《微积分I II》课程中英文简介.doc

统计学院微积分I II课程中英文简介Calculus 课程代码：120014A/120024ACourse Code：120014A/120024A课程名称：微积分I IICourse Name：Calculus I II学 时：64Periods：64学 分：4Credits：4考核方式：考试Assessment：Examination先修课程：无Preparatory Courses：None微积分是我校经济、管理类专业的一门必修课，为二学期课程。通过本课程的学习，使学生掌握微积分学的基本概念、基本理论及基本运算技能，逐步培养学生抽象概括问题的能力、逻辑推理能力、空间想象能力和比较熟练的运算能力，培养学生综合运用所学知识去分析和解决有关实际问题的能力，为学生学习后续课程和进一步获得数学知识奠定必要的数学基础。本课程的主要内容包括： 函数、极限与连续、导数与微分、中值定理与导数的应用、不定积分、定积分、无穷级数、多元函数微积分学、微分方程、差分方程。Calculus is an important two-semester basic compulsory for economics and management professional in our university. Though the studying of this course, students should maser basic concepts, basic theory and basic computing skills of calculus. The course can cultivate students ability of abstracting general problems, logical reasoning, spatial imagination and skilled computing. In addition, the course can cultivate students the ability to analyze and solve practical problems though using their knowledge learnt, and lay a basic for students to study relevant courses and further to acquire mathematical knowledge.The content of the course includes: functions, limits and continuity, derivative and differential mean value theorem and the application of derivatives, indefinite integral, definite integral, infinite series, multi-function calculus, differential equations, difference equations.微积分课程中英文简介Calculus课程代码：120033ACourse Code：120033A课程名称：微积分Course Name：Calculus学 时：48Periods：48学 分：3Credits：3考核方式：考试Assessment：Examination先修课程：无Preparatory Courses：None微积分是我校经济、管理类专业的一门重要基础必修课。通过本课程的学习，使学生掌握微积分学的基本概念、基本理论及基本运算技能。培养学生综合运用所学知识去分析和解决有关实际问题的能力，为学生学习有关专业课程和进一步获得数学知识奠定必要的数学基础。本课程的内容包括：函数、极限与连续、导数与微分、中值定理与导数的应用、不定积分。Calculus is an important basic compulsory for economics and management professional in our university. Though the studying of this course, students should maser basic concepts, basic theory and basic computing skills of calculus. The course can cultivate students the ability to analyze and solve practical problems though using their knowledge learnt, and lay a basic for students to study relevant courses and further to acquire mathematical knowledge.The content of the course includes: functions, limits and continuity, derivative and differential mean value theorem and the application of derivatives, indefinite integral.线性代数课程中英文简介Linear Algebra课程代码：120043ACourse Code：120043A课程名称：线性代数Course Name：Linear Algebra学 时：48Periods：48学 分：3Credits：3考核方式：考试Assessment：Examination先修课程：微积分Preparatory Courses：Calculus本课程是我校本科经济、管理类专业数学课中三门最重要的基础课之一，为一学期课程。通过本课程的学习，学生不仅能够获得线性代数的基本知识，而且能够得到“两个基本训练”即：代数学基本方法的训练、线性代数基本计算的训练；同时培养和训练了学生运用数学方法分析和解决问题的能力，扩展了学生的数学知识，为进一步学习有关专业课程提供必要的数学基础。本课程的内容包括：行列式（行列式的定义、性质和按行(列)展开、克莱姆法则），矩阵（矩阵运算、逆矩阵、分块矩阵、初等矩阵与初等变换、矩阵的秩），线性方程组与向量空间（欧氏空间），矩阵的特征值与特征向量，二次型（用配方法和正交变换法化二次型为标准形、正定二次型）。This course is one of the most important undergraduate basic courses of economics and management professional math in our university. Students can not only get a basic knowledge of linear algebra, and can obtain “two basic training”: the training about algebra basic methods and the training about basic knowledge of linear algebra. Meanwhile, the course will culture and train the ability of students using mathematics analyze and solve problems and expand the mathematical knowledge, as well as provide the necessary mathematical foundation to further learn relevant courses. The content of this course include: determinant (the definition, nature and by row (column) Expand, Cramers rule), matrix (matrix operations, inverse matrix, block matrix, elementary matrix with elementary transformation, rank of matrix), linear equations and vector space (Euclidean space), matrix eigenvalue and vector, the second type (with the Method and orthogonal transformation of the standard quadratic form, positive definite quadratic form). 