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[综合版版主]GOGO ^^

附4.GOGO的数学词汇

map

image

fixed point

composite function

one to one / injective

onto / surjective

bijective

inverse function

reciprocal

denominator

symmetric with respect to the y axis / the origin / the line y=x

abscissa

x/y intercept

ordinate

analytic geometry

parabola

hyperbola

conic sections 二次曲线系

coefficients

point-slope formula

directrix 准线         vertex  focus

latus rectum 过焦点平行于准线的弦

radius, center

tangent line

degenerate 退化

major axis / minor axis

eccentricity e=c/a

difference 差

branch 支

asymptotes 渐近线

focal axis

polynomial equations

quadratic polynomial 二次多项式

quadratic formula

discriminant判别式

division algorithm / remainder theorem

quotient

fundamental theorem of algebra

multiplicity 重根

conjugate radical 共轭根

the complex conjugate 共轭复数‘

monic (an=1)

the rational roots theorem

logarithm 对数 GRE用log x表示lnx

trigonometry 三角几何

complementary 互余

cos = complementary sine

tangent / cotangent / secant / cosecant

terminal side 终边

quadrant 象限

arbitrary angle 钝角

trig function 三角函数

periodicity 周期性 period

equidistant 等距

sequence 序列

convergent / divergent

(minus) infinity

monotonic 单调

bounded 有界

the sandwich (or squeeze) theorem

approach A from above (右逼近A)

continuous function

The Intermediate Value Theorem 中值定理

derivative 导数

secant line 割线

tangent line 切线

normal line 法线

differential 微分的

linear appropriation

implicit differentiation 隐函数求导

concave up (convex) f’’>0

concave down (concave) f’’<0

inflection point 拐点

local minimum / absolute minimum

critical point / stationary point (f’=0)

nth-derivative test fn>0 极小，反之极大

adjacent sides 毗连的边

relate rates  dy/dt= r dx/dt

indefinite integration 不定积分

intersect 曲线相交

rectangular (or Cartesian) coordinates

polar coordinates

cardioids 心形线 r=2a(1+cos(sita))

solids of revolution 旋转体

infinite series 无穷极数

harmonic series

p-series

alternation series

power series

the radius of convergence

the interval of convergence

arccosine function

arcsine function

domain

adjoint                伴随阵

determinant

expected value

probability density function

derivative

inflection point

rank

eigenvalue

eigenvetor

eigenspace

subset

polyhedron        多面体

vertices / vertex

inverse of the matrix

orthogonal        正交

height        多项式系数绝对值和+最高次

trace

polynomial

idempotent        幂等A2=A

nilpotent                幂零

scalar                数量阵

fixed point

the qth roots of unity

coset                陪集

dot/scalar product         点积

projAB        B在A的投影

cross product

triple scalar product                (A*B)•C

magnitude        模

parametric equation                参数方程

symmetric equation                (直线)对称式

generator, elements                cracking p111

arbitrary

level curve of height        等高线

contour curve                轮廓线(被平面截的截面)

hyperboloid                双曲面

circular poraboloid

cylindrical coordinates

spherical coordinates

partial derivative

directional derivatives

gradient

saddle point        cracking p131

Hessian matrix

line integral

The Fundamental Theorem of Calculus for Line Integral 势场内线积分只与起止点有关

gradient field        My=Nx

conservative        值与路值无关

Green Theorem                 cracking p152

ordinary/partial differential equation (ODE/PDE)

homogeneous of degree n         n阶齐次

exact differential

integrating function                积分因子

inconsistent                (线性方程组)无解

commutative                交换的

invertible                        可逆的

associative                传递性

coefficient matrix

augmented matrix        增广矩阵

Gaussian Elimination

echelon form

parameter                        参数

nullspace

linear combination

span                         几个向量的所有线性组合

trivial combination即linearly independent

basis        a minimal spanning set for a vector space

dimension                基中向量数

normal vector                法向量

column space / row space

Laplace expansions        即按某行/列展开

adjugate matrix        共轭矩阵

Cramer’s Rule                克莱莫法则

scalar                        数乘

linear operation=linear transformation

kernel / nullity / range / rank

Rank plus Nullity Theorem

Cayley-Hamilton Theorem                 p(A)=0

divisibility, factor, multiple

prime number, composite

greatest common divisor (gcd)

least common multiple (lcm)

the congruence equation ax=b(mod n)

the Euclidean Algorithm 欧氏算法 cracking p222

congruence                 余数

binary operation on S         S*SS

associate ：a•(b•c)=(a•b)•c  semigroup条件

identity        单位元

semigroup+identity=monoid

monoid+inverse=group

abelian group

general/special linear group

Sn symmetric group对称群(阶为n!)

