东北大学：某学院应用统计学专业《线性代数》课程教学大纲.pdf

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线性代数作为一种基本的数学工具在数学领域及其他科学领域，如控制理论、数值分析、信息与科学技术、最优化理论、管理科学等学科都有十分重要的应用。通过这门课程，学生可以了解矩阵分析在人类生活和社会发展中的重要地位和作用以及其深远的发展历史。同时学生能够系统掌握代数中的基本概念、基本理论和基本论证方法，提高学生从事科学研究的能力，为进一步学习其它专业课和从事专业研究打下基础。在奠定数学科学知识基础的同时，培养学生的基本运算能力、抽象思维能力、逻辑推理能力和运用所学的知识分析问题、解决问题的能力。培养科学精神、创新意识与应用意识。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。Linear algebra, as a basic mathematical tool, has been applied veryimportantin mathematics andotherscientificfields,suchas controltheory,numerical analysis, information and science and technology整体目标：optimization theory,management science and other disciplinesOverallObjectiveThrough this course, students can understand the important position androleofmatrixanalysisinhuman lifeand socialdevelopmentaswell asits far-reaching development history.At the same time, students cansystematically master the basic concepts, basic theories and basicdemonstration methods of algebra, improve the ability of students toengage in scientific research, and lay a foundation for further learningother specialized courses and engaging in professional research. At thesametimeof laying thefoundation ofmathematical scienceknowledgethe students'basic operation ability,abstract thinking ability,logicalreasoning ability and the ability to use the learned knowledge toanalyzeand solveproblemswill be cultivated.Cultivate scientific spirit, innovation consciousness and applicationconsciousness.Abilityto work as an individual, a team member and aleaderinamultidisciplinaryteam具有扎实的专业基础与学科特长，系统掌握统计与数据分析、智能仿真建模技术、量化管理优化技术、试验设计与分析、项目管理与决策及其相关领域的专门知识与技能。A solid professional foundation and competency, systematical1-1mastery of the specialized knowledge and skills in statistics anddata analysis, intelligent simulation modeling technology,（1）专业目标：quantitativemanagementoptimizationtechnology,Professional Abilityexperimental design and analysis, project management anddecision-making具有扎实的专业基础与学科特长，系统掌握信息通信系统、项目管理与决策及其相关领域专门知识与技能。1-2Have a solid professional foundation and subject expertisemastertheinformationand communicationsystem,project2 /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 线性代数作为一种基本的数学工具在数学领域及其他科学领域，如控制理论、数值分析、信息与科学技术、最优化理论、管理科学等学科都有十分重要的应用。通过这门课程，学生可以了解矩阵分析在人类生活和社会发展中的重要地位和作用以及其深远的发展历史。同时学生能够系统掌握代数中的基本概念、基本理论和基本论证方法，提高学生从事科学研究的能力，为进一步学习其它专业课和从事专业研究打下基础。在奠定数学科学知识基础的同时，培养学生的基本运算能力、抽象思维能力、逻辑推理能力和运用所学的知识分析问题、解决问题的能力。培养科学精神、创新意识与应用意识。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。 Linear algebra, as a basic mathematical tool, has been applied very important in mathematics and other scientific fields, such as control theory, numerical analysis, information and science and technology, optimization theory, management science and other disciplines. Through this course, students can understand the important position and role of matrix analysis in human life and social development as well as its far-reaching development history. At the same time, students can systematically master the basic concepts, basic theories and basic demonstration methods of algebra, improve the ability of students to engage in scientific research, and lay a foundation for further learning other specialized courses and engaging in professional research. At the same time of laying the foundation of mathematical science knowledge, the students' basic operation ability, abstract thinking ability, logical reasoning ability and the ability to use the learned knowledge to analyze and solve problems will be cultivated. Cultivate scientific spirit, innovation consciousness and application consciousness. Ability to work as an individual, a team member and a leader in a multidisciplinary team. （1）专业目标: Professional Ability 1-1 具有扎实的专业基础与学科特长，系统掌握统计与数据分析、智能仿真建模技术、量化管理优化技术、试验设计与分析、项目管理与决策及其相关领域的专门知识与技能。 A solid professional foundation and competency, systematical mastery of the specialized knowledge and skills in statistics and data analysis, intelligent simulation modeling technology, quantitative management optimization technology, experimental design and analysis, project management and decision-making. 1-2 具有扎实的专业基础与学科特长，系统掌握信息通信系统、项目管理与决策及其相关领域专门知识与技能。 Have a solid professional foundation and subject expertise, master the information and communication system, project

