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数学专业英语第三版课文翻译章本文将根据数学专业英语第三版课文《Step by Step Thinking》进行翻译。
"Step by Step Thinking"is an article that introduces the concept of step-by-step thinking in mathematics.It highlights the importance of breaking down complex problems into smaller,more manageable steps in order to solve them effectively.The article begins by stating that step-by-step thinking is a fundamental skill in mathematics.It emphasizes the need to approach problems by breaking them downinto smaller components,as this helps to clarify the problem and identify potential solutions.The author argues that this approach is not only applicable tomathematics but also to various other fields,as it promotes clearer thinking and problem-solving abilities.The article then discusses the step-by-step thinking process in more detail.It suggests that the first step is tocarefully read and understand the problem, ensuring that all relevant information is identified.This is followed by breaking the problem down into smaller sub-problems or steps,each of which can be solved individually.The author emphasizes the need to be systematic and organized during this process,as it helps to prevent mistakes and confusion.Furthermore,the article highlights the importance of logical reasoning in step-by-step thinking.It states that each step should be justified with logical reasoning,ensuring that the solution is based on sound mathematical principles.The author advises against skipping steps or making assumptions without proper justification,as this can lead to erroneous results.The article also provides examples to illustrate the step-by-step thinking approach.It presents a complex problem and demonstrates how breaking it down into smaller steps can simplify the solution process.By solving each step individually and logically connecting them,the problem can be solved effectively.In conclusion,"Step by Step Thinking" emphasizes the significance of step-by-step thinking in mathematics and problem-solving. It encourages readers to approach problems systematically,breaking them down into smaller components,and justifying eachstep with logical reasoning.This approach promotes clearer thinking and enhances problem-solving abilities,not only in mathematics but also in other disciplines.。
高数第一章知识点总结希望同学们在准备考研数学高数的复习过程中能够适当结合真题与模拟题，下面是精心收集的高数第一章知识点总结，希望能对你有所帮助。
篇一：高数第一章知识点总结高等数学是考研数学的重中之重，所占的比重较大，在数学一、三中占56%，数学二中占78%，重点难点较多。
具体说来，大家需要重点掌握的知识点有几以下几点：1.函数、极限与连续：主要考查极限的计算或已知极限确定原式中的常数;讨论函数连续性和判断间断点类型;无穷小阶的比较;讨论连续函数在给定区间上零点的个数或确定方程在给定区间上有无实根。
2.一元函数微分学：主要考查导数与微分的定义;各种函数导数与微分的计算;利用洛比达法则求不定式极限;函数极值;方程的的个数;证明函数不等式;与中值定理相关的证明;最大值、最小值在物理、经济等方面实际应用;用导数研究函数性态和描绘函数图形;求曲线渐近线。
3.一元函数积分学：主要考查不定积分、定积分及广义积分的计算;变上限积分的求导、极限等;积分中值定理和积分性质的证明;定积分的应用，如计算旋转面面积、旋转体体积、变力作功等。
4.多元函数微分学：主要考查偏导数存在、可微、连续的判断;多元函数和隐函数的一阶、二阶偏导数;多元函数极值或条件极值在与经济上的应用;二元连续函数在有界平面区域上的最大值和最小值。
此外，数学一还要求会计算方向导数、梯度、曲线的切线与法平面、曲面的切平面与法线。
5.多元函数的积分学：包括二重积分在各种坐标下的计算，累次积分交换次序。
数一还要求掌握三重积分，曲线积分和曲面积分以及相关的重要公式。
6.微分方程及差分方程：主要考查一阶微分方程的通解或特解;二阶线性常系数齐次和非齐次方程的特解或通解;微分方程的建立与求解。
差分方程的基本概念与一介常系数线形方程求解方法由于微积分的知识是一个完整的体系，考试的题目往往带有很强的综合性，跨章节的题目很多，需要考生对整个学科有一个完整而系统的把握。
最后凯程考研名师预祝大家都能取得好成绩。
