用英语表达数学

万书草堂 2019-10-26

展开全文

最近发现自己用英语描述数学语言的能力非常欠缺(做presentation和写报告完全不够用)，果断补补。本文整理用英语表达数学的一些问题。

目录 [hide]

1. 基本表达

1.1 四则运算
1.2 括号表达
1.3 比较
1.4 分数与小数
1.5 比例(ratio)
1.6 指数、方根和对数
1.7 集合(set)
1.8 函数
1.9 微积分
1.10 其他符号

2. 论文写作

1. 基本表达

1.1 四则运算

加、减、乘、除

plus, minus, times/multiplied by, divided by

1.2 括号表达

小括号(round bracket)、中括号(square bracket)、大括号(bracket)。

(a+b) bracket a plus b bracket

值得注意的是：

两个括号相乘，用over连接两括号，如a plus b into a minus b.
括号的内容被一个数除，说完括号内容，再用all is divide by…

1.3 比较

大于、小于、等于、约等于、小大于、小小于

equals/is equal to, greater than, less than, is approximately equal to, is not greater than, is not less than

1.4 分数与小数

(1)分数(fraction)

一般情况，分子(numerator)用基数词(cardinal number)表示，分母(denominator)用序数词(ordinal number)表示。值得注意的是：

分母为2或4，常用half和quarter表示，如3/4, three quarters
序数词(分母)被视为名词，因此，大于1用复数，如four fifths
带分数的(mixed fraction)，用and连接整数与分数
分母很大时，用over连接分子和分母，如one over a thousand and eighty-nine
代数里的分数用over
分母是一百的，读成percent

(2)小数(decimal fractions)

用point连接整数部分(the integral part)与小数部分，如zero/nought point two six.精确到3位数，correct to three significant figures.

四舍五入，rounding up or down，举例如下：

If the spreadsheet column is not wide enough to show all available decimal places, then the spreadsheet will round the number to the available column width.
Some items vary from month to month, like the phone bill for example, so track the amounts for a few months, take an average, and round up to the nearest $10.
Lastly, it stores the cleaned up and rounded value in the database.

1.5 比例(ratio)

比例为the ratio，冒号:读作to，举例如下：

21:7 – 3:1 the ratio of twenty one to seven is equal to the ratio of three to one
a:b∷c:d a is to b as c is to d

1.6 指数、方根和对数

(1)指数(exponentiation)

Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b and the exponent (or power) n.^[2]

2次方为squared，3次方为cubed或to the third，往后依次为to the fourth, to the fifth, … 举例如下：

three squared plus four cubed/to the third
a to the fifth/the fifth power of a
to the minus tenth power of a

值得注意的是，如果是负次方，则需要在序数前加minus。

(2)方根(nth root)

形式为：the * root of，2为squared，3为cubed，举例如下：

the squared root of a
the cubed root of a
x to the minus two third plus the fifth root of a squared

(3)对数(logarithm)

log_aN，a为底数(base)，N为真数(antilog/antilogarithm)，log_aN读成:

the log/logarithm of N to the base a
log N to the base a

1.7 集合(set)

空集：empty set
属于：x is a number of R 或 x is in R
子集：A is a subset of B
真子集：A is a proper subset of B 或 A is properly included in
交集：the intersection of A and B
并集：the union set of A and B
差集：the different set
α→β(α==>β)：α implies β 或 if β, then α.
α <==> β：α is equivalent to β 或 α holds if and only if B holds

1.8 函数

f(x)意为the function f of x 或 the value of function f at x，读作f of x 或 the value of f at x

Y – f^-1(x)为：y is the inverse of function f of x.
f: x→y读作：f maps x into y.
f_og读作：f circle g

1.9 微积分

微积分符号：the integral between the limits a and b of xy

导数：the differential coefficient of y with respect to x

1.10 其他符号

绝对值：the absolute value of x
无穷大：infinity
向量：vector a
求和：sigma 或 the summation of
求积：pi 或 the product of
x→y：x approaches the limit a 或 the implication ‘if x then a’