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1、Mathematics Symbols and Their English Explanations 1/2 a half or one half 1/3 a third or one third 2/3 two third 1/4 a quarter or one quarter;a fourth or one fourth 1/10 a tenth or one tenth 1/100 a one hundredth 1/1000 a one thousandth 1/1234 one over a thousand two hundred and thirty-four 3/4 thre
2、e fourths or three quarters 4/5 three fifths or four over five 113/300 one hundred and thirteen over three hundred 212two and a half 872two and seven over eight or two and seven eighths 813three and one eighth 314four and a third 43125a one hundred twenty-five and three fourths quarters 0.1(or.1)0 p
3、oint one or zero point one or nought point one 0.01(or.01)0 point 0 one or zero point zero one or nougth point nought one 0.25(or.25)nougth point two five or point two five 0.045 decimal point nought four five 2.35 two point three five 4.9four point nine recurring 3.0362three point nought three two
4、six,two six recurring 45.67 four five forth-five point six seven 38.72 three eight point seven two or thirty-eight decimal seven two 名师资料总结-精品资料欢迎下载-名师精心整理-第 1 页，共 16 页 -0.001(or.001)0 point 0 0 one nought point nought nought one or zero point zero zero one or point nought nought one+plus;positive _
5、 minus;negative plus or minus(or.)multiplied by;times(or/)divided by=is equal to;equals is identically equal to(or;=)is approximately equal to;approximately equals identical with=or not equal to or=approaches less than greater than much grater than equal to or less than equal to or greater than()rou
6、nd brackets;parentheses square brackets angular brackets braces intersection union is member of set is a subset of similar to;difference*denotes an operation 名师资料总结-精品资料欢迎下载-名师精心整理-第 2 页，共 16 页 -is equivalent to implies orempty set maps into therefore because:ratio sign,divided by,is to:equals,as(pr
7、oportion)varies as infinity square root of 3cube root of parallel to。degrees,minutes”secondsangle ABlength of line from A to B AB vector product of A and B;magnitude of A times magnitude of B times sine of the angle from A to B;AB sin ABABscalar product of A to B;magnitude of A times magnitude of B
8、times cosine of the angle form A to B;AB cosABI or j imaginary or square root of-1 or 2the imaginary cube roots of 1 pi;the ratio of the circumference of a circle to its diameter,approx.3.14159 e or the base of natural logarithms,approx.2.71828 名师资料总结-精品资料欢迎下载-名师精心整理-第 3 页，共 16 页 -the eccentricity o
9、f a conic section x!or xfactorial x nlog xlog x to the base n10log x or lgxlog x to the base 10(common logarithm)elog x or ln x log x to the base(natural logarithm or Naperian logarithm)M modulus of common logarithms 10loge=0.4343,(10logx=elog x0.4343)1Mel o g10=2.3026,(elog x=10logx2.3026)nxx x.xto
10、 n factors,the nth power of x,x to the power nnx or nx1the nth root of x,x to the power one over n th X a x approaches the limit a(the angle between the radius vector and the polar axis)the angle theta sigma the product of the terms indicated xthe absolute value of xxthe mean value of x;x bar bb pri
11、me bb double prime;b second prime bb triple prime 1bb sub one 2bb sub two mbb sub mxx dot,first derivative of x with respect to time xx two dot,second derivative of x with respect to time 名师资料总结-精品资料欢迎下载-名师精心整理-第 4 页，共 16 页 -exp x=xe(e=naperian log base)(abbreviation for xe)nmbb double prime sub mf
12、or F function f(x);F(x);(x)function f(or)of xy=f(x)y is a function of x(finite difference or increment)delta xor x(the increment of x)delta xxd(an increment of x considered as tending to zero)dee of x;dee x;differential of xyxddor xyDthe differential coefficient of y with respect to xthe first deriv
13、ative of y with respect to x2yd/2xdthe second derivative of y with respect x;nyd/nxdthe nth derivative of y with respect xy/uthe partial derivative of y with respect u,uwhere y is a function of u and another variable(or variables)F(x)the first derivative of function F of x with respect to xi/x+j/y+k
14、/zdel;nabla;vector differential operator n nth del(nabla)Laplacian operator 4!Factorial=1432line integral around a closed path integral abintegral between limits a and b名师资料总结-精品资料欢迎下载-名师精心整理-第 5 页，共 16 页 -Fvector Fx+y x plus y(a+b)bracket a plus b bracket closed a=b a equal b;a is equal to b;a is b
