1、本文格式為Word版，下載可任意編輯 數(shù)學(xué)專業(yè)英語第2章課后答案上課講義 此文檔僅供收集于網(wǎng)絡(luò)，如有侵權(quán)請聯(lián)系網(wǎng)站刪除 2.1 2.比:ratio 比例:proportion 利率:interest rate 速率:speed 除:pide 除法:pision 商:quotient 同類量:like quantity 項:term 線段:line segment 角:angle 長度:length 寬:width 高度:height 維數(shù):dimension 單位:unit 分?jǐn)?shù):fraction 百分?jǐn)?shù):percentage 3.(1)一條線段和一個角的比沒有意義,他們不是一致類型的量. (

2、2)對比式通過說明一個量是另一個量的多少倍做出的,并且這兩個量務(wù)必依據(jù)一致的單位. (5)為了解一個方程,我們務(wù)必移項,直到未知項單獨處在方程的一邊,這樣就可以使它等于另一邊的某量. 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

3、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. 2.2 2.初等幾何:elementary geometry 三角學(xué):trigonometry 余弦定理:Law of cosines 勾股定理/畢達哥拉斯定理:Gou-Gu theorem/Pythagoras

4、theorem 角:angle 銳角:acute angle 直角:right angle 同終邊的角:conterminal angles 仰角:angle of elevation 俯角:angle of depression 全 等:congruence 夾角:included angle 三角形:triangle 三角函 數(shù):trigonometric function 直角邊:leg 斜邊:hypotenuse 對邊:opposite side 臨邊:adjacent side 始邊:initial side 解三角形:solve a triangle 相互依靠:mutually d

5、ependent 表示成:be denoted as 定義為:be defined as 3.(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 are 只供學(xué)習(xí)與交流 此文檔僅供收集于網(wǎng)絡(luò)，如有侵權(quán)請聯(lián)系網(wǎng)站刪除 known, then th

6、e 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)假如一個角的頂點在一個笛卡爾坐標(biāo)系的原點并且它的始邊沿著x軸正方向，這

7、個角被稱為處于標(biāo)準(zhǔn)位置. (3)仰角和俯角是以一條以水平線為參考位置來測量的,假如正被觀測的物體在觀測者的上方,那么由水平線和視線所形成的角叫做仰角.假如正被觀測的物體在觀測者的下方,那么由水平線和視線所形成的的角叫做俯角. (5)假如我們知道一個三角形的兩條邊的長度和對著其中一條邊的角度,我們?nèi)绾谓膺@個三角形呢?這個問題有一點困難來回復(fù),由于所給的信息可能確定兩個三角形,一個三角形或者一個也確定不了. 2.3 2.素數(shù):prime 合數(shù):composite 質(zhì)因數(shù):prime factor/prime pisor 公倍數(shù):common multiple 正素因子: positive prim

8、e pisor 除法算式:pision equation 最大公因數(shù):greatest common pisor(G.C.D) 最小公倍數(shù): lowest common multiple(L.C.M) 整除:pide by 整除性:pisibility 過 程:process 證明:proof 分類:classification 剩余:remainder輾轉(zhuǎn)相除 法:Euclidean algorithm 有限集:finite set 無限的:infinitely 可數(shù)的countable 終止:terminate 與矛盾:contrary to 3.(1)We need to study b

9、y which integers an integer is pisible, 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 pisible by 1 and itself, can al

10、so be pisible 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)數(shù)論中一個重要的問題是哥德巴赫猜想,它是關(guān)于偶數(shù)作為兩個奇素數(shù)和的表示. (3)一個數(shù),形如2p-1的素數(shù)被稱為梅森素數(shù).求出5個這樣的數(shù). 只供學(xué)習(xí)與交流 此文檔僅供收集于網(wǎng)絡(luò)，如有侵權(quán)請聯(lián)系網(wǎng)站刪除 (5)任意給定的整數(shù)m和素數(shù)p,p的僅有的正因子是

11、p和1,因此僅有的可能 的p和m的正公因子是p和1.因此,我們有結(jié)論:假如p是一個素數(shù),m是任意整數(shù),那么p整除m,要么(p,m)=1. 2.4 2.集:set 子集:subset 真子集:proper subset 全集:universe 補 集:complement 抽象集:abstract set 并集:union 交集:intersection 元 素:element/member 組成:comprise/constitute 包含:contain 術(shù)語:terminology 概念:concept 上有界:bounded above 上界:upper bound 最小的上界:leas

12、t upper bound 完備性公理:completeness axiom 3.(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 becom