数学专业英语第八讲附数学课程英文表达.pptx

第二级,第三级,第四级,第五级,Mathematical English,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,Mathematical English,第二级,第三级,第四级,第五级,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,数学专业英语第八讲附数学课程英文表达,数学类,第一学年 几何与拓扑:,1,、,James R、Munkres,Topology,2,、,Basic Topology by Armstrong,3,、,Kelley,General Topology,:,4,、,Willard,General Topology,:一般拓扑学,5,、,Topology and geometry,:,6,、,Introduction to Topological Manifolds,7,、,From calculus to cohomology,代数:,1,、,Abstract Algebra,2,、,Algebra Lang,:标准得研究生一、二年级代数教材,难度很高,适合作参考书;,3,、,Algebra Hungerford,:标准得研究生一年级代数教材,适合作参考书;,4,、,Algebra M,Artin,:标准得本科生代数教材;,5,、,Advanced Modern Algebra by Rotman,:较新得研究生代数教材,很全面;,6,、,Algebra,:,a graduate course by Isaacs,:较新得研究生代数教材;,7,、,Basic algebra Vol I&II by Jacobson,:经典得代数学全面参考书,适合研究生参考。,分析基础:,1,、,Walter Rudin,Principles of mathematical analysis,:本科数学分析得标准参考书;,2,、,Walter Rudin,Real and plex analysis,:标准得研究生一年级分析教材;,3,、,Lars V、Ahlfors,plex analysis,:本科高年级与研究生一年级经典得复分析教材;,4,、,Functions of One plex Variable I,J、B、Conway,:研究生级别得单变量复分析经典;,5,、,Lang,plex analysis,:研究生级别得单变量复分析参考书;,6,、,plex Analysis by Elias M、Stein,:较新得研究生级别得单变量复分析教材;,7,、,Lang,Real and Functional analysis,:研究生级别得分析参考书;,8,、,Royden,Real analysis,:标准得研究生一年级实分析教材;,第二学年 代数:,1,、,mutative ring theory,by H、Matsumura,:较新得研究生交换代数标准教材;,2,、,mutative Algebra I&II by Oscar Zariski,Pierre Samuel,:经典得交换代数参考书;,3,、,An introduction to mutative Algebra by Atiyah,:标准得交换代数入门教材;,4,、,An introduction to homological algebra,by weibel,:较新得研究生二年级同调代数教材;,5,、,A Course in Homological Algebra by P、J、Hilton,U、Stammbach,:经典全面得同调代数参考书;,6,、,Homological Algebra by Cartan,:经典得同调代数参考书;,7,、,Methods of Homological Algebra by Sergei I、Gelfand,Yuri I、Manin,:高级、经典得同调代数参考书;,8,、,Homology by Saunders Mac Lane,:经典得同调代数系统介绍;,9,、,mutative Algebra with a view toward Algebraic Geometry by Eisenbud,:高级得代数几何、交换代数得参考书,最新得交换代数全面参考。,代数拓扑:,1,、,Algebraic Topology,A、Hatcher,:最新得研究生代数拓扑标准教材;,2,、,Spaniers“Algebraic Topology”,:经典得代数拓扑参考书;,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,:经典得研究生代数拓扑教材;,5,、,Fulton,Algebraic topology,:,a first course,:很好本科生高年级与研究生一年级得代数拓扑参考书;,6,、,Glen Bredon,Topology and geometry,:标准得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、经典得代数拓扑参考书;,8,、,A Concise Course in Algebraic Topology by J、P、May,:研究生代数拓扑得入门教材,覆盖范围较广;,9,、,Elements of Homotopy Theory by G、W、Whitehead,:高级、经典得代数拓扑参考书。,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 plex analysis,:标准研究生分析教材;,3,、,Halmos,”,Measure Theory”,:经典得研究生实分析教材,适合作参考书;,4,、,Walter Rudin,Functional analysis,:标准得研究生泛函分析教材;,5,、,Conway,A course of Functional analysis,:标准得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,:高级得研究生泛函分析教材;,8,、,Functional Analysis by Yoshida,:高级得研究生泛函分析参考书;,9,、,Measure Theory,Donald L、Cohn,:经典得测度论参考书。,微分拓扑 李群、李代数,1,、,Hirsch,Differential topology,:标准得研究生微分拓扑教材,有相当难度;,2,、,Lang,Differential and Riemannian manifolds,:研究生微分流形得参考书,难度较高;,3,、,Warner,Foundations of Differentiable manifolds and Lie groups,:标准研究生微分流形教材,有相当得篇幅讲述李群;,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,:李群得参考书;,6,、,Lectures on Lie Groups W、Y、Hsiang,:李群得参考书;,7,、,Introduction to Smooth Manifolds by John M、Lee,:较新得关于光滑流形得标准教材;,8,、,Lie Groups,Lie Algebras,and Their Representation by V、S、Varadarajan,:最重要得李群、李代数参考书;,9,、,Humphreys,Introduction to Lie Algebras and Representation Theory,SpringerVerlag,GTM9,:标准得李代数入门教材。,第三学年 微分几何:,1,、,Peter Petersen,Riemannian Geometry,:标准得黎曼几何教材;,2,、,Riemannian Manifolds:An Introduction to Curvature by John M、Lee,:最新得黎曼几何教材;,3,、,doCarmo,Riemannian Geometry、,:标准得黎曼几何教材;,4,、,M、Spivak,A prehensive Introduction to Differential Geometry IV,:全面得微分几何经典,适合作参考书;,5,、,Helgason,Differential Geometry,Lie groups,and symmetric spaces,:标准得微分几何教材;,6,、,Lang,Fundamentals of Differential Geometry,:最新得微分几何教材,很适合作参考书;,7,、,kobayashi/nomizu,Foundations of Differential Geometry,:经典得微分几何参考书;,8,、,Boothby,Introduction to Differentiable manifolds and Riemannian Geometry,:标准得微分几何入门教材,主要讲述微分流形;,9,、,Riemannian Geometry I、Chavel,:经典得黎曼几何参考书;,10,、,Dubrovin,Fomenko,Novikov“Modern geometry-methods and applications”Vol 13,:经典得现代几何学参考书。