高一英语大学专业选择指导练习题40题1. Which major is related to the study of living organisms?A. Computer ScienceB. BiologyC. MathematicsD. History答案解析：B。
Biology 是生物学，主要研究生物，与living organisms（生物体）相关。
Computer Science 是计算机科学，与生物体无关。
Mathematics 是数学，也不涉及生物体研究。
History 是历史，同样与生物体没有关系。
2. Which major focuses on the design and development of software?A. PhysicsB. ChemistryC. EngineeringD. Computer Science答案解析：D。
Computer Science 是计算机科学，专注于软件的设计和开发。
Physics 是物理学，与软件设计无关。
Chemistry 是化学，也不涉及软件。
Engineering 是工程学，范围比较广，但不是专门针对软件设计和开发。
3. Which major is concerned with the study of human behavior and mental processes?A. PsychologyB. EconomicsC. SociologyD. Literature答案解析：A。
Psychology 是心理学，研究人类行为和心理过程。
Economics 是经济学，主要研究经济现象。
Sociology 是社会学，关注社会现象。
Literature 是文学，与人类行为和心理过程的研究关系不大。
4. Which major deals with the management of financial resources?A. AccountingB. MarketingC. PhilosophyD. Art答案解析：A。
关于数学专业英语课程教学的一些探讨与体会【摘要】数学专业英语课程是面向数学系学生所开始的一门专业任选课，它具有英语、数学、英语与数学相结合等特点，要求学生具备一定的数学知识和英语知识。
本文针对数学专业英语教学的现状，结合此门课程所具有的特点，来探讨如何提高学生学习数学专业英语的乐趣，提高学生阅读数学专业英语文献的能力，同时介绍一些数学的前沿研究热点。
【关键词】数学专业英语；教学探讨；教学方法如今越来越多的本科生毕业后到国外进行研究生学习，首要面对的一个紧要问题就是要听懂国外教师上课。
虽然在出国之前经历过各种各样的英语考试，口语和听力有了一定的提高，但专业英语词汇量比较缺乏。
数学专业英语课是针对数学系本科生所开设的一门专业任选课，课程开设的目的是帮助本科生能掌握一定的数学专业词汇，提高阅读数学专业文献的能力，促进我国的数学教育与国际上的交流，紧跟国际数学的研究步伐。
此课程的开设有助于扩大本科生的视野，知道一些数学专业词汇的英文表达，进一步会撰写一篇英语科技论文。
我们学院通常在第四学期开设专业英语选修课，从前两年的教学效果来看，绝大部分学生对此门课程兴趣不大，抱着拿两学分的心态，因此在课堂不能和教师进行良好的互动，课堂浑然无趣。
本文从以下四个方面指出在教学中所存在的一些问题，并探讨数学专业英语课程的教学改革方法与策略。
一、教学课时量较少目前学院采用吴炯圻老师的数学英语课本-第二版，此门课程性质是专业任选课，安排总课时为32。
课本内容总共6章，分别介绍了数学专业的阅读和翻译初阶；精读课文；专业文选；数学英语专业论文写作基础；查阅英语数学文献的基本知识和数学文献常用英语词汇。
从课本内容来看，涉及内容较多，如第二章内容有12小节，从课时安排来看，要想讲完全部内容有难度，因此在课堂教学中，我们选取了与数学分析、高等代数和概率论与数理统计等学科相关的内容来讲解，如函数的思想；线性空间中的相关与无关集；概率论与数理统计中的基本术语，通过讲解这些内容，让同学们能够联想到之前学过的数学内容，从而会主动用专业英语来表述。
大学专业常见课程英文词汇大学英语,,,,,,College English高等数学,,,,,,Advanced Mathematics体育,,,,,,,,,Physical Education军事理论,,,,,,Military Theory机械制图,,,,,,Mechanical Graphing算法语言,,,,,,Algorithmic Language大学物理,,,,,,College Physics物理实验,,,,,,Experiment of College Physics线性代数,,,,,,Linear Algebra法律基础,,,,,,Fundamentals of Law普通物理,,,,,,General Physics普通物理实验室,,,,,,Lab of General Physics复变函数与积分变换,,,Functions of Complex V ariables & Integral Transformati ons电路理论,,,,,,,,,Theory of Circuitry电路测试技术,,,,,,Circuit Measurement Technology概率论与随机过程,,,Probability Theory & Stochastic Process信号与线性系统,,,,,,Signal & Linear System电子线路,,,,,,,,,Circuitry脉冲与数字电路,,,,,,Pulse & Numerical Circuitry金工实习,,,,,,Metalworking Practice电工实习,,,,,,Electrical Engineering PracticeCET-4,,,College English Test (Band 4)电子线路实验,,,Experiment in Electronic Circuitry微机原理,,,,,,Principle of Microcomputer电磁场与电磁波Electromagnetic Fields & Magnetic Waves电机电器与供电Motor Elements and Power Supply计算方法,,,,,,Computational Method软件技术基础,,,Basis of Software Technique微波技术,,,,,,Microwave Technique通讯原理,,,,,,Principle of Communication数字信号处理,,,Digital Signal Processing微机实验,,,,,,Experiment of Microcomputer计算机接口技术Computer Interface Technologyc 语言,,,,,, C languageCET-6,,,College English Test (Band 6)工业企业管理,,,Industrial Enterprise Management移动通讯,,,,,,Moving Communication光纤通讯系统,,,Fiber Optical Communication System可靠性技术导论Introduction to Reliability Technology卫星通信,,,,,,Satellite