Writing Math in LaTeX

Introduction

$\LaTeX$ is the universal standard for writing mathematical expressions. Coupled with modern editors like VS Code, Obsidian, or Overleaf, it allows you to write mathematics efficiently on a PC.

Why LaTeX?

With LaTeX, you can write absolutely anything in mathematics:

• Simple or complex equations with fractions, roots, indices
• Matrices, determinants, systems of equations
• Multiple integrals, partial derivatives
• Specialized symbols (quantum physics, set theory, logic)
• Commutative diagrams, graphs
• Musical notation, chess, chemistry...

The good news: It is impossible (and useless) to know all LaTeX commands by heart. There are thousands of them, and even experts regularly look up the exact syntax.

Learn progressively

Don't worry if you don't remember everything immediately. Mastery comes with practice. Commands you use often (fractions, sums, integrals) will naturally engrave themselves in your memory. For the rest, there are tools!

Detexify: Your Best Ally

Detexify is a magical tool that recognizes symbols drawn with the mouse:

1. Draw approximately the symbol you're looking for
2. The AI suggests corresponding LaTeX commands
3. Copy the command and use it in your document

Recommended workflow for beginners:

• Use Detexify every time you're looking for an unknown symbol
• Note the commands you use frequently
• After a few weeks, you'll naturally know the common symbols
• Create snippets for commands you type often (see following sections)

My personal advice

At first, keep Detexify open in a tab. Over time, you'll barely need it for common mathematics, but it will remain essential for rare or specialized symbols.

Learning objectives:

• Master basic mathematical syntax in LaTeX
• Be autonomous in learning new commands
• Use Detexify to quickly find symbols
• Create custom snippets to speed up typing
• Use LaTeX in different environments (Markdown, Overleaf)

Example of what you'll be able to do:

$$\displaystyle \boxed{ \left( \begin{smallmatrix} \color{red}\displaystyle \sum_{i=1}^{n}\frac{\alpha_i x^{i}}{i!} & \displaystyle \color{purple} \cancel{\int_{a}^{b} f(t)\,\mathrm{d}t}\\[4pt] \displaystyle \left.\frac{\partial^2 g}{\partial y^2}\right|_{y=0} & \displaystyle \color{green}\sqrt{\beta^2+\gamma^2} \end{smallmatrix} \right)_{x=\hat{\theta}_{\scriptscriptstyle 0}} \cdot \vec{v}_{\lfloor\gamma\rfloor} \;+\; \overbrace{\lim_{x\to0^{+}}\sum_{k=0}^{\infty}\frac{(-1)^k x^{2k}}{(2k)!}}^{\cos x} \;=\; \color{blue} \frac{\Gamma\!\bigl(\tfrac{1}{2}\bigr)}{\sqrt{\pi}} }$$

warning

What is written above is false, it's only for demonstration purposes!

Prerequisites & Installation

Several options are available for writing mathematical expressions in LaTeX.

Markdown on VS Code

Code editor with LaTeX rendering via extensions: code.visualstudio.com

Recommended extensions:

• Markdown Preview Enhanced
• Markdown All in One
• Markdown PDF

Markdown on Obsidian

Note-taking in Markdown with native LaTeX rendering: obsidian.md

Recommended plugins:

• Latex Suite
• Better Math in Callouts & Blockquotes

LaTeX on Overleaf (online)

Online, collaborative LaTeX IDE: overleaf.com

tip

Always load \usepackage{amsmath,amssymb,mathtools} in the preamble.

LaTeX on VS Code

Code editor with local LaTeX compilation: code.visualstudio.com

Add the LaTeX Workshop extension for compilation, snippets, and preview.

Install a LaTeX distribution:

• TeX Live: Recommended LaTeX distribution (Windows/macOS/Linux)
• MiKTeX: Lighter alternative to TeX Live

tip

Always load \usepackage{amsmath,amssymb,mathtools} in the preamble.

Math Modes

LaTeX offers two modes for writing mathematics. Understanding these modes is essential as they influence the rendering of symbols and spacing.

