数学专业英语第一讲.ppt
专业英语1_juntaoLi概要
数学专业英语 Juntao Li
Lecture 1 Introduction
引言
1.1 What is specialized English ? 什么是专业英语
普通英语（Common English, Ordinary English）
这个装置包括一个互感器和一个有两个电路的继电器系统。
其他常用的省略形式：
As already discussed 前已讨论
If so 倘若如此
As explained before 前已解释 As described above 如上所示
As previously mentioned 前已提到 When needed (necessary, feasible)必要时 Where feasible 在实际可行的场合
当前大部分资料都可以通过互联网传ger数据库？）
世界上科技情报资料的交流主要靠使用英语,对于数学、电子工程和 信息类等专业来说，绝大部分专业资料和信息都是以英语形式出版。
(2) 研究成果展示 专业英语写作能力
申报国家奖项 申请专利 发表学术论文：85％以上的科技资料都是以英语形式出版的
2.1 Grammar Features
③ 不定式
用不定式短语来替代表示目的和功能的从句或语句 (1) The capacity of individual generators is larger and larger so that the increasing demand of electric power is satisfied.
保险的作用就是保护电路。
2.1 Grammar Features
数学专业英语
vt.表明，标示，指示; 象征，暗示，预 示; [医]显示需要做…的治疗;
numerical[英][nju:ˈmerɪkl][美][nu:ˈmerɪkl]
adj.数字的，用数字表示的，数值的;
root[英][ru:t][美][rut, rʊt]
n.根，根源; 原因，本质; 祖先; [乐]和弦基音; vt.使生根; 使固定; 根源在于; 欢呼，喝彩; vi.生根; 根除;
n.身份; [逻]同一性; 个性; [数]恒等（式）;
arithmetic[英][əˈrɪθmətɪk][美][əˈrɪθmɪtɪk]
n.算术，计算; 算法;
algebraic[英][ˌældʒɪ'breɪɪk][美][ˌældʒəˈbreɪk]
adj.代数的，关于代数学的;
indicate[英][ˈɪndɪkeɪt][美][ˈɪndɪˌket]
你拿这个或那个都可以。
1. either…or…连接两个成分作主语时，谓语动 词通常与其靠近的主语保持一致。如： Either you or I am to go. 你或我必须有人去。 但在非正式文体中，有时也会一律用复数谓 语。如：If either David or Janet come, they will want a drink.
prep.在...的附近; 在...的周围
解方程意味着求未知项的值，为了求未知项的值，当 然，我们必须移项，直到未知项单独在方程的一边， 令其等于方程的另一边，求得未知项的值，这样我们 就解决了问题。
on one side…on the other side…一方面……另一方面……
脑筋急转弯：
Two little brother,One lives on one side,The other on the other side,They hear what you say But they do not see each other,Who are they?
1-1数学专业英语的基本特点精品PPT课件
• 由于数学内容的英语表达有特殊性，软件一般不能 代替专业英语学习。
• 把握数学英语专业的基本特点和阅读与翻译的基本 知识，才能进入数学专业英语的中心内容学习中。
数学专业英语的基本特点：
A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:). Suppose we want to write the ratio of 8 and 12. We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve.
3.主动语态句型也多数用于强调事实，而不是强调 10 行为发出者及其情感
例 Given 0 ， there exists a number N 0 such that| an a | for all n N .
表示“存在”的句型显然不表示主语a number N发出什么行为， 而表示满足的条件或具有某性质的主语存在这一事实。
强调“已被证明是正确的”，未指明是谁证明的，一般读者 只关心该猜想的研究现状。
例 Attention must be paid to the working temperature of the
machine. 应当注意机器的工作温度。 而很少说： You must pay attention to the working temperature of the machine .
10
Definition. Suppose that A is an n n matrix, with entries in R. We say that A is diagonalizable, if there exists an invertible matrix P, with entries in R, such that P-1AP is a diagonal matrix, with entries in R.
数学专业英语之课件一
• 3. Analysis of language – implication
蕴含
• 4. Analysis of language – equivalence
等价
• 5. Analysis of language – quantifiers
量词
• 6. Working with quantifiers
• 课程目标：帮助我们形成一种有益 的心智能力——我们祖先三千年前 形成的一种强大的思考方式.
