数学专业英语第2章课后答案上课讲义
课文2—AB数学专业英语翻译(第二版)吴炯圻
2-A Why study geometry?Why do we study geometry? The student beginning the study of this text may well ask, "What is geometry? What can I expect to gain from this study?2-A为什么研究几何学？为什么我们研究几何学？刚开始学习这篇文章的学生会疑问，“几何是什么？研究几何我们能学到什么呢？Many leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics. This is evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools.许多居领导地位的学术机构承认，所有学习这个数学分支的人都将得到很好的收益。
事实是，他们需要学习几何作为学校入学考试的先决条件。
Geometry had its origin long ago in the measurements by the Babylonians and Egyptians of their lands inundated by the floods of the Nile River. The greek word geometry is derived from geo, meaning "earth," and metron, meaning "measure." As early as 2000 B. C. we find the land surveyors of these people reestablishing vanishing landmarks and boundaries by utilizing the truths of geometry.很早以前，几何学源于测量被尼罗河的洪水淹没了的巴比伦人和埃及人的土地。
数学专业英语
数学专业英语课后答案2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
2.-第二章课后习题及答案
2.-第二章课后习题及答案D3. (Q4) What information is used by a processrunning on one host to identify a process running on another host?Answer: The IP address of the destination host and the port number of the destination socket.4. (Q6) Referring to Figure 2.4, we see thatnone of the application listed in Figure2.4 requires both no data loss and timing.Can you conceive of an application that requires no data loss and that is also highly time-sensitive?Answer: There are no good example of an application that requires no data loss and timing. If you know of one, send an e-mail to the authors5. (Q9) Why do HTTP, FTP, SMTP, and POP3 run on top of TCP rather than on UDP?Answer: The applications associated with those protocols require that all application data be received in the correct order and without gaps. TCP provides this service whereas UDP does not.6. (Q11) What is meant by a handshaking protocol?Answer: A protocol uses handshaking if the two communicating entities first exchange control packets before sending data to each other. SMTP uses handshaking at the application layer whereas HTTP does not.7. (Q13) Telnet into a Web server and senda multiline request message. Include inthe request message the If-modified-since:header line to force a response message with the 304 Not Modified status code.Answer: Issued the following command (in Windows command prompt) followed by the HTTP GET message to the “” web server:> telnet 80Since the index.html page in this web server was not modified since Fri, 18 May 2007 09:23:34 GMT, the following output was displayed when the above commands were issued on Sat, 19 May 2007. Note that the first 4 lines are the GET message and header lines input by the user and the next 4 lines (starting from HTTP/1.1 304 Not Modified) is the response from the web server.8. (Q14) Consider an e-commerce site thatwants to keep a purchase record for each of its customers. Describe how this can be done with cookies.Answer: When the user first visits the site, the site returns a cookie number.This cookie number is stored on the user’s host and is managed by the browser.During each subsequent visit (and purchase), the browser sends the cookie number back to the site. Thus the site knows when this user (more precisely, this browser) is visiting the site.9. (Q15) Suppose Alice, with a Web-basede-mail account (such as Hotmail or gmail), sends a message to Bob, who accesses his mail from his mail server using POP3.Discuss how the message gets from Alice’s host to Bob’s host. Be sure to list theseries of application-layer protocols that are used to move the message between the two hosts.Answer: Message is sent from Alice’s host to her mail server over HTTP. Alice’s mail server then sends the message to Bob’s mail server over SMTP. Bob then transfers the message from his mail server to his host over POP3.10. (Q10) Recall that TCP can be enhancedwith SSL to provide process-to-process security services, including encryption.Does SSL operate at the transport layer or the application layer? If the application developer wants TCP to be enhanced