algebraic_geometry_I
大学课程专业名称中英文对照
大学课程专业名称中英文对照关键词：大学课程专业名称中英文对照工学ENGINEERING课程中文名称课程英文名称高等数理方法Advanced Mathematical Method弹塑性力学Elastic-Plastic Mechanics板壳理论Theory of Plate and Shell高等工程力学Advanced Engineering Mechanics板壳非线性力学Nonlinear Mechanics of Plate and Shell复合材料结构力学Structural Mechanics of Composite Material弹性元件的理论及设计Theory and Design of Elastic Element非线性振动Nonlinear Vibration高等土力学Advanced Soil Mechanics分析力学Analytic Mechanics 随机振动Random Vibration数值分析Numerical Analysis基础工程计算与分析Calculation and Analysis of Founda tion Engineering 结构动力学StructuralDynamics 实验力学Laboratory Mechanics 损伤与断裂Damage and Fracture 小波分析WaveletAnalysis 有限元与边界元分析方法Analytical Method of Finite Element and Boundary Element 最优化设计方法Optimal Design Method 弹性力学Elastic Mechanics 高层建筑基础Tall BuildingFoundation 动力学Dynanics 土的本构关系Soil Constitutive Relation 数学建模Mathe maticalModeling 现代通信理论与技术Emerging Communications Theory and Technology 数字信号处理Digital Signal Processing 网络理论与多媒体技术Multi-media and Network Technolog y 医用电子学Electronics for Medicine 计算微电子学Computational Microelectronics 集成电路材料和系统电子学Material and System Electronics for In tegrated Circuits 网络集成与大型数据库C omputerNetwork Integrating Technology and Large scale Database 现代数字系统Modern Di gital System微机应用系统设计Microcomputer Application Design 计算机网络新技术Modern Com puter NetworkTechnologies 网络信息系统Network Information System 图像传输与处理Image Tran smission andProcessing 图像编码理论Theory of Image Coding 遥感技术Remote Sensing Techni ques 虚拟仪器系统设计Design of Virtual Instrument System 生物医学信号处理技术Signal Processin g forBiology and Medicine 光纤光学Fiber Optics VLSI的EDA技术EDA Techniques for VLSI 电子系统的ASIC技术ASIC Design Technologies VLSI技术与检测方法VLSI Techniques & Its E xamination 专题阅读或专题研究The Special Subject Study 信息论Information Theory 半导体物理学Semiconductor Physics 通信原理Principle of Communication 现代数理逻辑Modern MathematicalLogic 算法分析与设计Analysis and Design of Algorithms 高级计算机网络Advanced ComputerNetworks 高级软件工程Advanced Software Engineering 数字图像处理Digital Image Processing 知识工程原理Principles of Knowledge Engineering 面向对象程序设计Object-Oriented Programming形式语言与自动机Formal Languages and Automata 人工智能程序设计Artificial Intelli genceProgramming 软件质量与测试Software Quality and Testing 大型数据库原理与高级开发技术Principles of Large-Scale Data-Bas e and Advanced Development Technology 自然智能与人工智能Natural Intelligence and Artificial Intelligence Unix操作系统分析Analysis of Unix Sys tem 计算机图形学Computer Graphics Internet与Intranet技术Internet and Intranet Technol ogy 多媒体技术Multimedia Technology 数据仓库技术与联机分析处理Data Warehouse and OLA P 程序设计方法学Methodology of Programming 计算机信息保密与安全Secrecy and Security of Compu ter Information电子商务Electronic Commerce 分布式系统与分布式处理Distributed Systems and Dis tributedProcessing 并行处理与并行程序设计Parallel Processing and Parallel Programming 模糊信息处理技术Fuzzy Information Processing Technology 人工神经网络及应用Artificial Intellige nce andIts Applications Unix编程环境Unix Programming Environment 计算机视觉Computer Vision 高级管理信息系统Advanced Management Information Systems 信息系统综合集成理论及方法Theory andMethodology of Information n System Integration 计算机科学研究新进展Advances in ComputerScience 离散数学Discrete Mathematics 操作系统Operating System 数据库原理Prin ciples ofDatabase 编译原理Principles of Compiler 程序设计语言Programming Language 数据结构DataStructure 计算机科学中的逻辑学Logic in Computer Science 面向对象系统分析与设计Object-Oriented System Analysis and Design 高等数值分析Advanced Numeric Analysis 人工智能技术Artificial Intelligence Technology 软计算理论及应用Theory and Application of Soft-C omputing逻辑程序设计与专家系统Logic Programming and Expert Systems 模式识别Pattern Recognition 软件测试技术Software Testing Technology 高级计算机网络与集成技术Advanced Comp uter Networksand Integration Technology 语音信号处理Speech Signal Processing 系统分析与软件工具SystemAnalysis and Software Tools 计算机仿真Computer Simulation 计算机控制Computer Control 图像通信技术Image Communication Technology 人工神经网络及应用Artificial Intelligence and ItsApplications 计算机技术研究新进展Advances in Computer Technology 环境生物学E nvironmentalBiology 水环境生态学模型Models of Water Quality 环境化学Environmental Chemistr y 环境生物技术Environmental Biotechnology 水域生态学Aquatic Ecology 环境工程Environmental Engineering环境科学研究方法Study Methodology of Environmental Science 藻类生理生态学Ecol ogicalPhysiology in Algae 水生动物生理生态学Physiological Ecology of Aquatic Animal 专业文献综述Review on Special Information 废水处理与回用Sewage Disposal and Re-use 生物医学材料学及实验Biomaterials and Experiments 现代测试分析Modern Testing Technology and Metho ds 生物材料结构与性能Structures and Properties of Biomaterials 计算机基础Computer Basis 医学信息学Medical Informatics 计算机汇编语言Computer Assembly Language 学科前沿讲座Le ctures onFrontiers of the Discipline 组织工程学Tissue Engineering 生物医学工程概论Introduc tion toBiomedical Engineering 高等生物化学Advanced Biochemistry 光学与统计物理Optics andStatistical Physics 图像分析Image Treatment 数据处理分析与建模Data Analysis an dConstituting Model 高级数据库Advanced Database 计算机网络Computer Network 多媒体技术Technology of Multimedia 软件工程Software Engineering 药物化学Pharmaceutical Chemistry 功能高分子Functional Polymer InternetIntranet（英）InternetIntranet 程序设计方法学M ethodsof Programming InternetIntranet 高分子化学与物理Polymeric Chemistry and Physics 医学电子学Medical Electronics 现代仪器分析Modern Instrumental Analysis 仪器分析实验Instru mentalAnalysis Experiment 食品添加剂Food Additives Technology 高级食品化学Advanced FoodChemistry 食品酶学Food Enzymology 现代科学前沿选论Literature on Advances of Modern Science波谱学Spectroscopy 波谱学实验Spectroscopic Experiment 食品贮运与包装Food Pa ckaging 液晶化学Liquid Crystal Chemistry 高等有机化学Advanced Organic Chemistry 功能性食品FunctionFoods 食品营养与卫生学Food Nutrition and Hygiene 食品生物技术Food Biotechnol ogy 食品研究与开发Food Research and Development 有机合成化学Synthetic Organic Chemistry 食品分离技术Food Separation Technique 精细化工装备Refinery Chemical Equipment 食品包装原理Principle ofFood Packaging 表面活性剂化学及应用Chemistry and Application of Surfactant 天然产物研究与开发Research and Development of Natural Products 食品工艺学Food Technology 生物化学Biochemistry 食品分析Food Analysis 食品机械与设备Food Machinery and Equipme nt理学SCIENCE-----------------------------------------------------------理学SCIENCE课程中文名称课程英文名称矩阵分析Matrix Analysis面向对象程序设计方法Design Methods of Object Oriented Program李代数Lie Algebra代数图论Algebraic Graph Theory代数几何（I）Algebraic Geometry（I）泛函分析Functional Analysis论文选读Study on Selected PapersHopf代数Hopf Algebra基础代数Fundamental Algebra交换代数Commutative Algebra代数几何Algebraic GeometryHopf代数与代数群量子群Hopf Algebra , Algebraic Group and Qua ntum Group量子群表示Representation of Quantum Groups网络算法与复杂性Network Algorithms and Complexity组合数学Combinatorial Mathematics代数学Algebra半群理论Semigroup Theory计算机图形学Computer Graphics图的对称性Graph Symmetry代数拓扑Algebraic Topology代数几何（II）Algebraic Geometry（II）微分几何Differential Geometry多复变函数Analytic Functions of Several Complex Variab les代数曲面Algebraic Surfaces高维代数簇Algebraic Varieties of Higher Dimension数理方程Mathematics and Physical Equation偏微分方程近代方法The Recent Methods of Partial Differential E quations激波理论The Theory of Shock Waves非线性双曲型守恒律解的存在性The Existence of Solutions for Non - linearHyperbolic Conservation Laws粘性守恒律解的稳定性Stability of Solutions for Viscous Conservation Laws微分方程数值解Numerical Methods for Differential Equations小波理论与应用Warelet Theory and Application非线性方程组的数值解法Numerical Methods for No-linear System s of Equations网络算法与复杂性Network Algorithms and ComplexityGraph Theory 60近世代数Modern Algebra高等量子力学Advanced Quantum Mechanics统计力学Statistical Mechanics固体理论Solid State Theory薄膜物理Thin Film Physics计算物理学Computational Physics量子场论Quantum Field Theory非线性物理导论Introduction to Nonlinear Physics固体磁性理论Theory of Magnetism in SolidC语言科学计算方法Scientific Computation Method in C功能材料原理与技术Principle and Technology of Functional Materials 超高真空科学与技术Science and Technology of Ultrahigh Vacuum 60 现代表面分析技术Modern Technology of Surface Analysis现代传感技术Modern Sensor Technology数学模型与计算机模拟Mathematical Models and Computer Simulations 计算物理谱方法Spectral Method in Computational Physics蒙特卡罗方法在统计物理中的应用Applications of the Monte Carlo Method inStatistical Physics理论物理Theoretical Physics固体物理Solid-State Physics近代物理实验Contemporary Physics Experiments计算物理基础Basics of Computational Physics真空与薄膜技术Vacuum & Thin Film Technology高等光学Advanced Optics量子光学与统计光学Quantum Optics and Statistical Optics光电子学与光电信息技术Optoelectronics and Optoelectronic Information Technology图像处理与分析Image Processing and Analysis光纤通信系统System of Fiber Communications计算机网络Computer Networks光电检测与信号处理Optoelectronic Detection and Processing物理光学与光电子技术实验Experiments for Physical Optics and Op toelectronic Technology非线性光学Nonlinear Optics集成光学Integrated Optics光子学器件原理与技术Principle and Technology of Photonics Devices物理光学与信息光子学实验Physical Optics & Information Photonics Experiments现代激光医学Modern Laser Medicine生物医学光子学Biomedicine Photonics激光医学临床实践Clinical Practice for Laser Medicine光纤通信网络Networks of Fiber Communications光接入网技术Technology of Light Access Network全光通信系统All-Optical Communication Systems计算机图形学Computer Graphics信息光学Information Optics光子学专题Special Topics on Photonics激光与近代光学Laser and Contemporary Optics光电子技术Photoelectronic Technique微机系统与接口Micro Computer System and Interface智能仪器Intelligent Instruments高等无机化学Advanced Inorganic Chemistry量子化学(含群论) Quantum Chemistry(including Group Theory)高等分析化学Advanced Analytical Chemistry高等有机化学Advanced Organic Chemistry现代科学前沿选论Literature on Frontiers of Modern Science and Technology激光化学Laser Chemistry激光光谱Laser Spectroscopy稀土化学Rare Earth Chemistry材料化学Material Chemistry生物无机化学导论Bioinorganic Chemistry配位化学Coordination Chemistry膜模拟化学Membrane Mimetic Chemistry晶体工程基础Crystal Engineering催化原理Principles of Catalysis绿色化学Green Chemistry现代有机合成Modern Organic Synthesis无机化学Inorganic Chemistry物理化学Physics Chemistry有机化学Organic Chemistry分析化学Analytical Chemistry现代仪器分析Modern Instrumental