,代数几何:,1,、,Harris,Algebraic Geometry:a first course,:代数几何得入门教材;,2,、,Algebraic Geometry Robin Hartshorne,:经典得代数几何教材,难度很高;,3,、,Basic Algebraic Geometry 1&2 2nd ed、I、R、Shafarevich、,:非常好得代数几何入门教材;,4,、,Principles of Algebraic Geometry by giffiths/harris,:全面、经典得代数几何参考书,偏复代数几何;,5,、,mutative Algebra with a view toward Algebraic Geometry by Eisenbud,:高级得代数几何、交换代数得参考书,最新得交换代数全面参考;,6,、,The Geometry of Schemes by Eisenbud,:很好得研究生代数几何入门教材;,7,、,The Red Book of Varieties and Schemes by Mumford,:标准得研究生代数几何入门教材;,8,、,Algebraic Geometry I:plex Projective Varieties by David Mumford,:复代数几何得经典。,调与分析 偏微分方程,1,、,An Introduction to Harmonic Analysis,Third Edition Yitzhak Katznelson,:调与分析得标准教材,很经典;,2,、,Evans,Partial differential equations,:偏微分方程得经典教材;,3,、,Aleksei、A、Dezin,Partial differential equations,Springer-Verlag,:偏微分方程得参考书;,4,、,L、Hormander“Linear Partial Differential Operators,”I&II,:偏微分方程得经典参考书;,5,、,A Course in Abstract Harmonic Analysis by Folland,:高级得研究生调与分析教材;,6,、,Abstract Harmonic Analysis by Ross Hewitt,:抽象调与分析得经典参考书;,7,、,Harmonic Analysis by Elias M、Stein,:标准得研究生调与分析教材;,8,、,Elliptic Partial Differential Equations of Second Order by David Gilbarg,:偏微分方程得经典参考书;,9,、,Partial Differential Equations,by Jeffrey Rauch,:标准得研究生偏微分方程教材。,复分析 多复分析导论,1,、,Functions of One plex Variable II,J、B、Conway,:单复变得经典教材,第二卷较深入;,2,、,Lectures on Riemann Surfaces O、Forster,:黎曼曲面得参考书;,3,、,pact riemann surfaces Jost,:黎曼曲面得参考书;,4,、,pact riemann surfaces Narasimhan,:黎曼曲面得参考书;,5,、,Hormander”An introduction to plex Analysis in Several Variables”,:多复变得标准入门教材;,6,、,Riemann surfaces,Lang,:黎曼曲面得参考书;,7,、,Riemann Surfaces by Hershel M、Farkas,:标准得研究生黎曼曲面教材;,8,、,Function Theory of Several plex Variables by Steven G、Krantz,:高级得研究生多复变参考书;,9,、,plex Analysis:The Geometric Viewpoint by Steven G、Krantz,:高级得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,、抽象调与分析;,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得过程中穿插选修,本科毕业应有得水平 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,李群与李代数,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 puting 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,mutative 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 plex 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,子流形得几何,Submanifold Geometry,李群得表示论,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,常微分方程得几何理论,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,有限元方法得数学基础,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 puting,数值逼近,Numerical Approximation,保结构算法,Structure-Preserving Algorithms,多尺度分析,Multiscale Analysis,反问题中得数值方法,Numerical Methods for Inverse Problems,专业课,有限元方法,(2)Finite Element Methods(2),计算机图形学,puter Graphics,计算机辅助设计,puter-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 puting,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得数学基础,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,binatorial 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,binatorics 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,可持续发展得理论与实践,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,供应链管理与电子商务,Supply Chain Management&E-merce,电子商务与网络营销,Electronic merce 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,binatorial Mathematics,计算机算法设计与分析,The Design and Analysis of puter Algorithms,排队论,Queueing Theory,高级人工智能,Advanced Artificial Intelligence,计算机体系结构,puter System Architecture,软件开发与程序设计方法学,Software Development and Programming Methodology,高级计算机网络,Advanced puter Networks,计算机视觉与图像理解,puter Vision and Image Understanding,计算机通信网络安全,puter munication 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-puter Interface,高性能计算机系统,High Performance puter Systems,学科综合课,先进计算机与软件技术系统讲座,Topics in advanced puter 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,putability and plexity of puting,形式语言与自动机理论,Formal language and Automata theory,编译程序高级教程,pilers: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 puter Systems,计算语言学,putational 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,