Math Reading

 https://www.liangye.site/2019/03/15/math-english/

计数方法

• 小数(decimal; decimal number)
  0.5: zero point five; point five.
  10.875: ten point eight seven five.
• 小数舍入(rounding)
  1.2735 rounded to 3 decimal places is 1.274.
• 分数(fraction; fraction number)
  a/b: a over b.
  1/2: one half.
  1/100: one hundredth.
  分子: numerator; 分母: denominator.
• 百分数(percentage)
  10%: ten percent.
• 科学计数(scientific notation)
  1.23×103$1.23\times {10}^3$: 1.23 times ten to the power of three; 1.23 times ten to the third (参考幂运算).

基本运算

• 四则运算(Elementary arithmetic)
  𝑎+𝑏=𝑐$a+b=c$: a plus b equals c (plus是介词).
  𝑎−𝑏=𝑐$a-b=c$: a minus b equals c (minus是介词); b substracted from a leaves c.
  𝑎×𝑏=𝑐$a\times b=c$: a times b equals c (times是介词); a multiplied by b is c.
  𝑎÷𝑏=𝑐$a÷b=c$: a divided by b equals c.
  1/𝑥$1/x$: the reciprocal of x.
  3:5$3:5$: three to five.
• 乘方/幂运算(exponentiation)
  𝑎𝑛$a^n$: a to the n-th (power); a to the power of n; a raised to the n-th power.
  𝑥2$x^2$: x squared.
  𝑦3$y^3$: y cubed.
  指数: exponent.
  底数: base.
• 开方(radication)
  9‾√$\sqrt{9}$: the square root of 9.
  8‾√3$\sqrt[3]{8}$: the cube root of 8.
  𝑏√𝑛$\sqrt[n]{b}$: the n-th root of b.
• 对数(logarithm)
  log𝑏𝑥${\log }_{b}x$: the logarithm of x to base b.
  log𝑥, ln𝑥, log𝑒𝑥$\log x,\ln x,{\log }_{e}x$: the natural logarithm of x.
  lg𝑥, log10𝑥$\lg x,{\log }_{10}x$: the common logarithm of x.
  lb 𝑥, log2𝑥$\text{lb}x,{\log }_{2}x$: the binary logarithm of x.
• 阶乘(factorial)
  5!: five factorial.

基本符号

• 小括号() (parentheses)
  (2𝑥−6𝑦)−10$(2x-6y)-10$: the quantity two x minus six y, close quantity, minus ten;paren, two x minus six y, close paren, minus ten; left paren, two x minus six y, right paren, minus ten.
  𝑎(𝑥−𝑦)$a(x-y)$: a, parenthesis, x minus y, close parenthesis.
• 中括号[] (brackets)
• 大括号\{\} (brace)
• 斜线/ (slash)
• 反斜线\\ (backslash)
• 井号# (hash; number sign, pound sign)
• 与号& (ampersand)
  a & b: a and b.
• 星号* (asterisk, star)
  𝑥∗$x^{\ast }$: x star; x asterisk.
• 十字†$†$ (dagger)
• 撇号’ (apostrophe)
  𝑎′$a^{\prime }$: a prime (US); a dash (UK).
  𝑎″$a^{″}$: a double prime (US); a double dash (UK).
• 省略号⋯$\cdots$ (ellipsis)
  12+14+18+⋯$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots$: one half plus one quarter plus one eighth and so forth.
• 叹号! (exclamation mark)
• 逗号, (comma)
• 句号. (full stop, period)
• 问号? (question mark)

特殊数学符号

• 正负号±$\pm$ (plus-minus)
• 成比例∝$\propto$ (is proportional to)
• 无穷∞$\mathrm{\infty }$ (infinity)
• 上下标 (superscript, subscript)
  𝑎1$a_1$: a (sub) one.
  𝜀𝑖𝑗𝑘${\epsilon }_{ijk}$: epsilon (sub) ijk.
  𝑎𝑖$a^i$: a super i.
• 附加符号(diacritic)
  𝑎¯$\overline{a}$: a bar.
  𝑥̃ $\tilde{x}$: x tilde.
  𝑎̂ $\hat{a}$: a hat.
  𝑦˙$\dot{y}$: x dot.
  𝑥⃗ $\overrightarrow{x}$: vector x.

逻辑运算符号

• 相等=$=$ (equal, is equal to)
• 不等≠$\ne$ (is not equal to)
• 大于>$>$ (is greater than, is larger than)
• 小于<$<$ (is less than, is smaller than)
• 大于等于⩾$⩾$ (is greater than or equal to)
• 小于等于⩽$⩽$ (is less than or equal to)
• 约等于≈$\approx$ (is approximately equal to)
• 赋值:=$:=$ (is set to be, is defined to be)

代数与函数运算符号

• 绝对值(absolute value)
• 求和(summation)
  ∑𝑛𝑘=1𝑘2$\sum _{k=1}^n{k}^2$: the summation over k from 1 to n of k squared; the summation of k squared over k from 1 to n.
• 求积(product)
  ∏𝑛𝑘=11𝑘$\prod _{k=1}^n\frac{1}{k}$: the product over k from 1 to n of one over k.
• 函数(function)
  𝑓(𝑥)$f(x)$: f of x.
  参数、变量: argument.
• 反函数(inverse function)

微积分符号

• 极限(limit)
  lim𝑥→0𝑓(𝑥)$\underset{x\to 0}{lim}f(x)$: the limit as x approaches zero of f of x; the limit of f of x as x approaches zero.
• 导数(derivative)
  𝑓′(𝑥)$f^{\prime }(x)$: f prime of x; the derivative of f with respect to x.
  𝑑𝑦𝑑𝑥$\frac{dy}{dx}$: d y over d x; the derivative of y with respect to x.
  ∂𝑦∂𝑥$\frac{\mathrm{\partial }y}{\mathrm{\partial }x}$: partial y over partial x; d y over d x; the partial derivative of y with respect to x.
• 积分(integral)
  ∫∞0𝑓(𝑡)𝑑𝑡${\int }_0^{\mathrm{\infty }}f(t)dt$: the integral from t equals 0 to t equals infinity of f of t d t; the integral of f of t d t as t goes from 0 to infinity; integrate f of t d t from 0 to infinity.

方程的解

• the solution of equation
• the solution for x
• the key to the question