Inline vs Display Mode

Mode	Syntax	Usage	Rendering
Inline	$ ... $ or \( ... \)	Mathematics within running text	Compact, reduced indices/exponents
Display	$$ ... $$ or \[ ... \]	Equations centered on their own line	Enlarged, indices/exponents placed above/below

Example:

The Pythagorean theorem is written $a^2 + b^2 = c^2$ for a right triangle.

$$
\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}
$$

The Pythagorean theorem is written $a^2 + b^2 = c^2$ for a right triangle.

$$\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$$

Force display style in inline mode

Use \displaystyle to get enlarged rendering even in inline mode:

Compare $\sum_{i=1}^{n} i$ with $\displaystyle\sum_{i=1}^{n} i$ in the text.

Compare $\sum_{i=1}^{n} i$ with $\displaystyle\sum_{i=1}^{n} i$ in the text.

Professional tip

In inline mode, avoid \displaystyle as it disrupts line spacing. Rather prefer switching to display mode with $$ ... $$ for complex expressions.

Quick Symbol Reference

Basic Operators

LaTeX Command	Rendering	Description
\cdot	$\cdot$	Multiplication
\frac{a}{b}	$\frac{a}{b}$	Fraction
a_i, x^{n+1}	$a_i,\; x^{n+1}$	Indices and exponents
\sqrt[n]{x}	$\sqrt[n]{x}$	nth root
\sum_{k=0}^n	$\displaystyle\sum_{k=0}^n$	Sum
\int_a^b	$\displaystyle\int_a^b$	Integral
\prod_{i=1}^n	$\displaystyle\prod_{i=1}^n$	Product
\lim_{x \to 0}	$\displaystyle\lim_{x \to 0}$	Limit

Sets and Relations

Command	Rendering	Description
\in	$\in$	Belongs to
\notin	$\notin$	Does not belong to
\subset	$\subset$	Strict inclusion
\subseteq	$\subseteq$	Inclusion
\cup	$\cup$	Union
\cap	$\cap$	Intersection
\emptyset	$\emptyset$	Empty set
\mathbb{N}	$\mathbb{N}$	Natural numbers
\mathbb{Z}	$\mathbb{Z}$	Integers
\mathbb{Q}	$\mathbb{Q}$	Rational numbers
\mathbb{R}	$\mathbb{R}$	Real numbers
\mathbb{C}	$\mathbb{C}$	Complex numbers

Adaptive Delimiters

Delimiters \left and \right automatically adapt to the content size:

$\displaystyle( \frac{a}{b} )$ vs $\displaystyle\left( \frac{a}{b} \right)$

$\displaystyle( \frac{a}{b} )$ vs $\displaystyle\left( \frac{a}{b} \right)$

Delimiter	Static	Adaptive
Parentheses	( )	\left( \right)
Brackets	[ ]	\left[ \right]
Braces	\{ \}	\left\{ \right\}
Bars	| |	\left| \right|

Advanced Math Environments

align Environment

To align multiple equations on the & symbol:

\begin{align}
  f(x) &= x^2 + 2x + 1 \\
  &= (x + 1)^2
\end{align}

$$\begin{align} f(x) &= x^2 + 2x + 1 \\ &= (x + 1)^2 \end{align}$$

Numbering

align automatically numbers each line. To avoid numbering, use align* or add \nonumber on a specific line.

cases Environment: Piecewise Functions

Ideal for defining conditional functions:

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

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

Application in probability:

P(X = k) = \begin{cases}
  \binom{n}{k} p^k (1-p)^{n-k} & \text{if } k \in \{0,\ldots,n\} \\
  0 & \text{otherwise}
\end{cases}

$$P(X = k) = \begin{cases} \binom{n}{k} p^k (1-p)^{n-k} & \text{if } k \in \{0,\ldots,n\} \\ 0 & \text{otherwise} \end{cases}$$

Matrices: Types and Variants

LaTeX offers several matrix environments with different delimiters:

Environment	Delimiters	Code	Rendering
matrix	None	\begin{matrix} a & b \\ c & d \end{matrix}	$\begin{matrix} a & b \\ c & d \end{matrix}$
pmatrix	( )	\begin{pmatrix} a & b \\ c & d \end{pmatrix}	$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$
bmatrix	[ ]	\begin{bmatrix} a & b \\ c & d \end{bmatrix}	$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$
Bmatrix	{ }	\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}	$\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}$
vmatrix	| |	\begin{vmatrix} a & b \\ c & d \end{vmatrix}	$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$
smallmatrix	None	\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}	$\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}$

Practical usage: smallmatrix

smallmatrix is perfect for vectors and small matrices in inline mode, avoiding disruption of paragraph line spacing. Use it with \left( and \right) to add delimiters.