Analysis现代波谱学Modern Spectroscopy化学计量学Chemomtrics现代食品分析Modern Methods of Food Analysis天然产物化学Natural Product Chemistry天然药物化学Natural Pharmaceutical Chemistry现代环境分析与监测Analysis and Monitoring of Environment Pollution现代科学前沿选论Literature on Frontiers of Modern Science and Technology计算机在分析化学的应用Computer Application in Analytical Chemistry现代仪器分析技术Modern Instrument Analytical Technique分离科学Separation Science高等环境微生物Advanced Environmental Microorganism海洋资源利用与开发Utilization & Development of Ocean Resources立体化学Stereochemistry高等发光分析Advanced Luminescence Analysis激光光谱分析Laser Spectroscopy Analysis保健食品监督评价Evaluation and Supervision on Health Food s生物电化学Bioelectrochemistry现代技术与中药Modern Technology and Traditional Chinese Medicine高等有机化学Advanced Organic Chemistry中药新药研究与开发Study and Exploitation of Traditional Chinese Medicine药物化学研究方法Pharmaceutical Chemical Research Methods废水处理工程Technology of Wastewater Treatment生物与化学传感技术Biosensors & Chemical Sensors现代分析化学研究方法Research Methods of Modern Analytical Chemistry 神经生物学Neurobiology动物遗传工程Animal Genetic Engineering动物免疫学Animal Immunology动物病害学基础Basis of Animal Disease受体生物化学Receptor Biochemistry动物生理与分子生物学Animal Physiology and Molecular Biochemistry学科前沿讲座Lectures on Frontiers of the Discipline微生物学Microbiology细胞生物学Cell Biology生理学Physiology电生理技术基础Basics of Electricphysiological Technology生理学Physiology生物化学Biochemistry高级水生生物学Advanced Aquatic Biology藻类生理生态学Ecological Physiology in Algae水生动物生理生态学Physiological Ecology of Aquatic Animal 水域生态学Aquatic Ecology水生态毒理学Aquatic Ecotoxicology水生生物学研究进展Advance on Aquatic Biology水环境生态学模型Models of Water Quality藻类生态学Ecology in Algae生物数学Biological Mathematics植物生理生化Plant Biochemistry水质分析方法Water Quality Analysis水产养殖学Aquaculture环境生物学Environmental Biology专业文献综述Review on Special Information分子生物学Molecular Biology学科前沿讲座Lectures on Frontiers of the Discipline植物学Botany动物学Zoology普通生态学General Ecology生物统计学Biological Statistics分子遗传学Molecular Genetics基因工程原理Principles of Gene Engineering基因工程技术Technique for Gene Engineering基因诊断Gene Diagnosis基因组学Genomics医学遗传学Medical Genetics免疫遗传学Immunogenetics基因工程药物学Pharmacology of Gene Engineering高级生化技术Advanced Biochemical Technique基因治疗Gene Therapy肿瘤免疫学Tumour Immunology免疫学Immunology免疫化学技术Methods for Immunological Chemistry毒理遗传学Toxicological Genetics分子病毒学Molecular Virology分子生物学技术Protocols in Molecular Biology神经免疫调节Neuroimmunology普通生物学Biology生物化学技术Biochemic Technique分子生物学Molecular Biology生殖生理与生殖内分泌Reproductive Physiology & Reproductive Endocrinology生殖免疫学Reproductive Immunology发育生物学原理与实验技术Principle and Experimental Technology of Development免疫学Immunology蛋白质生物化学技术Biochemical Technology of Protein受精的分子生物学Molecular Biology of Fertilization免疫化学技术Immunochemical Technology低温生物学原理与应用Principle & Application of Cryobiology不育症的病因学Etiology of Infertility分子生物学Molecular Biology生物化学Biochemistry分析生物化学Analytical Biochemistry医学生物化学Medical Biochemistry医学分子生物学Medical Molecular Biology医学生物化学技术Techniques of Medical Biochemistry生化与分子生物学进展Progresses in Biochemistry and Molecular Biology高级植物生理生化Advanced Plant Physiology and Biochemistry拟南芥—结构与发育Arobidosis-Structure and Development开花的艺术Art of Flowering蛋白质结构基础Principle of Protein Structure生活在美国Living in America分子进化工程Engineering of Molecular Evolution生物工程下游技术Downstream Technique of Biotechnology仪器分析Instrumental Analysis临床检验与诊断Clinical Check-up & Diagnosis药理学Pharmacology文科方面：澳门历史研究|| Study of the History of Macao 办公管理|| Office Management 办公设备运用||Using Desktop Publishing in Business 比较管理学|| Comparative Management 比较诗学||Comparative Poetics 比较文化学|| Comparative Culturology 比较文学研究|| Study o fComparative Literature 必修课4－10学分|| Restricted (4-10 Credits needed) 病理生理学||Pathological Physiology 病理学|| Pathology 病理学|| Pathology 病理学|| Pathology 财务报告介绍|| An Introduction to Financial Accounting Statements 财务报告运用|| Using Fi nancialAccounting Statements 财务管理学|| Financial Management 财务会计学|| Financial Accounting财务理论与方法|| Finance Theory & Methods 财政与金融|| Finance 财政与金融学研究|| Studyof Finance 财政预算|| Preparing Financial Forecasts 产业经济学|| Industrial Econo mics 传统文化与现代化|| Tradition Culture and Modernizat ion 当代国际关系研究|| Contempor aryInternational Relations Studies 当代世界发展研究|| Contemporary World Developme nt Studies当代中国外交与侨务专题研究|| Monographic Studies of Diplomacy and Overseas Ch inese Affairsof Contemporary China 德语(第二外语) || German (2nd foreign language) 第一外语(英语) ||English (1st foreign language) 电力系统|| Power Electronic Systems 电子数据|| Dig italElectronics 电子通信|| Electronic Communications 电子原理|| Electrical Principles 断代文化史研究|| Study of Dynastic History of Culture 多媒体：多媒体应用开发|| Multimedia:Developing Multimedia Application 多用户操作系统|| Multi-User Operating Systems 耳鼻喉科学|| Otolaryngology 发展经济学|| Economics of Development 放射生态学|| Radioecolo gy 分布式应用程序的设计与开发：概况|| Distributed application Design and Development: An Int roduction分子细胞与组织生物学|| Molecular, Cellular and Tissue Biology 分子遗传学|| Molec ularGenetics 妇产科学|| Gynaecology & Obstetrics 妇产科学|| Gynaecology & Obstetric s 高级生物化学|| Advanced Bǐochemistry 高级水生生物学|| Advanced Hydrobiology 工程实践与应用||沟通（提升行业沟通技能）|| Communication (Developing a Communication Strategy for VocationalPurposes)沟通：实用技能|| Communication: Practical Skills管理经济学|| Management Economics管理经济学|| Managerial Economics管理决策|| Management Decision-Making管理决策|| Management Decisions管理理论研究|| Management Theory Studies管理理论与实践|| Management Theory & Practice管理学研究|| Management Research光化学|| Photochemistry国际关系案例分析|| Case Studies of International Affairs国际关系学导论|| Introduction of International Relations国际金融市场研究|| International Financial Market Study国际金融研究|| Study of International Finance国际经济关系研究|| International Economic Relations国际经济环境|| The International Economic Environment国际经济政治制度比较研究|| Comparative Researches on Intennational Economic & PoliticalStructure国际音标的应用|| Application of International Phonetic Alphabet国际战略与大国关系|| International Strategy国际政治经济学|| International Political Economy国际组织与国际制度|| International Organization and International System海外汉学|| Sinology Abroad海外华侨华人概论|| Researches on Overseas Chinese海外华人文学研究|| Study of Overseas Chinese Literature汉语词汇学|| Chinese Lexicology汉语方言调查|| Survey of Chinese Dialects汉语方言概要|| Outline of Chinese Dialects汉语方言学专书选读|| Selected Reading of Chinese Dialectology汉语方言研究|| Studies of Chinese Dialects汉语史名著选读|| Selected Reading of Chinese History汉语音韵学|| Chinese Phonology汉语语法史|| History of Chinese Grammar汉语语法学名著选读|| Selected Reading of Chinese Grammar宏观经济环境|| The Macro Economic Environment宏观经济学|| Macro-economics互联网：WEB服务器的管理|| Internet: Web Server Management互联网：电子商务入门|| Internet : Introducing E Commerce互联网：网络客户服务|| Internet : Internet Client Service互联网：网络配制与管理|| Internet: Configuration and Administration of Internet Servi ces华侨华人史|| History of Overseas Chinese华侨华人与国际关系|| Ethnic Chinese and International Relations环境生物学|| Environmental Biology回族史|| History of Chinese Muslims会计基本理论与方法|| Basic Theories & Approaches of计算数学1 || Mathematics of Computing 1计算数学2 || Mathematics of Computing 2解剖生理学|| Anatomical Physiology金融工程学|| Financial Engineering金融机构风险管理|| Risk Management by Financial Institution金融热点及前沿问题专题研究|| Research on Financia l Central & Up-to-date Issues经济数量分析方法|| Methods of Economic & Mathematic Analysis经济数量分析方法|| Methods of Economic Quantitative Analysis跨文化管理学|| Cross-Cultural Management临床血液病学|| Clinical Hematology马克思主义与当代科技革命|| Marxism & Contemporary Science & Techn ology Revo lution马克思主义与当代社会思潮|| Marxism & Contemporary Social Trends o f Thought 美术理论||Theory of Fine Art美术史|| History of Fine Art蒙古史|| History of the Mongols免疫生物学|| Immunobiology免疫学|| Immunology免疫学|| Immunology民族政策与民族理论研究|| Study of Policies and Theories on Nation alities明清档案|| Archives in Ming and Qing Dynasties模拟电路|| Analogue Electronics南海诸岛史研究|| Study of the History of Islands in the South Chi na Sea企业财务与资本营运|| Company Finance & Capital Operation企业管理理论与实务|| Theory & Practice of Business Management企业应用软件的开发：概况|| Enterprise Application Development: An Introduction 全球化研究|| Globalization Studies人工器官|| Artifical Organs人力资源管理研究方法|| Study Methods of Human Resource Management人体解剖学|| Human Anatomy人文地理文化学|| Culturology of Humane Geo graphy日常交流（法语/德语/意大利语/西班牙语1、2、3级）|| Basic communication in French/German/Italian/Spanish(Levels 1,2&3)日语(第二外语) || Japanese (2nd foreign language)软件开发：抽象数据结构|| Software Development: Abstract Data Structure软件开发：第四代开发环境|| Software Development: Fourth Generation Environment软件开发：高级编程|| Software Development: Advanced Programming软件开发：过程式程序设计|| Software Development: Procedural Programming软件开发：汇编语言和编程|| Software Development: Assembly Language and Interfa ceProgramming软件开发：结构设计方法|| Software Development: Structure Design Methods软件开发：开发计划|| Software Development: Program Planning软件开发：快速应用开发和原型技术|| Software Development: Rapid Applications Dev elopment andPrototyping软件开发：面向对象编程|| Software Development: Object Oriented Programming软件开发：面象对象设计|| Software Development: Object Oriented Design软件开发：事件驱动程序设计|| Software Development:: Event Driven Programming 软件开发：网站开发|| Software Development: Developing the WWW软件开发：应用软件开发|| Software商业法规|| Law for Business商业模式|| Structure of Business商业情报管理|| Business Information Management商业统计1 || Business Statistics 1商业统计2 || Business Statistics 2商业信息技术运用（电子数据表和Word处理应用软件）|| Using Information Technolog y in Business（Spreadsheets &Word Processing Applications）商业信息技术运用（数据库和Word处理应用软件）|| Using Information Technology in Business(Database & Word Processing Applications)社会语言学|| Sociolinguistics审计学|| Auditing生物材料|| Biomaterials生物材料测试技术|| Modern