Introduction to mathematical thingking
• 数学思维不等同于做数
• Mathematical thinking is not the same as doing mathematics – at
• 校园数学成功的关键是了解数学内部世界.相比而言， 数学思维的主要特征是考虑数学外部世界--种必要的 技能在当今世界.这门课帮助我们形成思维方式的关 键.
Introduction to mathematical thingking
• The primary audience is firstyear students at college or university who are thinking of majoring in mathematics or a mathematically-dependent subject, or high school seniors who have such a college career in mind.
学运算-至少不像数学那
least not as mathematics is
样是我们教育系统的主
typically presented in our school system. School math typically
《数学专业英语》课件
2 三角恒等式和方程 4 三角学在几何和物理中的应用
IV. Calculus
1 极限和连续性 4 定积分及其性质
2 导数及其性质
3 导数在优化和相关速
率中的应用
5 定积分在面积和体积计算中的应用
V. Linear Algebra
1 向量和向量运算 3 线性方程组
《数学专业英语》PPT课 件
探索数学专业英语的精髓，为您呈现一场精彩的数学之旅。
I. Introduction
- 数学的定义 - 数学在现代社会中的重要性 - 课程目标
II. Algebra
1 基础代数表达式和方程 3 多项式和因式分解
2 根式和指数 4 二次方程和函数
III. Trigonom etry
2 矩阵及其运算 4 特征值和特征向量
VI. Probability and Statistics
1 概率的基本概念 3 数据的统计度量
2 离散和连续概率分布 4 假设检验和置信区间
VII. Conclusion
1 课程内容回顾
2 数学在不同领域的未 3 继
数学专业英语
2 . 掌握概率论基本的表示方法。
11-A Predicates
Statements involving variables, such as “x>3”, “x+y=3”, “x+y=z” are often found in mathematical assertion and in computer programs.
Two types of quantification will be discussed here, namely, universal quantification and existential quantification . 这里讨论两种量词化方法，也就是全称量词化和存在 量词化。
※Many mathematical statements assert that a property is true for all values of a variable in a particular domain, called the universe of discourse.
Assume we have a probability space (S,B,P) associated with an experiment. Let A be an event, and suppose the experiment is performed and that its outcome is x. (In other words, let x be a point of S.) 假设有一个对应于某一个试验的概率空间(S,B,P) 。A 是一个事件，假设试验已经完成，结果是x(换句话说， x是S中的一个点)。 This outcome x may or may not belong to the set A. If it does, we say that the event A has occurred. 结果x可能属于集合A，也可能不属于A。如果属于， 则称事件A发生。
《数学专业英语》课件
The course provides learners with feedback on their performance and guidance on areas where improvement is needed to help them achieve their learning goals effectively
Basic mathematical terms
This includes words like "equation," "function," "integral," etc., which are essential for understanding mathematical concepts and e combinations of symbols that represent relationships between mathematical entities They are used to express mathematical ideas conceptually and precisely
感谢观看
THANKS
Application of Mathematics Professional English
Use English to write research articles for international journals or conferences, enabling more people to learn about and cite your article.