15、a b a is not equal b;a is not bab a plus or minus bab a is approximately equal to bab a is greater than bab a is much far greater than bab a is greater than or equal to bab a is not greater than bab a is less than bab a is much less than baba is less than or equal to baba is not less than baba is pe
16、rpendicular to bx=x approaches infinity aba is identically equal to b;a is of identity aangle aab a is parallel to bab the difference between a and baba varies directly as b11=1 one one is one 22=4 twice two is four 65=30 six times multiplied by five equals is equal to;are;makes;make thirty 30=65thi
17、rty is five times as large as six s=vt s equals is equal to v multiplied by t;s equals v times t1:2 the ratio of one to two 名师资料总结-精品资料欢迎下载-名师精心整理-第 6 页，共 16 页 -123=4 12 divided by 3 equals is 4 20:5=16:4 the ratio of 20 to 5 equals the ratio of 16 to 4;20 is to 5 as 16 is to 4 a:b:c:d a is to b as
18、c is to da+b=c a plus b is are;equals;is equal to cc-b=a c minus b is equals;is equal to a;b from c leaves av=tsv equals s divided by t;c is s over t7+37+3 12 is greater than 7 plus 3 72-16=56 72 minus 16 is equals;is equal to 56;16 from 72 leaves 56 2xx square;x squared;the square of x;the second p
19、ower of x;x to the second power 25=25 the second power of 5 is 25;5 square is 25;5 to the second power is equal to 25 3yy cube;y cubed;the cube of y;y to the third power;y to the third 10yy to the minus tenth(power)4=2the square root of 4 is equals plus or minus 2 3athe cube root of a 52xthe fifth r
20、oot of x square 518the square root of five hundred and eighteen 3930the cube root of nine hundred and thirty 3x=5 three times x equals 5 3x/5=2yx to the third power divided by five equals ysquared 名师资料总结-精品资料欢迎下载-名师精心整理-第 7 页，共 16 页 -2x+2y=10 x squared with y squared equals 10 a=tVVta equals v sub t
21、 minus v over divided by t(a+b-cfed)a plus b minus c multiplied by d,all divided by eequals f(8+6212)468.385eight plus six and five-eighths minus three decimal point six eight multiplied by four,all divided by two and a half 456719823余 13 23 into 4567 goes 198 times,and 13 remainder 45+70+152=267 45
22、,70 and 152 added together are 267%per cent 2%two per cent 000per mille 5000five per mille 83%three eighths(of one)per cent 0.3%point three per cent 21ton half ton 32ton tow third of a ton 43km three quarters of a kilometer 1.75km one point seven five kilometer 60hrmisixty miles per hour 20C0twenty
23、degrees 6 6 minutes 6 feet01 10 seconds 10 inches0C0zero degree Centigrade Celsius 名师资料总结-精品资料欢迎下载-名师精心整理-第 8 页，共 16 页 -100C0one a hundred degrees centigrade 32F0thirty-two degrees Fahrenheit Set theory,relations,functions X,YSet xXx is a member of the set XxXx is not a member of XAXAX,Set A is cont
24、ained in set XXAXA,A is not contained in XYXYX,Union of sets X and YYXYX.,Intersection of sets X and Y+,+,Symmetric difference of sets xiXi,Union of all the sets XxiXi,Intersection of all the sets X,0,Null set,empty set CXCXX,Complement of the set XX-Y,XY Difference of sets X and Y)(:),(),(xPxxPxxpx
25、The set of all x with the property p(x,y,z),(x,y,z)Ordered set of elements x,y,and z;to be distinguished from(x,y,z),for example(x,y,z)Unordered set,the set whose elements are x,y,z,and no others ,.,21aa,ia i=1,2.,n 1iniaThe set whose members are ia,where i is any whole number from 1 to n 名师资料总结-精品资
26、料欢迎下载-名师精心整理-第 9 页，共 16 页 -,.,21aa,ia i=1,2.,1iiaThe set whose members are ia,where i is any positive whole number YXCartesian product,set of all(x,y)such that YyXx,IiaiThe set whose elements are a,where IiXry,R x,y Relation,Equivalence relations,for example,congrucnce,Transitive relations,for examp
27、le,numerical order f:XfYfYXyXYX,Function,mapping,transformation YXfff111,Inverse mapping g。F Composite functions:(g。F)(x)=g(f(x)f(X)Image of X by f)(1XfInverse-image set,counter image 1-1,one-one Read“one-to-one correspondence”yxfDiagram:the diagram is commutative in case zwgAff=gPartial mapping,res
28、triction of function f to set AX,card X,XCardinal of the set A,d Denumerable infinity C,c,2 Power of continuum Order type of the set of positive integers Read“countably”名师资料总结-精品资料欢迎下载-名师精心整理-第 10 页，共 16 页 -Number,numerical functions 1(1)20(10)100 Read“from 1 to 20 in intervals of 1,and from 20 to 1