Testing Methods of Biomaterials生物分子的探测和操纵|| Signals Biomolecule Detection and Manipu lation生物力学|| Biomechanics生物流变学|| Biorheology生物信息学|| Bioinformatics生物医学工程前沿|| Advances in Biomedical Engineering生物医学信号处理与建模|| Biomedical Signal Processing and Modeling生物制片及电镜技术|| Biological Section and Electronic Microscope Technique 生物制片及电镜技术|| Biological Section and Electronic Microscope Technique生殖工程|| Reproductive Engineering世界经济与政治研究|| World Economy & Politics Studies水生动物生理生态学|| Physiological Ecology of Aquatic Animal水生生物学研究进展|| Study Progress on Aquatic Biology水域生态学|| Aquatic Ecology思想道德修养|| Understand of Ideology and Morality宋代政治制度研究|| Study of the Political System of Song Dynasty宋明理学史研究|| Study of the History of Neo-Confucianism in Son g and Ming Dy nasties提高个人成效|| Developing Personal Effectiveness通信工程|| Communication and Industry网络会计研究|| Network Accounting Studies微观经济环境|| The Micro Economic Environment微观经济学与宏观经济学|| Micro-economics & Macro-economics微型计算机系统|| Microcomputer Systems文化语言学|| Cultural Linguistics文献学|| Bibliography文学与文化|| Literature and Culture文艺美学|| Aesthetics of Literature and Art文艺学专题研究|| Special Study of Literature Theory西方史学理论|| Historical Theories in the West西方文论|| Western Literary Theories系统开发：关系数据库|| Systems Development: Rational Database Systems 系统开发概论|| Systems Development Introduction系统生态学|| System Ecology细胞超微结构|| Cell Ultrastructure细胞超微生物学|| Cell Ultramicrobiology细胞生长因子|| Cell Growth Factor现代公司会计研究|| Study of Modern Company Accounting现代汉语诗学|| Modern Chinese Poetics现代汉语语法研究|| Studies of Modern Chinese Grammar现代经济与金融理论研究|| Study of Modern Economy & Finance Theory现代商业复合信息|| Presenting complex Business Information现代商业信息|| Presenting Business Information现代审计理论与方法研究|| Study of Modern Audit Theories & Approac hes 香港历史研究|| Study of the History of Hong Kong项目管理|| Project Management项目设计|| Project Studies新制度经济学|| New Institutional Economics新制度经济学|| New Institutional Economics信息工程：应用软件|| Information Technology: Applications Software 1信息技术和信息系统|| Information Technology Information Systems and Services信息技术应用软件|| Information Technology Applications Software选修课总学分|| Total optional credits required血液分子细胞生物学|| Hematologicol Cell and Moleular Biology训诂学史|| History of Chinese Traditional Semantics亚太经济政治与国际关系|| Economy, Politics and International Rela tions in Asian-P acificRegion眼科学|| Ophthalmology眼科学|| Ophthalmology医学分子生物学|| Medical Molecular Biology医学基因工程|| Gene Engineering in Medicine医学统计学|| Medical Statistics医学图像处理|| Image Processing医学物理学|| Medical Physics医学信息学|| Medi-formatics医学遗传学|| Medical Genetics医学影像技术|| Medical Imaging Technigue医学影像诊疗与介入放射学|| Medical Imaging Diagnosis & Treatment and Intervenin g Radiology译介学|| Medio-Translatology音韵学史|| History of Chinese Phonology应用统计|| Applied Statistics应用统计|| Applied Statistics用户支持|| Providing Support to Users语义学|| Semantics藻类生理生态学|| Ecological Physiology in Algae增强团队合作意识|| Developing the Individual Within a Team政治学研究|| Politics Studies中国古代历史文献的考释与利用之一：宋史史料学之二：元史史料学之三：港澳史料学之四：边疆民族史料学|| Utilization and Interpretation of Ancient Chinese Historical Literature中国古代史的断代研究之一：宋史研究之二：元史研究之三：明清史研究|| Dynastic Histor y of China中国古代史的专题研究之一：宋元明清经济史之二：二十世纪宋史研究评价之三：中国文化史之四：中西文化交流史之五：港澳史研究之六：中国边疆民族史之七：西域史研究|| Stud ies ofHistory of China中国古代文化史|| History of Chinese Ancient Culture中国古代文化史|| History of Chinese Ancient Culture中国古代文论|| Ancient Chinese Literary Theories中国古典美学研究|| Study of Chinese Classical Aesthetics中国教育史|| History of Education in China中国经济问题研究|| Economic Problems Research in China中国经济问题研究|| Study of China＇s Economic Issues中国区域文化研究之一：岭南文化史之二：潮汕文化史|| Re search on Chinese Regi onal Culture中国少数民族文化专题研究|| Study of Special Subjects on Cultures of Chinese Mino rityNationality 中国思想史|| History of Chinese Ideologies 中国与大国关系史之一：中美关系史之二：中俄关系史之三：中英关系史之四：中日关系史|| History of Relations Between China andMajor Powers 中国与世界地区关系史之一：与中亚地区关系史之二：与东南亚地区关系史之三：与东北亚地区关系史之四：与南亚地区关系史|| History of Relations Between China and OtherRegions o f the World中国语言文学与文化|| Chinese Languages, Literatures and Cultures中外关系史名著导读|| Reading Guide of Famous Works on the History of Sino-Fore ign Relations中外关系史史料学|| Science of Historical Data on the History of S ino-Foreign Rela tions中外关系史研究|| Researches on the History of Sino-Foreign Relati ons中外史学理论与方法研究|| Researches on Theory and Method About Si no-Foreign HistoryScience中外文化交流史|| History of Sino-Foreign Cultural Exchanges中外文论|| Chinese and Western Literature Theories中西交通史|| History of Communication Between China and the West资本市场研究|| Study of Capital Market资本营运、财务与管理会计理论和方法研究|| Study of Theories & Appr oaches of Ca pitalOperation, Financial Management Accounting资本运营与财务管理研究|| Capital Operation and Financial Management Research 组织工程进展|| Advances in Tissue Engineering组织行为理论|| Organizational Behavior Theory。
第五章 1代数系统的概念
5-1 代数系统的引入
例2 下面均是二元运算的例子。 (1) A为集合，2A为其幂集。f : 2A×2A →2A 。f 可以 是∩、∪、-、。 (2) A={0,1}。f：AAA。f 可以是∧、∨、、 。
一般地，二元运算用符号“”、“◦”、“•”、 “△”、“◇”、“☆”等等表示，并将其写于 两个元素之间，如Z×Z→Z的加法：
定义5-2.1 设“”，“◦”均为集合A上的二元运 算。 (1) 若x, y∈A，都有xyA，则称“”运算在A 上是封闭的(Closed) 。即
xy( x A y A x y A) 在A上封闭
(2) 若x, y∈A，都有xy=yx，则称“”运算在A 上满足交换律(Commutativity) 。即
离散数学
(Discrete Mathematics)
第五章 代数结构(Algebraic Structure)
❖ 以具体代数为研究对象的经典代数，其研究内容、 基本理论和方法，主要反映在初等代数和高等代数 （工科的线性代数）两部分的现代教育中。
❖ 从19世纪早期由法国数学家Galois(1811-1832)创始， 近200年来经历起伏、逐渐成熟的代数系统，常被 人们冠以代数结构、抽象代数及近世代数(Modern Algebra)等美称。
xy(x A y A x y y x)
在A上可交换
5-2 运算及其性质
(3) 若x, y, z∈A，都有x(yz)=(xy)z，则称“” 运算在A上满足结合律(Associativity) 。即
在A上可结合 xyz( x A y A z A
x(y z) (x y) z)
(4) 若x, y, z∈A，都有x(y◦z)=(xy)◦(xz) ，则称 “”运算对“◦”运算满足左分配律； 若x, y, z∈A，都有(x◦y)z=(xz)◦(yz) ，则称“” 运算对“◦”运算满足右分配律。若二者均成立， 则称“”运算对“◦”运算满足分配律 (Distributivity) 。
大学各专业名称英文翻译——理科SCIENCE
大学各专业名称英文翻译——理科SCIENCE理科 SCIENCE课程中文名称课程英文名称矩阵分析 Matrix Analysis面向对象程序设计方法 Design Methods of Object oriented Program李代数 Lie Algebra代数图论 Algebraic Graph Theory代数几何（I） Algebraic Geometry（I）泛函分析 Functional Analysis论文选读 Study on Selected PapersHoof代数 Hoof Algebra基础代数 Fundamental Algebra交换代数 Commutative Algebra代数几何 Algebraic GeometryHoof代数与代数群量子群 Hoof Algebra , Algebraic Group and Qua numb G roup量子群表示 Representation of Quantum Groups网络算法与复杂性 Network Algorithms and Complexity组合数学 Combinatorial Mathematics代数学 Algebra半群理论 Semigroup Theory计算机图形学 Computer Graphics图的对称性 Graph Symmetry代数拓扑 Algebraic Topology代数几何（II） Algebraic Geometry（II）微分几何 Differential Geometry多复变函数 Analytic Functions of Several Complex Varian les代数曲面 Algebraic Surfaces高维代数簇 Algebraic Varieties of Higher Dimension数理方程 Mathematics and Physical Equation偏微分方程近代方法 The Recent Methods of Partial Differential Equatio ns激波理论 The Theory of Shock Waves非线性双曲型守恒律解的存在性 The Existence of Solutions for Non-linea r Hyperbolic Conservation Laws粘性守恒律解的稳定性 Stability of Solutions for Viscous Conservation Laws微分方程数值解 Numerical Methods for Differential Equations小波理论与应用 Wavelet Theory and Application非线性方程组的数值解法 Numerical Methods for No-linear System s of Eq uations网络算法与复杂性 Network Algorithms and Complexity Graph Theory 60近世代数 Modern Algebra高等量子力学 Advanced Quantum Mechanics统计力学 Statistical Mechanics固体理论 Solid State Theory薄膜物理 Thin Film Physics计算物理学 Computational Physics量子场论 Quantum Field Theory非线性物理导论 Introduction to Nonlinear Physics固体磁性理论 Theory of Magnetism in SolidC语言科学计算方法 Scientific Computation Method in C功能材料原理与技术 Principle and Technology of Functional Materials 超高真空科学与技术 Science and Technology of Ultrahigh Vacuum 60现代表面分析技术 Modern Technology of Surface Analysis现代传感技术 Modern Sensor Technology数学模型与计算机模拟 Mathematical Models and Computer Simulations计算物理谱方法 Spectral Method in Computational Physics蒙特卡罗方法在统计物理中的应用 Applications of the Monte Carlo Method in Statistical Physics理论物理 Theoretical Physics固体物理 Solid-State Physics近代物理实验 Contemporary Physics Experiments计算物理基础 Basics of Computational Physics真空与薄膜技术 Vacuum & Thin Film Technology高等光学 Advanced Optics量子光学与统计光学 Quantum Optics and Statistical Optics光电子学与光电信息技术 Optoelectronics and Optoelectronic Information Technology图像处理与分析 Image Processing and Analysis光纤通信系统 System of Fiber Communications计算机网络 Computer Networks光电检测与信号处理 Optoelectronic Detection and Processing物理光学与光电子技术实验 Experiments for Physical Optics and Optoelec tronic Technology非线性光学 Nonlinear Optics集成光学 Integrated Optics光子学器件原理与技术 Principle and Technology of Photonics Devices 物理光学与信息光子学实验 Physical Optics & Information Photonics Expe riments现代激光医学 Modern Laser Medicine生物医学光子学 Biomedicine Photonics激光医学临床实践 Clinical Practice for Laser Medicine光纤通信网络 Networks of Fiber Communications光接入网技术 Technology of Light Access Network全光通信系统 All-Optical Communication Systems计算机图形学 Computer Graphics信息光学 Information Optics光子学专题 Special Topics on Photonics激光与近代光学 Laser and Contemporary Optics光电子技术 Photo electronic Technique微机系统与接口 Micro Computer System and Interface智能仪器 Intelligent Instruments高等无机化学 Advanced Inorganic Chemistry量子化学(含群论) Quantum Chemistry(including Group Theory)高等分析化学 Advanced Analytical Chemistry高等有机化学 Advanced organic Chemistry现代科学前沿选论 Literature on Frontiers of Modern Science and Techno logy激光化学 Laser Chemistry激光光谱 Laser Spectroscopy稀土化学 Rare Earth Chemistry材料化学 Material Chemistry生物无机化学导论 Bioinorganic Chemistry配位化学 Coordination Chemistry膜模拟化学 Membrane Mimetic Chemistry晶体工程基础 Crystal Engineering催化原理 Principles of Catalysis绿色化学 Green Chemistry现代有机合成 Modern organic Synthesis无机化学 Inorganic Chemistry物理化学 Physics Chemistry有机化学 organic Chemistry分析化学 Analytical Chemistry现代仪器分析 Modern Instrumental Analysis现代波谱学 Modern Spectroscopy化学计量学 Chemistries现代食品分析 Modern