线性代数课程中英文简介Linear Algebra I课程代码：120053ACourse Code：120053A课程名称：线性代数Course Name：Linear Algebra学 时：48Periods：48学 分：3Credits：3考核方式：考试Assessment：Examination先修课程：微积分Preparatory Courses：Calculus本课程是我校本科经济、管理类专业数学课中三门最重要的基础课之一，为一学期课程。通过本课程的学习，学生不仅能够获得线性代数的基本知识，而且能够得到“两个基本训练”即：代数学基本方法的训练、线性代数基本计算的训练；同时培养和训练了学生运用数学方法分析和解决问题的能力，扩展了学生的数学知识，为进一步学习有关专业课程提供必要的数学基础。本课程的内容包括：行列式（行列式的定义、性质和按行(列)展开、克莱姆法则），矩阵（矩阵运算、逆矩阵、分块矩阵、初等矩阵与初等变换、矩阵的秩），线性方程组与向量空间（欧氏空间），矩阵的特征值与特征向量，二次型（用配方法和正交变换法化二次型为标准形、正定二次型）。This course is one of the most important undergraduate basic courses of economics and management professional math in our university. Students can not only get a basic knowledge of linear algebra, and can obtain “two basic training”: the training about algebra basic methods and the training about basic knowledge of linear algebra. Meanwhile, the course will culture and train the ability of students using mathematics analyze and solve problems and expand the mathematical knowledge, as well as provide the necessary mathematical foundation to further learn relevant courses. The content of this course include: determinant (the definition, nature and by row (column) Expand, Cramers rule), matrix (matrix operations, inverse matrix, block matrix, elementary matrix with elementary transformation, rank of matrix), linear equations and vector space (Euclidean space), matrix eigenvalue and vector, the second type (with the Method and orthogonal transformation of the standard quadratic form, positive definite quadratic form). 线性代数II课程中英文简介Linear Algebra II课程代码：120063ACourse Code：120063A课程名称：线性代数Course Name：Linear Algebra学 时：48Periods：48学 分：3Credits：3考核方式：考试Assessment：Examination先修课程：微积分Preparatory Courses：Calculus本课程是我校本科经济、管理类专业数学课中三门最重要的基础课之一，为一学期课程。通过本课程的学习，学生不仅能够获得线性代数的基本知识，而且能够得到“两个基本训练”即：代数学基本方法的训练、线性代数基本计算的训练；同时培养和训练了学生运用数学方法分析和解决问题的能力，扩展了学生的数学知识，为进一步学习有关专业课程提供必要的数学基础。本课程的内容包括：行列式（行列式的定义、性质和按行(列)展开、克莱姆法则），矩阵（矩阵运算、逆矩阵、分块矩阵、初等矩阵与初等变换、矩阵的秩），线性方程组与向量空间（欧氏空间），矩阵的特征值与特征向量，二次型（用配方法和正交变换法化二次型为标准形、正定二次型）。This course is one of the most important undergraduate basic courses of economics and management professional math in our university. Students can not only get a basic knowledge of linear algebra, and can obtain “two basic training”: the training about algebra basic methods and the training about basic knowledge of linear algebra. Meanwhile, the course will culture and train the ability of students using mathematics analyze and solve problems and expand the mathematical knowledge, as well as provide the necessary mathematical foundation to further learn relevant courses. The content of this course include: determinant (the definition, nature and by row (column) Expand, Cramers rule), matrix (matrix operations, inverse matrix, block matrix, elementary matrix with elementary transformation, rank of matrix), linear equations and vector space (Euclidean space), matrix eigenvalue and vector, the second type (with the Method and orthogonal transformation of the standard quadratic form, positive definite quadratic form). 