《数学专业英语》常用英文表达

MATHEMATICAL ENGLISHMATHEMATICAL ENGLISH Mathematical English ， School of Appl. Math. 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 and 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 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 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: 5 6read as 5 times 6 or 5 multiplied by 6 ,Over or is to or divided by 3 4 Example:read as 3 over 4, three quarters, 3 divided by 4 3,x= = 4 x Proportion : Example::1 2read as the ratio of 1 to 2 0 0 Percent, Per cent Example: 0 2 0 read as 2 Percent ‰Permille, per mille Example: 5‰read as 5 per mille 2. Basic signs of relationships = = Be equal to, equals Be identical with/to, be equivalent to 5cExample:read as c is identical with (to) 5, c is equivalent to 5 5 Be not equal to Example: 0cd a+坠+坠c plus d times a is not equals to 0 Be approximately equal to 3 0.429 7 3 divided by 7 is approximately Equal to zero point four two nine Example: , Be less than, be greater than Example: ,ab cda is less than b, c is greater than d ,３３ Be less than or equal to, be greater than or equal to Example:38x- ＃- ＃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:6c- -? ?c is far greater than minus 6 6 xA x belongs to A x is an element (or a member) of A x does not belong to A x is not an element (or a member) of A ABA 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 xA AB ∩AB UAB \A B Signs of elementary algebra Absolute value Example: 217x+=+=The absolute value of 2 times x plus 1 equals 7 !nFactorial n Example: !=鬃鬃55 4 3 2 1 Factorial 5 equals 5 times 4 times 3 times 2 times1 ΣThe sum of the terms indicated,summation of Example: 5 n n=1 sThe sum of sn from n equals 1 to 5 The product of the terms indicated Example: 1 n n a = = Product of all an from n equals 1 to infinity 7 max, min maximum value, minimum value Eampl