[转载]常用数学专业名词的英语_数学区间的英语读法

前言

因为最近将论文翻译成英文时,经常有一些数学的证明推理部分不知道怎么翻译,翻译网站的有些不是很精准,因此网上找到一篇相关的帖子,转载过来收藏和分享.如有侵权,立刻删文.
原文链接

数学分支的英文:

数学:mathematics 几何学:geometry 解析几何学:analytic geometry 三角学:trigonometry
算数学:arithmetic 代数学:algebra 逻辑学:logic 拓扑学:topology 分析学:analysis
集合论:set theory 数论:number theory 群论:group theory 图论:group theory
实分析:real analysis 复分析:complex analysis 点集拓扑:point-set topology
线性代数:linear algebra 抽象代数:abstract algebra 微积分:calculus

命题的英文:

命题:proposition
定理:theorem
公理:axiom
公设:postulate
定义:definition(名词);define(动词)
引理:lemma
原理:principle
推论:corollary
理论:theory
证明:proof(名词);prove(动词)
准则:criterion
法则:rule
律:law
公式:formula
猜想:conjecture或hypothesis
性质:property
推导:derivation(名词);derive(动词)
假设:ansatz
推广:generalization
预备知识:preliminary
“一个对…的定义"可译作"a definition of…”
“一个…的公式"可译作"a formula for…”
“推导…“可译作"derive …”
其中,“ansatz"指的"假设"一般指由我们目测出来的,符合条件的一个解
另外,在我们阐述一个命题的时候,“令”、“设"可译作"put"或"let"或"assume"或"suppose”,“使得"可译作"such that"或简写为"s.t.”,“反之亦然"可译作"vice versa”,“因为"可译作"since”,“所以"可译作"hence”,“即"可译作"namely”,“以B代表A"或"将A记作B"可译作"denote A by B"或"A is denoted (by) B”,”…成立"可译作”… hold",“根据…“可译作"by…”
对于人名定理/等式的命名:
当人名为一个人时,命名法为人名+’s(以单个s结尾的人名+’;以两个s结尾的人名+’s) +theorem/equation;当人名为多个人时,每个人名之间以”-"连接,不加’或’s
对于一些极其有名和常见的数学家定理,我们通常将其名字变为形容词,如:Pythagorean theorem,Euler’s equation
对于其他的人名数学名词的命名:
只需人名+数学名词,如:Taylor series
有时可将人名变为形容词再+数学名词,如:Gaussian function
需要特别提出的是,数学家笛卡尔(Descartes)在用于命名数学名词时,用的是他的拉丁文名Cartesius或其形容词形式Cartesian

数学中常见数词的英语:

基数词:即one-1,two-2,three-3,four-4…
序数词:即first-1,second-2,third-3,fourth-4…第n个可写作n-th
罗马数词:即I-1,II-2,III-3,IV-4,V-5,VI-6,VII-7,VIII-8,IX-9,X-10
拉丁数词:常用作"元"、“进制”、“项式”、“次”、“重”、“边形”、“面体"和"等分"等的前缀,即:
(由于拉丁语中六的开头既可以是hex-也可以是sex-,所以以下与六有关的,且以hex-或sex-为前缀的数词可以有两种形式,即sex-或hex-)
n-ary-n元的
unary-一元的,binary-二元的,ternary-三元的,quaternary-四元的,quinary-五元的,
senary-六元的,septenary-七元的,octonary-八元的,nonary-九元的,denary-十元的
n-ary-n进制的
unary-一进制的,binary-二进制的,ternary-三进制的,quaternary-四进制的,
quinary-五进制的,senary-六进制的,septenary-七进制的,octal-八进制的,
nonary-九进制的,decimal-十进制的,hexadecimal-十六进制的
n-nomial-n项式
monomial-单项式,binomial-二项式,trinomial-三项式,quadrinomial-四项式
n-ic-n次的
linear-一次的,quadratic-二次的,cubic-三次的,quartic-四次的,quintic-五次的,
sextic-六次的,septic-七次的,octic-八次的,nonic-九次的,decic-十次的
n-ple-n重的
single-一重的,double-二重的,triple-三重的,quadruple-四重的,quintuple-五重的,
sextuple-六重的,septuple-七重的,octuple-八重的,nonuple-九重的,decuple-十重的
n-gon-n边形
triangle-三角形,quadrilateral-四边形,quadrangle-四边形,pentagon-五边形,
hexagon-六边形,heptagon-七边形,octagon-八边形,enneagon-九边形,decagon-十边形
n-hedron-n面体
tetrahedron-四面体,pentahedron-五面体,hexahedron-六面体,
heptahedron-七面体,octahedron-八面体,enneahedron-九面体,decahedron-十面体
n-sect-n等分
bisect-二等分,trisect-三等分,quadrisect-四等分,quinsect-五等分
下面介绍一下两位数的拉丁数词前缀的构成方法:
十位数:
二十:icosi-(单独用时用icosa-,即二十边形:icosagon)
三十:triaconta-或triconta-
四十:tetraconta-或tessaraconta-
五十:pentaconta-或penteconta-
六十:hexaconta-或hexeconta-
七十:heptaconta-或hebdomeconta-
八十:octaconta-
九十:enneaconta-或eneneconta-
个位数:
一:-hena-
二:-di-
三:-tri-
四:-tetra-
五:-penta-
六:-hexa-
七:-hepta-
八:-octa-
九:-ennea-
十位数和个位数之间用”-kai-"连接,但有时也会省略
如:三十二边形:triacontadigon或triacontakaidigon

点的英文:

点:point 共线的:collinear 共面的:coplanar
“A,B,C三点共线"可译作"A,B,C are collinear”
“A,B,C,D四点共面"可译作"A,B,C,D are coplanar”
“在点A处"可译作"at point A”
轨迹:locus(复数:loci)

线的英文:

直线:line或straight line 射线:ray 线段:line segment
线段的长度:length of the line segment
射线的端点:the initial point of the ray
线段的端点:the endpoint of the line segment
线段的中点:the midpoint of the line segment
线段的中垂线:the perpendicular bisector of the line segment
线段的n等分点:the point of n-section of the line segment
“线段被点A平分"可译作"the line segment is bisected by A”
“线段被点An等分"可译作"the line segment is n-sected by A”
直线簇:pencil of lines 直线包络:envelope of lines
平行的:parallel 相交的:intersecting 垂直的:perpendicular
异面的:skew 共点的:concurrent
交点:intersection point或the point of intersection 公共点:point in common
“l1和l2的交点"可译作"the intersection point of l1 and l2”
“l1交l2于点A"可译作"l1 intersects l2 in A"或"l1 intersects l2 at A”
“l1以α度角与l2相交"可译作"l1 intersects l2 at α”
“通过点A的直线"可译作"the line passing through A"或"the line through A”
“直线上的一点"可译作"a point on the line”
“直线外的一点"可译作"a point outside the line”
“确定一条直线"可以做"determine a line”
“l1平行于l2"可译作"l1 is parallel to l2”
“l1垂直于l2"可译作"l1 is perpendicular to l2”
“由A到l的垂足"可译作"the foot of the perpendicular from A to l"或"a foot of A on l”
“l1与l2异面"可译作"l1 and l2 are skew”
“l1与l2共面"可译作"l1 and l2 are coplanar”
“l1,l2,l3三线共点"可译作"l1,l2,l3 are concurrent”

面的英文:

平面:plane 曲面:surface
交线:intersection line或line of intersection
“α和β的交线"可译作"the intersection line between α and β”
“面α和面β交于一条直线"可译作"α intersects β in a line”
“平面内的一点"可译作"a point on the plane"或"a point in the plane”
“平面内的一条直线"可译作"a line in the plane”
“点在面内"可译作"the point lies in the plane”
“线在面内"可译作"the line lies in the plane”

角的英文:

角:angle 对顶角:vertical angle 邻角:adjacent angle 二面角:dihedral angle
角的边:the side of the angle
角的顶点:the vertex of the angle
角的角平分线:the angle bisector of the angle
“l1和l2的夹角"可译作"the angle between l1 and l2”
“一个α度的角"可译作"an angle of α degrees"或"an angle measuring α degrees”
锐角:acute angle 直角:right angle 钝角:obtuse angle 平角:straight angle
余角:complementary angle 补角:supplementary angle
“角A的余角"可译作"the complementary angle to angle A”
“角A的补角"可译作"the supplementary angle to angle A”
“角A与角B互余"可译作"angle A and angle B are complementary”
“角A与角B互补"可译作"angle A and angle B are supplementary”
同位角:corresponding angle 内错角:alternate angle
同旁内角:consecutive interior angle

距离的英文:

距离:distance
“点A和点B的距离"可译作"the distance between A and B”
“点A到直线l的距离"可译作"the distance from A to l”

多边形的英文:

多边形:polygon n边形:n-gon
顶点:vertex(复数:vertices)或corner 边:side或edge
内角:interior angle 外角:exterior angle
凸多边形:convex polygon 凹多边形:concave polygon 圆内接多边形:cyclic polygon
等角多边形:equiangular polygon 等边多边形:equilateral polygon
正多边形:regular polygon 对偶多边形:dual polygon
全等多边形:congruent polygon 相似多边形:similar polygon
位似多边形:homothetic polygon 位似中心:homothetic center
“多边形A全等于多边形B"可译作"A is congruent to B"或"A and B are congruent”
“多边形A相似于多边形B"可译作"A is similar to B"或"A and B are similar”
“多边形A位似于多边形B"可译作"A is homothetic to B"或"A and B are homothetic”
对应边:corresponding side 对应角:corresponding angle
周长:perimeter 面积:area

三角形的英文:

三角形:triangle 对边:opposite side 邻边:adjacent side
“角A的对边"可译作"the opposite side to A"或"the side opposide to A”
“角A的邻边"可译作"the adjacent side to A"或"the side adjacent to A”
高:altitude或height 高的底:the base of the altitude
角平分线:angle bisection
内角平分线:internal angle bisector 外角平分线:external angle bisector
中线:median 中位线:bimedian
外心:circumcenter 垂心:orthocenter 内心:incenter 重心:centroid 旁心:excenter
外接圆:circumcircle或circumscribed circle 内切圆:incircle或inscribed circle
旁切圆:excircle或escirbed circle 九点圆:nine-point circle
等边三角形:equilateral triangle 等腰三角形:isosceles triangle
等腰三角形的腰:leg of the isosceles triangle
等腰三角形的底:base of the isosceles triangle
等腰三角形的顶角:vertex angle of the isosceles triangle
等腰三角形的底角:base angle of the isosceles triangle
黄金三角形:golden triangle
斜三角形:scalene triangle 锐角三角形:acute triangle 钝角三角形:obtuse triangle
直角三角形:right angle 斜边:hypotenuse 直角边:cathetus(复数:catheti)或leg
所夹的角:the included angle 所夹的边:the included side
正弦定理:law of sine 余弦定理:law of cosine

四边形的英文:

四边形:quadrilateral或quadrangle
对角线:diagonal
平行四边形:parallelogram 菱形:rhombus(复数:rhombi或rhombuses)
矩形:rectangle 正方形:square 筝形:kite 梯形:trapezoid(美)或trapezium(英)
等腰梯形:isosceles trapezoid 直角梯形:right trapezoid 不规则四边形:trapezium(美)
矩形的长:length of the rectangle 矩形的宽:width of the rectangle
梯形的底:base of the trapezoid
梯形的腰:leg of the trapezoid或lateral side of the trapezoid

圆的英文:

圆:circle 圆盘:disk 扇形:circle sector 弓形:circular segment 圆环:annulus
半圆:semicircle 单位圆:unit circle 圆系:pencil of circles
圆周:circumference 直径:diameter 半径:radius(复数:radii或radiuses) 圆心:center
弧:arc 弦:chord 割线:secant line 切线:tangent line
优弧:major arc 劣弧:minor arc
切点:point of tangency
圆的切线:tangent line to the circle
圆的周长:perimeter of the circle或circumference
圆周角:inscribed angle 圆心角:central angle 弦切角:tangent chord angle
弧所对的圆周角:inscribed angle subtended by the arc
圆周角所对的弧:arc subtended by the inscribed angle
圆幂定理:power-of-a-point theorem
内切:internally tangent 外切:externally tangent
两圆外离:the two circles are outside each other
两圆相交:the two circles intersects each other
两圆内含:one circle is inside the other
圆心距:center distance
圆的外切n边形:circumscribed n-gon to the circle
圆的内接n边形:inscribed n-gon to the circle

多面体的英文:

多面体:polyhedron(复数:polyhedra或polyhedrons) n面体:n-hedron
面:face 棱:edge 截面:section
柱体:cylinder 锥体:cone 台体:frustum(复数:frusta或frustums)
棱柱:prism 直棱柱:right prism 直n棱柱:right n-gonal prism 侧棱:lateral edge
平行六面体:parallelepiped 长方体:rectangluar cuboid 立方体:cube
长方体的长:length of the rectangular cuboid
长方体的宽:width of the rectangular cuboid
长方体的高:height of the rectangular cuboid
棱锥:pyramid 棱锥的顶点:apex of the pyramid 侧面:lateral face 底面:base face
正n棱锥:regular n-gonal pyramid
体积:volume 表面积:surface area 在某个方向上投影的周长:girth in a certain direction
主视图:front view 左视图:left side view 俯视图:top view
斜二测画法:cabinet projection
平行投影:parallel projection 中心投影:central projection

曲面图形的英语:

圆柱:circular cylinder或cylinder 圆锥:circular cone或cone 母线:generatrix
圆锥的顶点:apex of the circular cone或vertex of the circular cone
圆台:circular frustum
球面:sphere 球体:ball
球心:center 半径:radius 直径:diameter 测地线:geodesic
大圆:great circle 小圆:small circle
球的外切n面体:circumscribed n-hedron to the sphere
球的内接n面体:inscribed n-hedron to the sphere

空间变换的英文:

旋转:rotation(名词);rotate(动词)
旋转中心:center of rotation
旋转轴:axis of rotation
旋转面:plane of rotation
旋转角:angle of rotation
“绕…顺时针旋转α度角"可译作"rotate around…clockwise through the angle α”
“绕…逆时针旋转α度角"可译作"rotate around…counterclockwise through the angle α”
“旋转…体”(如旋转椭球体等)可译作"…of revolution"
平移:translation(名词);translate(动词)
“沿某一方向平移…“可译作"translate…in a certain direction”
对称:symmetry
“…是对称的"可译作”…has symmetry"或”…is symmetric"
轴对称的:axisymmetric 轴对称:reflection symmetry 对称轴:line of symmetry
中心对称的:centrosymmetric 中心对称:central symmetry
对称中心:center of symmetry
翻折:reflection(名词);reflect(动词)

几何作图的英语:

尺规作图:compass-and-straightedge construction
"作出…"可译作"create…"或"construct…“或"draw…”
“…的作法"可译作"construction of…”
“以A为圆心,r为半径作圆A"可译作"use A as center,r as radius,construct the circle A"或"construct the circle A with center at A and radius r”
“交…于点A"可译作"intersecting…in A"或"intersecting…at A”
“连接(联结)A,B"可译作"join A and B"或"connect A and B”
“过点A作l1平行于l"可译作"construct l1 parallel to l through A”
“过点A作l1垂直于l"可译作"construct l1 perpendicular to l through A”
“过顶点A引BC边上的高"可译作"drop the altitude of vertex A”
“延长AB"可译作"extend AB”

坐标系的英文:

坐标系:coordinate system或coordinates
坐标:coordinate
数轴:number line
直角坐标系:Cartesian coordinate system或rectangular coordinate system
直角坐标:Cartesian coordinate
坐标轴:coordinate axis或axis(复数:axes)
坐标轴的正方向:orientation for the axis
坐标原点:origin
单位长度:unit of length
横坐标:x-coordinate或abscissa
纵坐标:y-coordinate或ordinate
竖坐标:z-coordinate或applicate
横轴:abscissa或x-axis 纵轴:ordinate或y-axis 竖轴:applicate或z-axis
"在横轴上方"可译作"above the x-axis
“在横轴下方"可译作"below the x-axis”
象限:quadrant 卦限:octant
第一象限:quadrant I 第二象限:quadrant II 第三象限:quadrant III
第四象限:quadrant IV
第一卦限:octant I 第二卦限:octant II 第三卦限:octant III 第四卦限:octant IV
第五卦限:octant V 第六卦限:octant VI 第七卦限:octant VII 第八卦限:octant VIII
右手系:right-hand system 左手系:left-hand system
极坐标系:polar coordinate system
极坐标:polar coordinate
极点:pole 极轴:polar axis 极径:radial coordinate或radius
极角:angular coordinate或polar angle或azimuth
“将极坐标转化为直角坐标"可译作"convert polar coordinate to Cartesian coordinate”
螺线:spiral
柱坐标系:cylindrical coordinate system
柱坐标:cylindrical coordinate
原点:origin 极轴:polar axis 竖轴:longitudinal axis或cylindrical coordinate
极径:radial coordinate或radius 竖坐标:height或altitude
极角:angular coordinate或polar angle或azimuth
球坐标系:spherical coordinate system
球坐标:spherical coordinate
距离:radial distance或radius 方向角:azimuth angle
仰角:polar angle或zenith angle或inclination angle

线性规划的英文:

线性规划:linear programming 最优值:optimization
可行域:feasible region 目标函数:objective function 约束条件:problem constraint

圆锥曲线的英文:

圆锥曲线:conic section或conic 退化的:degenerate
椭圆:ellipse 抛物线:parabola 双曲线:hyperbola
标准方程:standard equation
离心率:eccentricity 半焦距:linear eccentricity 焦准距:focal parameter
焦点:focus(复数:foci) 准线:directrix 通径:latus rectum 顶点:vertex
长轴:major axis 短轴:minor axis 半长轴:semi-major axis 半短轴:semi-minor axis
双曲线的一支:an arm of the hyperbola或a branch of the hyperbola
渐近线:asymptote 等轴双曲线:rectangular hyperbola或equilateral hyperbola
实轴:transverse axis或major axis 虚轴:conjugate axis或imaginary axis
椭球面:ellipsoid 椭圆抛物面:elliptic paraboloid 双曲抛物面:hyperbolic paraboloid
单叶双曲面:hyperboloid of one sheet 双叶双曲面:hyperboloid of two sheets
马鞍面:the saddle surface(注意要加the,不加the则代表含有多个鞍点的曲面)
椭圆锥面:elliptic cone 椭圆柱面:elliptic cylinder 双曲柱面:hyperbolic cylinder
抛物柱面:parabolic cylinder 旋转椭球体:spheroid或ellipsoid of revolution

直角坐标方程的英文:

方程:equation 参数方程:parametric equation
标准方程:standard form
斜率:slope 截距:intercept 横截距:x-intercept 纵截距:y-intercept
一般式:general form
斜截式:slope-intercept form
点斜式:point-slope form
两点式:two-point form
截距式:intercept form

向量的英文:

向量:vector 数量:quantity 标量:scalar 有向线段:directed line segment
" “可读作"vector AB”," “可读作"n hat”
起点:initial point 终点:terminal point 模:magnitude或length或norm 方向:direction
自由向量:free vector 固定向量(胶着向量):bound vector
平行向量:parallel vector 共线向量:collinear vector 垂直向量:perpendicular vector
零向量:zero vector 单位向量:unit vector 列向量:column vector 行向量:row vector
向量加法:addition of vector 数乘:scalar multiplication
点乘:dot product 内积:inner product 数量积:scalar product
叉乘:cross product 向量积:vector product
混合积:mixed product或scalar triple product
线性无关的:linear independent
基底:basis 一组基底:a set of basis
标准基底:standard basis 正交基底:orthogonal basis 标准正交基底:orthonormal basis
“分解向量"可译作"decompose the vector”
方向向量:direction vector 法向量:normal vector 切向量:tangent vector

整数的英文:

整数:integer
数字:digit
正整数(positive integer):按小学＆初中学习的方法读即可。
零:zero(美式)nought(英式)
负整数(negative integer):负号读作"negative"(正式)或"minus"(不正式),如"-1"读作"negative one"或"minus one"
非零整数:nonzero integer或nonezero
非负的:nonnegative 非正的:nonpositive
“±"可读作"plus or minus”
自然数:natural number 后继数:successor
偶数:even number
奇数:odd number
奇偶性:parity

小数的英文:

小数:decimal
有限小数:小数点读作"point",按数字读,如:“0.25"读作"zero point two five”,“36.14"读作"thirty-six point one four”
有限小数:terminating decimal
无限循环小数:repeating decimal或recurring decimal
读法为在后面加个recurring,如:" “读作"zero point three recurring”
注:在小数点后的"0"亦可读成字母"o"的读音.如:“0.0205"可读作"zero point o two o five”
循环节:repepetend或reptend

分数的英文:

分数:fraction
分子:numerator
分母:denominator
“在分母上"可译作"in the denominator”
“在分子上"可译作"in the numerator”
一般的,分子用基数词,分母用序数词,分子>1时,分母用复数.如:" “读作"a third"或"one third”," “读作"two thirds”
特别地, 可读作"one half"
另外,比较复杂的分数亦可读成分子over分母,如" “亦可读作"one over three”," “读作"one over thirty”
真分数:proper fraction 假分数:improper fraction 繁分数:complex fraction
带分数:mixed numeral或mixed number或mixed fraction 连分数:continued fraction
" “可读作"two and three over five”
倒数:reciprocal
“数x的倒数"读作"the reciprocal of x”
裂项法:method of difference 约分:cancellation
比:ratio
“a:b"可读作"a to b”
“a:b=c:d"可读作"a is to b as c is to d”

有理数:

有理数:rational number或rational
无理数:irrational number或irrational

实数:

实数:real number或real
代数数:algebraic number
超越数:transcendental number
相反数:additive inverse或opposite number
“数x的相反数"可译作"the additive inverse of x"或"the opposite number of x”
绝对值(模):absolute value或norm或magnitude
“数x的绝对值"读作"the absolute value of x"或"the norm of x"或"the magnitude of x”

复数:

虚数:imaginary number
纯虚数:pure imaginary number
复数:complex number
实部:real part
虚部:imaginary part
“数x的实部"可译作"real part of x”
“数x的虚部"可译作"imaginary part of x”
共轭复数:conjugate complex number
“数x的共轭复数"可译作"conjugate complex number of x”
虚数一般不读中间的乘号,如"2i"读作"two i"
复平面:complex plane 辐角:argument 模:modulus
“数z的辐角"可译作"the argument of z”
“数z的模长"可译作"the modulus of z”