Methods of Food Analysis天然产物化学 Natural Product Chemistry天然药物化学 Natural Pharmaceutical Chemistry现代环境分析与监测 Analysis and Monitoring of Environment Pollution 现代科学前沿选论 Literature on Frontiers of Modern Science and Techno logy计算机在分析化学的应用 Computer Application in Analytical Chemistry 现代仪器分析技术 Modern Instrument Analytical Technique分离科学 Separation Science高等环境微生物 Advanced Environmental Microorganism海洋资源利用与开发 Utilization & Development of Ocean Resources立体化学 Stereochemistry高等发光分析 Advanced Luminescence Analysis激光光谱分析 Laser Spectroscopy Analysis保健食品监督评价 Evaluation and Supervision on Health Food s生物电化学 Bioelectrochemistry现代技术与中药 Modern Technology and Traditional Chinese Medicine高等有机化学 Advanced organic Chemistry中药新药研究与开发 Study and Exploitation of Traditional Chinese Medi cine药物化学研究方法 Pharmaceutical Chemical Research Methods废水处理工程 Technology of Wastewater Treatment生物与化学传感技术 Biosensors & Chemical Sensors现代分析化学研究方法 Research Methods of Modern Analytical Chemistry 神经生物学 Neurobiology动物遗传工程 Animal Genetic Engineering动物免疫学 Animal Immunology动物病害学基础 Basis of Animal Disease受体生物化学 Receptor Biochemistry动物生理与分子生物学 Animal Physiology and Molecular Biochemistry分析生物化学 Analytical Biochemistry学科前沿讲座 Lectures on Frontiers of the Discipline微生物学 Microbiology细胞生物学 Cell Biology生理学 Physiology电生理技术基础 Basics of Electrophysiological Technology 生理学 Physiology生物化学 Biochemistry高级水生生物学 Advanced Aquatic Biology藻类生理生态学 Ecological Physiology in Algae水生动物生理生态学 Physiological Ecology of Aquatic Animal 水域生态学 Aquatic Ecology水生态毒理学 Aquatic Ecotoxicology水生生物学研究进展 Advance on Aquatic Biology水环境生态学模型 Models of Water Quality藻类生态学 Ecology in Algae生物数学 Biological Mathematics植物生理生化 Plant Biochemistry水质分析方法 Water Quality Analysis水产养殖学 Aquaculture环境生物学 Environmental Biology专业文献综述 Review on Special Information分子生物学 Molecular Biology学科前沿讲座 Lectures on Frontiers of the Discipline植物学 Botany动物学 Zoology普通生态学 General Ecology生物统计学 Biological Statistics分子遗传学 Molecular Genetics基因工程原理 Principles of Gene Engineering高级生物化学 Advanced Biochemistry基因工程技术 Technique for Gene Engineering基因诊断 Gene Diagnosis基因组学 Genomics医学遗传学 Medical Genetics免疫遗传学 Immunogenetics基因工程药物学 Pharmacology of Gene Engineering 高级生化技术 Advanced Biochemical Technique基因治疗 Gene Therapy肿瘤免疫学 Tumor Immunology免疫学 Immunology免疫化学技术 Methods for Immunological Chemistry 毒理遗传学 Toxicological Genetics分子病毒学 Molecular Virology分子生物学技术 Protocols in Molecular Biology神经免疫调节 Neuroimmunology普通生物学 Biology生物化学技术 Biochemical Technique分子生物学 Molecular Biology生殖生理与生殖内分泌 Reproductive Physiology & Reproductive Endocrino logy生殖免疫学 Reproductive Immunology发育生物学原理与实验技术 Principle and Experimental Technology of Dev elopment免疫学 Immunology蛋白质生物化学技术 Biochemical Technology of Protein受精的分子生物学 Molecular Biology of Fertilization免疫化学技术 Immunochemical Technology低温生物学原理与应用 Principle & Application of Cryobiology不育症的病因学 Etiology of Infertility分子生物学 Molecular Biology生物化学 Biochemistry分析生物化学 Analytical Biochemistry医学生物化学 Medical Biochemistry医学分子生物学 Medical Molecular Biology医学生物化学技术 Techniques of Medical Biochemistry生化与分子生物学进展 Progresses in Biochemistry and Molecular Biology 高级植物生理生化 Advanced Plant Physiology and Biochemistry拟南芥—结构与发育 Arabidopsis-Structure and Development开花的艺术 Art of Flowering蛋白质结构基础 Principle of Protein Structure文档来源为:从网络收集整理.word版本可编辑.欢迎下载支持. 生活在美国 Living in America分子进化工程 Engineering of Molecular Evolution生物工程下游技术 Downstream Technique of Biotechnology仪器分析 Instrumental Analysis临床检验与诊断 Clinical Check-up & Diagnosis药理学 Pharmacology。
大学各专业名称英文翻译——理科SCIENCE
大学各专业名称英文翻译理科SCIENCE 理科SCIENCE课程中文名称课程英文名称矩阵分析Matrix Analysis面向对象程序设计方法Desig n Methods of Object orie nted Program 李代数Lie Algebra代数图论Algebraic Graph Theory代数几何（I ）Algebraic Geometry （I）泛函分析Functional Analysis论文选读Study on Selected PapersHoof 代数Hoof Algebra基础代数Fundamental Algebra交换代数Commutative Algebra代数几何Algebraic Geometry \ /Hoof 代数与代数群量子群Hoof Algebra , Algebraic Group and Qua numb G roup量子群表示Representation of Quantum Groups网络算法与复杂性Network Algorithms and Complexity组合数学Combinatorial Mathematics代数学Algebra半群理论Semigroup Theory计算机图形学Computer Graphics图的对称性Graph Symmetry代数拓扑Algebraic Topology代数几何(II ) Algebraic Geometry (II )微分几何Differential Geometry多复变函数Analytic Functions of Several Complex Varian les代数曲面Algebraic Surfaces高维代数簇Algebraic Varieties of Higher Dimension数理方程Mathematics and Physical Equation偏微分方程近代方法The Recent Methods of Partial Differential Equatio ns 激波理论The Theory of Shock Waves非线性双曲型守恒律解的存在性The Existe nee of Solutio ns for Non-li nea r Hyperbolic Con servati on Laws粘性守恒律解的稳定性Stability of Solutio ns for Viscous Con servation Laws微分方程数值解Numerical Methods for Differential Equations小波理论与应用Wavelet Theory and Application非线性方程组的数值解法Numerical Methods for No-li near System s of Eq uati ons网络算法与复杂性Network Algorithms and Complexity Graph Theory 60近世代数Modern Algebra高等量子力学Advaneed Quantum Mechanics统计力学Statistical Mechanics固体理论Solid State Theory薄膜物理Thin Film Physics计算物理学Computational Physics量子场论Quantum Field Theory非线性物理导论Introduction to Nonlinear Physics固体磁性理论Theory of Magnetism in SolidC语言科学计算方法Scientific Computation Method in C功能材料原理与技术Prin ciple and Tech no logy of Fun cti onal Materials超高真空科学与技术Scie nee and Techno logy of Ultrahigh Vacuum 60现代表面分析技术Modern Technology of Surface Analysis现代传感技术Moder n Sen sor Tech no logy数学模型与计算机模拟Mathematical Models and Computer Simulatio ns计算物理谱方法Spectral Method in Computational Physics蒙特卡罗方法在统计物理中的应用Applicatio ns of the Mon te Carlo Method in Statistical Physics理论物理Theoretical Physics固体物理Solid-State Physics近代物理实验Con temporary Physics Experime nts 计算物理基础Basics of Computational Physics真空与薄膜技术Vacuum & Thin Film Technology高等光学Advaneed Optics量子光学与统计光学Quantum Optics and Statistical Optics X光电子学与光电信息技术Optoelectr onics and Optoelectro nic In formatio n Tech no logy图像处理与分析Image Processing and Analysis光纤通信系统System of Fiber Communications计算机网络Computer Networks光电检测与信号处理Optoelectr onic Detect ion and Process ing物理光学与光电子技术实验Experime nts for Physical Optics and Optoelec tronic Tech no logy非线性光学Nonlinear Optics集成光学Integrated Optics光子学器件原理与技术Prin ciple and Tech no logy of Phot onics Devices物理光学与信息光子学实验Physical Optics & In formation Photo nics Expe rime nts现代激光医学Modern Laser Medicine生物医学光子学Biomedicine Photonics激光医学临床实践Clinical Practice for Laser Medicine光纤通信网络Networks of Fiber Communications光接入网技术Tech no logy of Light Access Network全光通信系统All-Optical Communication Systems计算机图形学Computer Graphics信息光学Information Optics光子学专题Special Topics on Photonics激光与近代光学Laser and Con temporary Optics光电子技术Photo electronic Technique微机系统与接口Micro Computer System and In terface智能仪器In tellige nt In strume nts高等无机化学Advaneed Inorganic Chemistry量子化学(含群论)Quantum Chemistry(including Group Theory) 高等分析化学Advaneed Analytical Chemistry高等有机化学Advaneed organic Chemistry现代科学前沿选论Literature on Fron tiers of Moder n Science and Tech no logy激光化学Laser Chemistry激光光谱Laser Spectroscopy稀土化学Rare Earth Chemistry材料化学Material Chemistry生物无机化学导论Bioinorganic Chemistry配位化学Coord in ati on Chemistry膜模拟化学Membrane Mimetic Chemistry晶体工程基础Crystal Engineering催化原理Principles of Catalysis绿色化学Green Chemistry现代有机合成Modern organic Synthesis无机化学Inorganic Chemistry物理化学Physics Chemistry有机化学organic Chemistry分析化学Analytical Chemistry现代仪器分析Modern Instrumental Analysis现代波谱学Modern Spectroscopy化学计量学Chemistries现代食品分析Modern Methods of Food Analysis天然产物化学Natural Product Chemistry天然药物化学Natural Pharmaceutical Chemistry现代环境分析与监测Analysis and Monitoring of Environment Pollution现代科学前沿选论Literature on Fron tiers of Moder n Science and Tech no logy计算机在分析化学的应用Computer Application in An alytical Chemistry现代仪器分析技术Modern Instrument Analytical Technique分离科学Separation Scienee高等环境微生物Advaneed Environmentai Microorganism海洋资源利用与开发Utilization & Development of Ocean Resources立体化学Stereochemistry高等发光分析Advaneed Luminescenee Analysis激光光谱分析Laser Spectroscopy Analysis保健食品监督评价Evaluation and Supervision on Health Food s生物电化学Bioelectrochemistry现代技术与中药Moder n Tech no logy and Traditi onal Chin ese Medici ne 高等有机化学Advaneed organic Chemistry中药新药研究与开发Study and Exploitation of Traditional Chinese Medi cine 药物化学研究方法Pharmaceutical Chemical Research Methods废水处理工程Tech no logy of Wastewater Treatme nt生物与化学传感技术Biose nsors & Chemical Se nsors现代分析化学研究方法Research Methods of Modern An alytical Chemistry神经生物学Neurobiology动物遗传工程Animal Genetic Engineering动物免疫学Animal Immunology动物病害学基础Basis of Animal Disease受体生物化学Receptor Biochemistry动物生理与分子生物学Animal Physiology and Molecular Biochemistry分析生物化学Analytical Biochemistry学科前沿讲座Lectures on Frontiers of the Discipline微生物学Microbiology细胞生物学Cell Biology生理学Physiology电生理技术基础Basics of Electrophysiological Tech no logy生理学Physiology生物化学Biochemistry高级水生生物学Advaneed Aquatic Biology藻类生理生态学Ecological Physiology in Algae水生动物生理生态学Physiological Ecology of Aquatic Ani mal 水域生态学Aquatic Ecology水生态毒理学Aquatic Ecotoxicology水生生物学研究进展Advanee on Aquatic Biology水环境生态学模型Models of Water Quality藻类生态学Ecology in Algae生物数学Biological Mathematics植物生理生化Plant Biochemistry水质分析方法Water Quality Analysis水产养殖学Aquaculture环境生物学Environmental Biology专业文献综述Review on Special Information分子生物学Molecular Biology学科前沿讲座Lectures on Frontiers of the Discipline 植物学Bota ny动物学Zoology普通生态学General Ecology生物统计学Biological Statistics分子遗传学Molecular Genetics基因工程原理Principles of Gene Engineering高级生物化学Advaneed Biochemistry基因工程技术Technique for Gene Engineering基因诊断Gene Diag no sis基因组学Genomics医学遗传学Medical Genetics免疫遗传学Immunogenetics基因工程药物学Pharmacology of Gene Engineering 高级生化技术Advaneed Biochemical Technique基因治疗Gene Therapy肿瘤免疫学Tumor Immuno logy \ /免疫学Immuno logy免疫化学技术Methods for Immunological Chemistry毒理遗传学Toxicological Genetics分子病毒学Molecular Virology分子生物学技术Protocols in Molecular Biology神经免疫调节Neuroimmunology普通生物学Biology生物化学技术Biochemical Technique分子生物学Molecular Biology生殖生理与生殖内分泌Reproductive Physiology & Reproductive En docri no logy生殖免疫学Reproductive Immuno logy发育生物学原理与实验技术Prin ciple and Experime ntal Techn ology of Developme nt免疫学Immuno logy蛋白质生物化学技术Biochemical Tech nology of Protein受精的分子生物学Molecular Biology of Fertilization免疫化学技术Immuno chemical Tech no logy低温生物学原理与应用Prin ciple & Application of Cryobiology不育症的病因学Etiology of In fertility分子生物学Molecular Biology生物化学Biochemistry分析生物化学Analytical Biochemistry医学生物化学Medical Biochemistry医学分子生物学Medical Molecular Biology医学生物化学技术Techniques of Medical Biochemistry生化与分子生物学进展Progresses in Biochemistry and Molecular Biology 高级植物生理生化Advaneed Plant Physiology and Biochemistry拟南芥一结构与发育Arabidopsis-Structure and Development开花的艺术Art of Flowering蛋白质结构基础Principle of Protein Structure生活在美国Living in America分子进化工程Engineering of Molecular Evolution生物工程下游技术Down stream Tech nique of Biotech no logy仪器分析Instrumental Analysis临床检验与诊断Clinical Check-up & Diagnosis 药理学Pharmacology。
