LaTeX-Tutorial
Published:
After more than half a year, I picked up LaTeX again to write algorithm homework and found that I had forgotten a ridiculous number of symbols. So I wrote this tutorial to record common LaTeX mathematical symbols and environments for future reference.
LaTeX Tutorial
1. Basic Syntax
1.1 Document Structure
\documentclass{article} % Document type
\usepackage{amsmath} % Math package
\usepackage{amssymb} % Math symbol package
\begin{document}
% Document content
\end{document}
1.2 Text Formatting
\textbf{bold text} % Bold
\textit{italic text} % Italic
\underline{underline} % Underline
\texttt{monospace text} % Typewriter font
2. Math Mode
2.1 Inline and Display Formulas
Inline formula: $E = mc^2$
Display formula: $$E = mc^2$$
Or:
\[ E = mc^2 \]
2.2 equation Environment
\begin{equation}
E = mc^2
\end{equation}
% Without numbering
\begin{equation*}
E = mc^2
\end{equation*}
3. Common Mathematical Symbols
3.1 Greek Letters
Lowercase letters:
\alpha α \beta β \gamma γ
\delta δ \epsilon ε \zeta ζ
\eta η \theta θ \iota ι
\kappa κ \lambda λ \mu μ
\nu ν \xi ξ \pi π
\rho ρ \sigma σ \tau τ
\upsilon υ \phi φ \chi χ
\psi ψ \omega ω
Uppercase letters:
\Gamma Γ \Delta Δ \Theta Θ
\Lambda Λ \Xi Ξ \Pi Π
\Sigma Σ \Upsilon Υ \Phi Φ
\Psi Ψ \Omega Ω
3.2 Operators
Basic operations:
+ plus - minus \times ×
\div ÷ \pm ± \mp ∓
\cdot · \ast * \star ⋆
Relational operators:
= = \neq ≠ < <
> > \leq ≤ \geq ≥
\ll ≪ \gg ≫ \approx ≈
\equiv ≡ \sim ∼ \simeq ≃
\propto ∝ \in ∈ \notin ∉
\subset ⊂ \subseteq ⊆ \supset ⊃
Logical symbols:
\land ∧ \lor ∨ \neg ¬
\implies ⟹ \iff ⟺ \forall ∀
\exists ∃ \nexists ∄ \emptyset ∅
3.3 Superscripts and Subscripts
x^2 % Superscript
x_i % Subscript
x^{2y} % Multi-character superscript
x_{ij} % Multi-character subscript
x_i^2 % Superscript and subscript together
3.4 Fractions and Roots
\frac{a}{b} % Fraction
\dfrac{a}{b} % Display-style fraction
\tfrac{a}{b} % Text-style fraction
\sqrt{x} % Square root
\sqrt[n]{x} % n-th root
3.5 Summation, Integrals, and Limits
\sum_{i=1}^{n} % Summation
\prod_{i=1}^{n} % Product
\int_{a}^{b} % Integral
\iint % Double integral
\iiint % Triple integral
\oint % Contour integral
\lim_{x \to \infty} % Limit
3.6 Brackets
() % Parentheses
[] % Square brackets
\{\} % Braces
\langle \rangle % Angle brackets
\lfloor \rfloor % Floor
\lceil \rceil % Ceiling
Automatic sizing:
\left( \frac{a}{b} \right)
\left[ \frac{a}{b} \right]
\left\{ \frac{a}{b} \right\}
4. Matrices
4.1 Basic Matrices
% Matrix without brackets
\begin{matrix}
a & b \\
c & d
\end{matrix}
% Parenthesized matrix
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
% Square-bracket matrix
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
% Brace matrix
\begin{Bmatrix}
a & b \\
c & d
\end{Bmatrix}
% Single-vertical-line matrix
\begin{vmatrix}
a & b \\
c & d
\end{vmatrix}
% Double-vertical-line matrix
\begin{Vmatrix}
a & b \\
c & d
\end{Vmatrix}
4.2 Ellipses
\dots % Low ellipsis
\cdots % Centered ellipsis
\vdots % Vertical ellipsis
\ddots % Diagonal ellipsis
5. Multi-Line Formulas
5.1 align Environment
\begin{align}
x &= a + b \\
y &= c + d \\
z &= e + f
\end{align}
5.2 cases Environment
f(x) = \begin{cases}
x^2 & \text{if } x \geq 0 \\
-x & \text{if } x < 0
\end{cases}
5.3 split Environment
\begin{equation}
\begin{split}
f(x) &= (x+1)^2 \\
&= x^2 + 2x + 1
\end{split}
\end{equation}
6. Special Symbols
6.1 Arrows
\rightarrow → \leftarrow ←
\Rightarrow ⇒ \Leftarrow ⇐
\leftrightarrow ↔ \Leftrightarrow ⇔
\uparrow ↑ \downarrow ↓
\Uparrow ⇑ \Downarrow ⇓
\mapsto ↦ \longmapsto ⟼
\longrightarrow ⟶ \Longrightarrow ⟹
6.2 Other Common Symbols
\infty ∞ \partial ∂
\nabla ∇ \hbar ℏ
\prime ′ \ldots …
\cdots ⋯ \vdots ⋮
\ddots ⋱ \angle ∠
\degree ° \circ ∘
\bullet • \cap ∩
\cup ∪ \triangle △
6.3 Fonts
\mathbb{R} % Blackboard bold
\mathcal{A} % Calligraphic
\mathfrak{A} % Fraktur
\mathbf{A} % Bold
\mathrm{A} % Roman
\mathit{A} % Italic
\mathsf{A} % Sans-serif
\mathtt{A} % Typewriter
7. Spacing Control
a\ b % Normal space
a\,b % Small space
a\:b % Medium space
a\;b % Large space
a\quad b % 1em space
a\qquad b % 2em space
a\!b % Negative space
8. Text Comments
\text{text content} % Insert text inside a formula
\mbox{text content} % Text box
9. Accents
\hat{a} â \bar{a} ā
\tilde{a} ã \dot{a} ȧ
\ddot{a} ä \vec{a} ā⃗
\widehat{ab} \widetilde{ab}
10. Common Theorem Environments
\usepackage{amsthm}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{corollary}{Corollary}
\newtheorem{definition}{Definition}
\begin{theorem}
Theorem content
\end{theorem}
\begin{proof}
Proof content
\end{proof}
11. Common Tips
11.1 Alignment
\begin{aligned}
&\text{left aligned} \\
&\text{content}
\end{aligned}
11.2 Numbering Control
\tag{1} % Manual tag
\notag % Remove numbering
\nonumber % Remove numbering
11.3 Colors
\usepackage{xcolor}
\textcolor{red}{red text}
\colorbox{yellow}{yellow background}
12. Best Practices
- Matching brackets: use
\leftand\rightto automatically adjust bracket size. - Long formulas: use
alignorsplitto break lines. - Matrices: choose an appropriate bracket type.
- Spacing: use
\,,\quad, and similar commands to adjust spacing. - Text: use
\text{}to insert text in formulas. - Symbols: define macros for complex symbols to simplify input.
% Custom command examples
\newcommand{\R}{\mathbb{R}}
\newcommand{\norm}[1]{\left\| #1 \right\|}
References
- Overleaf Documentation
- LaTeX Wikibook
- Detexify - handwritten LaTeX symbol recognition