四则运算:

加法:addition 加数:summand 被加数:augend 加数:addend
在两个数的加法中,这两个数要么都叫做summand,要么一个叫augend,一个叫addend,乘法类似。
减法:subtraction 被减数:minuend 减数:subtrahend
乘法:multiplication 乘数:factor 被乘数:multiplicand 乘数:multiplier
除法:division 被除数:dividend 除数:divisor 余数:remainder
加:add(动词),plus(介词)
减:subtract(动词);minus(介词)
乘:multiply(动词);times(介词)
除:divide(动词)
和:sum
差:difference
积:product 倍数:multiple
商:quotient 比:ratio
“2+3=5"可读作"two added by three is five"或"two plus three is five"或"the sum of two and three is five”
“5-3=2"可读作"five subtracted by three is two"或"five minus three is five"或"the difference of five and three is five”
“2×3=5"可读作"two multiplied by three is six"或"two times three is six"或"the product of two and three is six”
“6÷3=2"可读作"six divided by three is two"或"the quotient of six and three is two"或"the ratio of six and three is two”
“7除以2等于3余1"可读作"seven divided by three is three with remainder 3”
“以A加B"可译作"add B by A”
“以A减B"可译作"subtract B by A”
“以A乘B"可译作"multiply B by A”
“以A除B"可译作"divide B by A”
求和符号:summation symbol

指数(幂)的英文:

指数:exponent 幂:power 底数:base number 指数式:exponential
取幂:exponentiation(即:addition,subtraction,multiplication,division,exponentiation)
对数:logarithm 真数:antilogarithm
自然对数:natural logarithm 常用对数:common logarithm
平方:squared 立方:cubed 平方根:square root 立方根:cube root 根式:radical
连根式:nested radical 算数平方根:principal square root 被开方数:radicand
根号:radical sign或radix 阶乘:factorial
如:" “读作"two squared”;" “读作"two cubed”;" “读作"square root of two”;
" “读作"cube root of two”.
一般地,指数的读法是"底数 + raised to the + 真数的序数词 + power",如" “读作"two raised to the fifth power”.在复杂的字母运算时,“raised"和"power"亦可舍去,如”“可读作"e to the two pi i s t”.
类似地," “读作"fifth root of two”.而" “读作"two to the x power”," “读作"x root of two”,当n次方根作宾语而非定语时,可译作"the root of degree n"
而对数的读法则是"logarithm of + 真数 + to base + 底数"或"the base+底数+logarithm of +真数".如" “读作"logarithm of three to base two"或"the base-two logarithm of three”.“以…为底的对数"可译作"logarithm to base …”
换底公式:the formula for changing the base
“数x的阶乘"可读作"x factorial”.

三角函数的英语:

三角函数:trigonometric function
正弦:sine 余弦:cosine 正切:tangent 余切:cotangent 正割:secant 余割:cosecant
正弦线:sine line 余弦线:cosine line 正切线:tangent line
余割线:cosecant line 正割线:secant line 余切线:cotangent line
“sinx"读作"sine x"或"sine of x”
“这个角的正弦值"可译作"sine of this angle”
由于 ,所以外国人有一个口诀SOH-CAH-TOA
弧度:radian 角度:degree
“πrad"可读作"pi radians”
“180°"可读作"one hundred and eighty degrees”
“和差化积恒等式"可译作"sum-to-product identities”
“积化和差恒等式"可译作"product-to-sum identities”
“正弦的合角恒等式"可译作"sine of sum identities”
倍角公式:multiple-angle formula 二倍角公式:double-angle formula
降幂公式:power-reduction formula
正弦波:sine wave或sinusoid
振幅:amplitude 频率:frequency 周期:period 相位:phase
反三角函数:inverse trigonometric function
反正弦:arcsine 反余弦:arccosine 反正切:arctangent
反余割:arccosecant 反正割:arcsecant 反余切:arccotangent

代数式的英语:

即从左往右,按上文介绍的方式读,如:
“x+3y"可读作"x plus three y”(如果特意强调3和y之间是乘法关系,则可读作"x plus three times y")
代数式:algebraic expression 分式:fraction 根式:radical 指数式:exponential
有理式:rational expression 无理式:irrational expression
齐次式:homogeneous expression
n项式:n-nomial 多项式:polynomial n次式:n-ic expression
次数:degree 项:term 常数项:constant term 系数:coefficient 元:indeterminate
同类项:similar term或like term
“式P是二次的"可译作"P is of degree 2"或"P have degree 2"或"the degree of P is 2”
“x的系数"可译作"the coefficient of x”
“n次项系数"可译作"n-ic coefficient”
“x是式P的元"可译作"x is the indeterminate of P”
“以x为元的多项式P"可译作"a polynomial P in the indeterminate x"或"a polynomial P in x”
“元x上的指数"可译作"the exponent on the indeterminate x”
“n次齐次式"可译作"the polynomial homogeneous of degree n”
“a元b次c项式"可译作"a-ary b-ic c-nomial"或"c-term polynomial of degree b with a indeterminates”
如"二元二次三项式"可译作"binary quadratic trinomial"或"three-term polynomial of degree 2 with two indeterminates"
“按x的升幂展开的多项式P"可译作"the polynomial P in ascending powers of x”
“按x的降幂展开的多项式P"可译作"the polynomial P in descending powers of x”
展开:expansion
二项展开:binomial expansion
因式:factor 因式分解:factorization或factoring 分解因式:factor 长除法:long division
最简因式:irreducible factor
“P被分解因式为Q"可译作"P is factored as Q"或"P factors as Q”
“在…范围内分解因式"可译作"factor over…”
平方差公式:the difference of two squares
配方:complete the square
合并同类项:combine similar terms或combine like terms
十字相乘法:crisscross factorization

等式的英语:

等式:equality
等式"P=Q"可读作"P is equal to Q"(强调等式关系)或"P is Q"(不强调等式,只是陈述事实)或"P equals to Q"(不强调等式,只是陈述事实)
等号左边:left-hand-side或简写为L.E.F.
等式右边:right-hand-side或简写为R.H.S.
“在等号右边"可译作"on the right-hand-side”
“在等式两边"可译作"on the both sides of the equality”
“在等式两边同时加A"可译作"add both sides of thr equality by A”
减乘除类似
“将等式P带入到等式Q中"可译作"plug P into Q”
恒等式:identity

不等式的英语:

不等式:inequality
“P>Q"可读作"P is greater than Q”
“P<Q"可读作"P is less than Q”
“P≥Q"可读作"P is greater than or equal to Q”
“P≤Q"可读作"P is less than or equal to Q”

方程的英语:

方程:equation
解方程:solve the equation
未知数:unknown 常数:constant 系数:coefficient 参数:parameter
方程的解:the solution to the equation 增解:extraneous solution
方程的根:the root of the equation
方程组:system of equations 联立的:simultaneous
“a元b次方程组"可译作"system of a-ary b-ic equations"或"system of equations of degree b with a unknowns”
参数方程:parametric equation
不定方程:indeterminate equation
差分方程:difference equation
n阶差分:n-th difference
一元二次方程:unary quadratic equation,但通常省略unary,即quadratic equation
判别式:discriminant
一元二次方程求根公式:quadratic formula
重根:repeated root或double root

数论的英语:

质数:prime number或prime 互质的:coprime
合数:composite number或composite
因数:divisor
算术基本定理:fundamental theorem of arithmetic
质因数分解:prime factorization
标准分解式:canonical representation或standard form
最小公倍数:least common multiple
最大公因数:great common divisor
完全数:perfect number
平方数:square number或perfect square number
" “可读作"a divides b"或"a is a divisor of b"或"b is a multiple of a"或"a is divisible by b”
同余的:congruent 模n等价类:modulo n equivalence class
模n剩余系:residue system modulo n
模n完全剩余系:complete residue system modulo n
" “可读作"a and b are congruent modulo c”
不定方程:indeterminate equation

排列组合的英语:

排列:permutation 环排列:circular permutation
组合:combination
二项式定理:binomial theorem 二项式系数:binomial coefficient

图论的英语:

无序积:unordered pair
无向图:undirected graph 有向图:directed graph或digraph
顶点集:set of vertices或set of nodes 顶点:vertex或node
边集:set of edges 边:edge 有向边:directed edge
n阶图:graph of order n 标定图:labeled graph 非标定图:unlabeled graph
零图:null graph或empty graph 空图:null graph或order-zero graph
端点:end point或end 关联:incident 相邻:adjacent 环:loop
“边e与顶点v相关联"可译作"e is incident to v”
“顶点v1和v2相邻"可译作"v1 is adjacent to v2”
始点:tail或direct predecessor 终点:head或direct successor
孤立点:isolated vertex
邻域:neighborhood 闭邻域:closed neighborhood
关联集:incidence set 关联矩阵:incidence matrix
后继元集:set of successors 先驱元集:set of predecessors
平行边:multiple edge或parallel edge 多重图:multigraph 简单图:simple graph
度数:degree或valency 出度:outdegree 入度:indegree
最大度:maximum degree 最小度:minimum degree
最大出度:maximum outdegree 最小出度:minimum outdegree
最大入度:maximum indegree 最小入度:minimum indegree
度数列:degree sequence 出度列:outdegree sequence 入度列:indegree sequence
可图化的:graphic或graphical或realizable 同构的:isomorphic
完全图:complete graph 竞赛图:complete digraph 正则图:regular graph
子图:subgraph 母图:supergraph 真子图:proper subgraph
生成子图:spanning subgraph 导出的子图:induced subgraph
补图:complement 自补图:self-complement graph
“删除顶点v"可译作"delete v”
“加新边e"可译作"add e”
边的收缩:edge contraction
通路:path 简单通路:simple path 回路:cycle 简单回路:simple cycle
奇圈:odd cycle 偶圈:even cycle 长度:length
连通的:connected 连通图:connected graph 连通分支:connected component
短程线:shortest path 极大路径:longest path 距离:distance
割集:cutset 割点:cut-vertex 割边:cut-edge 桥:bridge
连通度:local connectivity 点连通的:vertex-connected 边连通的:edge-connected
“v1可达v2"可译作"v1 can reach v2”
弱连通的:weakly connected 强连通的:strongly connected
二部图:bipartite graph或bigraph
并图:union graph
树:tree 森林:forest 分支点:internal vertex
生成树:spanning tree 树枝:branch 树叶:leaf 弦:chord
基本圈:fundamental cycle 圈秩:cycle rank
基本割集:fundamental cutset 割集秩:cutset rank
最小生成树:minimum spanning tree
根树:rooted tree 树根:root 高度:height 层数:depth
父亲:parent 儿子:child(复数:children) 兄弟:sibling 祖先:ancestor 后代:descendent
有序树:ordered tree r叉树:r-ary tree 正则树:regular tree
完全树:perfect tree或complete tree
子树:subtree 左子树:left subtree 右子树:right subtree
平面图:planar graph 平面嵌入:planar embedding 非平面图:nonplanar graph
面:face 外部面:external face 内部面:internal face 次数:degree 边界:bound
极大平面图:maximal planar graph 极小非平面图:minimal nonplanar graph
同胚的:homeomorphic 对偶图:dual graph 自对偶图:self-dual graph
轮图:wheel graph
支配集:dominating set 支配数:domination number
极小支配图:minimal dominating set 最小支配图:minimum dominating set
“v1支配v2"可译作"v1 dominates v2”
独立集:independent set 独立数:independence number
极大独立集:maximal independent set 最大独立集:maximum independent set
点覆盖(集):vertex cover 点覆盖数:vertex covering number
极小点覆盖(集):minimal vertex cover 最小点覆盖(集):minimum vertex cover
“v1覆盖v2"可译作"v1 covers v2”
边覆盖(集):edge cover 边覆盖数:edge covering number
极小边覆盖:minimal edge cover 最小边覆盖:minimum edge cover
“e1覆盖e2"可译作"e1 covers e2”
边独立集:independent edge set 匹配:matching 匹配数:matching number
极大匹配:maximal matching 最大匹配:maximum matching
匹配边:matched edge 非匹配边:unmatched edge
饱和点:saturated vertex 非饱和点:unsaturated vertex
完美匹配:perfect matching或complete matching
交错路径:alternating path 可增广路径:augmenting path 交错圈:alternating cycle
完备匹配:perfect matching
点着色:vertex coloring 可着色的:colorable 色数:chromatic number
面着色:face coloring 可面着色的:face-colorable
边着色:edge coloring 可边着色的:edge-colorable 边色数:chromatic index

线性代数的英语:

线性代数:linear algebra
逆序数:inversion number 奇排列:odd permutation 偶排列:even permutation
行列式:determinant 行列式中的元:entry 行:row 列:column
n阶行列式:determinant of order n
“行列式D的转置"可译作"the transpose of the determinant D”
余子式:minor 代数余子式:cofactor 主子式:principal minor
“将行列式D按第n行展开"可译作"expand the determinant D along the n-th row”
主对角线:main diagonal 副对角线:antidiagonal
上三角行列式:upper triangular determinant 下三角行列式:lower triangular determinant
对角行列式:diagonal determinant
矩阵:matrix(复数:matrices) 阵元:entry
n阶方阵:square matrix of order n
左乘:pre-multiply或left multiply 右乘:post multiply或right-multiply
可交换的:commutative
行向量:row vector 列向量:column vector
零矩阵:zero matrix或null matrix 对角阵:diagonal matrix
单位阵:unit matrix或identity matrix
“矩阵M的转置"可译作"the transpose of the matrix M”
对称阵:symmetric matrix
“方阵的行列式"可译作"the determinant of the square matrix”
可逆的:invertible 非奇异的:nonsingular 逆矩阵:inverse
“矩阵M的逆阵"可译作"the inverse of the matrix M”
伴随矩阵:adjugate matrix
“将矩阵M分块"可译作"partition the matrix M”
初等行变换:elementary row operation 行等价的:row equivalent
初等列变换:elementary column operation 列等价的:column equivalent
初等变换:elementary operation
行阶梯形:row echelon form 列阶梯形:column echelon form
行最简形:reduced row echelon form 列最简形:reduced column echelon form
标准形:canonical form
“矩阵M是标准形"可译作"matrix M is in canonical form”
秩:rank 满秩的:have full rank 迹:trace
系数行列式:coefficient determinant 系数矩阵:coefficient matrix
增广矩阵:augmented matrix
n维向量:vector of dimension n 分量:decomposition
向量组:set of vectors 线性无关的:linearly independent 线性相关的:linear dependent
向量空间:vector space 维度:dimension 基底:basis
基础解系:fundamental system of solutions
正交的:orthogonal 正交矩阵:orthogonal matrix 正交化:orthogonalize
特征值:eigenvalue或characteristic value
特征向量:eigenvector或characteristic vector
相似矩阵:similar matrix 相似变换:similarity transformation
过渡矩阵:change of basis matrix
可对角化的:diagonalizable 对角化:diagonalize
二次型:quadratic form 标准型:diagonal form 规范型:signature
正定的:positive definite 负定的:negative definite
正惯性指数:positive index of inertia 负惯性指数:negative index of inertia
合同的:congruent
线性空间:linear space