Vocabulary-词汇表
vocabulary sumabnormal[æb'nɔ:məl] adj.反常的，不规则的absorb [əb'sɔ:b, -'zɔ:b] vt. 吸收；吸引；accumulation [ə,kju:mju'leiʃən] n. 积聚，累积acid-base indicator 酸碱指示剂actinide elements 锕系元素activated complex 活化络合物adsorb [æd'sɔ:b] vt. 吸附aggregation [,æɡri'ɡeiʃən] n. 聚合，聚集；聚集体algebraic sum 代数和alkali ['ælkəlai] n. 碱；可溶性无机盐adj.碱性alkali metal 碱金属allotrope['æləutrəup]n.同素异形体aluminum[ə'lju:minəm]n.铝amorphous[ə'mɔ:fəs]adj.无定形的amphiprotic [æmfi'prɔtik] adj. 两性的analogous to类推为；类同于analytical [,ænə'litik,-kəl] adj. 分析的and vice versa 反过来也一样；反之亦然anode ['ænəud] n.阳极，正极antiferromagnetic ['ænti,ferəumæɡ'netik]adj. 反铁磁性的approximate vt. 使…接近；近似； vi. 接近于；近似于adj. 大概的；近似的approximation [ə,prɔksi'meiʃən] n. 接近；近似值；近似aqueous ['eikwiəs] adj. 水的astronomy [ə'strɔnəmi] n. 天文学atmospheren.大气,气氛atomic radius原子半径carbonates n.碳酸盐chloride['klɔ:raid]n.氯化物deliquescence[,deli'kwesəns] n.潮解density['densiti]n.密度Autoionization [,ɔ:təu,aiənai'zeiʃən, -ni'z-] n. 自电离average n. 平均bactericide [bæk'tiəri,said] n.杀菌剂beadtest熔珠试验binary a.二元的bipyramid [bai'pirəmid] n. 双锥体bleaching agent漂白剂Bond Moment 键矩borax['bɔ:ræks]n.硼砂boron['bɔ:rɔn]n.硼brass [brɑ:s] n.黄铜buffer solution 缓冲溶液calomel ['kæləmel] n.甘汞；氯化亚汞Cartesian coordinates笛卡儿坐标直角坐标catalyst ['kætəlist] n. 催化剂cathode ['kæθəud] n. 阴极chiral ['kaiərəl] adj.手征的(指不能叠置于镜像上的分子)，手征性的；不对称的chromium ['krəumjəm] n.铬cobalt [kə'bɔ:lt, 'kəubɔ:lt] n.钴collision theory 碰撞理论combination of 的组合complementary [kɔmplə'mentəri] a.补充的complexation n. 络合；络合作用components n.组件；成份composition [,kɔmpə'ziʃən] n.组成configuration [kən,figju'reiʃən] n. 结构,布局,形态conjugate acid 共轭酸conjugate base 共轭碱constant ['kɔnstənt] adj. 不变的；恒定的；n. 常数；恒量consume [kən'sju:m] vt.消耗；耗尽；用掉coordination bond 配位键；配价键coordination compound 配位化合物[亦称作coordination complex]copper ['kɔpə] n.铜corresponding [,kɔris'pɔndiŋ] a 符合的,一致的,相同corundum[kə'rʌndəm]n.金刚砂，刚玉cosmochemistry [,kɔzmə'keməstri] n. 宇宙化学；天体化学counteract[,kauntə'rækt]vt.抵消；中和；covalent radius 共价半径crystal ['kristəl] n. 水晶；结晶，晶体；crystalsn.晶体cubic['kju:bik]n.立方晶系cyanide ['saiənaid] n.氰化物decomposition [,di:kɔmpə'ziʃən] n. 分解decompositionreaction分解反应deficient[di'fiʃənt]adj.有缺陷的degree of polymerization聚合度dehydration [,di:hai'dreiʃən] n.脱水depict [di'pikt] vt.描述desiccant ['desikənt] n.干燥剂diagonal[dai'æɡənəl] adj. 对角线的diamagnetic [,daiəmæɡ'netik] n. 反磁性体adj.反磁性的differentiating effect 区分效应diffraction [di'frækʃən] n. （光，声等的）衍射，绕射diluted[dai'lju:tid,di-]adj.稀释的dilution law n. 稀释律dimensional [di'menʃənəl, dai-] adj. 空间的；尺寸的dimensionless [di'menʃənlis; dai-] dj. 无量纲的dimensionsn.规模，大小dipole forces取向力discontinuous ['diskən'tinjuəs] a. 不连续的,中断的,间断的disorder [dis'ɔ:də] n. 混乱Dispersion forces色散力disproportionate [,disprə'pɔ:ʃənit] a.不成比例的disproportionating vi.,vt.(使)歧化disproportionation ['disprə,pɔ:ʃə'neiʃən]n.歧化作用distorted [dis'tɔ:tid] adj. 歪曲的；受到曲解的v. 扭曲distribution [,distri'bju:ʃən] n. 分配；分布dodecahedron [,dɔudekə'hi:drən] n. 12面体dual nature 二重性，双重性electrochemical cell 电化学电池electrode potential 电极电势；电极电位electrolysis [,ilek'trɔlisis] n.电解electromagnetic radiation 电磁辐射electron affinity 电子亲合性electron shell 电子壳层；电子壳；电子层electron subshells 电子亚层electronegativity [i'lektrəu,neɡə'tivəti] n.电负性；elementary substance单质emission [i'miʃən] n. 发射,射出,发行empirical [em'pirikəl] a. 经验主义的endothermic reaction 吸热反应enthalpy [en'θælpi] n. 焓,热函(符号H)[亦作heat content,total heat]enzyme ['enzaim] n. 酶equivalent [i'kwivələnt] adj. 等价的，相等的； n. 等价物，相等物essence ['esəns] n. 本质，实质；精华；香精excess [ik'ses, 'ekses] a.过量的excited state 受激状态；激发态exothermic reaction 放热反应facile ['fæsail] adj.灵巧的；温和的features ['fi:tʃə] n.特征；ferrimagnetic [,ferimæɡ'netic] dj.亚铁磁的ferromagnetic ['ferəumæɡ'netik] adj. 铁磁体；铁磁的fluorine ['flu（:）əri:n] n.氟fractional precipitation 分步沉淀fractionate ['frækʃəneit] vt.分离Fullerenes.富勒烯fundamental [,fʌndə'mentəl] adj. 基本的，根本的n. 基本原理；基本原则fused [fju:zd] v.熔化geometric isomer几何异构体geometry [dʒi'ɔmitri] n. 几何学germanium[dʒə:'meiniəm]n.锗granule ['ɡrænju:l] n.细粒，颗粒graphite ['ɡræfait] n. 石墨ground state n. 基态halide ['hælaid] n.卤化物adj.卤族的，卤化物的halogen ['hælədʒin] n.卤(素)helical ['helikəl] adj.螺旋形的heterogeneous [,hetərəu'dʒi:njəs] adj.由不同成分形成的；不均匀的；多相的hexagonal[hek'sæɡənəl]n.六方晶系homogeneous [,hɔmə'dʒi:niəs, ,həu-] adj. 同种的；均匀的homonuclear [,hɔmə'nju:kliə] adj. 同核的hybrid ['haibrid] n. 混合物； adj. 杂种的；混合的hybridization [,haibridai'zeiʃən, -di'z-] n.杂化hydridesn.氢化物hydrogen bond氢键hydrolysis [hai'drɔlisis] n. 水解作用hydroxide [hai'drɔksaid] n. 氢氧化物ignition[iɡ'niʃən]n.点火，点燃impurity defects杂质缺陷incubation period 发酵周期；孵育期；induced dipole forces诱导力inert [i'nə:t] adj. 惰性的；inert gas 惰性气体inevitable [in'evitəbl] adj. 必然的，不可避免的initially [i'niʃəli] adv. 最初innovation [,inəu'veiʃən] n. 创新，革新；新方法inorganic [inɔ:'ɡænik] adj. 无机的instantaneous [,instən'teinjəs] adj. 即时的；瞬间的；猝发的integer ['intidʒə] n. 整数interconvert [,intəkən'və:t] vt. 互变；互换ionization [,aiənai'zeiʃən; -ni'z-] n.电离作用ionization energy 电离能isoelectronic[,aisəuilek'trɔnik]adj.等电子的isolated system 孤立系统isomer ['aisəumə] n.同分异构体；同分异构物kinetic [ki'netik, kai-] adj. 运动的；活跃的kinetics [ki'netiks, kai-] n. 动力学lanthanide ['lænθənaid] n. 镧系元素lanthanide contraction 镧系收缩latent defect本征缺陷lattice['lætis]n.格子；晶格Le Chatelier's principle 勒夏特列原理lead[li:d]n.铅lectromotive force 电动势leveling effect. 拉平效应ligand ['liɡənd; 'lai-] n.配体；配位体liquid ammonia 液氨literature ['litərətʃə] n.文献；著作lithium ['liθiəm] n. 锂lithium aluminium hydride氢化铝锂litmus ['litməs] n. 石蕊lotion ['ləuʃən] n.洗液magnesium [mæɡ'ni:ziəm, -ʃi-]n. 镁magnetism ['mæɡnitizəm] n. 磁性，磁力；磁学magnitude ['mæɡnitju:d] n. 大小manganese [,mæŋgə'ni:z, 'mæŋgəni:z] n.锰matching ['mætʃiŋ] adj. 相配的；相称的；一致的n. 匹配v. 使…相配mechanism ['mekənizəm] n.原理medium ['mi:diəm, -djəm] n. 溶剂,介质melting point熔点Mercury ['mə:kjuri] n.水银metaboricacid偏硼酸metal alloy金属合金metalloid['metəlɔid]n.非金属；类金属；准金属metallurgy [me'tælədʒi, 'metələ:dʒi] n. 冶金；冶金术；冶金学metaperiodic acid偏高碘酸.. metatheticalreaction复分解反应methyl orange 甲基橙microstate ['maikrəusteit] n微观状态moist [mɔist] a.潮湿的,湿润的monoclinic [,mɔnəu'klinik] adj.单斜的；单斜晶体的monodentate.. 单配位基,单原子螯合配体Monoprotic acid 一元酸multiphase ['mʌltifeiz] adj. 多相的neutralization reaction 中和反应nickel ['nikl] n.镍Nitrates n. 硝酸盐nitrite ['naitrait] n.亚硝酸盐nitrogen ['naitrədʒən] n.氮nitrogen dioxide二氧化氮nitrous acid亚硝酸nonequivalent adj. 非等值的；非等效的octahedral [,ɔktə'hedrəl, -'hi:-] adj. 八面体的；有八面的odorless ['əudəlis] adj.没有气味的omit [əu'mit] vt. 省略optical isomer光学异构体order of magnitude 数量级organic [ɔ:'ɡænik] adj. 有机的orientation [,ɔ:rien'teiʃən, əu-] n. 方向；定向；overlap [,əuvə'læp, 'əuvəlæp] . 重叠；重复oxidation number 氧化值oxidizing agent 氧化剂paramagnetic [,pærəmæɡ'netik] adj. 顺磁性的；常磁性的n. 顺磁物质；顺磁体parameter [pə'ræmitə] n.参(变)数；参(变)量;参项passivate ['pæsiveit] vt.使钝化penetration [,peni'treiʃən] n. 侵入；突破；洞察力；渗透perchlorate [pə'kləureit] n.高氯酸盐Periodic law 周期律；门捷列夫氏定律periodic [,piəri'ɔdik] adj. 周期的，定期的periodic acid过碘酸；高碘酸peroxides n.过氧化物（peroxide的复数）petroleum[pi'trəuliəm,pə-]n.石油phase [feiz] n. 相phase boundary 相界面；相界线phenolphthalein [,fi:nɔl'fθæliin, -li:n] n. 酚酞phlogiston [flɔ'dʒistɔn, fləu-] n.燃素phosphate ['fɔsfeit] n.磷酸盐phosphorus ['fɔsfərəs] n.磷photon ['fəutɔn] n. [物]光子；辐射量子plastic ['plæstik,'plɑ:s-]adj.可塑的,弹性polarizability['pəulə,raizə'biləti]n.极化率polonium [pə'ləuniəm] n.钋polyphosphoric acid多磷酸polyprotic acid 多元酸positive ['pɔzətiv, -zi-] adj.积极的；正的，阳性的； n. 正片；正数potential [pə'tenʃ(ə)l] n. 电位，电势potential difference位差，势差；电位差precipitate [pri'sipitit, -teit] n. 沉淀物vt. 使沉淀precipitation [pri,sipi'teiʃən] n. 沉淀predict [pri'dikt] v. 预知,预言,预报pre-exponential factor指数前的因子prescript ['priskript, pri'skript] adj. 规定的；n.；规定promote [prəu'məut] vt.促进；提升propellent [prəu'pelənt] n.推进燃料proportional [prə'pɔ:ʃənl] a. 成比例的proton ['prəutɔn] n.质子；氕核proton acceptor质子受体proton donor 质子给予体pungent odor刺激气味purification [,pjuərifi'keiʃən]n.净化；提纯pyrophosphoric acid焦磷酸pyrosulfuric acid焦硫酸=disulfuric acid qualitative ['kwɔlitətiv, -tei-] adj. 定性的；质的，性质上的qualitative analysis 定性分析；定量分析quilibrium [,i:kwi'libriəm] n. 平静quotient ['kwəuʃənt] n.商radioactive [,reidiəu'æktiv] adj.放射性的；有辐射的rearranging [,ri:ə'reindʒ] n. 重排redox ['ri:dɔks] n. 氧化还原剂；氧化还原反应redox reaction 氧化还原反应reducing agent 还原剂releases vt.n. 释放repulsion [ri'pʌlʃən] n. 排斥reversible process 可逆过程rhombic sulfur斜方硫rhombohedraln.三方晶系rust [rʌst] n. 锈；生锈saturated ['sætʃəreitid] adj. 饱和的；深颜色的；渗透的v. 使渗透，使饱和seesaw ['si:sɔ:] adj. 互的；前后动的vi.上下来回摇动 vt. 使上下或来回摇动selenium [si'li:niəm] n.