Communications电视原理,,,,,,Television Operation数字图象处理,,,Digital Image Processing专业英语,,,,,,Specialty English情报检索,,,,,,Information Searches毕业设计,,,,,,Graduation Thesis自动控制理论,,,Automatic Control Theory模拟电子电路,,,Analogical Electronics数字电子电路,,,Digital Electronics资本主义经济,,,Economy of Capitalism马克思主义原理Principle of Marxism机械原理,,,,,,Principle of Mechanic机械设计,,,,,,Mechanic Design最优控制,,,,,,Optimum Control微机控制技术,,,Microcomputer Control Technology过程控制,,,,,,Procedure Control自动控制系统,,,Automatic Control System半导体变流技术Semiconductor converting Technique 运筹学,,,,,,Operational Research自动检测技术,,,Auto-Measurement Technique传感器原理,,,Principle of Sensing Device单片机原理,,,Principle of Single-Chip computer学科分类词汇Chinese语文English英语Japanese日语mathematics数学science理科gymnastics体育history历史algebra代数geometry几何geography地理biology生物chemistry化学biochemistry生物化学physics物理physical geography地球物理literature文学sociology社会学linguistics语言学psycology心理学philosophy哲学engineering工程学mechanical engineering机械工程学electronic engineering电子工程学medicine医学social science社会科学agriculture农学astronomy天文学economics经济学politics政治学comercial science商学biochemistry生物化学anthropology人类学languistics语言学accounting会计学law, jurisprdence法学banking银行学metallurgy冶金学finance财政学mass-communication大众传播学journalism新闻学atomic energy原子能学civil engineering土木工程architecture建筑学chemical, engineering化学工程accounting and satisics会计统计business administration工商管理library图书馆学diplomacy外交foreign language外文botany植物major主修。
数学是世界上最普遍、最实用的工具，也是一种语言，它的领域不仅仅局限于交流与沟通，是科学发展的标志，是大自然的破译密码，也是研究微观世界的重要工具。
数学在人类历史发展和社会生活中发挥着不可替代的作用，也是学习和研究现代科学技术必不可少的基本工具。
基础数学的知识与运用是个人与团体生活中不可或缺的一部分。
就像康托尔说过那样，数学的本质在于它的自由。
数学的自由体现在方方面面数学被应用在很多不同的领域上。
基础数学在生活中的运用范围广，与很多事物都有联系甚至是与其他学科有着密不可分的联系。
英语是当今世界上主要的国际通用语言之一，也是世界上最被广泛使用的第二语言，是欧盟和许多国际组织与英联邦国家的官方语言之一，也是联合国的工作语言之一。
英语的母语使用者数量位居世界第三，少于标准汉语和西班牙语，但上两个世纪英国和美国在文化、经济、军事、政治和科学上的领先地位使得英语成为一种国际语言，如今许多国际场合都使用英语作为沟通的媒介。
英语也是与电脑联系最密切的语言，大多数编程语言都与英语有联系，而且随着网络使用，使英文使用更为普及。
数学与英语是我们学习中最为基本也是最重要的两个学科。
这两个学科之间有着什么微小的联系，就是本论文主要介绍之处。
数学与英语有着非常紧密的关系，。
我校作为理工科院校，很多院系专业的学习经常运用到数学可以说每天的生活都离不开数学。
1《大学英语教学大纲》规定: 大学非英语专业的英语教学是由两个阶段来完成的, 即: 基础英语阶段和专业英语阶段, 其中专业英语是基础英语的后续课程. 就数学专业英语而言, 它是一门由本专业教师授课的涉及数学专业领域的英语教学课程. 学生通过大学1、2学年基础英语的学习, 在听、说、读、写、译等方面已经打下了一定的基础, 但离掌握英语的实用技能并灵活应用还有相当的一段差距, 数学专业英语教学在此基础上进一步提供了学习、使用、实践英语的课堂环境, 是学生结合专业知识使用英语, 培养英语的实用技能的重要环节. 学生通过数学专业英语的学习来掌握数学文章的文体、词法、词汇、表达、翻译、写作等方面的知识, 提高听、说、读、写、译等方面的基本交际技能, 培养学生利用英语交流和获取信息的能力和习惯, 为以后数学专业课的双语教学和未来从事中小学数学双语教学打下坚实的英语基础。
教案2015 ～2016 学年第一学期分院（部) 数学分院专业数学教育课程名称大学英语1课程代码授课班级2015级汉数学教育普专班授课教师廖雪莲职称助教教材创新大学英语综合教程高职高专版Book1新疆教育学院教务处制课程教案授课题目（或章节）Book 1 Unit 1Reception课型课时10课时教学目标1. Teach the students how to pick up a client at the airport.2. Train the students’ ability to plan a business reception and know some intercultural reception skills.3. Give the students a chance to exchange views on the texts to enable them to havea deeper understanding of the texts and to let the students be acquainted with some new words.4.Teach the students some practical reading skills and writing skills.