图了解：Theteaching content of graph theory and its application学习目标：Recognizein computer field, the main characteristics of simpleLearning Objectivesgraph, graph connectivity, vertex cut set and edge cutset, graph isomorphism, bipartite graph理解：握手定理，图的矩阵表示，欧拉回路与欧拉图，哈密Understand尔顿回路与哈密尔顿图，欧拉公式，平面图与树的概6 /10
6 / 10 depicting the practical engineering problems. 重点: Key Points 二元运算的特殊元素； Special elements of binary operation; 半群的证明； The proof of semigroup; 群的一般概念； The general concept of group; 群的基本性质； The basic properties of groups; 元素的阶； The order of elements; 陪集的求法； The solution of coset; 拉格朗日定理。 Lagrange theorem. 难点: Focal points 群的概念及其基本性质； The concept of group and its basic properties; 元素的阶； The order of elements; 整环与域的判定。 The determination of integral ring and field。 知识单元序号: Knowledge Unit No. 3 支撑教学目标: SLOs Supported 1-1,1-2,1-4,2-2 知识单元名称 Unit Title 图论 Graph Theory 知识点: Knowledge Delivery 图的一般概念与性质：图的基本概念、图的连通性、赋权图的最短 路径、图的矩阵表示 General concepts and properties of graph: basic concepts of graph, connectivity of graph, shortest path of weighted graph, matrix representation of graph 几种特殊的图：欧拉图、哈密尔顿图、二部图、平面图、树 Several special graphs: Euler graph, Hamiltonian graph, bipartite graph, planar graph, tree 学习目标: Learning Objectives 了解: Recognize 图论的教学内容及其在计算机领域中的应用，简单图 的主要特征，图的连通，点割集与边割集，图的同构， 二部图 The teaching content of graph theory and its application in computer field, the main characteristics of simple graph, graph connectivity, vertex cut set and edge cut set, graph isomorphism, bipartite graph 理解: Understand 握手定理，图的矩阵表示，欧拉回路与欧拉图，哈密 尔顿回路与哈密尔顿图，欧拉公式，平面图与树的概
念及性质Handshake theorem, matrix representation of graph.Euler circuit and Euler graph, Hamilton circuit andHamilton graph,Eulerformula,planar graphand tree赋权图的最短路径的求法，欧拉图与哈密尔顿图的判定方法，最小生成树和最优树的求取方法。掌握：The method of finding the shortest path of weightedMastergraph, the method of determining Euler graph andHamilton graph, the method of finding the minimumspanningtreeandtheoptimaltree认知大国工匠精神的内涵及时代意义，增强专业认同感、民族责任感。德育目标Understand the connotation and significance ofthe craftsman spirit of aMoral Objectivesgreat country and enhance our professional identity and sense ofnational responsibility握手定理的应用：Theapplicationof handshaketheorem;赋权图的最短路径的求法；How to find the shortest path of weighted graph;重点：图的各种矩阵表示方法；Key PointsVarious matrix representations of graphs欧拉图、哈密尔顿图的判定方法；The judgment method of Euler graph and Hamilton graph;最小生成树和最优树的求取方法。The method to get the minimum spanning tree and the optimal tree.赋权图的最短路径的求法；难点：Howtofind the shortest path of weighted graph;Focal points最小生成树和最优树的求取方法。The method to get the minimum spanning tree and the optimal tree.支撑教学目标：知识单元序号41-1,1-2,1-3,2-2Knowledge Unit No.SLOs Supported知识单元名称数理逻辑MathematicalLogicUnit Title命题逻辑：命题与联接词、命题公式及其分类、等值演算、其他联接词、对偶与范式、推理理论Propositional logic:propositions and connectives,propositional知识点：formula and its classification, equivalent calculus, other connectives,Knowledge Deliveryduality and paradigm,reasoning theory谓词逻辑：谓词公式及其解释、谓词公式的等值式与蕴含式、前束范式、谓词逻辑推理理论Predicate logic:predicate formula and its explanation, equivalent7/10
7 / 10 念及性质 Handshake theorem, matrix representation of graph, Euler circuit and Euler graph, Hamilton circuit and Hamilton graph, Euler formula, planar graph and tree 掌握: Master 赋权图的最短路径的求法，欧拉图与哈密尔顿图的判 定方法，最小生成树和最优树的求取方法。 The method of finding the shortest path of weighted graph, the method of determining Euler graph and Hamilton graph, the method of finding the minimum spanning tree and the optimal tree. 德育目标 Moral Objectives 认知大国工匠精神的内涵及时代意义，增强专业认同感、民族责任 感。 Understand the connotation and significance of the craftsman spirit of a great country and enhance our professional identity and sense of national responsibility. 重点: Key Points 握手定理的应用； The application of handshake theorem; 赋权图的最短路径的求法； How to find the shortest path of weighted graph; 图的各种矩阵表示方法； Various matrix representations of graphs; 欧拉图、哈密尔顿图的判定方法； The judgment method of Euler graph and Hamilton graph; 最小生成树和最优树的求取方法。 