硒sensitivity ['sensi'tiviti] n.敏感sequence ['si:kwəns] n. 序列；顺序shielding effect 屏蔽效应；屏蔽作用silica['silikə]n.二氧化硅silicon['silikən,-kɔn]n.硅silver ['silvə] n.银sodium hydrosulfite保险粉；连二硫酸钠solubility [,sɔlju'biləti] n.溶解性，可溶性；溶解度solubility product 溶度积spatial ['speiʃəl] adj. 空间的；存在于空间的；受空间条件限制的spectrum ['spektrəm] n.光谱；]频谱sphere[sfiə]n.球体sphericadj. 球的；球状的（等于spherical）spherical coordinates 球面坐标spin quantum number n. 自旋量子数spontaneous [spɔn'teiniəs] adj. 自发的statistical [stə'tistikəl] adj. 统计的；统计学的stereoisomer [,steriəu'aisəmə; ,stiə-] n.立体异构体stoichiometric coefficient 化学计量系数，化学计算系数stoichiometric equation 化学计算方程式sublimation [,sʌbli'meiʃən] n.升华subshell ['sʌbʃel] n.支壳层，亚壳层substitution [,sʌbsti'tju:ʃən] n. 代替；置换；代替物substitution reaction取代反应；置换反应subtracting [səb'trækt]n. 减法sulfates n. 硫化物；硫酸盐sulfide ['sʌlfaid] n.硫化物symmetry ['simitri] n. 对称（性）system ['sistəm] n. 系统tellurium [te'ljuəriəm, tə-]n.碲tetragonal[te'træɡənəl]n.四方晶系tetrahedral [,tetrə'hi:drəl; -'he-] adj.四面体的；由四面的thermochemistry [,θə:məu'kemistri] n. 热化学thiosulfate [,θaiəu'sʌlfeit] n.硫代硫酸盐thiosulfuric acid [,θaiəusʌl'fju:rik] 硫代硫酸tin[tin]n.锡titanium [tai'teiniəm, ti-]n.钛toxic ['tɔksik] a.有毒的triclinic[trai'klinik]n.三斜晶系trioxide n.三氧化物tungsten ['tʌŋstən] n.钨,unique [ju:'ni:k] adj. 唯一的valence bond 价键vanadium [və'neidiəm] n.钒velocity [vi'lɔsəti] n. 速率；迅速；周转率vigorously adv. 活泼地virulent['virjulənt]adj.剧毒的volatile ['vɔlətail] adj.爆炸性的；不稳定的；挥发性的voltaic cell n. 伏打电池；原电池volume ['vɔlju:m] n. 体积VSEPR 价层电子对互斥理论zinc [ziŋk] n.锌。
理科课程英文翻译
有机化学 Organic Chemistry
分析化学 Analytical Chemistry
现代仪器分析 Modern Instrumental Analysis
现代波谱学 Modern Spectroscopy
化学计量学 Chemomtrics
激光与近代光学 Laser and Contemporary Optics
光电子技术 Photoelectronic Technique
微机系统与接口 Micro Computer System and Interface
智能仪器 Intelligent Instruments
高等无机化学 Advanced Inorganic Chemistry
废水处理工程 Technology of Wastewater Treatment
生物与化学传感技术 Biosensors & Chemical Sensors
现代分析化学研究方法 Research Methods of Modern Analytical Chemistry
神经生物学 Neurobiology
动物遗传工程 Animal Genetic Engineering
光纤通信系统 System of Fiber Communications
计算机网络 Computer Networks
光电检测与信号处理 Optoelectronic Detection and Processing
物理光学与光电子技术实验 Experiments for Physical Optics and Op
固体物理 Solid-State Physics
美国数学参考书目
美国数学本科生、研究生基础课程参考书目在网上找书的时候恰好看到这个，看着觉得的确是经典书目大全，贴在这里供学弟学妹们参考：）其中所谓第几学年云云，各校要求不同，像我所在的学校，一般学生第一年选三到四门基础课（代数、分析、几何三大类中至少各挑一门），学年末进行qualifying笔试。
第二年开始选自己喜爱方向的高级课程，并通过qualifying口试。
第三年开始做research，并通过第二语言考试（法语或德语或俄语，一般人都选法语，因为代数几何经典大作都是法语的）. 而Princeton 就没有基础课，只有seminar类型的课。
第一学年几何与拓扑：1、James R. Munkres, Topology：较新的拓扑学的教材适用于本科高年级或研究生一级；2、Basic Topology by Armstrong：本科生拓扑学教材；3、Kelley, General Topology：一般拓扑学的经典教材，不过观点较老；4、Willard, General Topology：一般拓扑学新的经典教材；5、Glen Bredon, Topology and geometry：研究生一年级的拓扑、几何教材；6、Introduction to Topological Manifolds by John M. Lee：研究生一年级的拓扑、几何教材，是一本新书；7、from calculus to cohomology by Madsen：很好的本科生代数拓扑、微分流形教材。
代数：1、Abstract Algebra Dummit：最好的本科代数学参考书，标准的研究生一年级代数材；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。
数学教材列表
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;
第一学年
几何与拓扑：
1、James R. Munkres, Topology：较新的拓扑学的教材适用于本科高年级或研究生一年级;
2、Basic Topology by Armstrong：本科生拓扑学教材;
3、Kelley, General Topology：一般拓扑学的经典教材，不过观点较老;
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. I.R.Shafarevich.：非常好的代数几何入门教材;
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。
6、Complex Analysis by Elias M. Stein：较新的研究生级别的单变量复分析教材;
一阶复结构形变中产生Hodge数跳跃的障碍公式的解析证明
一阶复结构形变中产生Hodge数跳跃的障碍公式的解析证明林洁珠;叶轩明【摘要】Let X be a compact complex manifold, and let π:x→ B be a small deformation of X, the dimensions of the Dolbeault cohomology groupsHp(Xt ,Ωpxt) may vary under this deformation. The author studied the deformation obstructions of a (p, q) class in the central fiber X. In particular, He obtained an explicit formula for the obstructions. The first order obstruction is proved in another way by using Dolbeault cohomology.%设X为一个紧致复流形,考虑X的任一复结构形变族π:x→B,则X的微分形式层的上同调群H(ρ)(X(t),Ω(ρ)X(t))的维数在此变化过程中可能产生跳跃现象.相关文献作者通过研究X各阶形变中微分形式层的上同调群等价类元素在延拓过程中的障碍来研究这一跳跃现象,得到了产生此障碍的公式.文中将给出1阶障碍公式的另一个用Dolbeault上同调计算的证明.【期刊名称】《中山大学学报（自然科学版）》【年(卷),期】2012(051)006【总页数】4页(P17-20)【关键词】Hodge数;复结构形变;障碍;Kodaira Spencer类【作者】林洁珠;叶轩明【作者单位】广州大学数学与信息科学学院//数学与交叉学科广东普通高校重点实验室,广东广州510006;中山大学数学与计算科学学院,广东广州510275【正文语种】中文【中图分类】O186设X为一紧致复流形, π∶χ→B 是以复流形X为中心纤维的复结构形变簇。
代数几何学
代数几何学代数几何研究就是平面解析几何与三维空间解析几何的推广。
大致说来，它是研究n维仿射空间或n维射影空间中多项式方程组的零点集合构成的几何对象之特性及其上的三大结构：代数结构，拓扑结构和序结构。
此三大结构系Bourbaki 学派（布尔巴基）提出，用来统摄结构数学，数学中凡是具有结构特征的板块，均由这三大母结构及其混合构成。
对于1元n次方程的解，我们有很好的结果，即代数学基本定理：在复数域C内，任意1元n次方程一定有n个零点（重复了几次算几重）。
但是，若把情况改变一下，由1元变成 n元，复数域变成任意基域K，现要讨论由m个n元方程构成的方程组在K内的公共零点的情况，容易发现，情况要比1元时复杂得多，此时，用相同的方法已无济于事，必须创造新的方法，融入新的思想。
正是这样的内在的发展要求，使得代数几何在20世纪发生了一场革命，即库恩意义上的范式的彻底改变。
其中蕴涵的新的数学思想，不仅革新了代数几何本身，而且也革新了整个数学界的思考方式，给经典的数学家们在思想上带来了深深的震撼！重要性在20世纪数学史上，代数几何学（Algebraic Geometry）始终处于一个核心的地位，这从数学界的主要大奖之一，Fields奖（菲尔兹奖）的获得者情况即可看出，从1936年颁发首届Fields奖算起，到2002年在中国举行的国际数学家大会上颁发的第24届Fields奖为止，总共有45位40岁以下的青年数学家获奖，其中大约有1/3的人，其获奖的工作或多或少与代数几何有一定的联系，这说明代数几何的研究是相当活跃的，一直是Dieudonne意义上的主流数学。
为什么代数几何的研究会常盛不衰？因为在代数几何了有大量未解决的问题，而且这些难题涉及其他许多学科，正是这些难题和其他学科的刺激，使得代数几何充满了活力，充满了令人神往的创造的生长点。
发展史Dieudonne把代数几何学的历史分为七个时期：前史（prehistory，Ca.400BC-1630A.D），探索阶段（Exploration，1630-1795），射影几何的黄金时代（1795-1850），Riemann（黎曼）和双有理几何的时代（1850- 1866），发展和混乱时期（1866-1920），涌现新结构和新思想的时期（1920-1950），最后的一个阶段，也就是代数几何史上最辉煌的时期，层（sheaf）和概型（Scheme）的时代（1950-）。
【优质】美国大学数学教材
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；
9、Folland, Real analysis：标准的研究生一年级实分析教材。
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。
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；
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；
研究生英语阅读教程（提高版）第三版第六课原文
研究⽣英语阅读教程（提⾼版）第三版第六课原⽂A Beautiful MindSylvia Nasar[1]John Forbes Nash, Jr. —mathematical genius, inventor of a theory of rational behavior, visionary of the thinking machine —had been sitting with his visitor, also a mathematician, for nearly half an hour. It was late on a weekday afternoon in the spring of 1959, and, though it was only May, uncomfortably warm. Nash was slumped in an armchair in one corner of the hospital lounge, carelessly dressed in a nylon shirt that hung limply over his unbelted trousers. His powerful frame was slack as a rag doll’s, his finely molded features expressionless. He had been staring dully at a spot immediately in front of the left foot of Harvard professor George Mackey, hardly moving except to brush his long dark hair away from his forehead in a fitful, repetitive motion. His visitor sat upright, oppressed by the silence, acutely conscious that the doors to the room were locked. Mackey finally could contain himself no longer. His voice was slightly querulous, but he strained to be gentle. “How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof... how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you ...?”[2]Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake.“Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”[3]The young genius from Bluefield, West Virginia—handsome, arrogant, and highly eccentric—burst onto the mathematical scene in 1948. Over the next decade, a decade as notable for its supreme faith in human rationality as for its dark anxieties about mankind's survival, Nash proved himself, in the words of the eminent geometer Mikhail Gromov, “the most remarkable mathematician of the second half of the century.”Games of strategy, economic rivalry, computer architecture, the shape of the universe, the geometry of imaginary spaces, the mystery of prime numbers—all engaged his wide-ranging imagination. His ideas were of the deep and wholly unanticipated kind that pushes scientific thinking in new directions.[4]Geniuses, the mathematician Paul Halmos wrote, “are of two kinds: the ones who are just like all of us, but very much more so, and the ones who, apparently, have an extra human spark. We can all run, and some of us can run the mile in less than 4 minutes; but there is nothing that most of us can do that compares with the creation of the Great G-minor Fugue.”Nash’s genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences. It wasn’t merely that his mind worked faster, that his memory was more retentive, or that his power of concentration was greater. The flashes of intuition were nonrational. Like other great mathematical intuitionists —Georg Friedrich Bernhard Riemann, Jules Henri Poincare, Srinivasa Ramanujan—Nash saw the vision first, constructing the laborious proofs long afterward. But even after he’d try to explain some astonishing result, the actual route he had taken remained a mystery to others who tried to follow his reasoning. Donald Newman, a mathematician who knew Nash at MIT in the 1950s, used to say about him that “everyone else would climb a peak by looking for a path somewhere on the mountain. Nash would climb another mountain altogether and from that distant peak would shine a searchlight back onto the first peak”[5]No one was more obsessed with originality, more disdainful of authority, or more jealous of his independence. As a young man he was surrounded by the high priests of twentieth-century science—Albert Einstein, John von Neumann, and Norbert Wiener—he joined no school, became no one's disciple, got along largely without guides or followers. In almost everything he did—from game theory to geometry—he thumbed his nose at the received wisdom, current fashions, established methods. He almost always worked alone, in his head, usually walking, often whistling Bach. Nash acquired his knowledge of mathematics not mainly from studying what other mathematicians had discovered, but by rediscovering their truths for himself. Eager to astound, he was always on the lookout for the really big problems. When he focused on some new puzzle, he saw dimensions that people who really knew the subject (he never did) initially dismissed as naive or wrongheaded. Even as a student, his indifference to others' skepticism, doubt, and ridicule was awesome.