教学重点1.Knowing how to pick up a client at a airport.2. Email writingeful words and expressions: reception activity track flight pick up entertain available greet plan invite hospitality spa land serve baggage dinner specialty recommend see off celebrate教学难点1. Planning a business reception2. Tenses3. Writing an invitation via email教学方法Interactive approach Situational teaching approach Teamwork methodTask-based teaching method教具PPTBlackboard11. The first two-class-hour session for Warm-up & Unit task (Text A)2. The second two-class-hour session for Section A Tips for Business Reception3. The third two-class session for Section B Reading4. The fourth two-class-hour session for Exercises and grammar5. The last two-class-hour session for Listening comprehension and email writingWarm-up and Unit task (Text A)Step 1 Lead-in: Business reception1. Warm-up questions: What is business reception?A business reception means the first step o impress your client. A good reception can help the following negotiation and the following deals. Reception includes meeting the clients at the airport, reserving hotel rooms for clients, planning recreational activities to entertain clients and hosting a dinner for clients, too.2. The Ss read warm-up 1 and match the names of different activities with their pictures.3. Invite 1-2 Ss to present their answers.4.Invite 3-4 Ss to express their ideas according to the sample.Step 2 Warm-up 21. Ss read Warm-up22.Ask Ss to do a pair work. Try the quiz and check the score for their partner.3.Invite a student to present his/her partner’s result.4.The teacher help to explain some difficult language points.5.Introduce more intercultural business reception skills.Step 3 Assignments1. preview text ASection A Tips for Business ReceptionStep 1 Warm-up questions1. How to track flights status?2. How to pick up your clients?Step2 Reading231. Jigsaw reading let the students share the tips for business reception.2. Rank the steps of picking a client up at the airport.Step 3 Language PointsThe Ss choose some useful expressions and sentences from the passage, and then the teacher demonstrates their usage. The following should be chosen and practiced. The Ss should make up at least two sentences using the chosen phrases in groups.1. reception [ri'sep ʃən] n . 接见；接待；迎接 ;招待会；欢迎会 ;接纳；接受；容纳;【无线电、电视】接收；接收能力; (饭店、旅馆等处的)接待处，招待处 e.g. The reception is over.招待会到此结束。
大学数学专业英语教材IntroductionMathematics plays a crucial role in various fields and industries, and studying mathematics at the university level requires a solid foundation in both the subject itself and the English language. A well-designed mathematics textbook for university students in the field of mathematics can effectively integrate mathematical concepts with English language learning. In this article, we will explore the essential features and requirements of a comprehensive English textbook for mathematics students at the university level.Chapter 1: Fundamental ConceptsThe first chapter of the textbook should cover the fundamental concepts of mathematics, introducing students to the basic principles that underpin the subject. It should provide concise explanations and definitions, supplemented with examples and illustrations to aid comprehension. Additionally, this chapter should include exercises to reinforce learning and promote critical