Mathematical Notation¶

Material for MkDocs supports mathematical notation through the Arithmatex extension, enabling LaTeX math rendering with MathJax or KaTeX.

Overview¶

Mathematical notation provides:

LaTeX syntax support - Industry-standard math typesetting
Inline and block math - Equations within text or standalone
Equation numbering - Automatic equation references
Math environments - Matrices, alignments, and more
Custom macros - Define reusable notation
Accessibility - Screen reader compatible output

Configuration¶

Basic Setup¶

Enable Arithmatex in mkdocs.yml:

markdown_extensions:
  - pymdownx.arithmatex:
      generic: true

extra_javascript:
  - javascripts/mathjax.js
  - https://polyfill.io/v3/polyfill.min.js?features=es6
  - https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js

MathJax Configuration¶

Create docs/javascripts/mathjax.js:

window.MathJax = {
  tex: {
    inlineMath: [["\\(", "\\)"]],
    displayMath: [["\\[", "\\]"]],
    processEscapes: true,
    processEnvironments: true
  },
  options: {
    ignoreHtmlClass: ".*|",
    processHtmlClass: "arithmatex"
  }
};

document$.subscribe(() => {
  MathJax.typesetPromise()
})

Basic Usage¶

Inline Math¶

Use \(...\) for inline equations:

The Pythagorean theorem states that \(a^2 + b^2 = c^2\).

Einstein's famous equation is \(E = mc^2\).

Result:

The Pythagorean theorem states that \(a^2 + b^2 = c^2\).

Einstein's famous equation is \(E = mc^2\).

Display Math¶

Use \[...\] for display equations:

\[
\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}
\]

Result:

\[ \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi} \]

Common Mathematical Expressions¶

Greek Letters¶

Lower	Upper	LaTeX
\(\alpha\)	\(A\)	`\alpha`, `A`
\(\beta\)	\(B\)	`\beta`, `B`
\(\gamma\)	\(\Gamma\)	`\gamma`, `\Gamma`
\(\delta\)	\(\Delta\)	`\delta`, `\Delta`
\(\epsilon\)	\(E\)	`\epsilon`, `E`
\(\theta\)	\(\Theta\)	`\theta`, `\Theta`
\(\lambda\)	\(\Lambda\)	`\lambda`, `\Lambda`
\(\pi\)	\(\Pi\)	`\pi`, `\Pi`
\(\sigma\)	\(\Sigma\)	`\sigma`, `\Sigma`
\(\omega\)	\(\Omega\)	`\omega`, `\Omega`

Operators and Relations¶

Addition: \(a + b\)
Subtraction: \(a - b\)
Multiplication: \(a \times b\) or \(a \cdot b\)
Division: \(a \div b\) or \(\frac{a}{b}\)
Equal: \(a = b\)
Not equal: \(a \neq b\)
Less than: \(a < b\)
Greater than: \(a > b\)
Less or equal: \(a \leq b\)
Greater or equal: \(a \geq b\)
Approximately: \(a \approx b\)

Superscripts and Subscripts¶

Superscript: \(x^2\), \(x^{n+1}\)
Subscript: \(x_i\), \(x_{i,j}\)
Combined: \(x_i^2\), \(x_{i,j}^{k+1}\)

Result:

Superscript: \(x^2\), \(x^{n+1}\) Subscript: \(x_i\), \(x_{i,j}\) Combined: \(x_i^2\), \(x_{i,j}^{k+1}\)

Fractions¶

Simple: \(\frac{1}{2}\)
Complex: \(\frac{x^2 + 3x + 2}{x - 1}\)
Nested: \(\frac{1}{1 + \frac{1}{x}}\)

Result:

Simple: \(\frac{1}{2}\) Complex: \(\frac{x^2 + 3x + 2}{x - 1}\) Nested: \(\frac{1}{1 + \frac{1}{x}}\)

Roots¶

Square root: \(\sqrt{x}\)
Nth root: \(\sqrt[n]{x}\)
Complex: \(\sqrt{x^2 + y^2}\)

Result:

Square root: \(\sqrt{x}\) Nth root: \(\sqrt[n]{x}\) Complex: \(\sqrt{x^2 + y^2}\)

Advanced Mathematics¶

Calculus¶

Derivatives:

\[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]

\[ \frac{d}{dx}(x^n) = nx^{n-1} \]

Integrals:

\[ \int_a^b f(x)\,dx = F(b) - F(a) \]

\[ \int_0^{\pi} \sin(x)\,dx = 2 \]

Partial Derivatives:

\[ \frac{\partial f}{\partial x} = \lim_{h \to 0} \frac{f(x+h,y) - f(x,y)}{h} \]

Linear Algebra¶

Matrices:

\[ A = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \]

Determinant:

\[ \det(A) = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc \]

Vector notation:

\[ \vec{v} = \begin{bmatrix} v_1 \\ v_2 \\ v_3 \end{bmatrix} \]

Set Theory¶

\[ A \cup B = \{x : x \in A \text{ or } x \in B\} \]

\[ A \cap B = \{x : x \in A \text{ and } x \in B\} \]

\[ A \setminus B = \{x : x \in A \text{ and } x \notin B\} \]

Summations and Products¶

Summation:

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

Product:

\[ \prod_{i=1}^{n} i = n! \]

Series:

\[ \sum_{n=0}^{\infty} \frac{x^n}{n!} = e^x \]

Equation Environments¶

Aligned Equations¶

\[ \begin{align} 2x + 3y &= 7 \\ x - y &= 1 \end{align} \]

