附4.GOGO的数学词汇
map
image
fixed point
composite function
one to one / injective
onto / surjective
bijective
inver 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 ctions 二次曲线系
coefficients
point-slope formula
lolicondirectrix 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 equationsthetimes
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 / cant / cocant
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
quence 序列
convergent / divergent
(minus) infinity安魂弥撒
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
cant 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the influence
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
interct 曲线相交
化妆品常识rectangular (or Cartesian) coordinates
polar coordinates
cardioids 心形线 r=2a(1+cos(sita))
solids of revolution 旋转体
infinite ries 无穷极数
harmonic ries
p-ries
alternation ries
power ries
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
subt
polyhedron 多面体
vertices / vertex
inver 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
cot 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
韩语班
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
conrvative 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 t 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
小学一年级拼音教学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*SS
associate ：a•(b•c)=(a•b)•c migroup条件
identity 单位元
migroup+identity=monoid
monoid+inver=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
racismgenerators 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
老外教你十分钟看懂中国ring with unity 幺环
commutative ring
词组翻译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
subt > supert
universal t
complement of B relative to A A-B
union / interction
symmetric difference (A-B)U(B-A)
Cartesian product 笛卡尔积
open / clod interval
cardinality (cardinal number) 元素数
countably infinite
algebraic numbers cracking p267
power t 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 ts on S: E
指the power t 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)
esntial 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 ts
singleton
Lebesgue measurable function
Lebgue 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