management and decision-making and related fields ofexpertise and skills具有扎实的专业基础与学科特长，系统掌握大数据与人工智能系统、项目管理与决策及其相关领域专门知识与技能。Have a solid professional foundation and subject expertise1-3systematically master big data and artificial intelligencesystems, project management and decision-making and relatedfields of expertise and skills具有卓越的技术素养和突出的应用统计学实践能力，具备在应用统计学及其相关领域通过科学技术理论和方法创造性的解决复杂问题、从事学术前沿问题研究的能力。Have excellent technical literacy and outstanding practical1-4ability of applied statistics,have theability to creativelysolvecomplexproblemsthroughscientificandtechnologicaltheoriesand methods in Applied Statisticsand related fields,andengage in the research of academic frontier problems融入辩证唯物主义哲学思想，提升学生对概念、定理的认识深度和对本质的把握，促进学生辩证思维能力的培养。Integrate dialectical materialism philosophy thought, improve2-1students'understandingdepth of concept, theorem and grasp ofessence,and promote the cultivation of studentsdialecticalthinking ability线性代数的理论不仅渗透到了数学的许多分支中，而且在理论物理、理论化学、工程技术、国民经济、生物技术、航天、航海等领域中都有着广泛的应用。该课程对于培养学生的逻（2）德育目标：辑推理和抽象思维能力、空间直观和想象能力具有重要的作Essential Quality用。The theory of linear algebra has not only penetrated into many2-2branches of mathematics,but alsohas a wide range ofapplications in theoretical physics, theoretical chemistry,engineering technology,national economy,biotechnology,aerospace, navigation and other fields. This course plays animportant role in cultivating students' logical reasoning andabstract thinking ability, spatial intuition and imaginationability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SLOs1、理学知识：具有扎实的数指标点1-1：具有较强的演绎推理能力、学基础，能够将数学、自然准确计算能力、分析归纳能力、抽象思科学和专业知识用于解决复维能力，掌握数学、自然科学和相关专杂实际问题。业知识，并使用其建立正确的数学、物1-1. 1-2Science knowledge: have a理学等模型以解释复杂实际问题。solid mathematicalHave strong deductive reasoning ability,foundation, be able to useaccurate calculation ability,analytical and3/10

3 / 10 management and decision-making and related fields of expertise and skills. 1-3 具有扎实的专业基础与学科特长，系统掌握大数据与人工智能系统、项目管理与决策及其相关领域专门知识与技能。 Have a solid professional foundation and subject expertise, systematically master big data and artificial intelligence systems, project management and decision-making and related fields of expertise and skills. 1-4 具有卓越的技术素养和突出的应用统计学实践能力，具备在应用统计学及其相关领域通过科学技术理论和方法创造性的解决复杂问题、从事学术前沿问题研究的能力。 Have excellent technical literacy and outstanding practical ability of applied statistics, have the ability to creatively solve complex problems through scientific and technological theories and methods in Applied Statistics and related fields, and engage in the research of academic frontier problems. （2）德育目标: Essential Quality 2-1 融入辩证唯物主义哲学思想，提升学生对概念、定理的认识深度和对本质的把握，促进学生辩证思维能力的培养。 Integrate dialectical materialism philosophy thought, improve students' understanding depth of concept, theorem and grasp of essence, and promote the cultivation of students' dialectical thinking ability. 2-2 线性代数的理论不仅渗透到了数学的许多分支中，而且在理论物理、理论化学、工程技术、国民经济、生物技术、航天、航海等领域中都有着广泛的应用。该课程对于培养学生的逻辑推理和抽象思维能力、空间直观和想象能力具有重要的作用。 The theory of linear algebra has not only penetrated into many branches of mathematics, but also has a wide range of applications in theoretical physics, theoretical chemistry, engineering technology, national economy, biotechnology, aerospace, navigation and other fields. This course plays an important role in cultivating students' logical reasoning and abstract thinking ability, spatial intuition and imagination ability. 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 1、理学知识：具有扎实的数学基础，能够将数学、自然科学和专业知识用于解决复杂实际问题。 Science knowledge: have a solid mathematical foundation, be able to use 指标点 1-1：具有较强的演绎推理能力、准确计算能力、分析归纳能力、抽象思维能力，掌握数学、自然科学和相关专业知识，并使用其建立正确的数学、物理学等模型以解释复杂实际问题。 Have strong deductive reasoning ability, accurate calculation ability, analytical and 1-1, 1-2

