Standard Keyboard Notation for IFoA Examinations.
自从 IFoA 英国精算师协会全面采用在线开卷考试，前六门基础科目的Paper A（纸考科目）均要求提交 Word（不可手写）。为便于协会批卷查重，IFoA 对考试提交的 Word 中数学公式的书写进行了严格的规定。总结来说，不得采用Word自带的数学公式编辑器或其他插件（如Mathtype等），而需要写成纯文本形式（类似LaTex代码），官方称为Standard Keyboard Notation。需要写较多数学公式的科目主要有前六门中的：CM1、CM2、CS1、CS2和高级阶段的 SP6、SP9，准备考这些科目的同学要注意认真听讲啦。
Jackie 根据 IFoA 的 Examinations Handbook 中的 Standard Keyboard Notation 部分，和历年真题答案中使用的符号总结了一份符号写法，具体可以分为四个部分：
- General mathematical notation
- Statistical notation
- Compound interest functions
- Life table functions
General mathematical notation
| Meaning | Notation | Standard Keyboard Notation |
|---|---|---|
| Multiplication | \(\times\) | * |
| Division | \(\div\) | / |
| Approximately equal | \(\approx\) | ~= OR approx. = OR c. = |
| Inequalities | \(a \geq b\) and \(c \leq d\) | a >= b and c <= d |
| Proportionality | \(a \propto b\) | a is proportional to b |
| Square root | \(\sqrt{\ldots}\) | sqrt(…) |
| Superscripted letters | \(a^x\) | a^x |
| Subscripted letters | \(X_{i j}\) | X_ij OR Xij |
| Exponential | \(e^{x}\) | exp(x) OR e^x |
| Accented symbols | \(\hat{b}, \bar{X}\) | b^hat, X^bar OR bhat, Xbar |
| Greek letters | \(\mu, \sigma, \alpha, \beta, \theta, \varphi, \lambda, \eta, \rho, \delta\) | Use the typed word for the letter e.g. mu, sigma, alpha, beta,
theta, phi, lambda, eta, rho, delta. Match case of Greek letter, for
example phi for φ and PHI for Φ. OR; an Arabic alternative where available e.g. a, b instead of alpha, beta, d for delta or D for DELTA. |
| Infinity symbol | \(\infty\) | Infinity OR Inf |
| Derivatives | \(f^{\prime}(x), f^{\prime \prime}(x), \delta f / \delta s\) | f'(x), f''(x), df/ds OR df/dx, d2f/dx2 |
| Integral | \(\int_{a}^{b} f^{\prime}(t) d t\) | INT(a,b):f'(t) dt OR Integral over a to b (f’(t)) OR int(a,b)[ … ] |
| Solved Integral | \(=[f(t)]_{a}^{b}\) | = [f(t)]:(a,b) |
| Summation | \(\sum_{t=a}^{b} \mu_{t}\) | sigma(a,b): mu(t) OR sum(a,b): mu(t) OR Sum over a to b (mu(t)) OR Sum(a,b)[ ... ] |
| Product | \(\prod_{a}^{b} f(x)\) | Product (a,b):f(x) OR product over a to b(f(x)) |
Statistical notation
| Meaning | Notation | Standard Keyboard Notation |
|---|---|---|
| Expected values | \(E(\ldots)\) | E(…) |
| Conditional expectation | \(E(X \mid Y)\) | E(X given Y) |
| Variance | \(V(\ldots)\) | V(…) |
| Covariance | \(\operatorname{cov}(\ldots)\) | Cov(…) |
| Distributions | \(\chi_{m}^{2}\) | chi-squared_m OR chi-squared with m degrees of freedom |
| Binomial Coefficient | \(\left(\begin{array}{l}n \\ r\end{array}\right)\) | n choose r OR choose (n, r) |
Compound interest functions
| Notation or Meaning | Standard Keyboard Notation |
|---|---|
| \(i^{(p)}\) | i(p) |
| \(d^{(p)}\) | d(p) |
| \(\delta\) | delta |
| \(v^n\) | v^n |
| \(\sx{\angln}\) | s:<n> |
| \(\axz{}{}{}{\angln}\) | abar:<n> |
| \(\ax{}{}{(p)}{\angln}\) | a(p):<n> |
| \(\actsymb{}{}{(Ia)}{}{\angln}\) | (Ia):<n> |
| \(f_{t, r}\) | f_t,r |
Life table functions
| Notation or Meaning | Standard Keyboard Notation |
|---|---|
| \(\frac{l_{y}}{l_{x}}\) | Ly/Lx |
| \(\frac{l_{y}^{(m)}}{l_{x}^{(m)}}\) | Ly(m)/Lx(m) |
| \(\frac{d_{x}}{l_{y}}\) | dx/Ly |
| \(\px{k}{x}\) | kpx |
| \(\px{k}{[x]}\) | kp[x] |
| \(\qx{m|}{x}\) | m|qx |
| \(\px{}{xy}\) | px:y |
| \(\px{t}{xy}\) | tpx:y |
| \(\qx{n}{\overset{2}{x}y}\) | nq:x(2):y |
| \(\axzz{}{}{}{\endowxn}\) | adue:x :<n> |
| \(\axzz{}{}{}{x}\) | adue:x |
| \(\ax{}{}{(p)}{x}\) | a(p):x |
| \(\axzz{}{}{}{xy}\) | adue:x :y |
| \(\axzz{}{}{}{\joint{xy}}\) | adue:(x:y)bar |
| \(\axzz{}{}{}{\endow{xy}{n}}\) | adue:x :y:<n> |
| \(\axzz{}{}{(p)}{\endow{xy}{n}}\) | adue(p):x :y:<n> |
| \(\axzz{}{}{}{x|y}\) | adue:x|y |
| \(\axzz{}{}{}{\overset{m}{x}|\overset{f}{y}}\) | a:x(m)|y(f) |
| \(\axzz{m|}{}{}{x}\) | m|adue:x |
| \(A_x\) | A:x |
| \(\actsymb{n|}{}{\bar{A}}{}{x}\) | n|Abar:x |
| \(\actsymb{n|}{2}{A}{}{x}\) | n|2A:x |
| \(\Ax{}{}{}{\endowxn}\) | EA:x :<n> |
| \(\Axz{}{}{}{\endowxn}\) | EAbar:x :<n> |
| \(\Ax{}{}{}{\termxn}\) | TA:x :<n> |
| \(\Ax{}{}{}{\pureendow{[x]}{n}}\) | PE:[x]:<n> |
| \(\actsymb{}{}{(IA)}{}{\termxn}\) | I(TA):x :<n> |
| \((a p)_{x}\) | ap(x) |
| \((a q)_{x}^{k}\) | aq(x):k |
| \(\mu_{x}^{k}\) | mu(x):k |
| \(\Vx{t}{}\) | tV |
| \(\actsymb{t}{}{V}{(f)}{}\) | tV(f) |
| \(\actsymb{t}{}{p}{\joint{HH}}{x}\) | tpxHHbar |
可以看到，一般化的数学公式输入较为简单，但利息理论和寿险精算部分的符号输入相对繁琐。为简化输入，Jackie 和 Keke 合作完成了一个符号自动化输入工具，欲知后事如何，且听下篇推文分解~
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