Mathematical Expressions

mdsvr supports rendering mathematical expressions using LaTeX syntax, following the GitHub standard for writing math in Markdown.

Math rendering is powered by LaTeX syntax — a widely used markup language for mathematical notation.

Inline Expressions

To include a math expression inline within your text, delimit the expression with a dollar symbol $:


  

    
    
    
  

  
This sentence uses `$` delimiters to show math inline: $\sqrt{3x-1}+(1+x)^2$

renders as:

This sentence uses $ delimiters to show math inline: 3x−1+(1+x)2\sqrt{3x-1}+(1+x)^2

Alternatively, you can use the \`...\` syntax to explicitly declare inline math, which is useful when the expression contains characters that overlap with Markdown syntax:


  

    
    
    
  

  
This sentence uses $` and `$ delimiters to show math inline: $`\sqrt{3x-1}+(1+x)^2`$

renders as:

This sentence uses and and delimiters to show math inline: E=mc2E = mc^2

Block Expressions

To add a math expression as a block, start a new line and delimit the expression with two dollar symbols $$:


  

    
    
    
  

  
**The Cauchy-Schwarz Inequality**

$$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$

renders as:

The Cauchy-Schwarz Inequality

(∑k=1nakbk)2≤(∑k=1nak2)(∑k=1nbk2)\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)

Alternatively, you can use the math code block syntax to display a math expression as a block. With this syntax, you don’t need to use $$ delimiters:


  

    
    
    
  

  
**The Cauchy-Schwarz Inequality**

```math
\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
```

renders as:

The Cauchy-Schwarz Inequality

(∑k=1nakbk)2≤(∑k=1nak2)(∑k=1nbk2)\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)

Writing Dollar Signs in Line with and Within Mathematical Expressions

To display a dollar sign as a character in the same line as a mathematical expression, you need to escape the non-delimiter $ to ensure the line renders correctly.

Within a math expression, add a \ symbol before the explicit $:


  

    
    
    
  

  
This expression uses `\$` to display a dollar sign: $\sqrt{\$4}$

renders as:

This expression uses \$ to display a dollar sign: $4\sqrt{\$4}

Outside a math expression, but on the same line, use span tags around the explicit $:


  

    
    
    
  

  
To split <span>$</span>100 in half, we calculate \$100/2

renders as:

To split $100 in half, we calculate 100/2100/2

Common Examples

Fractions and Roots


  

    
    
    
  

  
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Summations and Integrals


  

    
    
    
  

  
$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$

$$\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}$$
∑i=1ni=n(n+1)2\sum_{i=1}^{n} i = \frac{n(n+1)}{2}
∫−∞∞e−x2 dx=π\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}

Matrices


  

    
    
    
  

  
$$
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
=
\begin{pmatrix}
ax + by \\
cx + dy
\end{pmatrix}
$$
(abcd)(xy)=(ax+bycx+dy)\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} ax + by \\ cx + dy \end{pmatrix}

Greek Letters and Symbols


  

    
    
    
  

  
$\alpha, \beta, \gamma, \delta, \epsilon, \theta, \lambda, \mu, \pi, \sigma, \phi, \omega$

$\leq, \geq, \neq, \approx, \equiv, \infty, \partial, \nabla, \in, \subset, \cup, \cap$

α,β,γ,δ,ϵ,θ,λ,μ,π,σ,ϕ,ω\alpha, \beta, \gamma, \delta, \epsilon, \theta, \lambda, \mu, \pi, \sigma, \phi, \omega

≤,≥,≠,≈,≡,∞,∂,∇,∈,⊂,∪,∩\leq, \geq, \neq, \approx, \equiv, \infty, \partial, \nabla, \in, \subset, \cup, \cap

Aligned Equations


  

    
    
    
  

  
$$
\begin{aligned}
(a+b)^2 &= (a+b)(a+b) \\
        &= a^2 + ab + ba + b^2 \\
        &= a^2 + 2ab + b^2
\end{aligned}
$$
(a+b)2=(a+b)(a+b)=a2+ab+ba+b2=a2+2ab+b2\begin{aligned} (a+b)^2 &= (a+b)(a+b) \\ &= a^2 + ab + ba + b^2 \\ &= a^2 + 2ab + b^2 \end{aligned}

Syntax Summary

Syntax Type Example
$...$ Inline $E = mc^2$
\`...\` Inline \`E = mc^2\`
$$...$$ Block $$E = mc^2$$
```math Block Code block with math language

Further Reading

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