数学词汇

2024年4月14日发(作者：中考宝典数学试卷分析)

附的数学词汇

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