数学专业英语第八讲附数学课件程英文表达.ppt

美国的大学数学研究生教材v.s.中国科学院数学研究生课程,数学类第一学年 几何与拓扑：1、James R.Munkres,Topology2、Basic Topology by Armstrong3、Kelley,General Topology：4、Willard,General Topology：一般拓扑学5、Topology and geometry：6、Introduction to Topological Manifolds7、From calculus to cohomology,代数：1、Abstract Algebra 2、Algebra Lang：标准的研究生一、二年级代数教材，难度很高，适合作参考书；3、Algebra Hungerford：标准的研究生一年级代数教材，适合作参考书；4、Algebra M,Artin：标准的本科生代数教材；5、Advanced Modern Algebra by Rotman：较新的研究生代数教材，很全面；6、Algebra：a graduate course by Isaacs：较新的研究生代数教材；7、Basic algebra Vol I&II by Jacobson：经典的代数学全面参考书，适合研究生参考。,分析基础：1、Walter Rudin,Principles of mathematical analysis：本科数学分析的标准参考书；2、Walter Rudin,Real and complex analysis：标准的研究生一年级分析教材；3、Lars V.Ahlfors,Complex analysis：本科高年级和研究生一年级经典的复分析教材；4、Functions of One Complex Variable I，：研究生级别的单变量复分析经典；5、Lang,Complex analysis：研究生级别的单变量复分析参考书；6、Complex Analysis by Elias M.Stein：较新的研究生级别的单变量复分析教材；7、Lang,Real and Functional analysis：研究生级别的分析参考书；8、Royden,Real analysis：标准的研究生一年级实分析教材；,第二学年 代数：1、Commutative ring theory,by H.Matsumura：较新的研究生交换代数标准教材；2、Commutative Algebra I&II by Oscar Zariski,Pierre Samuel：经典的交换代数参考书；3、An introduction to Commutative Algebra by Atiyah：标准的交换代数入门教材；4、An introduction to homological algebra,by weibel：较新的研究生二年级同调代数教材；5、A Course in Homological Algebra by P.J.Hilton,U.Stammbach：经典全面的同调代数参考书；6、Homological Algebra by Cartan：经典的同调代数参考书；7、Methods of Homological Algebra by Sergei I.Gelfand,Yuri I.Manin：高级、经典的同调代数参考书；8、Homology by Saunders Mac Lane：经典的同调代数系统介绍；9、Commutative Algebra with a view toward Algebraic Geometry by Eisenbud：高级的代数几何、交换代数的参考书，最新的交换代数全面参考。,代数拓扑：1、Algebraic Topology,A.Hatcher：最新的研究生代数拓扑标准教材；2、Spaniers“Algebraic Topology”：经典的代数拓扑参考书；3、Differential forms in algebraic topology,by Raoul Bott and Loring W.Tu：研究生代数拓扑标准教材；4、Massey,A basic course in Algebraic topology：经典的研究生代数拓扑教材；5、Fulton,Algebraic topology：a first course：很好本科生高年级和研究生一年级的代数拓扑参考书；6、Glen Bredon,Topology and geometry：标准的研究生代数拓扑教材，有相当篇幅讲述光滑流形；7、Algebraic Topology Homology and Homotopy：高级、经典的代数拓扑参考书；8、A Concise Course in Algebraic Topology by：研究生代数拓扑的入门教材，覆盖范围较广；9、Elements of Homotopy Theory by G.W.Whitehead：高级、经典的代数拓扑参考书。,实分析、泛函分析：1、Royden,Real analysis：标准研究生分析教材；2、Walter Rudin,Real and complex analysis：标准研究生分析教材；3、Halmos，”Measure Theory”：经典的研究生实分析教材，适合作参考书；4、Walter Rudin,Functional analysis：标准的研究生泛函分析教材；5、Conway,A course of Functional analysis：标准的研究生泛函分析教材；6、Folland,Real analysis：标准研究生实分析教材；7、Functional Analysis by Lax：高级的研究生泛函分析教材；8、Functional Analysis by Yoshida：高级的研究生泛函分析参考书；9、Measure Theory,Donald L.Cohn：经典的测度论参考书。,微分拓扑 李群、李代数 1、Hirsch,Differential topology：标准的研究生微分拓扑教材，有相当难度；2、Lang,Differential and Riemannian manifolds：研究生微分流形的参考书，难度较高；3、Warner,Foundations of Differentiable manifolds and Lie groups：标准研究生微分流形教材，有相当的篇幅讲述李群；4、Representation theory:a first course,by W.Fulton and J.Harris：李群及其表示论标准教材；5、Lie groups and algebraic groups,by A.L.Onishchik,E.B.Vinberg：李群的参考书；6、Lectures on Lie Groups：李群的参考书；7、Introduction to Smooth Manifolds by John M.Lee：较新的关于光滑流形的标准教材；8、Lie Groups,Lie Algebras,and Their Representation by V.S.Varadarajan：最重要的李群、李代数参考书；9、Humphreys,Introduction to Lie Algebras and Representation Theory,SpringerVerlag,GTM9：标准的李代数入门教材。