The matrix $\left(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\right)$ is invertible if $ad - bc \neq 0$.

The matrix $\left(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\right)$ is invertible if $ad - bc \neq 0$.

Complete example: system of linear equations:

\begin{bmatrix}
  1 & 2 & 3 \\
  4 & 5 & 6 \\
  7 & 8 & 9
\end{bmatrix}
\begin{pmatrix}
  x \\
  y \\
  z
\end{pmatrix}
=
\begin{pmatrix}
  b_1 \\
  b_2 \\
  b_3
\end{pmatrix}

$$\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix}$$

Speed Up Input with Snippets

Snippets transform a shortcut into predefined code. Example: fr + Tab → \frac{•}{•}

Snippets in VS Code

Initial Setup

1. Ctrl/Cmd + Shift + P → Preferences: Configure User Snippets
2. Choose latex.json (or markdown.json for Markdown)
3. Add your snippets in JSON format

Anatomy of a VS Code Snippet

"sum": {
  "prefix": "sum",                    // Shortcut to type
  "body": "\\sum_{i=$1}^{$2} $3",     // Generated code
  "description": "Sum"                // Description (optional)
}

Properties of a snippet:

• prefix: The shortcut to type (e.g., sum)
• body: The generated LaTeX code (escape backslashes: \\)
• description: Description displayed in autocompletion

Smart navigation (tab stops): $1, $2, $3 define where the cursor is positioned. After insertion, your cursor is placed on $1, then Tab moves to $2, etc.

Default values: ${1:value} defines a default value for the tab stop.

Examples of Useful Snippets

Add these snippets to your latex.json or markdown.json configuration:

{
  "fraction": {
    "prefix": "fr",
    "body": "\\frac{$1}{$2}$0",
    "description": "Fraction a/b"
  },
  "sum": {
    "prefix": "sum",
    "body": "\\sum_{${1:i}=${2:0}}^{${3:n}} $0",
    "description": "Sum with bounds"
  },
  "integral": {
    "prefix": "int",
    "body": "\\int_{${1:a}}^{${2:b}} ${3:f(x)} \\,\\mathrm{d}${4:x}$0",
    "description": "Definite integral"
  },
  "limit": {
    "prefix": "lim",
    "body": "\\lim_{${1:x} \\to ${2:0}} $0",
    "description": "Limit"
  },
  "matrix": {
    "prefix": "mat",
    "body": [
      "\\begin{${1|matrix,pmatrix,bmatrix,vmatrix|}}",
      "\t$2",
      "\\end{${1|matrix,pmatrix,bmatrix,vmatrix|}}"
    ],
    "description": "Matrix with choice of delimiters"
  },
  "cases": {
    "prefix": "cas",
    "body": [
      "\\begin{cases}",
      "\t$1 & \\text{if } $2 \\\\",
      "\t$3 & \\text{if } $4",
      "\\end{cases}$0"
    ],
    "description": "Piecewise function (2 cases)"
  },
  "align": {
    "prefix": "ali",
    "body": [
      "\\begin{align${1:*}}",
      "\t$2 &= $3 \\\\",
      "\t&= $4",
      "\\end{align${1:*}}$0"
    ],
    "description": "Equation alignment"
  }
}

Advanced technique: multiple choices

The ${1|option1,option2,option3|} syntax displays a dropdown menu upon insertion. Used in the mat snippet above to choose the matrix type.

Snippets in Obsidian with Latex Suite

Latex Suite is the reference extension for writing mathematics quickly in Obsidian. It transforms the writing experience by enabling input as fluid as with pen on paper.

Installation:

1. Open Obsidian → Settings → Community plugins options
2. Search for "Latex Suite" in the plugin browser
3. Click Install, then Enable

Key features:

Feature	Description	Example
Auto-expansion	Automatic expansion without pressing Tab	// → \frac{•}{•}
Visual mode	Transformation of selected text	Select x+y then S → \sqrt{x+y}
Context-aware	Snippets active only in math mode	@a works in $$...$$ only
Regex triggers	Advanced patterns for auto-formatting	x2 → x_{2} automatically
Variables	Predefined symbols to simplify regex	${GREEK} for all Greek letters

Anatomy of a Latex Suite Snippet

A Latex Suite snippet is a JavaScript object with 4 main properties:

{
  trigger: "//",                    // Trigger: text that activates the snippet
  replacement: "\\frac{$0}{$1}$2",  // Replacement: generated LaTeX code
  options: "mA",                    // Options: context and behavior
  priority: 1,                      // Execution priority. In case of conflict, the snippet with the highest priority will be preferred (optional)
  description: "Quick fraction",    // Description (optional)
  flags: "i"                        // Regex flags (optional)
}

Options explained:

Option	Meaning	Description
t	Text mode	Snippet active outside math environments
m	Math mode	Snippet active in $$...$$ or $...$
M	Block math mode	Snippet active in $$...$$
n	Inline math mode	Snippet active in $...$
c	Code mode	Snippet active in ``` ```
A	Auto-expand	Automatic expansion without Tab
v	Visual	Snippet active when text is selected
w	Word boundary	Requires a space or line start before the trigger
r	Regex	The trigger is a regular expression

Tab stops with $0, $1, $2:

As in VS Code, tab stops define where the cursor is positioned after expansion:

{ trigger: "sum", replacement: "\\sum_{${0:k}=${1:0}}^{${2:n}} $3", options: "mA" }

• ${0:k}: First stop with default value "k"
• ${1:0}: Second stop with default value "0"
• $3: Last stop without default value

{ trigger: "begin", replacement: "\\begin{$1}\n  $2\n\\end{$1}", options: "MA" }

Here, the first stop $1 is automatically reused in \end{...}.

Advanced regex triggers:

Snippets can use regex to detect patterns:

{
  trigger: "([A-Za-z])(\\d)",      // Detects letter + digit
  replacement: "[[0]]_{[[1]]}",    // [[0]] = letter, [[1]] = digit
  options: "rmA"                   // r = regex
}

Example: x2 → x_{2} automatically

Predefined variables:

The default_snippet_variables.js file defines constants to simplify regex:

{
  "${GREEK}": "alpha|beta|gamma|delta|...",
  "${SYMBOL}": "parallel|nabla|hbar|...",
  "${UNITS}": "V|A|Hz|kg|m|..."
}

Usage in a snippet:

{
  trigger: "\\\\(${GREEK})([A-Za-z])",
  replacement: "\\[[0]] [[1]]",    // Inserts a space after Greek letters
  options: "rmA"
}

My Personal Configuration

I've created a complete configuration with over 250 snippets optimized for mathematics and physics. This configuration is the result of two years of daily note-taking.

• default_snippets.js (custom snippets)
• default_snippet_variables.js (variables and symbols)

Complete configuration

The snippets cover:

• Automatic Obsidian callouts
• Advanced mathematical symbols
• Physical units (automatic detection: 10Hz → 10\text{Hz})
• Shortcuts for sequences and series: uu → $(u_{n})_{n\in\mathbb{N}}$, ff → $(f_{n})_{n\in\mathbb{N}}$, SS → $(S_{n})_{n\in\mathbb{N}}$
• Automatic conversion of isolated letters to math mode

I advise you to read the document even diagonally to discover them and know that they exist, so you can come back later with a ctrl+f.

Installation:

1. Copy the contents of the two files above
2. In Obsidian: Settings → Latex Suite → Snippets
3. Paste the contents of default_snippets.js in the text area
4. Go to Snippets variables
5. Paste the contents of default_snippet_variables.js

Recommended configuration

I highly recommend using my configuration as a base, then customize it according to your needs.

Examples of snippets from my configuration

1. Quick entry to math mode

Shortcut	Result	Description
ml	$\displaystyle •$	Inline math mode with displaystyle
dm	$$\n•\n$$	Display math mode (block)

2. Fractions and operations

Shortcut	Result	Description
//	\frac{•}{•}	Quick fraction
sr	^{2}	Square
cb	^{3}	Cube
sq	\sqrt{•}	Square root
ee	e^{•}	Exponential

3. Greek letters with @

The @ prefix allows quick insertion of Greek letters:

Shortcut	Result	Shortcut	Result
@a	\alpha	@G	\Gamma
@b	\beta	@D	\Delta
@g	\gamma	@T	\Theta
@d	\delta	@L	\Lambda
@e	\varepsilon	@S	\Sigma
@t	\theta	@O	\Omega
@l	\lambda	@P	\Pi
@p	\varphi
@o	\omega
@s	\sigma