[6]Nash’s faith in rationality and the power of pure thought was extreme, even for a very young mathematician and even for the new age of computers, space travel, and nuclear weapons. Einstein once chided him for wishing to amend relativity theory without studying physics. His heroes were solitary thinkers and supermen like Newton and Nietzsche. Computers and science fiction were his passions. He considered “thinking machines”, as he called them, superior in some ways to human beings. At one point, he became fascinated by the possibility that drugs could heighten physical and intellectual performancedd9 He was beguiled by the idea of alien races of hyper-rational beings who had taught themselves to disregard all emotion. 10 Compulsively rational, he wished to turn life’s decisions—whether to take the first elevator or wait for the next one, where to bank his money, what job to accept, whether to marry—into calculations of advantage and disadvantage, algorithms or mathematical rules divorced from emotion, convention, and tradition. Even the small act of saying an automatic hello to Nash in a hallway could elicit a furious “Why are you saying hello to me?”[7]His contemporaries, on the whole, found him immensely strange. They described him as “aloof ”, “haughty”, “without affect”, “detached”, “spooky”, “isolated”and “queer”, Nash mingled rather than mixed with his peers. Preoccupied with his own private reality, he seemed not to share their mundane concerns. His manner—slightly cold, a bit superior, somewhat secretive—suggested something “mysterious and unnatural”. His remoteness was punctuated by flights of grrulousness about outer space and geopolitical trends, childish pranks, and unpredictable eruptions of anger. But these outbursts were, more often than not, as enigmatic as his silences. “He is not one of us”was a constant refrain. Amathematician at the Institute for Advanced Study remembers meeting Nash for the first time at a crowded student party at Princeton:I noticed him very definitely among a lot of other people who were there. He was sitting on the floor in a half-circle discussing something. He made me feel uneasy. He gave me a peculiar feeling. I had a feeling of a certain strangeness. He was different in some way. I was not aware of the extent of his talent. I had no idea he would contribute as much as he really did.[8]But he did contribute, in a big way. The marvelous paradox was that the ideas themselves were not obscure. In 1958, Fortune singled Nash out for his achievements in game theory, algebraic geometry, and nonlinear theory, calling him the most brilliant of the younger generation of new ambidextrous mathematicians who worked in both pure and applied mathematics. Nash's insight into the dynamics of human rivalry —his theory of rational conflict and cooperation —was to become one of the most influential ideas of the twentieth century, transforming the young science of economics the way that Mendel’s ideas of genetic transmission, Darwin’s model of natural selection, and Newton’s celestial mechanics reshaped biology and physics in their day.。
《代数几何》课程大纲
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*教材或参考资料 (Textbooks & Other Materials)
（必含信息：教材名称，作者，出版社，出版年份，版次，书号） 1. Daniel bump, Algebraic Geometry, World Scientific 1998. 2. W. Futon, Introduction to Intersection Theory in Algebraic Geometry, CBMS Regional Conference Series in Mathematics 54 (1983). 3. W. Futon, Intersection Theory, Springer- Verlag(1984). 4. D. Mumford, The Red Book of varieties and Schemes, Lecture Notes in Mathematics 1358 , Springer- Verlag (1988). J. P. Serre, Faisceaux algébriques cohérents , Ann. of Math. 61 (1955), 197-278.
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Algebraic Geometry-A Problem Solving Approach英文精品课件
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1.1. Conics over the Reals
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1.2. Changes of Coordinates
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1.3. Conics over the Complex Numbers
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1.4. The Complex Projective Plane ℙ2
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1.5. Projective Change of Coordinates
Richard Belshoff
Missouri State University
Lynette Boos
Trinity College1
Ryan Brown
Georgia College & State UnivMinnesota State University2
University of Maine, Presque Isle
Brian Snyder
Lake Superior State University
Caryn Werner
Allegheny College
1Also Providence College 2Jim passed away January 23, 2009
188
Chapter 3. Higher Degree Curves
195
3.1. Higher Degree Polynomials and Curves
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3.2. Higher Degree Curves as Surfaces
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3.3. B´ezout’s Theorem
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3.4. Regular Functions and Function Fields
大学各专业名称英文翻译——_理科_SCIENCE
大学各专业名称英文翻译——理科SCIENCE课程中文名称课程英文名称矩阵分析Matrix Analysis面向对象程序设计方法Design Methods of Object oriented Program李代数Lie Algebra代数图论Algebraic Graph Theory代数几何（I）Algebraic Geometry（I）泛函分析Functional Analysis论文选读Study on Selected PapersHoof代数Hoof Algebra基础代数Fundamental Algebra交换代数Commutative Algebra代数几何Algebraic GeometryHoof代数与代数群量子群Hoof Algebra , Algebraic Group and Qua numb Group 量子群表示Representation of Quantum Groups网络算法与复杂性Network Algorithms and Complexity组合数学Combinatorial Mathematics代数学Algebra半群理论Semigroup Theory计算机图形学Computer Graphics图的对称性Graph Symmetry代数拓扑Algebraic Topology代数几何（II）Algebraic Geometry（II）微分几何Differential Geometry多复变函数Analytic Functions of Several Complex Varian les代数曲面Algebraic Surfaces高维代数簇Algebraic Varieties of Higher Dimension数理方程Mathematics and Physical Equation偏微分方程近代方法The Recent Methods of Partial Differential Equations激波理论The Theory of Shock Waves非线性双曲型守恒律解的存在性The Existence of Solutions for Non-linear Hyperbolic Conservation Laws粘性守恒律解的稳定性Stability of Solutions for Viscous Conservation Laws微分方程数值解Numerical Methods for Differential Equations小波理论与应用Wavelet Theory and Application非线性方程组的数值解法Numerical Methods for No-linear System s of Equations网络算法与复杂性Network Algorithms and Complexity Graph Theory 60近世代数Modern Algebra高等量子力学Advanced Quantum Mechanics统计力学Statistical Mechanics固体理论Solid State Theory薄膜物理Thin Film Physics计算物理学Computational Physics量子场论Quantum Field Theory非线性物理导论Introduction to Nonlinear Physics固体磁性理论Theory of Magnetism in SolidC语言科学计算方法Scientific Computation Method in C功能材料原理与技术Principle and Technology of Functional Materials超高真空科学与技术Science and Technology of Ultrahigh Vacuum 60现代表面分析技术Modern Technology of Surface Analysis现代传感技术Modern Sensor Technology数学模型与计算机模拟Mathematical Models and Computer Simulations计算物理谱方法Spectral Method in Computational Physics蒙特卡罗方法在统计物理中的应用Applications of the Monte Carlo Method in Statistical Physics理论物理Theoretical Physics固体物理Solid-State Physics近代物理实验Contemporary Physics Experiments计算物理基础Basics of Computational Physics真空与薄膜技术Vacuum & Thin Film Technology高等光学Advanced Optics量子光学与统计光学Quantum Optics and Statistical Optics光电子学与光电信息技术Optoelectronics and Optoelectronic Information Technology图像处理与分析Image Processing and Analysis光纤通信系统System of Fiber Communications计算机网络Computer Networks光电检测与信号处理Optoelectronic Detection and Processing物理光学与光电子技术实验Experiments for Physical Optics and Optoelectronic Technology 非线性光学Nonlinear Optics集成光学Integrated Optics光子学器件原理与技术Principle and Technology of Photonics Devices物理光学与信息光子学实验Physical Optics & Information Photonics Experiments现代激光医学Modern Laser Medicine生物医学光子学Biomedicine Photonics激光医学临床实践Clinical Practice for Laser Medicine光纤通信网络Networks of Fiber Communications光接入网技术Technology of Light Access Network全光通信系统All-Optical Communication Systems计算机图形学Computer Graphics信息光学Information Optics光子学专题Special Topics on Photonics激光与近代光学Laser and Contemporary Optics光电子技术Photo electronic Technique微机系统与接口Micro Computer System and Interface智能仪器Intelligent Instruments高等无机化学Advanced Inorganic Chemistry量子化学(含群论) Quantum Chemistry(including Group Theory)高等分析化学Advanced Analytical Chemistry高等有机化学Advanced organic Chemistry现代科学前沿选论Literature on Frontiers of Modern Science and Technology 激光化学Laser Chemistry激光光谱Laser Spectroscopy稀土化学Rare Earth Chemistry材料化学Material Chemistry生物无机化学导论Bioinorganic Chemistry配位化学Coordination Chemistry膜模拟化学Membrane Mimetic Chemistry晶体工程基础Crystal Engineering催化原理Principles of Catalysis绿色化学Green Chemistry现代有机合成Modern organic Synthesis无机化学Inorganic Chemistry物理化学Physics Chemistry有机化学organic Chemistry分析化学Analytical Chemistry现代仪器分析Modern Instrumental Analysis现代波谱学Modern Spectroscopy化学计量学Chemistries现代食品分析Modern Methods of Food Analysis天然产物化学Natural Product Chemistry天然药物化学Natural Pharmaceutical Chemistry现代环境分析与监测Analysis and Monitoring of Environment Pollution现代科学前沿选论Literature on Frontiers of Modern Science and Technology 计算机在分析化学的应用Computer Application in Analytical Chemistry现代仪器分析技术Modern Instrument Analytical