全部书籍

1 Primary & Middle School Mathematics1–9 年级在线 2 High School Mathematics10–12 年级在线 3 University Mathematics — Year 1本科一年级在线 4 University Mathematics — Year 2本科二年级在线 5 University Mathematics — Year 3本科三年级在线

1 Primary & Middle School Physics1–9 年级在线 2 High School Physics10–12 年级在线 3 University Physics — Year 1本科一年级在线 4 University Physics — Year 2本科二年级在线 5 University Physics — Year 3本科三年级在线

1 School Chemistry — Grades 1 to 121–12 年级在线 2 University Chemistry — Year 1本科一年级在线 3 University Chemistry — Year 2本科二年级在线 4 University Chemistry — Year 3本科三年级在线

1 Primary & Middle School Biology1–9 年级在线 2 High School Biology10–12 年级在线 3 University Biology — Year 1本科一年级在线 4 University Biology — Year 2本科二年级在线 5 University Biology — Year 3本科三年级在线

1 Primary & Middle School Earth and Space Sciences1–9 年级在线 2 High School Earth and Space Sciences10–12 年级在线 3 University Earth and Space Sciences — Year 1本科一年级在线 4 University Earth and Space Sciences — Year 2本科二年级在线 5 University Earth and Space Sciences — Year 3本科三年级在线

1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

全部游戏 Math Fuse Word Reactor Atlas Dash

应用关于

Coach

English Français Español Nederlands Português हिन्दी العربية Bahasa Indonesia 简体中文 বাংলা

登录开始阅读

书籍暂未推出简体中文版——当前显示英文版。

Mathematics · 术语表

什么是 Power？

又称： exponent

Definition 56.1 Primary & Middle School Mathematics · 第 56 章 — Powers

For a number $a$ and a whole number $n \geq 1$ :

a^n = \underbrace{a \times a \times \dots \times a}_{n \text{ factors}},

read “ $a$ to the (power) $n$ ”; $a$ is the base, $n$ the exponent. Special names: $a^2$ is “ $a$ squared”, $a^3$ “ $a$ cubed”. By convention:

a^1 = a, \qquad a^0 = 1 \ (a \neq 0), \qquad a^{-n} = \frac{1}{a^n}.

Powers of 2: each bar is twice the previous one. Growth by repeated multiplication runs away much faster than growth by repeated addition. — Powers of $2$ : each bar is twice the previous one. Growth by repeated multiplication runs away much faster than growth by repeated addition.

示例

Example 56.2

$3^4 = 3 \times 3 \times 3 \times 3 = 81$ ; $10^3 = 1000$ ; $5^{-2} = \frac{1}{25} = 0.04$ ; $(-2)^3 = -8$ and $(-2)^4 = +16$ (Example 54.5). Watch out: $a^n$ is not $a \times n$ : $2^5 = 32$ , not $10$ .

Example 56.4

2^3 \times 2^5 = 2^8 = 256, \qquad \frac{7^6}{7^4} = 7^2 = 49, \qquad \left(5^2\right)^3 = 5^6, \qquad 2^4 \times 5^4 = 10^4 .

A trap: the rules apply to a common base (or a common exponent, for the last one). No rule simplifies $2^3 \times 5^2$ — just compute: $8 \times 25 = 200$ .

在原文中阅读 →

Definition 63.7 Primary & Middle School Mathematics · 第 63 章 — Fractions and Powers

For a real number $a$ and a positive integer $n$ , the power $a^n$ is the product of $n$ factors equal to $a$ :

a^n = \underbrace{a \times a \times \dots \times a}_{n \text{ factors}} .

By convention $a^0 = 1$ (for $a \neq 0$ ), and negative exponents denote inverses:

a^{-n} = \frac{1}{a^n}.

示例

Example 63.13

The Earth–Sun distance is about $149\,600\,000$ km $= 1.496 \times 10^8$ km. The size of a water molecule is about $0.000\,000\,000\,28$ m $= 2.8 \times 10^{-10}$ m. To compute with such numbers, group the decimal parts and the powers of ten:

(3 \times 10^5) \times (2.5 \times 10^{-2}) = (3 \times 2.5) \times 10^{5 + (-2)} = 7.5 \times 10^{3}.

在原文中阅读 →

Definition 30.8 High School Mathematics · 第 30 章 — Matrices and Graphs

For a square matrix $A$ and $k \in \N$ , $A^k = A \times \dots \times A$ ( $k$ factors), with $A^0 = I$ .

在原文中阅读 →