,第三学年 微分几何：1、Peter Petersen,Riemannian Geometry：标准的黎曼几何教材；2、Riemannian Manifolds:An Introduction to Curvature by John M.Lee：最新的黎曼几何教材；3、doCarmo,Riemannian Geometry.：标准的黎曼几何教材；4、M.Spivak,A Comprehensive Introduction to Differential Geometry IV：全面的微分几何经典，适合作参考书；5、Helgason,Differential Geometry,Lie groups,and symmetric spaces：标准的微分几何教材；6、Lang,Fundamentals of Differential Geometry：最新的微分几何教材，很适合作参考书；7、kobayashi/nomizu,Foundations of Differential Geometry：经典的微分几何参考书；8、Boothby,Introduction to Differentiable manifolds and Riemannian Geometry：标准的微分几何入门教材，主要讲述微分流形；9、Riemannian Geometry I.Chavel：经典的黎曼几何参考书；10、Dubrovin,Fomenko,Novikov“Modern geometry-methods and applications”Vol 13：经典的现代几何学参考书。,代数几何：1、Harris,Algebraic Geometry:a first course：代数几何的入门教材；2、Algebraic Geometry Robin Hartshorne：经典的代数几何教材，难度很高；3、Basic Algebraic Geometry 1&2 2nd ed.：非常好的代数几何入门教材；4、Principles of Algebraic Geometry by giffiths/harris：全面、经典的代数几何参考书，偏复代数几何；5、Commutative Algebra with a view toward Algebraic Geometry by Eisenbud：高级的代数几何、交换代数的参考书，最新的交换代数全面参考；6、The Geometry of Schemes by Eisenbud：很好的研究生代数几何入门教材；7、The Red Book of Varieties and Schemes by Mumford：标准的研究生代数几何入门教材；8、Algebraic Geometry I:Complex Projective Varieties by David Mumford：复代数几何的经典。,调和分析 偏微分方程 1、An Introduction to Harmonic Analysis,Third Edition Yitzhak Katznelson：调和分析的标准教材，很经典；2、Evans,Partial differential equations：偏微分方程的经典教材；3、，Partial differential equations，Springer-Verlag：偏微分方程的参考书；4、L.Hormander“Linear Partial Differential Operators,”I&II：偏微分方程的经典参考书；5、A Course in Abstract Harmonic Analysis by Folland：高级的研究生调和分析教材；6、Abstract Harmonic Analysis by Ross Hewitt：抽象调和分析的经典参考书；7、Harmonic Analysis by Elias M.Stein：标准的研究生调和分析教材；8、Elliptic Partial Differential Equations of Second Order by David Gilbarg：偏微分方程的经典参考书；9、Partial Differential Equations，by Jeffrey Rauch：标准的研究生偏微分方程教材。,复分析 多复分析导论 1、Functions of One Complex Variable II，：单复变的经典教材，第二卷较深入；2、Lectures on Riemann Surfaces O.Forster：黎曼曲面的参考书；3、Compact riemann surfaces Jost：黎曼曲面的参考书；4、Compact riemann surfaces Narasimhan：黎曼曲面的参考书；5、Hormander”An introduction to Complex Analysis in Several Variables”：多复变的标准入门教材；6、Riemann surfaces,Lang：黎曼曲面的参考书；7、Riemann Surfaces by Hershel M.Farkas：标准的研究生黎曼曲面教材；8、Function Theory of Several Complex Variables by Steven G.Krantz：高级的研究生多复变参考书；9、Complex Analysis:The Geometric Viewpoint by Steven G.Krantz：高级的研究生复分析参考书。,专业方向选修课：1、多复分析；2、复几何；3、几何分析；4、抽象调和分析；5、代数几何；6、代数数论；7、微分几何；8、代数群、李代数与量子群；9、泛函分析与算子代数；10、数学物理；11、概率理论；12、动力系统与遍历理论；13、泛代数。数学基础：1、halmos,native set theory；2、fraenkel,abstract set theory；3、ebbinghaus,mathematical logic；4、enderton,a mathematical introduction to logic；5、landau,foundations of analysis；6、maclane,categories for working mathematican。应该在核心课程学习的过程中穿插选修,本科毕业应有的水平 分析：Walter Rudin,Principles of mathematical analysis；Apostol,mathematical analysis；M.spivak,calculus on manifolds；Munkres,analysis on manifolds；Kolmogorov/fomin,introductory real analysis；Arnold,ordinary differential equations。,代数：linear algebra by Stephen H.Friedberg；linear algebra by hoffman；linear algebra done right by Axler；advanced linear algebra by Roman；algebra,artin；a first course in abstract algebra by rotman。几何：do carmo,differential geometry of curves and surfaces；Differential topology by Pollack；Hilbert,foundations of geometry；James R.Munkres,Topology。