Summary and Outlook
01
Deepen the understanding of mathematical English vocabulary and grammar
数学专业英语1
数学专业英语1学专业英语－How to Write Mathematics?How to Write Mathematics?------ Honesty is the Best PolicyThe purpose of using good mathematical language is, of course, to make the u nderstanding of the subject easy for the reader, and perhaps even pleasant. The style should be good not in the sense of flashy brilliance, but good in the se nse of perfect unobtrusiveness. The purpose is to smooth the reader’s wanted, not pedantry; understanding, not fuss.The emphasis in the preceding paragraph, while perhaps necessary, might see m to point in an undesirable direction, and I hasten to correct a possible misin terpretation. While avoiding pedantry and fuss, I do not want to avoid rigor an d precision; I believe that these aims are reconcilable. I do not mean to advise a young author to be very so slightly but very very cleverly dishonest and to gloss over difficulties. Sometimes, for instance, there may be no better way t o get a result than a cumbersome computation. In that case it is the author’s duty to carry it out, in public; the he can do to alleviate it is to extend his s ympathy to the reader by some phrase such as “unfortunately the only known proof is the following cumbersome comp utation.”Here is the sort of the thing I mean by less than complete honesty. At a certa in point, having proudly proved a proposition P, you feel moved to say: “Not e, however, that p does not imply q”, and then, thinking that you’ve done a good expositor y job, go happily on to other things. Your motives may be per fectly pure, but the reader may feel cheated just the same. If he knew all abo ut the subject, he wouldn’t be reading you; for him thenonimplication is, qui te likely, unsupported. Is it obvious? (Say so.) Will a counterexample be suppl ied later? (Promise it now.) Is it a standard present purposes irrelevant part of the literature? (Give a reference.) Or, horrible dictum, do you merely mean th at you have tried to derive q from p, you failed, a nd you don’t in fact know whether p implies q? (Confess immediately.) any event: take the reader into y our confidence.There is nothing wrong with often derided “obvious”and “easy to see”, b ut there are certain minimal rules to their use. Surely when you wrote that so mething was obvious, you thought it was. When, a month, or two months, or six months later, you picked up the manuscript and re-read it, did you still thi nk that something was obvious? (A few months’ripening always improves ma nuscripts.) When you explained it to a friend, or to a seminar, was the someth ing at issue accepted as obvious? (Or did someone question it and subside, mu ttering, when you reassured him? Did your assurance demonstration or intimida tion?) the obvious answers to these rhetorical questions are among the rules th at should control the use of “obvious”. There is the most frequent source o f mathematical error: make that the “obvious”is true.It should go without saying that you are not setting out to hide facts from the reader: you are writing to uncover them. What I am saying now is that you should not hide the status of your statements and your attitude toward them eit her. Whenever you tell him something, tell him where it stands: this has been proved, that hasn’t, this will be proved, that won’t. Emphasize the importan t and minimize the trivial. The reason saying that they are obvious is to put t hem in proper perspecti e for the uninitiated. Even if your saying so makes an occasional readerangry at you, a good purpose is served by your telling him how you view the matter. But, of course, you must obey the rules. Don’t le t the reader down; he wants to believe in you. Pretentiousness, bluff, and conc ealment may not get caught out immediately, but most readers will soon sense that there is something wrong, and they will blame neither the facts nor them selves, but quite properly, the author. Complete honesty makes for greatest clar ity.---------Paul R.Haqlmosvocabularyflashy 一闪的 counter-example 反例unobtrusiveness 谦虚dictum 断言；格言forestall 阻止，先下手deride嘲弄anticipate 预见 subside沉静pedantry 迂腐；卖弄学问 mutter出怨言，喃喃自语fuss 小题大做 intimidation威下reconcilable 使一致的 rhetorical合符修辞学的gloss 掩饰 pretentiousness自命不凡alleviate 减轻，缓和bluff 欺骗implication 包含，含意concealment隐匿notes1. 本课文选自美国数学学会出版的小册子How to write mathematics 中Paul R.Halmos. 的文章第9节2. The purpose is smooth the reader’way, to anticipates his difficulties and to forestall them. Clarit y is what’s wanted, not pedantry; understanding, not fuss.意思是：目的是为读者扫清阅读上的障碍，即预先设想读者会遇到什么困难，并力求避免出现这类困难。
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1、了解文献查阅是做科研必不可少的能力； 2、掌握关键词索引查阅办法、学科分类查阅等办法。
学习本课程的基本要求：
1、认真自学好教材，并勾画出学习重点。 /中国知网翻译助手 2、积极参与本课程的讨论，做好听课笔记。 3、按时独立完成平时作业。
f (x) M For all x D ，where M is a constant.