概率论与数理统计课程中英文简介Probability and Mathematics Statistics课程代码：120074A/120073ACourse Code：120074A/120073A课程名称：概率论与数理统计Course Name：Probability and Mathematics Statistics学 时：64/48Periods：64/48学 分：4/3Credits：4/3考核方式：考试Assessment：Examination先修课程：微积分Preparatory Courses：Calculus概率论与数理统计课程是各专业本科生的一门重要的公共基础课程，是硕士研究生入学全国统一考试中必考的数学课程之一。概率论是一门研究随机现象统计规律性数量关系的数学学科，而数理统计是研究如何有效地收集整理和分析随机影响的数据，并做出统计推断、预测或者决策的一门学科，它是以概率论为基础的。概率论与数理统计课程是学生由确定性思维进入随机性思维的入门课程、也是大学唯一的一门进行随机思维培养和训练的课程，是整个随机数学这个庞大体系的基石。通过对本门课程的学习，不仅为其他专业课的学习提供有力工具（如西方经济学），而且可以掌握一定的随机思维，拓宽学生的视野，从根本上改变和完善学生的思维方式使学生对定性与定量方法的理解上一个更高的层次，启发学生的想象力及创造力，培养学生观察、分析、解决问题的能力。本课程涉及的知识面广泛，与实践联系紧密，是应用性较强的一门课程。Probability and Mathematics Statistics course is an important public basic course for undergraduate in each major and is one of the mathematics curriculums of compulsory in the National Graduate Entrance Examination. Probability theory is a mathematics discipline of studying of the quantitative relation of statistical regularity of random phenomena, while mathematical statistics based on Probability theory is a discipline which studies how to compile and analyze data of random influence effectively and makes statistical inference, forecasting, or decision-making. Probability and mathematical statistics is an introductory course for students from deterministic thought to random thought, also is the only course that teach and practice random thought in University, and is the foundation of this huge system in all random mathematics. Through this course, students not only learn powerful tool for other professional courses (for instance economics), but also master random thought in some degrees and broaden their horizons. It fundamentally changes and improves the thinking way for students so that they can understand the qualitative and quantitative methods to a higher level, inspires students imagination and creativity, and cultivates students abilities to observe, analyze and problem-solving. This course covers a broad range of knowledge, closely links with the practice, and has a wide application.概率论课程中英文简介Probability Theory课程代码：120084A/120083ACourse Code：120084A/120083A课程名称：概率论Course Name：Probability Theory学 时：64/48Periods：64/48学 分：4/3Credits：4/3考核方式：考试Assessment：Examination先修课程：高等数学Preparatory Courses：Advanced Mathematics高等代数Advanced Algebra概率论是以具有不确定性的随机现象为研究对象，以探讨和研究随机现象的统计规律性为任务的一个数学分支，是继续学习数理统计、随机过程，以及与概率理论相关的课程的基础。概率论是一门应用性很强的数学学科，广泛地应用于金融、保险，证券，工程技术和自然学科中，是各学科中分析与解决问题的基本工具，概率论与不同的问题结合形成许多分支。通过本课程的教学实践，一方面要求学生理解概率论的基本理论和基本计算方法，为后续课程的学习打下必要的基础；另一方面要求学生能够运用基本的概率模型、理论和方法解决实际应用中的简单概率问题。在本课程的执行过程中，内容的选取和讲解都考虑到了学生以后的发展，使学生主要掌握随机事件、随机变量的概念；掌握随机变量的分布及数字特征的计算，掌握大数定律及中心极限定理的实际应用等内容。Probability theory is a branch of mathematics which takes nondeterministic random phenomenon as study object and takes the statistics rule of random phenomena of exploring and studying as tasks. Also if you are going to continue learning statistics, stochastic processes and courses related to the probability theory. Probability theory is a mathematical discipline of strong application. It is widely used in finance, insurance, securities, engineering technology and science. Probability theory is a basic tool to analyze and solve problem in several disciplines, which combines with different problems to form many branch. Through the course of teaching practice, on the one hand, requiring students to understand the basic theory of probability theory and basic calculation method, so as to lay the necessary foundations of subsequent courses；On the other hand, requiring students to apply their basic probability model, theory and methods to solve simple probability questions of real-world application.In the course of the execution process, the selection and interpretation of content take the students future development into account. Making the students largely master the concept of random event and random variables, distributes and calculation, the practical application of the law of large numbers and the Central limit theorem and so on.