S3为最小的6阶非阿贝尔对称群

alternating group 置换群(同上)

polygon                多边形

equilateral triangle 等边三角形

isosceles triangle        等腰三角形

Dn nth dihedral group :order(Dn)=2n

additive group of integers modulo n

multiplicative group of integers modulo p

cyclic group

Klein four-group, or viergruppe

proper subgroup

nontrivial subgroup

generators                 生成元

finitely generated

isomorphism                同构

homomorphism         同态

monomorphism        单同态

epimorphism                满同态

endomorphism                自同态

automorphism                自同构

direct product         (a, b) cracking p237

direct sum                 同上if abelian

elementary divisors

/ invariant factors                cracking p238

normal subgruoup        正规子群

inner automorphism induced by a

unity                        环乘法单位元

unit                                存在乘法逆的非零元素

ring with unity                幺环

commutative ring

subring

characteristic

ring of integers

ring of integers modulo n (Zn, +, •)

ring of Gaussian integers  Z(i)

ring of polynomials in x over R        R[x]

ring of real-valued functions on R         RR        交换幺环

evaluation (or substitution) homomorphism at a         cracking p249

Frobenius endomorphism f(a)=app  is a prime number

binomial theorem        二项式定理

integral domain                整环

left/right zero divisor        零因子

cancellation law                a!=0, ac=ab, them c=b

division ring                        无零因子的环

field= commutative division ring

又，有限整环是域

strictly-skew field= noncommutative division ring体

real quatenion                        四元素体

Boolean ring                        该环中元素idempotent

subset > superset

universal set

complement of B relative to A                A-B

union / intersection

symmetric difference        (A-B)U(B-A)

Cartesian product                笛卡尔积

open / closed interval

cardinality (cardinal number)                元素数

countably infinite

algebraic numbers                 cracking p267

power set of A

levels of infinity

cardinal number of continuum

transcendental numbers

combination, permutation

binomial coefficient

pigeonhole principle         抽屉原理

probability

Boolean algebra (or algebra) of sets on S: E

指the power set of S 的子集

probability measure on E  cracking p274

distribution function

variance, standard deviation

the normal distribution        正态分布

standard normal distribution

binomial distribution        二项分布

imaginary unit i

principle argument         幅角主值

sample space (S), outcomes (S中元素), events(E中元素，S的子集)

independent独立, mutually exclusive相斥

Bernoulli trials

polar form, exponential form

principal logarithm

principal value of zw

hyperbolic function 双曲函数

Laplace equation / harmonic uxx+uyy=0

entire function                        在复平面内解析

disk of convergence

punctured open disk        cracking p312

singularity, isolated singularity

pole of order n

simple pole (n=1) double pole (n=2)

essential singularity

annulus                                环面

singular (or principal ) part / analytic part

residue

Hausdorff space

indiscrete / trivial topology

interior, exterior, boundary, limit point, closure

interior+boundary=closure

lower-limit topology        B=[a,b)

connected

covering, open covering

compactness

norm of a point                cracking p290

Euclidean metric                欧氏度量

square metric

open map != continuous        一来一去，方向反

homeomorphism = continuous + open map

upper bound, bounded above

lub=suremum (sup)

glb=infimum (inf)

complete space = no holes

Lebesgue measurable sets

singleton

Lebesgue measurable function

Lebsegue integrable

step function                cracking p296

index of a group        子群中元素的最小公共阶

tangent                        相切

loop                         循环

inradius                        内径

trajectory                        轨迹

centroid                        重心

cluster

partial fraction expansion

sufficient / necessary condition

[Last edited by goasuplease on 2005-12-21 at 17:32]