mathematics, natural scienceinductive ability, abstract thinking ability,andprofessional knowledgetomastermathematics,natural scienceandrelated professional knowledge, and use itsolve complexpracticalproblems.toestablishcorrectmathematicalphysicaland other models toexplain complexpracticalproblems.2-1能运用应用统计学的基本原理分析、识别和阐述与本专业相关的复杂实际问1、问题分析：能够借助应题。1-2, 1-3, 2-1用统计学的基本原理、方法Capable of analyzing, identifying and和手段，识别、表达、并通elaboratingcomplexpracticalproblems过文献研究分析复杂实际问related to this major with the applying of题，以获得有效结论。thebasicprinciples ofApplied Statistics2-2能够应用数学、自然科学和工程学的Problem analysis: with the基本原理、方法和手段，针对实际复杂help of the basic principles.工程问题设计针对性的技术方案，并综methodsandmeansofapplied合运用文献、科学基座和技术手段予以statistics, we can identify,解决。express and analyze complex1-3, 1-4, 2-1, 2-2Capable of drawing on the basic principlespractical problems throughliterature research,so astoof applied statistics to design targetedobtaineffectiveconclusionsschemesfor complexpracticalproblems,and using literature, scientific theories andtechnical means to solve them.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 ofknowledge unit(1)理论教学Lecture知识单元序号支撑教学目标11-1, 1-2, 1-3, 1-4Knowledge Unit NoSLOs Supported知识单元名称矩阵乘法和行列式Unit TitleMatrixmultiplication and determinants矩阵的定义Definition of matrix矩阵的初等变换，行最简型矩阵，矩阵的运算Fundamental transformation of matrix,Thesimplestrow form of知识点：matrix,ComputationofmatrixKnowledge Delivery分块矩阵，矩阵运算性质，矩阵的逆Blockmatrix,propertiesofmatrixcomputation,Inverseofmatrix初等矩阵；行列式定义，行列式的运算Fundamental matrix, Definition of determinant, Computation ofdeterminant4/10

4 / 10 mathematics, natural science and professional knowledge to solve complex practical problems. inductive ability, abstract thinking ability, master mathematics, natural science and related professional knowledge, and use it to establish correct mathematical, physical and other models to explain complex practical problems. 1、问题分析: 能够借助应用统计学的基本原理、方法和手段，识别、表达、并通过文献研究分析复杂实际问题，以获得有效结论。 Problem analysis: with the help of the basic principles, methods and means of applied statistics, we can identify, express and analyze complex practical problems through literature research, so as to obtain effective conclusions. 2-1 能运用应用统计学的基本原理分析、识别和阐述与本专业相关的复杂实际问题。 Capable of analyzing, identifying and elaborating complex practical problems related to this major with the applying of the basic principles of Applied Statistics. 1-2, 1-3, 2-1 2-2 能够应用数学、自然科学和工程学的基本原理、方法和手段，针对实际复杂工程问题设计针对性的技术方案，并综合运用文献、科学基座和技术手段予以解决。 Capable of drawing on the basic principles of applied statistics to design targeted schemes for complex practical problems, and using literature, scientific theories and technical means to solve them. 1-3, 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: Knowledge Unit No. 1 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 矩阵乘法和行列式 Matrix multiplication and determinants 知识点: Knowledge Delivery 矩阵的定义 Definition of matrix 矩阵的初等变换，行最简型矩阵, 矩阵的运算 Fundamental transformation of matrix, The simplest row form of matrix, Computation of matrix 分块矩阵，矩阵运算性质，矩阵的逆 Block matrix, properties of matrix computation, Inverse of matrix 初等矩阵；行列式定义，行列式的运算 Fundamental matrix, Definition of determinant, Computation of determinant