高等数学课程中英文简介Calculus I课程代码：120096A/120095ACourse Code：120096A/120095A课程名称：高等数学Course Name：Calculus I学 时：96/80Periods：96/80学 分：6/5Credits：6/5考核方式：考试Assessment：Examination先修课程：中学数学Preparatory Courses：School Mathematics高等数学是大学一年级的重要基础理论课。内容包括一元函数与极限、导数与微分、微分中值定理与导数的应用、不定积分、定积分、定积分的应用、微分方程等方面的基本概念、基本理论和基本运算技能，为学习后继课程和进一步获得数学知识奠定必要的数学基础。在传授知识的同时，通过各个教学环节逐步培养学生的抽象能力、逻辑推理能力、空间想象能力、运算能力和自学能力，还有特别注意培养学生具有综合运用所学知识去分析问题和解决问题的能力。本课程的特点是尊重数学的系统性，注重直观描述与实际背景，注重增强学生用数学的意识，培养学生使用数学的能力，让学生初步涉及数学建模。Higher Mathematics is an important basis theory course for the first year at college. Its Contents include function of one variable and limit value, derivative and differential, the application of differential mean value theorem and derivatives, indefinite integral, definite integral, the application of definite integral, the basic concepts, theory and computing skills of differential equations and other aspects.While imparting knowledge to students, this course can train the students ability of abstract, logical reasoning, spatial imagination, computing power and self-learning in each teaching link, especially pay attention to cultivate students ability of taking a global view of analyzing issues and solving problems with learned knowledge. This course is characterized by respect for systematicness of mathematics, which is focusing on visual description and practical background, also on enhancing students awareness of using mathematics and cultivating students ability of using mathematics so as to enable students initially involved in mathematical modeling.高等数学课程中英文简介Calculus II课程代码：120106A/120105ACourse Code：120106A/120105A课程名称：高等数学IICourse Name：Calculus II学 时：96/80Periods：96/80学 分：6/5Credits：6/5考核方式：考试Assessment：Examination先修课程：中学数学Preparatory Courses：School Mathematics高等数学是大学一年级的重要基础理论课。内容包括空间解析几何与向量代数、多元函数微分法及其应用、重积分、曲线积分与曲面积分、无穷级数等方面的基本概念、基本理论和基本运算技能，为学习后继课程和进一步获得数学知识奠定必要的数学基础。在传授知识的同时，通过各个教学环节逐步培养学生的抽象能力、逻辑推理能力、空间想象能力、运算能力和自学能力，还有特别注意培养学生具有综合运用所学知识去分析问题和解决问题的能力。本课程的特点是尊重数学的系统性，注重直观描述与实际背景，注重增强学生用数学的意识，培养学生使用数学的能力，让学生初步涉及数学建模。Higher Mathematics II is an important basis theory course for the first year at college. Its Contents include the basic concept, theory and computing skills of analytic geometry and vector algebra, multi-function differential method and its application, re-integration, the curve integral and surface integral, infinite series and so on. It will lay the foundations of mathematics for students follow-up courses so as to further access to the necessary mathematical knowledge.While imparting knowledge to students, this course can train the students ability of abstract, logical reasoning, spatial imagination, computing power and self-learning in each teaching link, especially pay attention to cultivate students ability of taking a global view of analyzing issues and solving problems with learned knowledge. This course is characterized by respect for systematicness of mathematics, which is focusing on visual description and practical background, also on enhancing students awareness of using mathematics and cultivating students ability of using mathematics so as to enable students initially involved in mathematical modeling.