Cases¶

\[ f(x) = \begin{cases} x^2 & \text{if } x \geq 0 \\ -x^2 & \text{if } x < 0 \end{cases} \]

Matrix Operations¶

\[ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} x + 2y \\ 3x + 4y \end{bmatrix} \]

Physics and Engineering¶

Classical Mechanics¶

Newton's Second Law: [ F = ma = mfrac{d^2x}{dt2} ]

Kinetic Energy: [ K = frac{1}{2}mv^2 ]

Quantum Mechanics¶

Schrödinger Equation: [ ihbarfrac{partial}{partial t}Psi = hat{H}Psi ]

Wave Function: [ Psi(x,t) = Ae^{i(kx - omega t)} ]

Electromagnetics¶

Maxwell's Equations: [ begin{align} nabla cdot mathbf{E} &= frac{rho}{epsilon_0} \ nabla cdot mathbf{B} &= 0 \ nabla times mathbf{E} &= -frac{partial mathbf{B}}{partial t} \ nabla times mathbf{B} &= mu_0mathbf{J} + mu_0epsilon_0frac{partial mathbf{E}}{partial t} end{align} ]

Statistics and Probability¶

Distributions¶

Normal Distribution: [ f(x) = frac{1}{sigmasqrt{2pi}}e^{{-frac{1}{2}left(frac{x-mu}{sigma}right)}2} ]

Binomial Distribution: [ P(X = k) = binom{n}{k}p^k(1-p) ]

Statistical Measures¶

Mean: [ bar{x} = frac{1}{n}sum_{i=1}^{n}x_i ]

Standard Deviation: [ sigma = sqrt{frac{1}{n}sum_{i=1}^{n}(x_i - bar{x})^2} ]

Custom Macros¶

Define reusable macros in your MathJax configuration:

window.MathJax = {
  tex: {
    macros: {
      RR: "\\mathbb{R}",
      CC: "\\mathbb{C}",
      NN: "\\mathbb{N}",
      ZZ: "\\mathbb{Z}",
      QQ: "\\mathbb{Q}",
      norm: ["\\lVert #1 \\rVert", 1],
      abs: ["\\lvert #1 \\rvert", 1],
      inner: ["\\langle #1, #2 \\rangle", 2]
    }
  }
};

Usage: - Real numbers: \(\mathbb{R}\) - Complex numbers: \(\mathbb{C}\) - Natural numbers: \(\mathbb{N}\) - Norm: \(\lVert x \rVert\) - Inner product: \(\langle x, y \rangle\)

Best Practices¶

1. Clarity¶

Use spacing and alignment for readability:

\[
\int_0^1 \frac{x^2 - 1}{x + 1} \, dx
\]

2. Accessibility¶

Provide context for equations:

The quadratic formula, \(x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\),
solves equations of the form \(ax^2 + bx + c = 0\).

3. Performance¶

For pages with many equations, consider lazy loading:

MathJax = {
  tex: {
    inlineMath: [['\\(', '\\)']],
    displayMath: [['\\[', '\\]']]
  },
  options: {
    lazyMargin: "200px"
  }
};

4. Mobile Responsiveness¶

Use scrollable containers for wide equations:

.arithmatex {
  overflow-x: auto;
  max-width: 100%;
}

Troubleshooting¶

Common Issues¶

Equations not rendering: Check MathJax is loaded
Incorrect spacing: Use \, for thin space, \; for medium
Escaping issues: Double backslashes in Markdown
Performance: Reduce equation complexity

Debug Mode¶

Enable MathJax debugging:

window.MathJax = {
  options: {
    menuOptions: {
      settings: {
        assistiveMml: true,
        collapsible: true,
        explorer: true
      }
    }
  }
};

Examples in Context¶

Algorithm Complexity¶

The time complexity of binary search is \(O(\log n)\), while linear search is \(O(n)\).

For a balanced binary tree with \(n\) nodes, the height is \(h = \lfloor \log_2 n \rfloor + 1\).

Machine Learning¶

The cost function for linear regression: [ J(theta) = frac{1}{2m}sum_{i=1}^{{m}(h_theta(x}) - y^{(i)})2 ]

Gradient descent update rule: [ theta_j := theta_j - alphafrac{partial}{partialtheta_j}J(theta) ]

Financial Mathematics¶

Compound interest formula: [ A = Pleft(1 + frac{r}{n}right)^{nt} ]

Black-Scholes option pricing: [ C = S_0N(d_1) - Ke^{-rt}N(d_2) ]

Mathematical Notation¶

Overview¶

Configuration¶

Basic Setup¶

MathJax Configuration¶

Basic Usage¶

Inline Math¶

Display Math¶

Common Mathematical Expressions¶

Greek Letters¶

Operators and Relations¶

Superscripts and Subscripts¶

Fractions¶

Roots¶

Advanced Mathematics¶

Calculus¶

Linear Algebra¶

Set Theory¶

Summations and Products¶

Equation Environments¶

Aligned Equations¶

Cases¶

Matrix Operations¶

Physics and Engineering¶

Classical Mechanics¶

Quantum Mechanics¶

Electromagnetics¶

Statistics and Probability¶

Distributions¶

Statistical Measures¶

Custom Macros¶

Best Practices¶

1. Clarity¶

2. Accessibility¶

3. Performance¶

4. Mobile Responsiveness¶

Troubleshooting¶

Common Issues¶

Debug Mode¶

Examples in Context¶

Algorithm Complexity¶

Machine Learning¶

Financial Mathematics¶

See Also¶