Technique分离科学Separation Science高等环境微生物Advanced Environmental Microorganism海洋资源利用与开发Utilization & Development of Ocean Resources立体化学Stereochemistry高等发光分析Advanced Luminescence Analysis激光光谱分析Laser Spectroscopy Analysis保健食品监督评价Evaluation and Supervision on Health Food s生物电化学Bioelectrochemistry现代技术与中药Modern Technology and Traditional Chinese Medicine高等有机化学Advanced organic Chemistry中药新药研究与开发Study and Exploitation of Traditional Chinese Medicine 药物化学研究方法Pharmaceutical Chemical Research Methods废水处理工程Technology of Wastewater Treatment生物与化学传感技术Biosensors & Chemical Sensors现代分析化学研究方法Research Methods of Modern Analytical Chemistry 神经生物学Neurobiology动物遗传工程Animal Genetic Engineering动物免疫学Animal Immunology动物病害学基础Basis of Animal Disease受体生物化学Receptor Biochemistry动物生理与分子生物学Animal Physiology and Molecular Biochemistry分析生物化学Analytical Biochemistry学科前沿讲座Lectures on Frontiers of the Discipline微生物学Microbiology细胞生物学Cell Biology生理学Physiology电生理技术基础Basics of Electrophysiological Technology生理学Physiology生物化学Biochemistry高级水生生物学Advanced Aquatic Biology藻类生理生态学Ecological Physiology in Algae水生动物生理生态学Physiological Ecology of Aquatic Animal水域生态学Aquatic Ecology水生态毒理学Aquatic Ecotoxicology水生生物学研究进展Advance on Aquatic Biology 水环境生态学模型Models of Water Quality藻类生态学Ecology in Algae生物数学Biological Mathematics植物生理生化Plant Biochemistry水质分析方法Water Quality Analysis水产养殖学Aquaculture环境生物学Environmental Biology专业文献综述Review on Special Information分子生物学Molecular Biology学科前沿讲座Lectures on Frontiers of the Discipline 植物学Botany动物学Zoology普通生态学General Ecology生物统计学Biological Statistics分子遗传学Molecular Genetics基因工程原理Principles of Gene Engineering高级生物化学Advanced Biochemistry基因工程技术Technique for Gene Engineering基因诊断Gene Diagnosis基因组学Genomics医学遗传学Medical Genetics免疫遗传学Immunogenetics基因工程药物学Pharmacology of Gene Engineering 高级生化技术Advanced Biochemical Technique基因治疗Gene Therapy肿瘤免疫学Tumor Immunology免疫学Immunology免疫化学技术Methods for Immunological Chemistry 毒理遗传学Toxicological Genetics分子病毒学Molecular Virology分子生物学技术Protocols in Molecular Biology神经免疫调节Neuroimmunology普通生物学Biology生物化学技术Biochemical Technique分子生物学Molecular Biology生殖生理与生殖内分泌Reproductive Physiology & Reproductive Endocrinology生殖免疫学Reproductive Immunology发育生物学原理与实验技术Principle and Experimental Technology of Development 免疫学Immunology蛋白质生物化学技术Biochemical Technology of Protein受精的分子生物学Molecular Biology of Fertilization免疫化学技术Immunochemical Technology低温生物学原理与应用Principle & Application of Cryobiology不育症的病因学Etiology of Infertility分子生物学Molecular Biology生物化学Biochemistry分析生物化学Analytical Biochemistry医学生物化学Medical Biochemistry医学分子生物学Medical Molecular Biology医学生物化学技术Techniques of Medical Biochemistry生化与分子生物学进展Progresses in Biochemistry and Molecular Biology高级植物生理生化Advanced Plant Physiology and Biochemistry拟南芥—结构与发育Arabidopsis-Structure and Development开花的艺术Art of Flowering蛋白质结构基础Principle of Protein Structure生活在美国Living in America分子进化工程Engineering of Molecular Evolution生物工程下游技术Downstream Technique of Biotechnology仪器分析Instrumental Analysis临床检验与诊断Clinical Check-up & Diagnosis 药理学Pharmacology。
代数几何学
1代数几何学在20世纪数学史上，代数几何学（Algebraic Geometry）始终处于一个核心的地位，这从数学界的主要大奖之一，Feilds奖的获得者情况即可看出，从1936年颁发首届Fields奖算起，到2002年在中国举行的国际数学家大会上颁发的第24届Fields奖为止，总共有45位40岁以下的青年数学家获奖，其中大约有1/3的人，其获奖的工作或多或少与代数几何有一定的联系，这说明代数几何的研究是相当活跃的，一直是Dieudonne意义上的主流数学。
为什么代数几何的研究会常盛不衰？因为在代数几何了有大量未解决的问题，而且这些难题涉及其他许多学科，正是这些难题和其他学科的刺激，使得代数几何充满了活力，充满了令人神往的创造的生长点。
代数几何到底研究什么呢？简单的说，就是研究n维仿射空间或n维射影空间中多项式方程组的零点及其上的三大结构：代数结构，拓扑结构和序结构。
此三大结构系Bourbaki学派提出，用来统摄结构数学，数学中凡是具有结构特征的板块，均由这三大母结构及其混合构成。
对于1元n次方程的解，我们有很好的结果，即代数学基本定理：在复数域C内，任意1元n次方程一定有n个零点（重复了几次算几重）。
但是，若把情况改变一下，由1元变成n元，复数域变成任意基域K，现要讨论由m个n元方程构成的方程组在K内的公共零点的情况，容易发现，情况要比1元时复杂得多，此时，用窗同的方法已无济于事，必须创造新的方法，融入新的思想。
正是这样的内在的发展要求，使得代数几何在20世纪发生了一场革命，即库恩意义上的范式的彻底改变。
其中蕴涵的新的数学思想，不仅革新了代数几何本身，而且也革新了整个数学界的思考方式，给经典的数学家们在思想上带来了深深的震撼！Dieudonne把代数几何学的历史分为七个时期：前史（prehistory，Ca.400BC-1630A.D），探索阶段（Exploration，1630-1795），射影几何的黄金时代（1795-1850），Riemann和双有理几何的时代（1850- 1866），发展和混乱时期（1866-1920），涌现新结构和新思想的时期（1920-1950），最后的一个阶段，也就是代数几何史上最辉煌的时期，层（sheaf）和概形（Scheme）的时代（1950-）。
Principles_of_Algebraic_Geometr_Griffiths_Harris
Includes bibliographical references.
1. Geometry, Algebraic. I. Harris, Joseph,
1951- jointauthor.il. Title.
QA564.G64
516'.35
78-6993
ISBN 0-471-05059-8
Printed in the United States of America
A number of principles guided the preparation of the book. One was to develop only that general machinery necessary to study the concrete geometric questions and special classes of algebraic varieties around which the presentation was centered.
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我对数学感兴趣英语作文
The Fascination of Mathematics: My Journeyof DiscoveryMathematics has always held a special place in my heart. It's not just a subject taught in school; it's a language that describes the universe, a tool that unlocks thesecrets of the world. Ever since I can remember, I've been fascinated by the elegance and power of mathematical concepts.As a child, my curiosity was piqued by the simple actof counting. The numbers seemed to have a magic of their own, and I was captivated by the idea of infinity - the concept that there are more numbers than there are stars in the sky. As I grew older, my interest in mathematics deepened, and I found myself drawn to the mysteries of algebra, geometry, and calculus.Algebra, in particular, fascinated me with its abilityto represent unknown quantities with letters and solve problems using abstract symbols. The beauty of algebraic equations lies in their simplicity and precision; theyoffer a concise way to express complex relationships andfind solutions to problems that would otherwise be impossible to solve.Geometry, on the other hand, revealed the beauty of shapes and patterns in the world. From the symmetry of a snowflake to the geometry of a spacecraft, I saw the invisible hand of mathematics at work everywhere. Geometry taught me about spatial reasoning and visualization skills that have been invaluable in my life and career.Calculus, the study of rates of change, opened up a whole new world of understanding. It explained the principles of motion and acceleration, allowing me to grasp the physics of the universe in a new way. Calculus also introduced me to the concept of limits and infinity, topics that have fascinated philosophers and mathematicians for centuries.But the appeal of mathematics isn't just intellectual; it's also emotional. The sense of accomplishment I feel when I solve a difficult problem or understand a complex concept is immense. Mathematics gives me a sense of purpose and direction, and it's a field that I can constantly grow and learn in.As I've delved deeper into the world of mathematics,I've discovered that it's not just a subject; it's a way of thinking. Mathematical thinking has taught me to be logical, analytical, and problem-solving. It has helped me todevelop a mindset of curiosity and exploration, always seeking to understand the underlying principles and structures of the world.In conclusion, my interest in mathematics is not just a hobby or a subject of study; it's a passion that drives me. The beauty and power of mathematical concepts continue to captivate me, and I'm excited to explore the mysteries of this fascinating field for the rest of my life. Mathematics, after all, is the language of the universe, and I'm honored to be a part of its ongoing conversation.**数学的魅力：我的发现之旅**数学在我心中一直占有着特殊的位置。
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5.有限态射
(1)环的有限扩张(2)有限态射(3)有限态射的定义方程
(4)双有理等价(5)有限态射的正规化
6.纤维的维数
7.纤维的不可约性
8.纤维的光滑性
(1)映射的微分(2)纤维的光滑点(3)光滑点的邻域是完全交(4)映射在光滑点处的解析表示
(1)代数簇（仿射）(2)代数簇上的有理函数域
6.域的单扩张----约化为一个方程
(1)分裂域(2)域的可分扩张(3)有限单扩张
(4)代数簇双有理等价于超曲面
7.诺特规范化定理----约化为规范方程
(1)有限代数(2)整性与有限性(3)诺特正规化(4)代数簇的函数域的结构
Chapter 2.解方程的代数理论
课程简介模板
代数几何I课程简介
课程名称
代数几何I
课程代码
∕
课程英文名称
Algebraic Geometry I
任课教师
任课教师职称
课程类别
第二层次
学时
4
学分
4
授课方式
主讲
主要内容简介
本课程属于第二层次课程，面向代数组的全体学生。这门课从解方程的思想出发，并以此为线索，由浅入深地介绍了代数几何的基础内容。它承接了本科生的《高等代数与解析几何》、《代数几何基础》等课程内容，也为今后学习代数几何后续课程提供了基础。
代数几何I ----代数簇理论
(周课时: 4，第二学期开设)
Chapter 1.解方程的基本理论
1.希尔伯特基定理----约化为有限个方程
(1)背景(2)希尔伯特基定理的证明
2.希尔伯特零点定理----方程组有无解的判别法
(1)判别方程组是否有解(2)诺特正规化引理(3)结式的性质(4)零点定理的证明(5)零点定理的等价形式.
(5)映射光滑点组成Zariski开集(6)主要定理的证明
9.射影代数簇
(1)射影空间(2)方程组在无穷远处的解(3)射影齐次坐标与仿射坐标(4)齐次坐标环
(5)射影代数簇上的有理函数与正则函数(6)不可约代数簇的维数
Chapter 4.代数曲线
1.代数曲线的局部性质
(1)代数曲线介绍(2)平面代数曲线(3)曲线的重数与切线
2.平面曲线的局部相交数
3.贝祖定理
(1)贝祖定理(2)曲线的拐点
4.诺特定理与Cayley-Bacharach定理
5.有理函数的零点与极点的重数计算
6.L(D)的定义与计算
7.L(D)的基本性质
8.Riemann-Roch定理及其证明
9.三次曲线的群结构和分类
(1)标准方程(2)群结构(3)三次曲线的几何(4)有理点计算(5)三次曲线的分类与j不变量
Hartshorne<Algebraic Geometry>
5.代数簇的维数理论
(1)不可约真子簇的维数(2)分式环中的素理想链(3) Q(x)的素理想链
6.整闭整环上的整扩张
(1)整闭性是局部性质(2)理想上的整元(3)构造素理想(4)下降定理
7.方程的个数与解的维数
(1)主要结果(2) Krull主理想定理的证明(3)高度和维数的定理证明
(4)不可约分支维数的定理证明
3.根理想----约化为既约方程组
(1)去掉方程中的指数幂(2)根理想(3)方程组同解的判别法
4.理想的准素分解----约化为不可约方程组
(1)方程组的分解(2)方程组的不可约分解
(3)不可约方程组解集的不可约性(4)准素分解的唯一性
(5)极小准素分解(6)不可约分支的性质
5.代数簇的有理函数域----方程的解的维数
1.坐标函数环
(1)坐标函数环的定义(2)极大理想与方程的解
2.环的整扩张
(1)例子(2)环的整扩张(3)整环的整闭包
(4)环的整同态、有限同态、有限型同态
3.代数簇的正规化
(1)正规化(2)迹与域的扩张(3)整元的特征多项式
(4)整闭包的有限性证明(5)诺特环上的有限生成模
4.局部化技巧
(1)分式环(2)分式模(3)局部性质(4)分式环的性质
Chapter3.代数簇的几何
1.代数簇的切空间
(1)解方程与隐函数定理(2)方程组的线性化与切空间(3)切空间的维数
2.光滑代数簇
(1)代数簇上的光滑点(2)零维诺特局部环
(3)一维诺特局部整环(4)曲线在光滑点处
3.正规代数簇
(1)正规簇上的奇点集(2)正规簇上的正则函数(3)正规簇上的子
4.代数簇之间的态射
10.Riemann-Roch定理的应用
(1)相伴线性系的性态(2)曲线典范映射的性态(3)亏格0曲线的分类
(4)亏格1线的分类(5)亏格2曲线的分类
(6)超椭圆曲线(7)非超椭圆曲线
11.曲线上的有理微分形式与Hurwitz公式
考核方式
闭卷考试
教材
谈胜利《交换代数与代数几何基础》
参考书目及文献
M.F.Atiya,I.G.Macdonald<Introductionto Commutative Algebra>