高等代数课程中英文简介Higher Algebra课程代码：120114ACourse Code：120114A课程名称：高等代数Course Name：Higher Algebra学 时：64Periods：64学 分：4Credits：4考核方式：考试Assessment：Examination先修课程：无Preparatory Courses：None本课程是统计学专业的一门专业基础课程，是学习离散数学、微分方程、泛函分析等课程的基础。本课程的教学目标是，使学生获得数学基本思想方法和行列式、线性方程组、矩阵、二次型、线性空间、线性变换、欧氏空间等方面的系统知识。它一方面使学生熟悉和掌握本课程所涉及的现代数学中的重要思想方法，为后继课程提供所需的基础理论知识；另一方面还能提高学生抽象思维、逻辑推理和代数运算能力，对提高学生的思维能力，开发学生智能、加强“三基”（基础知识、基本理论、基本方法）及培养学生创造型能力等起到重要作用。本课程的主要内容为多项式理论和线性代数理论，即因式分解和代数基本定理，行列式、线性方程组、矩阵、二次型，线性空间、欧几里得空间的相关理论。具体包括以下内容:行列式的定义和性质、行列式的计算方法、Cramer法则；向量空间、向量的线性相关性、线性方程组有解的判别定理、线性方程组解的结构等；矩阵的运算、逆矩阵和矩阵方程；二次型的标准形、唯一性、正定二次型；线性变换的矩阵、基变换和坐标变换公式、线性变换的特征值及特征向量、矩阵的对角化；欧几里得空间、标准正交基、正交变换、实对称矩阵的标准形。The course is an important professional basic course of the Financial Mathematics. It is the basic to study the course of Discrete Mathematics, differential equations, functional analysis and so on.The teaching objective of course is to provide students with the basic way of thinking and the system of knowledge of determinant, linear equations, matrix, quadratic, linear space, linear transformations and Euclidean space and so on. On the one hand, it enables students to know and master an important way of thinking about the modern mathematics in this course. And then provide some follow-up course for the basic theories and knowledge. On the other hand, it can improve the students，ability of abstract thinking, logical reasoning and algebra capacity. It plays an important role in improving students thinking ability and developing intelligent students, strengthening the Three Basics (basic knowledge, basic theory and method) and cultivating students creative ability.The main contents of this course are polynomial theory and linear algebra theory which is factorization and the fundamental theorem of determinant, linear equations, matrix, quadratic, linear space, linear transformations and Euclidean space. Specifically, this course includes the following contents: factorization and the fundamental theorem of algebra, the determinant of the definition and nature of the method of calculating the determinant, Cramer rule; vector space, vector of the linear correlation, linear equations solvable discriminant theorem, linear equations structure; matrix operations, inverse matrix and the matrix equation; the Standard Form of Quadratic, Unique, positive definite quadratic; Linear transformation matrix, Based transformation and coordinate transformation formula, Linear transformation of values and Eigen vectors, Diagonalization of Matrices, Euclidean space, orthonormal basis, orthogonal transformation, the standard form of real symmetric matrices数学分析课程中英文简介Mathematical Analysis课程代码：120127ACourse Code：120127A课程名称：数学分析Course Name：Mathematical Analysis学 时：112Periods：112学 分：7Credits：7考核方式：考试Assessment：Examination先修课程：空间解析几何Preparatory Courses：Space Analytic Geometry数学分析课程是金融数学专业与统计学专业的一门重要基础课。数学分析的基本思想是极限论，主要是通过微分和积分两种特殊的极限运算从微观和宏观两个方面来研究函数。通过本课程的学习，使学生能够正确理解数学分析的基本概念、基本理论，掌握数学分析的基本方法，并具备较熟练的演算技能和初步的应用能力。数学分析一方面为后继课程（概率论、复变函数、实变函数、微分方程等）提供必要的基础知识，另一方面，数学分析所体现的分析数学思想、逻辑推理方法、处理问题的技巧，对培养学生分析问题，解决问题的能力有着重要作用。数学分析是其中的第一部分。数学分析的基本内容如下：实数集与函数、数列极限、函数极限、连续函数、导数与微分、不定积分、定积分及其应用、反常积分。Mathematical Analysis course is an important basic course of Financial Mathematics and Statistics professionals. The basic idea of this course is the limit theory. From both the micro and macro aspects, this theory research function mainly through two special l