逻辑用语的英语:

真命题:true proposition 假命题:false proposition
逆命题:converse of the proposition 否命题:inverse of the proposition
逆否命题:contrapositive of the proposition
逻辑联结词:logical connective
且:and 或:or 非:not
合取:conjunction 析取:disjunction 否定:negation
合取范式:conjunction normal form 析取范式:disjunction normal form
主合取范式:principal conjunction normal form
主析取范式:principal disjunction normal form
极大项:maximal term 极小项:minimal term
对于任意:for all… 存在:there exists… 存在性:existence 唯一性:uniqueness
全称量词:universal quantifier 特称量词(存在性量词):existential quantifier
全称命题:universal proposition 特称命题(存在性命题):existential proposition
量词辖域:scope of quantifier
前束范式:prenex normal form
如:“这个命题中全称量词的辖域"可译作"the scope of universal quantifier in this proposition”.
当且仅当:if and only if或简写为"iff"(也有人说"exactly if")
蕴涵:implication 前件:antecedent 后件:consequent
“A推出B"可读作"A implies B”
等价:equivalence或material equivalence
“A和B等价"可译作"A is equivalent to B”
等值:equivalence或logical equivalence
真值:truth value
真值表:truth table
论域:discourse domain
n元真值函数:n-ary truth valued function
形式语言系统:formal language system 形式演算系统:formal calculation system
自然逻辑推理系统:natural logical deductive system

四种条件的英文:

充分性:necessity 必要性:sufficiency
充分条件:sufficient condition
必要条件:necessary condition
充要条件:necessary and sufficient condition
充分不必要条件:sufficient but not necessary condition
必要不充分条件:necessary but not sufficient condition(以上两个较少用)
“A是B的充要条件"可译作"A is the necessary and sufficient condition of B"或"A is necessary and sufficient for B”

集合的英文:

集合:set 元素:element 子集:subset 真子集:proper subset 集族:collection of sets
“由…组成的集合"可译作"a set of…”
“x是A的元素"可译作"x is an element of A”
“x属于A"可读作"x belongs to A”
“x不属于A"可读作"x does not belong to A”
“B是A的子集"可译作"B is a subset of A”
"B包含于A"可读作"B is consisted in A "
“A包含B"可读作"A contains B"或"A includes B”
集合的描述方法:
列举法:extensional notation 描述法:set-builder notation Venn图:Venn Diagram
空集:empty set 非空集合:nonempty set或nonempty 全集:universal set
幂集:power set
偏序集:partially ordered set或poset 全序集:totally ordered set或chain
最小元:least element 最大元:greatest element
极小元:minimal element 极大元:maximal element
n元集合:n-ary set或set with n elements
基数(势):cardinality或cardinal number或cardinal
"A的基数(势)“可译作"the cardinality of A"或"the cardinal number of A"或"the cardinal of A”
“A和B基数相等"可译作"A and B have the same cardinality"或"A and B have the same cardinal number"或"A and B have the same cardinal”
“A和B等势"可译作"A and B are equinumerous"或"A is equinumerous to B”
有穷集:finite set 无穷集:infinite set
可数的:countable或enumerable 不可数的:uncountable或denumerable
至多可数的:at most countable

区间的英文:

区间:interval 端点:endpoint
“区间I的一个端点"可译作"an endpoint of I”
开区间:segment或open interval 闭区间:interval或closed interval
半开半闭区间:half-open interval
左开区间:left-open interval 右开区间:right-open interval
左闭区间:left-closed interval 右闭区间:right-closed interval
“左闭右开区间"可译作"left-closed and right-open interval”
(区间的)长度:diameter或length或size

集合运算的英文:

并集:union 交集:intersection 补集:complement
笛卡尔乘积:Cartesian product 对称差:symmetric difference
“A和B的并集"可读作"the union of A and B”
“A和B的交集"可读作"the intersection of A and B”
“A与B在某些元素上相交"可译作"A intersects B at some elements”
“B在A中的补集"可读作"the complement of B in A”
“A和B的笛卡尔乘积"可读作"the Cartesian product of A and B”
“A和B的对称差"可读作"the symmetric difference of A and B”
不交的:disjoint
“A和B不交"可记作"A and B are disjoint”

点集拓扑的英语:

度量:metric 度量空间:metric space 可分度量空间:separable metric space
完备度量空间:complete metric space 范数:norm
赋范空间:space equipped with norm
邻域:neighborhood “点p的邻域的半径"可译作"the radius of the neighborhood of p”
“一个以r为半径的邻域"可译作"a neighborhood of radius r”
极限点:limit point 内点:interior point 孤立点:isolated point 聚点:condensation point
开集:open set 闭集:closed set 连通集:connected set 紧集:compact set
有界集:bounded set 完备集:perfect set 隔离集:separated set
闭包:closure 内部:interior
开的:open 闭的:closed 连通的:connected 紧的:compact 紧性:compactness
有界的:bounded 完备的:perfect 隔离的:separated 稠密的:dense 凹的:concave
凸的:convex
注意:perfect所指的"完备"是该集合是闭的且该集合的所有点都是该集合的极限点;
complete所指的"完备"是该度量空间的所有柯西列都收敛
“A相对X是开的"可译作"A is open relative to X”
“A是B的闭包"可译作"A is a closure of B”
上界:upper bound 下界:lower bound
有上界:be bounded above或be above bounded
有下界:be bounded below或be below bounded
上确界:least upper bound或supremum 下确界:greatest lower bound或infimum
“A的一个上界"可译作"an upper bound of A”
开覆盖:open cover 有限子覆盖:finite subcover

关系的英语:

有序对(序偶):ordered pair
关系:relation 空关系:empty relation 全域关系:universal relation
恒等关系:identity relation 逆关系:inverse relation n元关系:n-ary relation
“A和B的关系"可译作"the relation between A and B”
“A上的关系"可译作"the relation over A”
“xRy"可读作"x is R-related to y”
关系矩阵:relation matrix 关系图:relation graph
定义域:domain 值域:range或codomain 域:field
“关系R的定义域"可读作"the domain of R”
“关系R的值域"可读作"the range of R"或"the codomain of R”
“关系R的域"可读作"the field of R”
准确地讲,“range"和"codomain"的意思并非完全一样.
比如说,A={1},B={5,6,7},C={5,6},R={<1,5>,<1,6>},那么R的"domain"是A,R的"range"是B,而R的"codomain"既可以是B也可以是C
右复合:right composition 左复合:left composition
“A对B的右复合"可译作"the right composition of A to B”
限制:restriction 像:image
“R在A上的限制"可译作"the restriction of R over A”
“A在R下的像"可译作"the image of A under R”
自反性:reflexivity 对称性:symmetry 传递性:transitivity
自反的:reflexive 对称的:symmetric 传递的:transitive
反自反的:irreflexive 反对称的:antisymmetric
自反闭包:reflexive closure 对称闭包:symmetric closure 传递闭包:transitive closure
“R在A上的自反闭包"可译作"the reflexive closure of R over A”
等价关系:equivalence relation 等价类:equivalence class 商集:quotient set
划分:partition 划分块:block of partition
“x关于R的等价类"可读作"the equivalence of x by R”
“A关于R的商集"可读作"the quotient set of A by R”
“A的一个划分"可译作"a partition of A”
偏序关系:partial order 全序关系:total order 线序关系:linear order
注意以上三种关系的英语中都不需要加上"relation”
覆盖:cover
“a覆盖b"可译作"a covers b"或"b is covered by a”

