数学专业英语(15).doc

Mathematical English 15: Mathematical Symbols and Their ReadingMathematical EnglishDr. Xiaomin ZhangEmail: Mathematical Symbols38.72 three eight point seven two two point zero three two six, two six recurring a half or one half a quarter or one quarter; a fourth or one fourth one hundred twenty five and three quarters four fifths or four over five one hundred and thirteen over three hundred a over ba+b=c a plus b (the sum of a and b) is equal to (equals) cc-b=a c minus b (the difference of a and b) is equal to (equals) aab=c a times (multiplied by) b (the product of a and b) is equal to (equals) ccb=a c divided by b (the quotient of a and b) is equal to (equals) aa : b=c : d the ratio of a to b equals the ratio of c to d.ab a is approximately equal to (approximately equals) bab a is identically equal to (identical to) bab (mod p) a is congruent to b (modulo p)ab a is not equal to (identical to) bab a is greater than bab a is less than or equal to bab a is greater than or equal to bab a varies directly as ba/b a is parallel to bab a is perpendicular to b a bara a primea a double primes|a| the absolute value of aa2 a squareda3 a cubedan a to the power n (the nth power) the square root of a the cube root of a the nth root of aex exponential function of x (to the base e)logax logarithm of x to the base alnx logarithm of x (to the base e)y=f(x) y is a function f of x inverse function (mapping) of f image of X by mapping f inverse image of X by mapping f total differential of the function f derivative of the function f with respect to xthe second derivative of the function f with respect to xthe nth derivative of the function f with respect to x partial derivative of the function f with respect to x, where f is a function of x and other variables an indefinite integral of the function f with respect to x definite integral of the function f with respect to x from a to b the sum of all ai, where i is any integer from 1 to n the product of all ai, where i is any integer from 1 to n open interval from a to b closed interval from a to b half open interval from a to b, open at the left interval closed at the left a, infinite to the right one over the square root of x approaches zero as x approaches infinity (the limit of one over the square root of x as x approaches infinity is zero) limit of f(x) as x approaches a from the left limit superior limit inferior approaches 1 as n approaches infinity is bounded as n approaches infinity approaches 0 as n approaches infinity increases, approaching the limit b decreases, approaching the limit bA transpose of the matrix AA* adjoint of the matrix AtrA trace of the matrix A|A|, detA determinant of the matrix AAx the image of x under the transformation AAB scalar product (dot product, inner product) of A and B AB vector product (cross product, outer product) of A and BAB the direct sum of A and B not p (negation) p and q (conjuntion) p or q (disjuntion) p implies q (implication) p is equivalent to q (equivalence, i.e. p if and only if q) for all e greater than 0 there exists a d greater than 0x is a member (element) of the set XA is contained in set XA is not contained in set XA contains B as a subset union of sets A and B intersection of sets A and B union of all sets Ai intersection of all sets Ai empty set complement of set A difference of set A and B the set of all pairs (x, y) with the property the sum of x squared and y squared is less than r squared the set of all x with the property P the set whose members are ai, where i is any integer from 1 to n the set whose members are ai, where i is any positive integer closure of X boundary of XintX interior of Xdim X dimension of X P(A) the probability that the event A occurs P(A)=P(B) events A and B are equally likely (the probability that the event A occurs is equal to that of B)P(A)P(B) event A is more likely than B (the probability that the event A occurs is greater than that of B)P(A)P(B) event A is at least as likely as B