thinking.Chapter 2: AlgebraAlgebra is a cornerstone of mathematics, and this chapter should delve into its key theories and principles. It should cover topics such as equations, inequalities, functions, and matrices. The textbook should present clear explanations of concepts, accompanied by real-life applications to demonstrate the practical relevance of algebra.Chapter 3: CalculusCalculus is essential for advanced mathematics and the study of other disciplines such as physics and engineering. The textbook should guide students through both differential and integral calculus, ensuring a thorough understanding of concepts like limits, derivatives, and integrals. Practical examples and exercises should be incorporated to enhance students' problem-solving skills.Chapter 4: Probability and StatisticsIn this chapter, the textbook should introduce students to probability theory and statistical analysis. The content should cover topics such as probability distributions, hypothesis testing, and regression analysis. The inclusion of real-world data sets and case studies can foster students' ability to apply statistical methods effectively.Chapter 5: Discrete MathematicsDiscrete mathematics is vital in areas like computer science and cryptography. This chapter should explore concepts such as set theory, logic, graph theory, and combinatorics. The textbook should present clear explanations of these topics, accompanied by relevant examples and exercises to consolidate understanding.Chapter 6: Linear AlgebraLinear algebra is widely applicable in various fields, including computer science and physics. This chapter should cover vector spaces, linear transformations, and eigenvalues. Emphasis should be placed on theconnections between linear algebra and other mathematical disciplines, demonstrating its practical significance.Chapter 7: Number TheoryNumber theory explores the properties and relationships of numbers, and it forms the basis for cryptographic algorithms and computer security systems. This chapter should introduce students to prime numbers, modular arithmetic, and cryptographic algorithms. Examples and exercises should be given to develop students' problem-solving skills in the realm of number theory.Chapter 8: Numerical AnalysisNumerical analysis involves using algorithms to solve mathematical problems on computers. This chapter should cover topics such as interpolation, numerical integration, and numerical solutions of equations. The textbook should provide step-by-step guidance on implementing numerical algorithms, allowing students to develop practical coding skills.ConclusionA comprehensive English textbook for university-level mathematics students should provide a solid foundation in mathematical concepts while simultaneously enhancing students' English language proficiency. By incorporating clear explanations, practical examples, and engaging exercises, this textbook can foster a deep understanding of mathematics within an English language learning context. Such a resource will empower students to pursue further studies in mathematics and apply their skills in various professional domains.。
