数学专业英语之课件一
数学专业英语第一讲.ppt
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；
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。
高数双语课件section1_5.pptx
kind [第一类间断点] of the function; all other discontinuous points are called discontinuity of the second kind[第二类间断点].
y
y
O
x
First kind
x O
Second Kind
11
The Classification of Discontinuous Points
Finish.
7
The Continuity of Function
2x 1, 1 x 0
Example
Prove
f
(
x
)
x
2
3,
0 x1
does not continuous at
x0 .
Proof Since f (0) 3 and
xlim0 f ( x) xlim0( x2 3) 3 f (0)
x) sin( x0)
2cos
x0
x 2
sin
x 2
then
lim
x0
y
2
lim cos
x0
x0
x 2
sin
x 2
0.
Hence sin x is continuous at x x0. Since, x0 is arbitrary point
in the interval (,), we have sin x C(,) .
(
x0
)
x x0
lim
x x0
f (x) f (x)
f ( x0)
.
f ( x0)
4
The Continuity of Function
《数学专业英语》课件
Introduction to Mathematics Professional EnglishMathematics Professional English VocabularyGrammar and Expression in Mathematical English
01
Definition and Importance
Course content: covering basic mathematical vocabulary, mathematical formulas and symbols, academic paper reading and writing, academic speeches and communication, mathematical literature translation, and other aspects.
Course objectives and content
Course objective: To cultivate students' mastery of basic vocabulary, grammar, and expression in mathematics related English, and to improve their English reading, writing, communication, and translation abilities in the field of mathematics.
English interface of software and tools
Learn how to read and understand English documentation for mathematical software and tools, master the professional terms and expressions in the documentation, and lay a foundation for in-depth learning and application.
数学专业英语(吴炯圻-第2版)2-9-2-10课件
我们马上就会发现(9.1)的每一个解都一定是f(x)=Cex 这种形式，这里C可以是任何常数。
The study of differential equations is one part of mathematics that, perhaps more than any other, has been directly inspired by mechanics, astronomy, and mathematical physics.
近年来，在数学和许多各种不同的领域中，矩阵的应 用一直以惊人的速度不断增加。在研究量子力学时， 矩阵理论在现代物理学上起着主要的作用。
Matrix methods are used to solve problems in applied differential equations, specifically, in the area of aerodynamics, stress and structure analysis. One of the most powerful mathematical methods for psychological studies is factor analysis, a subject that makes wide use of matrix methods.
1. 理解微分方程的分类。 2. 理解矩阵学习的重要性。
Or a radioactive substance may be disintegrating at a known rate and we may be required to determine the amount of material present after a given time.
《高等数学课件-全英文版(英语思维篇)》
Discover the Fundamental Theorem of Calculus and its significance in integration.
Riemann Sums
Explore Riemann sums as a method for approximating definite integrals.
Functions and Graphs
Types of Functions
Discover the different types of functions and their graphical representations.
Graph Plotting
Learn how to plot and analyze functions using mathematical tools and software.
Differentiation
1
Derivative Definition
Learn the definition and basic rules
Chain Rule
2
of differentiation.
Discover how to differentiate
composite functions using the
Work and Energy
Explore how integration is used to calculate work and energy in various scenarios.
Differential Equations
1
Introduction to Differential
《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
(高等数学英文课件)1.4 Continuity
x0 ,a_0__ 时_f (x) 为 x0
连续函数.
提示: f(0)0, f (0) f (0) a
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1.4.3
Intermediate Value Theorem for Continuous Functions
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例. 证明方程 x34x210在区间(0,1) 内至少有
一个根 .
证: 显然 f(x ) x 3 4 x 2 1 C [0 ,1 ],又 f(0)10, f(1)20
故据零点定理, 至少存在一点(0,1),使 f()0,即 34210
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1.4
Continuity
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xl ix0m f(x)f(x0)
f(x 0 ) f(x 0 ) f(x 0 )
Left-continuous Right-continuous
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Corollary
• Suppose that f is continuous on the closed interval [a,b]. If f(a) f(b)<0, then there must be at least one number c on the open interval (a,b) such that f(c) = 0.
y ytaxn
O
x
2
y y sin 1 x
高等数学【线性代数】英文版课件1
dy 2 dx + y = x d2 y = −k2 y dx2 2y 5 d3 y + d 2 + cos x = dx3 dx dy sin dx + tan−1 y = 1
0
Ordinary Differential Equations Lecture Notes
Definition (1.2.3) The order of the highest derivative occurring in a differential equation is called the order of the differential equation. In Example 1.2.2
Ordinary Differential Equations Lecture Notes
School of Physical and Mathematical Sciences Nanyang Technological University
August 2010
Ordinary Differential Equations Lecture Notes
Ordinary Differential Equations Lecture Notes
1.2. Basic Ideas and Terminology
Begin with a very general definition of a differential equation. Definition (1.2.1) A differential equation is an equation involving one or more derivatives of an unknown function. Examples (1.2.2) The following are all differential equations.
(高等数学英文课件)1.3 Limits Involving Infinity
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1.3
Limits Involving Infinity
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1.3.1 Finite Limits as x … 1.3.2 Rules for Limits 1.3.3 Horizontal Asymptotes 1.3.4 Infinite Limits 1.3.5 Vertical Asymptotes 1.3.6 Oblique Asymptotes
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1.3.4
Infinite Limits
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x
x1
0
上式中分子多项式的次数应为零,
故有1－a=0,a－b=0,由此得 a=b=1
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1.3.3
Horizontal Asymptotes
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limsinx, limsinx.
x
x
11
lim , lim .
x x x0
x0
_________________________________________________
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• 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
流课程.校园数学主要集
focuses on learning procedures 中在学习函数去去解决
量词加工
• 7. Proofs
证明
• 8. Proofs involving quantifiers
量词证明
• 9. Elements of number theory
数论原理
10. Beginning real a要的学生是在 大学校园的大一 学生，他们主修 的是数学或与数 学相关的课题， 或高中毕业班的 学生有考考大学 的决心.
About the student
• They will need mathematical thinking to succeed in their major. Because mathematical thinking is a valuable life skill, however, anyone over the age of 17 could benefit from taking the course.
课程目标 数学思维简介
课程大纲
About the course
• The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.
to solve highly stereotyped problems. Professional
非常刻板问题.专业数学
mathematicians think a certain 家考虑一些特定的方法
way to solve real problems, problems that can arise from the
• 他们这类人需要数学思维去使他们的主 修成功.因为数学思维是一门有益的生 活技能，并且，任何超过17岁的人都能 从中获益.
Course syllabus
• Instructor’s welcome and introduction
• 1. Introductory material
目录
• 2. Analysis of language – the logical combinators 逻辑联结词
来解决实际问题，这些
everyday world, or from science, 问题来源于日常生活世
or from within mathematics itself.
界或者科学，或者来源 于数学本身.
Introduction to mathematical thingking
• The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.