,一、数学类学科基础课 抽象代数Abstract Algebra李群和李代数 Lie Groups and Lie Algebras代数拓扑Algebraic Topology微分流形Differentiable Manifolds黎曼曲面 Riemann Surfaces微分几何 Differential Geometry泛函分析 Functional Analysis 偏微分方程概论Introduction to Partial Differential Equations随机数学概论 Introduction to Mathematics of Randomness 最优化计算方法Optimization Computing Methods数值分析 Numerical Analysis,1、基础数学（070101）专业基础课解析数论 Analytic Number Theory表示论引论 Introduction to Representation Theory 交换代数与同调代数 Commutative Algebra and Homological Algebra代数几何Algebraic Geometry算术代数几何Arithmetic Algebraic Geometry微分拓扑 Differential Topology黎曼几何 Riemannian Geometry算子理论Operator Theory动力系统 Dynamical Systems几何分析基础 Foundation of Geometric Analysis非线性泛函分析 Nonlinear Functional Analysis 近代复分析 Modern Complex Analysis 近代实分析 Modern Real Analysis,专业课代数表示论选讲Topics on Representation Theory代数数论选讲Topics on Algebraic Number Theory微分几何选讲Topics on Differential Geometry子流形的几何 Submanifold Geometry 李群的表示论Representation Theory of Lie Groups变分方法及其应用 Variational Method and Its Applications 几何测度论 Geometric Measure Theory常微分方程的几何理论Geometrical Theory in Ordinary Differential Equations测度论Measure Theory椭圆型方程 Elliptic Differential Equations 抛物型方程 Equations of Parabolic Type,2、计算数学（070102）专业基础课微分方程数值解 Numerical Solutions of Differential Equations有限元方法的数学基础 The Mathematical Bases of Finite Element Methods数值线性代数 Numerical Linear Algebra科学工程计算概论 An Introduction to Scientific and Engineering Computing数值逼近 Numerical Approximation保结构算法 Structure-Preserving Algorithms多尺度分析Multiscale Analysis反问题中的数值方法 Numerical Methods for Inverse Problems,专业课有限元方法(2)Finite Element Methods(2)计算机图形学 Computer Graphics计算机辅助设计 Computer-Aid Design小波分析及其应用 Wavelets and Their Applications函数逼近论 Approximation Theory of Functions分形及其应用 Fractals and Their Applications并行计算方法引论 Introduction to Parallel Computing,3、概率论与数理统计（070103）专业基础课高等概率论Advanced Probability Theory高等数理统计Mathematical Statistics线性统计分析 Linear Statistical Analysis平稳过程与时间序列分析Stationary Stochastic Processes and Time Series Analysis抽样调查 Survey Sampling试验设计与分析Design and Analysis of Experiments 随机过程Stochastic Processes统计软件Statistics Software,专业课随机过程选讲 Topics on Stochastic Processes非参数统计 Non-parametric Statistics可靠性理论 Reliability Theory数理统计选讲 Topics on Mathematical Statistics高等随机过程 Advanced Course in Stochastic Processes平稳过程与时间序列分析(2)Stationary Stochastic Processes and Time Series Analysis（2）,4、应用数学（070104）专业基础课偏微分方程(2)Partial Differential Equation非线性可积系统 Integrable System数学物理方法 Methods of Mathematical Physics常微分方程(2)Ordinary Differential Equations(2)经典力学与量子力学的数学基础 Mathematical Methods of Classical and Quantum Mechanics,专业课随机过程选讲 Topics on Stochastic Processes非参数统计 Non-parametric Statistics可靠性理论 Reliability Theory数理统计选讲 Topics on Mathematical Statistics高等随机过程 Advanced Course in Stochastic Processes平稳过程与时间序列分析(2)Stationary Stochastic Processes and Time Series Analysis（2）,5、运筹学与控制论（070105）专业基础课规划论 Mathematical Programming随机运筹学Stochastic Operations Research图与网络流理论 Graph Theory and Network Flow Theory线性控制系统理论 Linear System Control Theory非线性控制系统理论Theory of Nonlinear Control Systems随机控制系统理论 Theory of Stochastic Control Systems组合优化Combinatorial Optimization运筹学通论 Principles of Operational Research(OR)对策论 Game Theory 决策分析Decision Analysis,专业课组合数学与图论 Combinatorics and Graphs数理经济学 Mathematical