29、00 in intervals of 10”const constant a0 The number A is nonnegative,or,the matrix A is positive definite,or,the matrix A has nonnegative entries xy Read“x divides y”xy mod p Read“x congruent to y modulo p”.1.,1110210aaaaaContinued fractions x1sinarc sine of xsinh sinus hyperbolicus,the hyperbolic si
30、ne a,b Closed interval a,b,a,b Half-open Interval(open at the right)(a,b),a,b Open interval a,a,Interval closed at the left,infinite to the right,),(Set of all real numbers max xxf(x),max f(x)Xx Maximum of f(x)when x is in the set Xmin Minimum sup,1.u.b.Supremum,least upper bound inf,g.1.b.Infimum,g
31、reatest lower bound lim sup,limlimit superior lim inf,limlimit inferior l.i.m.limit in the mean,ireiyxzieIvuwi,Complex variables 名师资料总结-精品资料欢迎下载-名师精心整理-第 11 页，共 16 页 -Z,zComplex conjugate Re,Real part Im,Imaginary part arg Argument),(),(,),(),(yxDvuDyxvuJacobian,functional determinant Exdxf)()(Integ
32、ral(for example,Lebesgue integral)of function f over set E with respect to measure f(n)log n as nf(n)/log n approaches 1 as nf(n)=0(log n)as nf(n)/log n is bounded as nf(n)=0(log n)f(n)/log n approaches zero f(x)b,f(x)b f(x)increases,approaching the limit bf(x)b,f(x)b f(x)decreases,approaching the l
33、imit ba.e.,p.p.almost everywhere ess sup essential superemum)(),(,00XCXCCspace of continuous function,baCCkkthe class of functions having continuous kth derivative(on a,b )Csame as CLipaLipa,lipschitz class of function pL,Lp,Lpa,b space of functions having integrable absolute pth power(on a,b)Lsame
34、as L(C,a),(C,p)cesaro summablity 名师资料总结-精品资料欢迎下载-名师精心整理-第 12 页，共 16 页 -Special function x The integral part of x knknnCCK,),(Binomial coefficient n!/k!(n-k)!)(pnLegendre symgol xexexp,Exponential function sinhx,coshx,tanhx Hyperbolic functions snx,cnx,dnx Jacobi elliptic functions(x)Weierstrass elli
35、ptic function)(xGamma function)(xJvBessel function)(xXxCharacteristic function of the set X X(x)=1 in case x X,otherwise X(x)=0 sgn x Signum:sgn 0=0.while sgn x=x xfor x0)(xDirac delta function Algebra,tensors,operators+,.,T。，law of composition in algebraic systems e,0 Identity,unit,neutral element(
36、of an additive system)e,1,I,Identity,unit,neutral element(of a general algebraic system)e,e,E,P idempotent 1aInverse of aHom(M,N)Group of all homomorphisms of M into N G/H Factor group,group of cosets K:k Dimension of K over k 名师资料总结-精品资料欢迎下载-名师精心整理-第 13 页，共 16 页 -,+Direct sumTensor product,Kronecke
37、r product Exterior product,Grassmann product xrxX,Vector),(,.,yxYXInner product,scalar product,dot product xYX,y Outer product,vector product,cross product xxxx,Norm of the vector x Ax,xA The image of x under the transformation A ijKronecker delta:jforiwhile0,1AAtAAtt,Transpose of the matrix A AA,Ad
38、joint,Hermitian conjugate of ATr A,Sp A Trace of the matrix A Det A,ADeterminant of the matrix A)(,),(xfnfxfnnFinite differences x0,x1,x0,x1,x2,0 xx0,xif Divided differences gradff,Read“gradient of f”divv,.v Read“divergence of v”curlV,v,rot v Read“curl of v”,2div grad Laplacian X,Y Poisson bracket,o
39、r commutator,or Lie product GL(n,R)Full linear group of degree n over field R0(n,R)Full orthogonal group SO(n,R),O(n,R)Special orthogonal group 名师资料总结-精品资料欢迎下载-名师精心整理-第 14 页，共 16 页 -Topology nEEuclidean n space nSn sphere(p,q),d(p,q)Metric,distance(between points p and q)XcclXXX,Closure of the set X
40、FrX,frX,Xbdry X Frontier,boundary of XInt X,X Interior of X2Tspace Hausdorff space aFUnion of countably many closed sets GIntersection of countably many open sets Dim X dimensionality,dimension of X),(),(AXXnnHimotopy groups)(),;,(),(XHGAXHXHnnHomology groups)(),;,(),(XHGAXHXHnnCohomology groups Pro
41、bability and statistics X,Y Random variables P(X2),Pr(X2)Probability that X2P(X2)(Y1)Conditional probability E(X),E(X)Expectation of XE(XY)1 Conditional expectation of(X/Y)C.d.f.Cumulative distribution function p.d.F.Probability density function c.f.Characteristic function xMean(especially,sample mean)?名师资料总结-精品资料欢迎下载-名师精心整理-第 15 页，共 16 页 -.,dsStandard deviation var,2VarVariance iji,321Moments of a distribution Coefficient of correlation 34.12Partial correlation coefficient 考试时间：本周五（11-26）早上 9：0011：30.考试地点：教东 B106 名师资料总结-精品资料欢迎下载-名师精心整理-第 16 页，共 16 页 -