with SSL, what does the developer have to do?Answer: SSL operates at the application layer. The SSL socket takes unencrypteddata from the application layer, encrypts it and then passes it to the TCP socket. If the application developer wants TCP to be enhanced with SSL, she has to include the SSL code in the application.11. (Q16) Print out the header of an e-mailmessage you have recently received. How many Received: header lines are there?Analyze each of the header lines in the message.Answer: from 65.54.246.203 (EHLO ) Received：(65.54.246.203) bywith SMTP; Sat, 19 May 200716:53:51 -0700from ([65.55.135.106]) by Received: with MicrosoftSMTPSVC(6.0.3790.2668); Sat, 19 May 2007 16:52:42 -0700Received: from mail pickup service by with MicrosoftSMTPSVC; Sat,19 May 200716:52:41 -0700Message-ID:<BAY130-F26D9E35BF59E0D18A819AFB9310@p hx.gbl>Received: from 65.55.135.123 byby130fd.bay130.hotmail.msn.com with HTTP; Sat, 19 May 200723:52:36 GMTFrom: "prithula dhungel"<prithuladhungel@>To: prithula@Bcc:Subject: Test mailDate: Sat, 19 May 2007 23:52:36 +0000Mime-Version:1.0Content-Type: Text/html; format=flowedReturn-Path: prithuladhungel@Figure: A sample mail message headerReceived: This header field indicates the sequence in which the SMTP servers send and receive the mail message including the respective timestamps.In this example there are 4 “Received:”header lines. This means the mail message passed through 5 different SMTP servers before being delivered to the receiver’s mail box. The last (forth) “Received:” heade r indicates the mail message flow from the SMTP server of the sender to the second SMTP server in the chain of servers. The sender’s SMTP server is at address 65.55.135.123 and the second SMTP server in the chain is . The thir d “Received:” header indicates the mail message flow from the second SMTPserver in the chain to the third server, and so on.Finally, the first “Received:” header indicates the flow of the mail message from the forth SMTP server to the last SMTP server (i.e. the receiver’s mail server) in the chain.Message-id: The message has been given this numberBAY130-F26D9E35BF59E0D18A819AFB9310@ph x.gbl(by. Message-id is a unique string assigned by the mail system when the message is first created.From: This indicates the email address of the sender of the mail. In the given example, the sender is prithuladhungel@To: This field indicates the email address of the receiver of the mail. In the example, the receiver is prithula@Subject: This gives the subject of the mail (if any specified by the sender). In the example, the subject specified by the sender is “Test mail”Date: The date and time when the mail was sent by the sender. In the example, the sender sent the mail on 19th May 2007, at time 23:52:36 GMT.Mime-version: MIME version used for the mail. In the example, it is 1.0.Content-type: The type of content in the body of the mail message. In the example, it is “text/html”.Return-Path: This specifies the emailaddress to which the mail will be sent if thereceiver of this mail wants to reply to the sender. This is also used by the sender’s mail server for bouncing back undeliverable mail messages of mailer-daemonerror messages. In the example, the return path is“prithuladhungel@”.12. (Q18) Is it possible for anorganization’s Web serve r and mail server to have exactly the same alias fora hostname (for example, )? Whatwould be the type for the RR that contains the hostname of the mail server?Answer: Yes an organization’s mail server and Web server can have the same alias for a host name. The MX record is used to map the mail server’s host name to its IP address.13. (Q19) Why is it said that FTP sends control information “out-of-band”?Answer: FTP uses two parallel TCP connections, one connection for sending control information (such as a request to transfer a file) and another connection for actually transferring the file. Because the control information is not sent over the same connection that the file is sent over, FTP sends control information out of band.14. (P6) Consider