The method to get the minimum spanning tree and the optimal tree. 难点: Focal points 赋权图的最短路径的求法； How to find the shortest path of weighted graph; 最小生成树和最优树的求取方法。 The method to get the minimum spanning tree and the optimal tree. 知识单元序号: Knowledge Unit No. 4 支撑教学目标: SLOs Supported 1-1,1-2,1-3,2-2 知识单元名称 Unit Title 数理逻辑 Mathematical Logic 知识点: Knowledge Delivery 命题逻辑：命题与联接词、命题公式及其分类、等值演算、其他联 接词、对偶与范式、推理理论 Propositional logic: propositions and connectives, propositional formula and its classification, equivalent calculus, other connectives, duality and paradigm, reasoning theory 谓词逻辑：谓词公式及其解释、谓词公式的等值式与蕴含式、前束 范式、谓词逻辑推理理论 Predicate logic: predicate formula and its explanation, equivalent
formula and implicationformula of predicateformula,toe in paradigm,reasoning theory of predicate logic命题逻辑的基本概念，命题联结词的概念，谓词逻辑了解：的基本概念Thebasic concepts of propositional logic,propositionalRecognizeconnectives and predicatelogic命题逻辑的等值式与蕴涵式，命题公式的真值表，主合取范式及主析取范式理解：Equivalence and implication of propositional logic学习目标：Understandtruth table of propositional formula,principalLearning Objectivesconjunctiveparadigm andprincipaldisjunctiveparadigm等值公式的证明方法，命题逻辑的推理过程，谓词逻辑等值演算，谓词逻辑推理过程掌握：The proof method of equivalent formula, reasoningMasterprocess of propositional logic, equivalent calculus ofpredicatelogic,reasoningprocess ofpredicate logic认知大国工匠精神的内涵及时代意义，增强专业认同感、民族责任感。德育目标Understand the connotation and significance of the craftsman spirit ofaMoral Objectivesgreat country and enhance our professional identity and sense ofnational responsibility命题公式的真值表；The truth table of propositional formula等值公式的证明方法；The proof method of equivalent formula;主合取范式及主析取范式：重点：Main conjunctiveparadigmandmaindisjunctiveparadigmKey Points命题逻辑的推理过程；Thereasoningprocess ofpropositional logic谓词逻辑等值演算；Predicate logicequivalentcalculus谓词逻辑推理规则。Inference rules of predicate logic主合取范式及主析取范式：Main conjunctive paradigm and main disjunctive paradigm;难点：命题逻辑的推理过程；Focal pointsThe reasoning process of propositional logic;谓词逻辑推理规则。Inference rules of predicate logic8/10
8 / 10 formula and implication formula of predicate formula, toe in paradigm, reasoning theory of predicate logic 学习目标: Learning Objectives 了解: Recognize 命题逻辑的基本概念，命题联结词的概念，谓词逻辑 的基本概念 The basic concepts of propositional logic, propositional connectives and predicate logic 理解: Understand 命题逻辑的等值式与蕴涵式，命题公式的真值表，主 合取范式及主析取范式 Equivalence and implication of propositional logic, truth table of propositional formula, principal conjunctive paradigm and principal disjunctive paradigm 掌握: Master 等值公式的证明方法，命题逻辑的推理过程，谓词逻 辑等值演算，谓词逻辑推理过程 The proof method of equivalent formula, reasoning process of propositional logic, equivalent calculus of predicate logic, reasoning process of predicate logic 德育目标 Moral Objectives 认知大国工匠精神的内涵及时代意义，增强专业认同感、民族责任 感。 Understand the connotation and significance of the craftsman spirit of a great country and enhance our professional identity and sense of national responsibility. 重点: Key Points 命题公式的真值表； The truth table of propositional formula; 等值公式的证明方法； The proof method of equivalent formula; 主合取范式及主析取范式； Main conjunctive paradigm and main disjunctive paradigm; 命题逻辑的推理过程； The reasoning process of propositional logic; 谓词逻辑等值演算； Predicate logic equivalent calculus; 谓词逻辑推理规则。 Inference rules of predicate logic. 难点: Focal points 主合取范式及主析取范式； Main conjunctive paradigm and main disjunctive paradigm; 命题逻辑的推理过程； The reasoning process of propositional logic; 谓词逻辑推理规则。 Inference rules of predicate logic
