How to display complex mathematical concepts with simple code

How to display complex mathematical concepts with simple code
0

Working with Mathjax

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bitkcor uses Mathjax, a JavaScript display engine for mathematics that works in all browsers. We’re excited to see how y’all put this to work in conversation. Use two dollar signs ($$) to open and close MathJax.

When you write this:

$$ 
\alpha, A 
$$

you will see this:

\alpha, A

Table of Contents

  1. Automatic Sizing
  2. Brackets & Brace Delimiters
  3. Cauchy’s Integral Formula
  4. Curl of Vector Field
  5. Define Christoffel Symbols
  6. Define Curly Braces
  7. Delimiter, Invisible Delimiter
  8. Delimiter, Nested Delimiter Sizing Examples
  9. Double Angle Formula for Cosines
  10. Fractions & Binomials
  11. Fractions, Continued
  12. Fractions, Embed Fractions in Fractions
  13. Limits
  14. Limit Integral Above & Below Symbol
  15. Limits Over Multiple Lines
  16. Manual Sizing
  17. Modular Operators
  18. Multiply Two Numbers
  19. Operators
  20. Powers and Indices
  21. Quadratic Formula
  22. Roots
  23. Sums & Integrals
  24. Standard Deviation
  25. Standard Symbols
  26. Other Common Symbol Commands

Automatic Sizing

$$
\left(\frac{x^2}{y^3}\right)
$$
\left(\frac{x^2}{y^3}\right)
$$
P\left(A=2\middle|\frac{A^2}{B}>4\right)
$$
P\left(A=2\middle|\frac{A^2}{B}>4\right)

Brackets & Brace Delimiters

$$
( a ), [ b ], \{ c \}, | d |, \| e \|,
\langle f \rangle, \lfloor g \rfloor,
\lceil h \rceil, \ulcorner i \urcorner
$$
( a ), [ b ], \{ c \}, | d |, \| e \|, \langle f \rangle, \lfloor g \rfloor, \lceil h \rceil, \ulcorner i \urcorner

Cauchy's Integral Formula

$$
f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz
$$
f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz

Curl of Vector Field

$$
\vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i} + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k}
$$
\vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i} + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k}

Define Christoffel Symbols

$$
(\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i \left( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m \right)
$$
(\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i \left( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m \right)