an HTTP client that wantsto retrieve a Web document at a given URL.The IP address of the HTTP server is initially unknown. What transport and application-layer protocols besides HTTP are needed in this scenario?Answer:Application layer protocols: DNS and HTTPTransport layer protocols: UDP for DNS;TCP for HTTP15. (P9) Consider Figure2.12, for whichthere is an institutional network connected to the Internet. Suppose that the average object size is 900,000 bits and that the average request rate from the institution’s browsers to the origin servers is 10 requests per second.Also suppose that the amount of time it takes from when the router on the Internet side of the access link forwards an HTTP request until it receives the response is two seconds on average (see Section 2.2.5). Model the total average response times as the sum of the averageaccess delay (that is, the delay from Internet router to institution router) and the average Internet delay. For the average access delay, use △/(1-△β), where △ is the average time required to send an object over the access link and β is the arrival rate of objects to the access link.a. Find the total average response time.b. Now suppose a cache is installed in theinstitutional LAN. Suppose the hit rate is 0.6. Find the total response time.Answer:a.T he time to transmit an object of sizeL over a link or rate R is L/R. The average time is the average size of the object divided by R:Δ= (900,000 bits)/(1,500,000 bits/sec) = 0.6 secThe traffic intensity on the link is (1.5requests/sec)(0.6 sec/request) = 0.9. Thus, the average access delay is (0.6 sec)/(1 - 0.9) = 6 seconds. The total average response time is therefore 6 sec + 2 sec = 8 sec.b.T he traffic intensity on the access linkis reduced by 40% since the 40% of the requests are satisfied within the institutional network. Thus the average access delay is (0.6 sec)/[1 –(0.6)(0.9)] = 1.2 seconds. The responsetime is approximately zero if the request is satisfied by the cache (which happens with probability 0.4); the average response time is 1.2 sec + 2 sec = 3.2 sec for cache misses (which happens 60% of the time). So the average response time is (0.4)(0 sec) +(0.6)(3.2 sec) = 1.92 seconds. Thus theaverage response time is reduced from 8 sec to 1.92 sec.16. (P12) What is the difference betweenMAIL FROM: in SMTP and From: in the mail message itself?Answer: The MAIL FROM: in SMTP is a message from the SMTP client that identifies the sender of the mail message to the SMTP server. The From: on the mail message itself is NOT an SMTP message, but rather is just a line in the body of the mail message.17. (P16) Consider distributing a file of F= 5 Gbits to N peers. The server has an upload rate of u= 20 Mbps, and each peers=1 Mbps and an has a download rate of diupload rate of u. For N = 10, 100, and 1,000 and u = 100 Kbps, 250 Kbps, and 500 Kbps, prepare a chart giving the minimumdistribution time for each of the combinations of N and u for both client-server distribution and P2P distribution.Answer: For calculating the minimum distribution time for client-server distribution, we use the following formula:D cs = max {NF/u s , F/d min }Similarly, for calculating the minimum distribution time for P2P distribution, we use the following formula:D P2P = max{F/u s ,F/d min ,NF/( u s +∑u i n i=1 )}Where,F = 5 Gbits = 5 * 1024 Mbitsu s = 20 Mbpsd min = d i = 1 MbpsClient Server:N10 100 1000200 Kbps 10240 51200 512000u 600 Kbps 10240 51200 512000 1Mbps 10240 51200 512000Peer to Peer:N10 100 1000200 Kbps 10240 25904.3 47559.33 U 600 Kbps 10240 13029.6 16899.641 Mbps 10240 10240 10240。
数学专业英语翻译2-1
Mathematicians study conceptions and propositions, Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. Formulas ,figures and charts are full of different symbols. Some of the best known symbols of mathematics are the Arabic numerals 1,2,3,4,5,6,7,8,9,0 and the signs of addition “+”, subtraction “-” , multiplication “×”, division “÷” and equality “=”. 数学家研究的是概念和命题，公理，公设，定义和定理都 是命题。符号是数学中一个特殊而有用的工具，常用于表 达概念和命题。 公式，图形和图表都是不同的符号……..
