数学专业英语

• shkdchsuo

  2011-05-19
  1，The following are...2，the compound proposition ... and its converse...3，all choices of truth values of the variables.....4，the final columns of...5，where the truth values of P and Q agree6，to reason with these senteces (reasoning with logical expressions)7，.....pertains to all people.8，this is more compact9，rule of inference10，in equal measure
• shkdchsuo

  2011-05-17
  1，a propositional function2，the symbol for negation3，the universe of discourse consists of...4，Many mathematical statements assert that....5，there is an element with a certain property6，be phrased in term of sth7，specify values 简称“赋值”
• shkdchsuo

  2011-05-14
  1，the proof ...is valid for...2，The same argument with S and T interchanged...3，We denote ....as an n-tuple...4，by contraction from...5，hold trivially 显然成立6，the underlying linear sapce 基础线性空间7，by induction on...8，there is associated...9，in many diverse fields...10，make wide use of...11，use ... to good advantage12，read with understanding13，be reduced to...14，this belief is now known to be untenable...15，Specifically for this case,...16，equations in n unknwowns17，in the sense that...18，polynomial in x [关于]x 的多项式
• shkdchsuo

  2011-05-13
  1，It is easy to check that....2，the solution of...were exhibited as...3，without any concern regarding the meaning and validity of such formulas.4，...by present-day standards.5，....independently and almost simultaneously proposed...6，....real numbers endowed with certain special properties.7，From the definition of...., it is possible to deduce ....8，By use of ....9，the same strict inequality holds for...10，but the proof is not easy to give at this stage.11，the foregoing definition agrees with that given in Chapter 812，This is logically equivalent to the statement that...13，To prove this, it suffices to show that...14，The results holds trivially ,,,,15，the subspace spanned by S16，reduces to....
• shkdchsuo

  2011-05-12
  1，The study of differential equations.....2，....so their study is of practical importance3，...near the end of this chapter.4，mathematical theories of much generality5，A more thorough study of ....is carried out in Volume ..6，it is customary to write...7，By.....is meant....8，we shall begin our study of ...with....9，the expression ...has various special forms10，where ...is assumed to be ....11，the ...equation has infinitely many solutions,...12，In actual practice,...13，to fix the position function14，In some respects,...15，this terminology originated in mechanics16，a large variety of ...
• shkdchsuo

  2011-05-11
  1，we conclude that...2，Thus the line segment ....has the direction....3，In the notation of logarithms,...4，It is important to realize....5，it follows that....6，computation by means of logarithms7，...is used mainly for theoretical purposes.8，in the counterclockwise sense9，in the form of an equation10，These equations are called differential equations, and their study forms one of the most challenging branches of mathematics.11，....are classified under two main headings: ......
• shkdchsuo

  2011-05-10
  1，A quantity that can take on ..... values2，....these values need not have any definite relations one to another.3，As stated before, ....4，....formula ..is valid5，all we need to prove is that...6，as illustrated in Fig. 2-7-17，If..., the proof is similar,...8，in the foregoing section,..9，when x changes from x to x+h10，....may be stated as follows11，the rate of change of position with respect to time12，In the example worked out in section 7.213，a way of obtaining.....14，We make the convention that ...15，This agrees with the fact that...16，the difference quotient ....has the value m....17，A line for which ...has slope 1.
• shkdchsuo

  2011-05-06
  1，In everyday usage of the language,....2，....these words have ...meanings.3，the common use of the term...4，The important thing here is that.....5，....how to carry on after a given start.6，the essential thing is that....7，For brevity, the notation.... is used to denote...8，Unless otherwise specified, ......9，The main question we are concerned with here is to....10，To treat this problem,....11，The analogy carries over to.... as well,.12，and we leave it for the reader to define the symbols.....13，The basic rules for dealing with........also hold for.....14，formulate these theorems
• shkdchsuo

  2011-05-06
  1，be illustrated schematically2，....are called ....., or, more briefly,...3，schematic representations of...4，.....expressed in function notation.5，plot 画（草图）6，.....has the property that...7，the inverse function to f8，Observe that....9，in the general case,...10，the equation... may have no solutions at all11，.....to admit an inverse function12，It is desirable to know that ...13，the rise of modern analysis14，In the extended sense,...15，.....serves many a practical purpose16，Not speciified by....17，some other form of description18，admit of no...19，desireable to serve as .....20，.....is incorporated in.....
• shkdchsuo

  2011-05-04
  1，....find the equation of ....2，a compact mathematical notation3，"the graph of the set of ordered pairs"4，.....will readily infer that...5，..geometrical figure6，one may be tempted to believe that...7，descibe.....in a quantitative fashion8，If the edges have length x,....9，.....less than or equal to......10，....too limited in its scope11，many stages of genearlziation12，This may be ....., but it need not be.
• shkdchsuo