Define Curly Braces

$$
\left\{\frac{x^2}{y^3}\right\}
$$
\left\{\frac{x^2}{y^3}\right\}

Delimiter, Invisible Delimiter

$$
\left.\frac{x^3}{3}\right|_0^1
$$
\left.\frac{x^3}{3}\right|_0^1

Delimiter, Nested Delimiter Sizing Examples

``` $$ \frac{\mathrm d}{\mathrm d x} \left( k g(x) \right) $$ ```
\frac{\mathrm d}{\mathrm d x} \left( k g(x) \right)
$$
\frac{\mathrm d}{\mathrm d x} \big( k g(x) \big)
$$
\frac{\mathrm d}{\mathrm d x} \big( k g(x) \big)

Double Angle Formula for Cosines

$$
\cos(\theta+\phi)=\cos(\theta)\cos(\varphi)−\sin(\theta)\sin(\varphi)
$$
\cos(\theta+\phi)=\cos(\theta)\cos(\varphi)−\sin(\theta)\sin(\varphi)

Fractions & Binomials

$$
\frac{n!}{k!(n-k)!} = \binom{n}{k}
$$
\frac{n!}{k!(n-k)!} = \binom{n}{k}

Fractions, Continued

$$
\begin{equation}
  x = a_0 + \cfrac{1}{a_1 
          + \cfrac{1}{a_2 
          + \cfrac{1}{a_3 + \cfrac{1}{a_4} } } }
\end{equation}
$$
\begin{equation} x = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{a_4} } } } \end{equation}

Fractions, Embed Fractions in Fractions

$$
\frac{\frac{1}{x}+\frac{1}{y}}{y-z}
$$
\frac{\frac{1}{x}+\frac{1}{y}}{y-z}

Greek Letters

$$
\alpha, Α, \beta, Β, \gamma, \Gamma, \pi, \Pi, \phi, \varphi, \mu, \Phi
$$
\alpha, Α, \beta, Β, \gamma, \Gamma, \pi, \Pi, \phi, \varphi, \mu, \Phi

Limits

$$
\lim_{x \to \infty} \exp(-x) = 0
$$
\lim_{x \to \infty} \exp(-x) = 0
$$
a \bmod b
$$
a \bmod b
$$
x \equiv a \pmod{b}
$$
x \equiv a \pmod{b}

Limit Integral Above & Below Symbol

$$
\int\limits_a^b
$$
\int\limits_a^b

Limits Over Multiple Lines

$$
\sum_{\substack{
   0<i<m \\
   0<j<n
  }} 
 P(i,j)
$$
\sum_{\substack{ 0<i<m \\ 0<j<n }} P(i,j)

Manual Sizing

$$
( \big( \Big( \bigg( \Bigg(
$$
( \big( \Big( \bigg( \Bigg(

Modular Operators

$$
a \bmod b
$$
a \bmod b
$$
x \equiv a \pmod{b}
$$
x \equiv a \pmod{b}

Multiply Two Numbers

$$
\begin{equation}
\frac{
    \begin{array}[b]{r}
      \left( x_1 x_2 \right)\\
      \times \left( x'_1 x'_2 \right)
    \end{array}
  }{
    \left( y_1y_2y_3y_4 \right)
  }
\end{equation}
$$
\begin{equation} \frac{ \begin{array}[b]{r} \left( x_1 x_2 \right)\\ \times \left( x'_1 x'_2 \right) \end{array} }{ \left( y_1y_2y_3y_4 \right) } \end{equation}

Operators

$$
\cos (2\theta) = \cos^2 \theta - \sin^2 \theta
$$
\cos (2\theta) = \cos^2 \theta - \sin^2 \theta

Powers and Indices

$$
k_{n+1} = n^2 + k_n^2 - k_{n-1}
$$
k_{n+1} = n^2 + k_n^2 - k_{n-1}

Surround power with brackets {} for powers with more than one digit.

$$
n^{22}
$$
n^{22}
$$
f(n) = n^5 + 4n^2 + 2 |_{n=17}
$$
f(n) = n^5 + 4n^2 + 2 |_{n=17}

Quadratic Formula

$$
x = {-b \pm \sqrt{b^2-4ac} \over 2a}
$$
x = {-b \pm \sqrt{b^2-4ac} \over 2a}

Roots

Use the \sqrt command to create a square root surrounded by an expression.

$$
\sqrt{\frac{a}{b}}
$$
\sqrt{\frac{a}{b}}
$$
\sqrt[n]{1+x+x^2+x^3+\dots+x^n}
$$
\sqrt[n]{1+x+x^2+x^3+\dots+x^n}

Sums and Integrals

$$
\sum_{i=1}^{10} t_i
$$
\sum_{i=1}^{10} t_i
$$
\int_0^infty \mathrm{e}^{-x}\,\mathrm{d}x
$$
\int_0^infty \mathrm{e}^{-x}\,\mathrm{d}x

Standard Deviation

$$
\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}
$$
\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}

Standard Symbols

$$
+ - =  ! / ( ) [ ] < > | ' : *
$$
+ - = ! / ( ) [ ] < > | ' : *

Other Common Symbol Commands

\sum \sum \prod \prod \coprod \coprod
\bigoplus \bigoplus \bigotimes \bigotimes \bigodot \bigodot
\bigcup \bigcup \bigcap \bigcap \biguplus \biguplus
\bigsqcup \bigsqcup \bigvee \bigvee \bigwedge \bigwedge
\int \int \oint \oint \iint \iint
\iiint \iiint \iiiint \iiiint \idotsint \idotsint
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