四、教学安排TeachingSchedule注：可根据实际情况增减行数Note: Please add/reduce lines based on subject.学时(周)Hour(Week)教学内容Teaching Content理论实验课外实践集中实践LECT.EXP.PBLPRAC.12集合论SetTheory12代数系统Algebraic System12图论Graph Theory12数理逻辑Mathematical Logic48总计Total五、教学方法TeachingMethodology注：可根据实际情况增减行数或修改内容Note: Please add/reduce lines or revise content based on subject.勾选Check教学方法与特色TeachingMethodology&Characters多媒体教学：基于信息化设备的课堂教学团Multi-media-based lecturing实践能力传授：理论与行业、实际案例相结合团Combiningtheorywithindustrialpracticalproblems课程思政建设：知识讲授与德育相结合团Knowledgedeliverywithethic educationPBL教学：问题驱动的分组学习与交流口Problem-based learning其他：口Other:六，成绩评定Assessment注：可根据实际情况增减行数或修改内容Note:Please add/reduce lines or revise content based on subject考核环节：环节负责人：赵媛平时BehaviorDirectorAssessment Content给分形式：课程总成绩比重(%)：50百分制MarksResult TypePercentage(%)9/10
9 / 10 四、教学安排 Teaching Schedule 注：可根据实际情况增减行数 Note: Please add/reduce lines based on subject. 教学内容 Teaching Content 学时(周) Hour(Week) 理论 LECT. 实验 EXP. 课外实践 PBL 集中实践 PRAC. 集合论 Set Theory 12 代数系统 Algebraic System 12 图论 Graph Theory 12 数理逻辑 Mathematical Logic 12 总计 Total 48 五、教学方法 Teaching Methodology 注：可根据实际情况增减行数或修改内容 Note: Please add/reduce lines or revise content based on subject. 勾选 Check 教学方法与特色 Teaching Methodology & Characters 多媒体教学：基于信息化设备的课堂教学 Multi-media-based lecturing 实践能力传授：理论与行业、实际案例相结合 Combining theory with industrial practical problems 课程思政建设：知识讲授与德育相结合 Knowledge delivery with ethic education ☐ PBL 教学：问题驱动的分组学习与交流 Problem-based learning ☐ 其他: Other: 六、成绩评定 Assessment 注：可根据实际情况增减行数或修改内容 Note: Please add/reduce lines or revise content based on subject. 考核环节: Assessment Content 平时 Behavior 环节负责人: Director 赵媛 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 50
平时成绩以学生出勤和学生作业完成情况综合评定，其中，学生出勤占平时成绩的40%，学生作业完成情况占平时成绩的60%。考核方式According to attendance and assignments performance of the students,Measuresthe mark is evaluated,where attendance accounts for 40%,assignmentsperformanceaccountsfor60%.考核环节：环节负责人：赵媛期末FinalAssessment ContentDirector给分形式：课程总成绩比重(%):50百分制MarksResult TypePercentage (%)考核方式：考试，2小时答题。MeasuresExamination, twohours.七，改进机制ImprovementMechanism注：未尽事宜以教学团队以及学院教学指导委员会商定为准。Note: Matters not covered in this file shall be determined by TAB of SSTC, NEU.教学大纲改进机制SubjectSyllabusImprovementMechanism考核周期(年):修订周期(年)：44Check Period (YR)Revise Period (YR)课程负责人根据课程教学内容与人才培养目标组织课程团队讨论并修改教学大纲，报分管教学工作副院长审核后由执行院长批准。改进措施：The subject coordinator shall be responsibleforthe syllabus discussionMeasuresand improvement, and the revised version shall be submitted to deputydean(teachingaffairs)for reviewingthen to executive dean forapprovement.成绩评定改进机制AssessmentImprovementMechanism考核周期(年)修订周期(年)：11Check Period (YR)Revise Period (YR)课程负责人根据课程教学内容、课堂教学效果以及成绩分布，对课程教学方法和成绩评定环节进行改进，并同步优化评定办法。改进措施The subject coordinator shall revise the syllabus based on the teachingMeasurescontent,effectandresultdistributionwhileoptimizetheassessmentmeasures.10/10
10 / 10 考核方式: Measures 平时成绩以学生出勤和学生作业完成情况综合评定，其中，学生出 勤占平时成绩的 40%，学生作业完成情况占平时成绩的 60%。 According to attendance and assignments performance of the students, the mark is evaluated, where attendance accounts for 40%, assignments performance accounts for 60%. 考核环节: Assessment Content 期末 Final 环节负责人: Director 赵媛 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 50 考核方式: Measures 考试，2 小时答题。 Examination, two hours. 七、改进机制 Improvement Mechanism 注：未尽事宜以教学团队以及学院教学指导委员会商定为准。 Note: Matters not covered in this file shall be determined by TAB of SSTC, NEU. 教学大纲改进机制 Subject Syllabus Improvement Mechanism 考核周期(年): Check Period (YR) 4 修订周期(年): Revise Period (YR) 4 改进措施: Measures 课程负责人根据课程教学内容与人才培养目标组织课程团队讨论 并修改教学大纲，报分管教学工作副院长审核后由执行院长批准。 The subject coordinator shall be responsible for the syllabus discussion and improvement, and the revised version shall be submitted to deputy dean (teaching affairs) for reviewing then to executive dean for approvement. 成绩评定改进机制 Assessment Improvement Mechanism 考核周期(年): Check Period (YR) 1 修订周期(年): Revise Period (YR) 1 改进措施: Measures 课程负责人根据课程教学内容、课堂教学效果以及成绩分布，对课 程教学方法和成绩评定环节进行改进，并同步优化评定办法。 The subject coordinator shall revise the syllabus based on the teaching content, effect and result distribution while optimize the assessment measures