  2011-05-03
  1，As mentioned earlier,...2，.....we do not talk about area by itself, instead, we talk about the area of something.3，....the subject of analytic geometry4，Figure 2-5 illustrates some examples.5，The point with coordinates (3,2) lies........6，...we agree that....7，Points (a,b) with both a and b positive.....8，with appropriate regard for signs,..9，We shall discuss ....in more detail later on; for the present we confine our attention to.....10，For example, consider a circle of radius r with its center at the origin......11，and suppose P has coordinates (x,y)12，a right triangle whose legs have lengths .....13，and hence,......14，......be intemately intertwined.15，as needed.16，elementary concepts of plane analytic geometry17，the rudiments of calculus18，drawing graph of function
• shkdchsuo

  2011-04-30
  1，Since the natural numbers do not terminate or repeat。。。2，Let us first turn our attention to fractios,3，Now for algebraical expressions,。。
• shkdchsuo

  2011-04-27
  1，。。listing each of elements would be tedious.2，。。would be impossible because they go on forever.3，。。reduce many mathematical concepts to their logical foundations4，outside the scope of this book5，a single entity6，belong to or to be contained in the set7，contain or be composed of its elements8，..and from this generality the theory derive its power.9，reduce to 化简为，归结为10，Strictly speaking,..11，in a careful treatment of。。12，we shall not enter into the details of such proofs13，。。all the field axioms and the order axioms are satisfied by Q14，to the left / right of15，as illustrated in Figrue ..16，it is customary to 。。17，the ordering relation18，the point x lies to the left of ..19，without any reference to geometry20，geometric arguments21，..are presented in analytic form22，这里 ...
• shkdchsuo

  2011-04-26
  1，Notations for denoting sets2，elements are designated by 。。3，When convenient, we shall designate sets by。。4，Two sets A and B are said to be equal。。5，According to this definition, 。。6，the definition requires that we call these sets equal.7，。。we may form new sets,8，all even integers less than 10.9，A is contained in B or that B contains A10，set inclusion11，The statemet 。。does not rule out 。。12，be designated as。。13，as analogous to 。。14，conceptually distinct from。。15，be thought of as 。。16，the shaded portion17，。。of this type18，the underlying set19，"talk of" 原意是谈论，这里转译为“表述”
• shkdchsuo

  2011-04-24
  1，。。joined, straight line segments,。。2，。。any line segment joining two points on the circle.3，From the definition it should be apparent that 。。4，A diameter divides a circle into two arcs termed semicircles,。。5，vanish 消失，变成零6，。。a fixed ray l having endpoint O,7，These functions are of fundamental importance in the study of trigonometry.8，Let us now take up the solution of right triangles.9，To solve a triangle is to 。。
• shkdchsuo

  2011-04-22
  1，The ratio of one quantity to anther like quantity。。2，。。all the rules governing a fraction apply to ratio3，the ratio 3 to 44，The 3 and 4 are called the terms of the ratio.5，a ratio is a quotient of like quantities6，quantities of the same kinds7，Unless there is an important reason to the contrary,。。8，the final ratio of width to length is。。9，parenthesis = round bracket10，Why study geometry?11，The Greek word geomerty is derived from geo, meaning "earth", and metron, meaning "measure".12，by utilizing the truths of geometry13，Solids and planes14，Common examples of solids are。。15，。。are called ....or simply 。。16，。。is termed a line segment17，When no confusion may result,。。
• shkdchsuo

  2011-04-21
  1，the proof of most of geometrical theorems2，equation 方程（常用）；等式（少用）// equality 等式（少用）；相等（常用）3，alike 相同的或一样的4，。。or simply an equation 或简称方程5，to move and change the terms 移项和变形6，The study of arithmetic begings with。。7，。。instead of special cases, we often consider general statements8，。。long or complicated statements9，。。generalizing many specific statements10，grouping symbols11，do the addition, do the multiplication
• shkdchsuo

  2011-04-20
  1，To deal with some more complex practical problems，。。2，。。analytic geometry and calculus, which belong to the higher mathematics.3，Mathematicians study conceptions and propositions.4，Axioms, postulates, definitions and theorems are all propositions.5，symbols Vs signs (例句看区别)6，the centric place of mathematical methods。。7，An equation is a statement of the equality between。。8， on the peprformance of the indicated operation9，An identity is true。。10，An equation which is true。。11，To obtain the root or roots of an equation。。12，To solve an equation。。13，。。almost every problem gives us one or more statements that 。。（结合7体会statement用法）
• shkdchsuo

  2011-04-19
  1，Equations are of two kinds----。。2，The formulas differ only in the signs preceding their left numbers.3，词的添加的一个重要理由是需要重复译出。4，After checking 经检验，5，An equilateral triangle is one with all its sides equal.6，signs and symbols of mathematiics7，The statement of the Gauss Theorem is as follows. (高斯定理叙述如下。)8，We call a triangle an abtuse triangle when one angle is an obtuse angle.9，无人称语句“It....”可照样译成无人称句，必要时也可以译成人称句。10，It should be noted that 应当指出11，It was found that 人们发现12，increase (be, go up) by three times 增加3倍increase three times 增加2倍13，decrease by 60% 降低了60% decrease to 40% 降到了原来的40%14，shortened three times 缩短到(原来的)1/3
• shkdchsuo

  2011-04-13
  The rotation of the line on x-axis forms a conicoid.Now we investigate the integrability of the functions. (现在，我们来研究....)