4. Sets and symbols with double capitals

Shortcut	Result	Description
RR	$\mathbb{R}$	Real numbers
CC	$\mathbb{C}$	Complex numbers
NN	$\mathbb{N}$	Natural numbers
ZZ	$\mathbb{Z}$	Integers
KK	$\mathbb{K}$	Generic field
LL	$\mathcal{L}$	Function space
MM	$\mathcal{M}$	Matrix space

5. Automatic indices

Snippets automatically detect common indices:

x2     →  x_{2}           (numeric indices)
xii    →  x_{i}           (indices i, j, k, n, m)
xip1   →  x_{i+1}         (indices with +)
xim2   →  x_{i-2}         (indices with -)

6. Accents and modifiers

Type a letter followed by:

Suffix	Result	Example	Preview
vec	\vec{•}	xvec → \vec{x}	$\vec{x}$
dot	\dot{•}	xdot → \dot{x}	$\dot{x}$
ddot	\ddot{•}	xddot → \ddot{x}	$\ddot{x}$
bar	\bar{•}	xbar → \bar{x}	$\bar{x}$
hat	\hat{•}	xhat → \hat{x}	$\hat{x}$

7. Derivatives and integrals

Shortcut	Result	Example preview	Description
par	\frac{\partial •}{\partial •}	$\frac{\partial f}{\partial x}$	Partial derivative
pa2	\frac{\partial^{2} •}{\partial •^{2}}	$\frac{\partial^{2} f}{\partial x^{2}}$	Second derivative
ddt	\frac{d}{dt}	$\frac{d}{dt}$	Time derivative
int	\int_{0}^{\infty} • \, d•	$\int_{0}^{\infty} f(x) \, dx$	Integral with bounds
oinf	\int_{0}^{\infty} • \, d•	$\int_{0}^{\infty} f(x) \, dx$	Integral from 0 to infinity
infi	\int_{-\infty}^{+\infty} • \, d•	$\int_{-\infty}^{+\infty} f(x) \, dx$	Integral over R

8. Quick matrices

Shortcut	Result	Example preview	Description
pmat	\begin{pmatrix}\n•\n\end{pmatrix}	$\begin{pmatrix} a&b\\c&d \end{pmatrix}$	Matrix with parentheses
bmat	\begin{bmatrix}\n•\n\end{bmatrix}	$\begin{bmatrix} a&b\\c&d \end{bmatrix}$	Matrix with brackets
vmat	\begin{vmatrix}\n•\n\end{vmatrix}	$\begin{vmatrix} a&b\\c&d \end{vmatrix}$	Determinant
cases	\begin{cases}\n•\n\end{cases}	$\begin{cases} 0&\text{if } x=0\\1&\text{otherwise} \end{cases}$	Piecewise function

9. Visual mode: selection transformations

Select text then press:

Key	Transformation	Example	Preview
S	\sqrt{...}	x+1 → \sqrt{x+1}	$\sqrt{x+1}$
U	\underbrace{...}_{•}	a+b → \underbrace{a+b}_{•}	$\underbrace{a+b}_{•}$
O	\overbrace{...}^{•}	a+b → \overbrace{a+b}^{•}	$\overbrace{a+b}^{•}$
C	\cancel{...}	x → \cancel{x}	$\cancel{x}$

Practical Exercises

#	Task	Educational objective
1	Write a sheet containing A1 level differentiation formulas	Master align and cases environments
2	Create a VS Code snippet for the matrix environment	Automate input
3	Import the document on Overleaf and share it with a classmate	Discover revision mode

Resources

Documentation and Online Tools

• Overleaf – Learn LaTeX in 30 Minutes - Complete introduction
• Detexify - Find LaTeX symbols by drawing - Draw a symbol to find the LaTeX command
• MathJax Documentation - TeX Syntax - Complete TeX syntax
• MathJax Macros - List of available macros - List of available macros
• LaTeX Math Cheat Sheet - Quick reference
• LaTeX Wikibook - Community documentation

Obsidian Configuration Files

• Open default_snippets.js - Latex Suite snippets configuration
• Open default_snippet_variables.js - Variables and symbols for Latex Suite

tip

These files contain over 250 snippets optimized for quick input of mathematics, physics, and chemistry in Obsidian. See the Snippets in Obsidian section for installation instructions.