抽象代数的英语:

抽象代数:abstract algebra
运算:operation 二元运算:binary operation
可交换的:commutative 可结合的:associative 幂等的:idempotent
可消去的:cancellative
在……下的封闭性:closure under……
……的交换律:commutative law of…… 交换性:commutativity
……的结合律:associative law of…… 结合性:associativity
……的消去律:cancellative law of…… 消去性:cancellation
可左消去的:left-cancellative 可右消去的:right-cancellative
单位元:identity element 逆元:inverse element
零元:absorbing element或zero element或annihilating element
同态:homomorphism 单同态:monomorphism 满同态:epimorphism
自同态:endomorphism
同构:isomorphism 自同构:automorphism 同态像:homomorphic image
代数结构:algebraic structure 子代数:subalgebra 真子代数:proper subalgebra
群:group 半群:semigroup 幺半群(独异点):monoid 平凡群:trivial group
基础集:underlying set 阶:order 周期:period 四元群:four-group
“n阶群"可译作"the group of order n”
子群:subgroup 正规子群:normal subgroup
“由a生成的子群"可译作"subgroup generated by a”
"子群的中心"可译作"center of the subgroup "
陪集:coset 左陪集:left coset 右陪集:right coset
“陪集H在群G中的指数"可译作"index of H in G”
循环群:cyclic group 生成元:generator 无限循环群:infinite cyclic group
置换群:permutation group 对称群:symmetry group
“n元置换群"可译作"the permutation group of degree n”
环:ring 交换环:commutative ring 非零因子环:domain 整环:integral domain
理想:ideal
A法相对于B法是可分配的:A is distributive with respect to B
分配率:distribution law
域:field
格:lattice 分配格:distributive lattice 钻石格:diamond lattice 五角格:pentagon lattice
有界格:bounded lattice
全上界:join或least upper bound 全下界:meet或greatest lower bound
有补格:complemented lattice 补元:complement element

映射的英语:

映射:mapping 逆映射:inverse mapping
满射的:surjective 满射:serjection
单射的:injective 单射:injection
双射的:bijective 双射:bijection
“f是从A到B的映射"可译作"f is a mapping of A into B"或"f maps A into B”
“f是从A到B的满射"可译作"f is a mapping of A onto B"或"f maps A onto B"或"f is a surjection from A to B"或"f is a surjective mapping of A to B”
“f是从A到B的单射"可译作"f is a 1-1 mapping of A into B”,可读作"f is a one-to-one mapping of A into B",亦可译作"f is an injection from A to B"或"f is an injective mapping of A into B"
“f是从A到B的双射"可译作"f is a bijection from A to B"或"f is a bijective mapping of A to B"或"f is a 1-1 correspondece between A and B”
“建立起一个映射"可译作"set up a mapping”

数列的英语:

数列:sequence 项:term 下标:subscript或index(数列中专用) 子列:subsequence
邻项:consecutive term 连续的项:successive term
首项:initial term或first term 末项:last term 第n项:the n-th term
一般项:general term
通项公式:formula for general term
有穷数列:finite sequence 无穷数列:infinite sequence或stream
单调数列:monotonic sequence 单调性:monotonicity
单调递增:monotonically increase 单调递减:monotonically decrease
“……的数列"可译作"a sequence of ……”
常数列:constant sequence
等差数列:arithmetic progression 等比数列:geometric progression
公差:common difference 公比:common radio或common quotient
等差中项:arithmetic mean 等比中项:geometric mean
“a和b的等差中项"可译作"the arithmetic mean between a and b”
递推关系:recurrence relation 初值:initial condition或seed value
n阶的:n-th-order 线性的:linear 非线性的:nonlinear 齐次的:homogeneous
非齐次的:non-homogeneous或inhomogeneous
线性递推数列:linear recurrence sequence或简写为LRS
常系数一阶齐次递推关系:first-order homogeneous recurrence relation with constant coefficients
特征多项式:characteristic polynomial或auxiliary polynomial
生成函数:generating function 特征根:characteristic root或eigenvalue
迭代:iteration(名词);iterate(动词)

函数的英语:

函数:function 定义域:domain 值域:codomain或range(关于codomain和range的区别参看上文)
像:image 原像:preimage或inverse image 限制:restriction 延拓:expansion
图像:graph
“A在f下的像"可译作"the image of A under f”
“B在f下的原像"可译作"the preimage of B under f"或"the inverse image of B under f”
“g是f的限制"可译作"g is a restriction of f”
“f是g的延拓"可译作"f is an expansion of g”
“f的图像"可译作"the graph of f”
不动点:fixed point或invariant point 零点:zero
" “读作"f of x”
" “读作"y evaluated at n”
" “读作"f prime of x”;" “读作"f hat of x”;" “读作"f star of x”;" “读作"f bar of x”;" “读作"f sub n of x"或"f n of x”
单射函数:injective function 满射函数:surjective function 双射函数:bijective function
复合函数:composite function 反函数:inverse function 可逆函数:invertible function
"g(f(x))“读作"g of f of x”
变量:variable 自变量:argument或independent variable
因变量:value或dependent variable
单变量函数:single-variable function或univariate function 一元函数:unary function
多变量函数:multivariable function或multivariate function n元函数:n-ary function
单值函数:single-valued function 多值函数:multivalued function
隐函数:implicit function
分支:branch
“该多值函数的主支"可译作"the principal branch of this multivalued function”
奇函数:odd function 偶函数:even function 奇偶性:parity
单调函数:monotonic function 单调性:monotonicity
单调递增:monotonically increase 单调递减:monotonically decrease
分段函数:piecewise function
常函数:constant function 一次函数:linear function n次函数:n-ic function
多项式函数:polynomial function 正比例函数:directly proportional function
反比例函数:inversely proportional function
“y与x成正比"可译作"y is directly proportional to x”
“y与x成反比"可译作"y is inversely proportional to x”
三角函数:trigonometric function 双曲函数:hyperbolic function
反三角函数:inverse trigonometric function
指数函数:exponential function 对数函数:logarithm function或logarithmic function
凹函数:concave function 凸函数:convex function 凹凸性:concavity
上凹的:concave up 下凹的:concave down
周期函数:periodic function 周期:period 最小正周期:primitive period
“一个以2为周期的函数"可译作"a function with period two”
超越函数:transcendental function 初等函数:elementary function
“函数y在a处无意义"可译作"y is annihilated at a"或"y is undefined at a”
极值:local extremum或relative extremum(复数:extrema)
极大值:local maximum或relative maximum(复数:maxima)
极小值:local minimum或relative minimum(复数:minima)
最值:global extremum或absolute extremum(复数:extrema)
最大值:global maximum或absolute maximum(复数:maxima)
最小值:global minimum或absolute minimum(复数:minima)

二次函数的英语:

二次函数:quadratic function 顶点:vertex 对称轴:axis of symmetry
交点式:factored form 顶点式:vertex form
开口向上:open upward 开口向下:open downward

极限的英语:

极限:limit 右极限:right limit 左极限:left limit 子列极限:subsequential limit
上极限:limit superior或superior limit或supremum limit或upper limit
下极限:limit inferior或inferior limit或infimum limit或lower limit
……的极限:limit of ……
收敛:converge 收敛的:convergent 收敛性:convergence
发散:diverge 发散的:divergent 发散性:divergence
“f在a处收敛"可译作"f converges at a”
趋向于:tend to或go to或approach
从右趋向于:tend to……from the right或go to……from the right或:approach……from the right
从左趋向于:tend to……from the left或go to……from the left或:approach……from the left
无穷大:infinity 无穷小:infinitesimal
" “可读作"the limit of an as n tends to /goes to /approaches infinity”
“在a处f的极限"可译作"the limit of f at a”
等价无穷小:equivalent infinitesimal
" “可读作"f of x is little-o of x raised to the forth power”
" “可读作"f of x is big-O of x raised to the forth power”
不定式:indeterminate form
滤子基:filter base

级数的英语:

级数:series 有穷级数:finite series 无穷级数:infinite series
部分和:partial sum
几何级数:geometric series 调和级数:harmonic series
交错级数:alternating series
绝对收敛:convergent absolutely 条件收敛:convergent conditionally
分部求和法:summation by parts
幂级数:power series
收敛半径:radius of convergence 收敛圆盘:disk of convergence
根值审敛法:root test
比值审敛法:ratio test
比较审敛法:comparison test

连续的英语:

连续:continuous 不连续的:discontinuous
连续性:continuity 间断点:discontinuity 奇点:singularity
可去间断点:removable discontinuity 跳跃间断点:jump discontinuity
无穷间断点:essential discontinuity或infinite discontinuity
第一类间断点:discontinuity of the first kind
第二类间断点:discontinuity of the second kind
逐点连续的:pointwise continuous 一致连续的:uniformly continuous
中值定理:intermediate value theorem
右连续的:right-continuous 左连续的:left-continuous

导数的英语:

导数的英语:
导数:derivative 导函数:derivative function或derivative
可导的:have the derivative或differentiable(在不引起混淆的情况下)
变化率:rate of change 瞬时变化率:instantaneous rate of change
“y关于x的导数"可译作"the derivative of y with respect to x”
链式法则:chain rule
高阶导数:higher-order derivative或higher derivative
n阶导数:n-th derivative或derivative of order n
" “可读作"d y d x"或"d y over d x”
" “可读作"d squared y over d x squared”
" “可读作"f prime of x”
" “可读作"f double prime of x"或"f prime prime of x”

微分的英语:

微分:differential 可微的:differentiable 微分法:differentiation 求微分:differentiate
常微分:ordinary differential
“y对于x的微分"可译作"the differential of y with respect to x”
“y在a处可微"可译作"y is differentiable at a”
线性主部:principal linear part或principal part
微分形式:differential form

导数几何意义的英语:

曲线:curve 光滑的:smooth
切向量:tangent vector 主法向量:principal normal vector 次法向量:binormal vector
“曲线在点A处的切线"可译作"the tangent line to the curve at A”
驻点:critical point或stationary point 拐点:inflection point 鞍点:saddle point
尖点:cusp 叉点:crunode 孤立点:acnode
曲率:curvature 曲率半径:radius of curvature 挠率:torsion
渐伸线:involute 渐屈线:evolute
悬链线:catenary 摆线:cycloid 旋轮线:roulette 星形线:astroid 蔓叶线:cissoid
蚌线:conchoid 环索线:strophoid 双纽线:lemniscate n叶玫瑰线:rose with n petals
心形线:cardioid

积分的英语:

积分:integral 可积的:integrable 积分法:integration 求积分:integrate
被积函数:integrand 积分限:limit of integral 积分常数:constant of integral
" “可读作"the integral of f of x d x”
" “可读作"the integral from a to b of f of x d x”
" “可读作"the double integral over region R of f of x y d x d y”
定积分:definite integral 不定积分:indefinite integral或antiderivative
反常积分:improper integral 瑕点:singularity
换元积分法:integration by substitution 分部积分法:integration by parts
微积分基本定理:fundamental theorem of calculus
可求长的:rectifiable

微分方程的英语:

微分方程:differential equation 微分算子:differential operator
常微分方程:ordinary differential equation或简写为O.D.E.
偏微分方程:partial differential equation或简写为P.D.E.
时滞微分方程:delay differential equation或简写为D.D.E.
随机微分方程:stochastic differential equation或简写为S.D.E.
微分方程组:system of differential equations
初值:initial condition或seed value
积分曲线:integral curve
n阶微分方程:differential equation of order n
自治的:autonomous 线性的:linear 非线性的:nonlinear
齐次的:homogeneous 非齐次的:non-homogeneous或inhomogeneous
系数:coefficient
n阶的:n-th-order 如:二阶的:second-order
特解:particular solution 通解:general solution
积分因子:integrating factor
特征方程:characteristic equation
常数变易法:variation of parameters或variation of constants
分离变量法:separation of variables

多变量微积分的英语:

等值线:contour line
偏导数:partial derivative 偏微分:partial differential 全微分:total differential
混合导数:mixed derivative
" “可读作"partial f over partial x”
" “可读作"partial squared f over partial x partial y”
“f关于x的偏导数"可译作"the partial derivative of f with respect to x”
梯度:gradient 散度:divergence 旋度:curl
重积分:multiple integral n重积分:n-ple integral 累次积分:iterated integral
曲线积分(线积分):line integral 曲面积分(面积分):surface integral
闭路积分:closed integral 路径无关的:path independent 通量:flux

复变函数的英语:

复变函数:complex-valued function或complex function
解析函数:analytic function 调和函数:harmonic function
无穷远点:infinity
“在无穷远点"可译作"at infinity”
孤立奇点:isolated singularity 本性奇点:essential singularity
可去奇点:movable singularity
极点:pole m级极点:pole of order m 零点:zero m级零点:zero of order m
留数:residue 共形映射:conformal map

积分变换的英语:

积分变换:integral transform
核:kernel function或integral kernel或nucleus
反变换:inverse transform
卷积:convolution
62.函数列的英语:
逐点收敛的:pointwise convergent 一致收敛的:uniformly convergent
逐点有界的:pointwise bounded 一致有界的:uniformly bounded
逐点连续的:pointwise continuous 一致连续的:uniformly continuous
等度连续的:equicontinuous 一致闭包:uniform closure
连续可导的:continuously differentiable
“在…消失"可译作"vanish at…”
上确范数:supremum norm

统计的英语:

统计学:statistics
总体:population 个体:unit 样本:sample 样本容量:sample size
数据:datum(复数:data)
抽样调查(抽查):sampling 普查:census
频率:frequency 频率分布:frequency distribution
柱状图:histogram 组:bin 组距:width
条形图:bar chart 折线图:line chart 饼图:pie chart
平均数:mean 算数平均数:arithmetic mean 几何平均数:geometric mean
调和平均数:harmonic mean 加权平均数:weighted mean 权:weight
众数:mode 中位数:median
极差:range 方差:variance 标准差:standard deviation

概率的英语:

概率:probability 事件:event 互斥事件:complementary event 独立的:independent
基本事件:elementary event
不可能事件:impossible event 随机事件:random event 必然事件:certain event
“……的概率"可译作"probability of……”
随机实验:random experiment 条件概率:conditional probability
等可能性:equiprobability
古典概型:classical interpretation of probability
几何概型:geometric interpretation of probability
随机变量:random variable
概率分布:probability distribution 概率分布函数:probability distribution function
概率质量函数:probability mass function 概率密度函数:probability density function
分布列:distribution series
二项分布:binomial distribution 超几何分布:hypergeometric distribution
正态分布:normal distribution
期望值(数学期望):expected value 众数:mode 中位数:median 支集:support
偏度:skewness 方差:variance 标准差:standard deviation