第二章 精读课文——入门必修
数学与计: useful terms and definitions of Mathematics,
equation
Difficult points:
Some mathematical terms
Requirements: 1. 掌握所讲课文的生词和词组 2. 理解并掌握课外作业里面的汉译英 3. 理解所讲段落的翻译技巧与方法
1－A What is mathematics
Actuarial Mathematics2
例1.8答案
A (7 ) 1 0 0 0 (1 j ) e
8 3
2 0 0 0 (1 j ) e
2
3
2 0 0 0e
2
1 0 0 0 1 .0 2 5 e
8
0 .0 9
2 0 0 0 1 .0 2 5 e
2
0 .0 9
2000e
0 .0 6
2 3
13130
利息度量二——利率和贴现率
期末计息——利率
第n期利率
in
I (n) A ( n 1)
期初计息——贴现率
第n期贴现率
dn I (n) A(n)
单利场合利率与贴现率的关系
I (n) A(n) a ( n ) a ( n 1) a (n) i 1 in
单利的实质利率逐期递减，复利的实质利率保持 恒定。
时，相同单复利场合，单利计息比复利计 息产生更大的积累值。所以短期业务一般单利计 息。
t 1
时，相同单复利场合，复利计息比单利计 息产生更大的积累值。所以长期业务一般复利计 息。
t 1
单/复利场合积累函数示图
a 5
4
3
2
1 0 1 t 2 3
L
tn
方法：建立现金流分析方程（求值方程） 原则：在任意时间参照点，求值方程等号两边现时值相等。
例1.5：求本金
某人为了能在第7年末得到1万元款项，他愿意 在第一年末付出1千元，第3年末付出4千元， 第8年末付出X元，如果以6%的年利率复利计 息，问X=？
例1.6答案
以第7年末为时间参照点，有
数学专业英语课后答案
2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
最新数学专业英语课后答案(1)
2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
数学专业英语课后答案
2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
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数学专业英语第2章课后答案上课讲义2.12.比:ratio 比例:proportion 利率:interest rate 速率:speed 除:divide 除法:division 商:quotient 同类量:like quantity 项:term 线段:line segment 角:angle 长度:length 宽:width高度:height 维数:dimension 单位:unit 分数:fraction 百分数:percentage3.(1)一条线段和一个角的比没有意义,他们不是相同类型的量.(2)比较式通过说明一个量是另一个量的多少倍做出的,并且这两个量必须依据相同的单位.(5)为了解一个方程,我们必须移项,直到未知项独自处在方程的一边,这样就可以使它等于另一边的某量.4.(1)Measuring the length of a desk, is actually comparing the length of the desk to that of a ruler.(3)Ratio is different from the measurement, it has no units. The ratio of the length and the width of the same book does not vary when the measurement unit changes.(5)60 percent of students in a school are female students, which mean that 60 students out of every 100 students are female students.2.22.初等几何:elementary geometry 三角学:trigonometry 余弦定理:Law of cosines 勾股定理/毕达哥拉斯定理:Gou-Gu theorem/Pythagoras theorem 角:angle 锐角:acute angle 直角:right angle 同终边的角:conterminal angles 仰角:angle of elevation 俯角:angle of depression 全等:congruence 夹角:included angle 三角形:triangle 三角函数:trigonometric function直角边:leg 斜边:hypotenuse 对边:opposite side 临边:adjacentside 始边:initial side 解三角形:solve a triangle 互相依赖:mutually dependent 表示成:be denoted as 定义为:be defined as3.(1)Trigonometric function of the acute angle shows the mutually dependent relations between each sides and acute angle of the right triangle.(3)If two sides and the included angle of an oblique triangle areknown, then the unknown sides and angles can be found by using the law of cosines.(5)Knowing the length of two sides and the measure of the included angle can determine the shape and size of the triangle. In other words, the two triangles made by these data are congruent.4.(1)如果一个角的顶点在一个笛卡尔坐标系的原点并且它的始边沿着x轴正方向，这个角被称为处于标准位置.(3)仰角和俯角是以一条以水平线为参考位置来测量的,如果正被观测的物体在观测者的上方,那么由水平线和视线所形成的角叫做仰角.如果正被观测的物体在观测者的下方,那么由水平线和视线所形成的的角叫做俯角.(5)如果我们知道一个三角形的两条边的长度和对着其中一条边的角度,我们如何解这个三角形呢?这个问题有一点困难来回答,因为所给的信息可能确定两个三角形,一个三角形或者一个也确定不了.2.32.