3、能用英语书写文章摘要、学术会议通知、 学术交流信件等。同时培养简单的英语会 话能力。 4、为部分优秀学生攻读研究生奠定数学专 业英语的基础，同时让大部分同学了解数 学专业英语与生活英语的区别，为今后走 上工作岗位，特别是服务于IT业或外资企 业有独当一面的能力。
课程学习安排
❖ 课程类别：专业任选课 ❖ 课程学时：总学时32 ❖ 学 分：1
数学专业英语 第一讲
为什么要学习数学专业英语？
❖ 数学学科发展需要：20世纪90年代计算机科学技术 的迅速发展宣告了人类信息时代的到来。数学，这 个古老而又优雅的学科获得了新的发展动力和发挥 作用的舞台。
❖ 现在国际数学教育与研究交流日益频繁，很多最新 的研究成果是以英文形式呈现的。专业人员需要有 阅读翻译英语，甚至用英文写作论文的能力。对于 学习数学的学生和准备从事数学研究的人员，在掌 握了公共英语的基本
Eg1:Given 0 ，there exists a number N>0 such that an a for all n N .
Eg2: Since h(x) is harmonic on neighborhood of
B(a,r), we have h(x)d (x) h(a) . B
本课程分四部分讲解：
精选课文：1、理解数学专业文章和一般英语文章写作的不同；
2、掌握数学一般的主要不同专业文章中的基本术语和普遍常用 词汇，英文习作的一般习惯。
专业文选：1、掌握数学英语专业文献和普通英语文章的不同；
2、了解专业文献方面知识。
英文数学论文写作基础：掌握英文论文的基本写作格式、
用词和符号等方面的规范。
特点二：科学内容的完整性与表达形式的精 炼性要求
1、长句较多 2、非限定动词使用频率高
Eg1: By introducing a new smoothing function, the problem is approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions.
2. 被动语态出现频率高，应用范围广
Eg1:The Fermat Conjecture has been proved to be true.
Eg2: The function idea may be illustrated schematically in many ways. 见P54
3. 主动语态句型也多数用于强调事实，而 不是强调行为发出者及其情感
3、名词化结构及其他简化表达的形式也较常出现 Eg1: The line rotates on x-axis, which forms a conicoid.
The rotation of the line on x-axis forms a conicoid.
特点三：数学的专业性十分典型
1、数学符号、公式和图表到处可见 2、专业术语是构建数学大厦的砖瓦 Eg: integer, diameter, differential, triangle 3、半专业性术语穿插频繁、词义多变 Eg: function, power, set,right
1.1 数学专业英语的基本特点
特点一：注意对客观事实与真理的描述
1. 时态常用一般现在时
Eg1: Equations are of two kinds-identities and equations of condition.见P19
Eg2: A right angle is a 90 angle. 见P31
知识的基础上，如果希望较快地掌握阅读英文 版数学教程和科研资料的基本方法，进一步学 习数学专业英语是必须的。
❖由于数学内容的英语表达有其特殊性，阅读 时不仅要靠个人在公共英语上的基本功，而且 还要靠数学基本知识的掌握及其运用的能力。
开设本课程目的
1、为数学专业本科大学生阅读英文数学文章 和发表数学英文文章做培训，同时扩大学生英 语知识面，为相关大学生的研究生考试做英语 保温和一定强化。 2、掌握数学专业词汇，培养快速阅读数学专业 英语的能力。了解数学的学科分类，英文学术 论文摘要的检索，数学文章的英译汉和汉译英 的技巧。
4、数学词汇的形式多样、数量庞大 Icosahedral，heptagon(七边形） heliciods
Algebra(代数)，geometry(几何)，trigonometry （三角学），isosceles triangles（等腰三角形）等
合成词：right-handed(system)右手系 jump-function(跳跃函数)
派生词：irregularity（非正则性）、inhomogeneous （非齐次的）、idempotence（幂等性）
以数学家名字命名的术语：Jacobian(雅克比行列 式），Laplacian(拉普拉斯算符)，
5、表示条件、推理根据的句型相对固定 (1)用if、when、as为连接词的条件从句 The function f(x) approaches infinity as x tends to zero.
(2)用if、when、as为连接词的条件从句
Suppose D is an open set with its closure in G.
(3) 用such that 为连接词的从句表示条件或不种条 件 Suppose f(x) is a function on a domain D such that