Economics,二、管理类管理科学与工程：学科基础课 高级管理学 Advanced Management 现代管理数学方法 Modern Managerial Mathematics微观经济学 Microeconomics宏观经济学 Macroeconomics高级运筹学 Operations Research应用统计 Applied Statistics计量经济学 Econometrics生产与运作管理Production and Operation Management技术创新管理 Technology Management,战略管理 Strategic Management战略信息管理 Strategic Information Management决策支持系统 Decision Support Systems决策分析 Decision Analysis管理系统工程 System Engineering in Management科技政策 S&T Policy 工业工程与管理 Industrial Engineering and Management管理信息系统 Management Information System项目管理 Project Management,专业课企业财务管理 Financial Management of Enterprises管理会计学 Managerial Accounting市场营销学 Marketing当代西方财务管理理论与实务Contemporary Corporate Finance-Theory and Practice会计学原理 Principles of Financial Accounting财务会计 Financial Accounting决策财务分析 Financial Analysis of Operation Decisions可持续发展的理论与实践 Sustainable Development in Theory and Practice优选学Optimum Seeking Methods国际贸易与金融International Trade and Finance投入产出分析及应用 Input-Output Technology and Application,金融经济学Financial Economics金融工程Financial Engineering投资分析 Investment Analysis物流管理 Logistics Management组织行为学 Organization Behavior制度经济学 Institutional Economics网络经济概论 The Economics of Networks人力资源管理 Human Resources Management经济控制论Economic Control Theory供应链管理和电子商务Supply Chain Management&E-Commerce电子商务与网络营销 Electronic Commerce and Cyber-Marketing产业组织理论 The Theory of Industry Organization国际金融 International Finance金融投资学 Financial Investments,三、计算机科学类计算机科学与技术（0812）一级学科课程：学科基础课数理逻辑Mathematical Logic组合数学 Combinatorial Mathematics计算机算法设计与分析 The Design and Analysis of Computer Algorithms排队论 Queueing Theory高级人工智能 Advanced Artificial Intelligence计算机体系结构 Computer System Architecture软件开发和程序设计方法学Software Development and Programming Methodology高级计算机网络 Advanced Computer Networks计算机视觉与图像理解 Computer Vision and Image Understanding计算机通信网络安全 Computer Communication Network Security高级软件工程Advanced Course on Software Engineering人机交互界面理论与技术 Principle of Human-Computer Interface高性能计算机系统 High Performance Computer Systems,学科综合课 先进计算机和软件技术系统讲座 Topics in advanced computer and software technology,计算机软件与理论：专业基础课可计算性与计算复杂性 Computability and Complexity of Computing 形式语言与自动机理论 Formal language and Automata theory编译程序高级教程 Compilers:An Advanced Course数据库技术 Database Technology分布式操作系统 Distributed Operating Systems软件理论基础The Foundations of Software Theory软件工程Software Engineering软件测试与软件可靠性Software Testing and Software Reliability,程序设计语言理论Theory of Programming Languages并行处理Parallel Process信息论与编码Information Theory and Coding人工智能原理The Principles of Artificial Intelligence形式语义学引论Introduction to Formal Semantics数值分析 Numerical Analysis分布式多媒体计算机系统 Distributed Multimedia Computer Systems计算语言学 Computational Linguistics现代密码学理论与实践Contemporary CryptographyTheory and Practice代数基础与有限域Algebraic Foundations and Finite Fields,专业课程序的形式验证Program Formal Validation统计学方法及其工程应用Statistical Methods for Engineers操作系统高级教程 Advanced Course of Operating Systems进程代数 Process Algebra软件体系结构 Software Architecture网络分布计算理论和技术 Theory and Technology of Network and Distributed Computing多元统计分析 Multivariate Analysis实时系统理论与方法Theory and Methods of Real-time Systems安全信息系统概论Introdution to Information System Security计算数论Computational Number Theory理论密码学 Theoretical Cryptography量子信息处理 Quantum Information Processing,