素数:prime 合数:composite 质因数:prime factor/prime divisor 公倍数:common multiple 正素因子: positive prime divisor 除法算式:division equation 最大公因数:greatest common divisor(G.C.D) 最小公倍数: lowest common multiple(L.C.M) 整除:divide by 整除性:divisibility 过程:process 证明:proof 分类:classification 剩余:remainder辗转相除法:Euclidean algorithm 有限集:finite set 无限的:infinitely 可数的countable 终止:terminate 与矛盾:contrary to3.(1)We need to study by which integers an integer is divisible, that is , what factor it has. Specially, it is sometime required that an integer is expressed as the product of its prime factors.(3)The number 1 is neither a prime nor a composite number;A composite number in addition to being divisible by 1 and itself, can also be divisible by some prime number.(5)The number of the primes bounded above by any given finite integer N can be found by using the method of the sieve Eratosthenes.4.(1)数论中一个重要的问题是哥德巴赫猜想,它是关于偶数作为两个奇素数和的表示.(3)一个数,形如2p-1的素数被称为梅森素数.求出5个这样的数.(5)任意给定的整数m和素数p,p的仅有的正因子是p和1,因此仅有的可能的p和m的正公因子是p和1.因此,我们有结论:如果p是一个素数,m是任意整数,那么p整除m,要么(p,m)=1.2.42.集:set 子集:subset 真子集:proper subset 全集:universe 补集:complement 抽象集:abstract set 并集:union 交集:intersection 元素:element/member 组成:comprise/constitute包含:contain 术语:terminology 概念:concept 上有界:bounded above 上界:upper bound 最小的上界:least upper bound 完备性公理:completeness axiom3.(1)Set theory has become one of the common theoretical foundation and the important tools in many branches of mathematics.(3)Set S itself is the improper subset of S; if set T is a subset of S but not S, then T is called a proper subset of S.(5)The subset T of set S can often be denoted by {x}, that is, T consists of those elements x for which P(x) holds.(7)This example makes the following question become clear, that is, why may two straight lines in the space neither intersect nor parallel.4.(1)设N是所有自然数的集合,如果S是所有偶数的集合,那么它在N中的补集是所有奇数的集合.(3)一个非空集合S称为由上界的,如果存在一个数c具有属性:x<=c对于所有S中的x.这样一个数字c被称为S的上界.(5)从任意两个对象x和y，我们可以形成序列（x，y），它被称为一个有序对，除非x=y，否则它当然不同于（y，x）.如果S和T是任意集合，我们用S*T表示所有有序对（x,y),其中x术语S，y属于T.在R.笛卡尔展示了如何通过实轴和它自己的笛卡尔积来描述平面的点之后，集合S*T 被称为S和T的笛卡尔积.2.52.竖直线:vertical line 水平线:horizontal line 数对:pairs of numbers 有序对:ordered pairs 纵坐标:ordinate 横坐标:abscissas 一一对应:one-to-one 对应点:corresponding points圆锥曲线:conic sections 非空图形:non vacuous graph 直立圆锥:right circular cone 定值角:constant angle 母线:generating line 双曲线:hyperbola 抛物线:parabola 椭圆:ellipse退化的:degenerate 非退化的:nondegenerate 任意的:arbitrarily 相容的:consistent 在几何上:geometrically 二次方程:quadraticequation 判别式:discriminant 行列式:determinant3.(1)In the planar rectangular coordinate system, one can set up aone-to-one correspondence between points and ordered pairs of numbers and also a one-to-one correspondence between conic sections and quadratic equation.(3)The symbol can be used to denote the set of ordered pairs （x，y）such that the ordinate is equal to the cube of the abscissa.（5）According to the values of the discriminate，the non-degenerate graph of Equation （iii）maybe known to be a parabola， a hyperbolaor an ellipse.4.（1）在例1，我们既用了图形，也用了代数的代入法解一个方程组（其中一个方程式二次的，另一个是线性的）。