行列式定义，分块矩阵定义，线性方程组定义了解：Definition of determinant, block matrix, linear equationRecognizesystem初等变换方法，矩阵的逆求法理解：学习目标：Fundamental transformation methodLearning ObjectivesUnderstandMethod of inverse of matrix矩阵运算性质，行列式的运算掌握：Properties of matrix computation,Computation ofMasterdeterminant2-1理解高等数学理论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 theadvanced mathematics inMoral Objectivesdepictingthepracticalengineeringproblems初等变换方法，矩阵的逆求法重点：Fundamental transformation method.Key PointsMethod of inverse of matrix难点：矩阵运算性质，行列式的运算Focal pointsPropertiesofmatrixcomputation,Computationofdeterminant知识单元序号支撑教学目标：21-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称线性方程组和向量空间Unit TitleSystems of linear equations and Vector spaces向量，向量空间，向量子空间Vectors,Vectorspaces,Subspacesofvectorspaces生成集和线性无关，基和维数Spanning sets and linearindependence,Basis anddimension;知识点：矩阵的秩和线性方程组Rankofamatrixand systemsof linearKnowledge Deliveryequations;坐标和基变换Coordinatesandchangeofbasis内积空间，正交基,施密特正交化过程Innerproductspaces,Orthonormal bases, Gram-schmidt process向量，向量空间，向量子空间,Vectors，Vector了解：spaces,Subspacesofvector spacesRecognize生成集，基和维数Spanningsets,Basisanddimension坐标和基变换；Coordinatesandchangeofbasis；理解：内积，正交和正交集Innerproducts,OrthogonalandUnderstand学习目标：orthonormal sets;Learning Objectives线性相关和线性无关，Lineardependenceand linearindependence;掌握：矩阵的秩和线性方程组RankofamatrixandsystemsMasterof linearequations:施密特正交化过程Gram-schmidtprocess德育目标2-2认知当前全球，数学理论的发展对提升中国工程关键技术及核Moral Objectives心竞争力的重要意义。5/10

5 / 10 学习目标: Learning Objectives 了解: Recognize 行列式定义, 分块矩阵定义，线性方程组定义 Definition of determinant, block matrix, linear equation system 理解: Understand 初等变换方法，矩阵的逆求法 Fundamental transformation method, Method of inverse of matrix 掌握: Master 矩阵运算性质，行列式的运算 Properties of matrix computation, Computation of determinant 德育目标 Moral Objectives 2-1 理解高等数学理论知识对于刻画工程实践问题的重要意义。 Understand the significant meanings of the advanced mathematics in depicting the practical engineering problems. 重点: Key Points 初等变换方法，矩阵的逆求法 Fundamental transformation method, Method of inverse of matrix 难点: Focal points 矩阵运算性质，行列式的运算 Properties of matrix computation, Computation of determinant 知识单元序号: Knowledge Unit No. 2 支撑教学目标: SLOs Supported 1-1，1-2 知识单元名称 Unit Title 线性方程组和向量空间 Systems of linear equations and Vector spaces 知识点: Knowledge Delivery 向量,向量空间,向量子空间 Vectors,Vector spaces, Subspaces of vector spaces 生成集和线性无关, 基和维数 Spanning sets and linear independence，Basis and dimension；矩阵的秩和线性方程组 Rank of a matrix and systems of linear equations；坐标和基变换 Coordinates and change of basis 内积空间，正交基,施密特正交化过程 Inner product spaces,Orthonormal bases, Gram-schmidt process 学习目标: Learning Objectives 了解: Recognize 向量,向量空间,向量子空间,Vectors, Vector spaces,Subspaces of vector spaces 生成集,基和维数 Spanning sets, Basis and dimension; 理解: Understand 坐标和基变换；Coordinates and change of basis；内积, 正交和正交集 Inner products, Orthogonal and orthonormal sets；掌握: Master 线性相关和线性无关,Linear dependence and linear independence; 矩阵的秩和线性方程组 Rank of a matrix and systems of linear equations；施密特正交化过程 Gram-schmidt process 德育目标 Moral Objectives 2-2 认知当前全球，数学理论的发展对提升中国工程关键技术及核心竞争力的重要意义