《数学专业英语》常用英文表达

1、MATHEMATICAL ENGLISH,Aim of the Course:,Expected progress in the following aspects:,. Reading skills of the original mathematical articles and books,. Writing skills of mathematical and other scientific articles,. Translating skills of mathematical articles:both translation from Chinese to English a

2、nd English to Chinese,* Reading, writing and translation of mathematical materials should be brife, simple, exact and easy to be understood,2,Some English expressions of numbers:,The set of numbers consists of real numbers and pure imaginary numbers shown as follows,Complex numbers(C),Pure imaginary

3、 numbers(I),Real numbers(R),Rational numbers(Q),Irrational numbers(Q),Integers(Z),Fractions(F),Natural numbers(N), Zero, Negatives of Natural Numbers,Notice: Reading of Integers one, ten, hundred, thousand, ten thousand, hundred thousand, million. Ten million, hundred million, billion,3,Expressions

4、of some basic mathematical signs:,1. General signs of operation,+ Plus, positive,- Minus, negative,Example: 2+3 read as two plus three,Example: 6-2 read as six minus two, Plus or minus, Positive or negative,Example: read as equals plus or minus 3,Multiplied by, times,Example:,read as 5 times 6 or 5

5、multiplied by 6,Over or is to or divided by,Example:,read as 3 over 4, three quarters, 3 divided by 4,4,Proportion,Example:,read as the ratio of 1 to 2,Percent, Per cent,Example:,read as 2 Percent,Permille, per mille,Example:,read as 5 per mille,2. Basic signs of relationships,Be equal to, equals,Be

6、 identical with/to, be equivalent to,Example:,read as c is identical with (to) 5, c is equivalent to 5,5,Be not equal to,Example:,c plus d times a is not equals to 0,Be approximately equal to,3 divided by 7 is approximately Equal to zero point four two nine,Example:,Be less than, be greater than,Exa

7、mple:,a is less than b, c is greater than d,Be less than or equal to, be greater than or equal to,Example:,x is greater than or equal to minus 3 and less than or equal to 8,Be far less than, be far greater than,Example:,c is far greater than minus 6,6,x belongs to A,x is an element (or a member) of

8、A,x does not belong to A,x is not an element (or a member) of A,A is contained in B or A is a subset of B,A contains B or B is a subset of A,A cap B or A meet B or A intersection B,A cup B or A join B or A union B,A minus B or the difference between A and B,6,Signs of elementary algebra,Absolute val

9、ue,Example:,The absolute value of 2 times x plus 1 equals 7,Factorial n,Example:,Factorial 5 equals 5 times 4 times 3 times 2 times1,The sum of the terms indicated,summation of,Example:,The sum of sn from n equals 1 to 5,The product of the terms indicated,7,max, min maximum value, minimum value,Maxi

10、mum value of the series a1 to an,Powers and roots,x cubed,x to the fourth ,or x to the power four,x to the nth ,or x to the power n,x to the power minus n,x inverse,cube root (of) x,8,Imaginary number and two common irrational numbers,ratio of the circumference of a circle to its diameter,approximat

11、e value 3.1415926,9,fourth root (of) x,nth root (of) x,x plus y all squared,x over y all squared,Some signs in elemetary analysis,Intervals,Open interval,The open interval,refers,to the set of all real numbers x between left endpoint a to the right endpoint b(excluding a and b)with axb.,Closed inter

12、val,The closed interval,refers,to the set of all real numbers x between left endpoint a to the right endpoint b (including a and b) with,Half open(closed) interval,The half open interval,refers,real numbers x between left endpoint a to the right endpoint b (including a but not b) with,to the set of

13、all,10,Function,Example:,The function of x,equals a times the square of x plus b times x plus c,where a is not equal to zero.,Approach, tend to,limit,11,infinity,The limit as x approaches zero from above,The limit as x approaches zero from below,the integral from zero to infinity,double integral over the domain D,triple integral over the domain D,12,f prime x, f dashed x,Example:,