LaTeX Tutorial Series: Mathematical Typesetting

A clear and practical guide to math typesetting in LaTeX

After learning the basic layout settings in LaTeX, it is time to move to its strongest feature: mathematical typesetting.

In many technical fields, formulas are not optional. We use them to define models, report results, and explain proofs. Word processors can handle simple equations, but they often become hard to manage when formulas get long or structured. LaTeX solves this problem with a full math system that is precise and consistent.

Basic Math Setup

Before writing advanced formulas, we should load the right packages. The most common set is the AMS package family:

Table 1: AMS package family

Package	Main purpose
amsmath	Extra math environments: alignment, multi-line equations, cases, matrices
amssymb	More math symbols
amsfonts	Extra math fonts
amsthm	Theorem-style environments

Inline vs Display Math

LaTeX has two main math modes:

• Inline math: appears inside normal text
• Display math: shown on its own line

Inline math

Common syntax:

Table 2: Inline math syntax

Syntax	Note
$...$	Most common
\(...\)	Native LaTeX form
\begin{math}...\end{math}	Longer form

\documentclass{article}
\usepackage{amsmath}

\begin{document}

$a^2 + b^2 = c^2$
\( a^2 + b^2 = c^2 \)
\begin{math} a^2 + b^2 = c^2 \end{math}

\end{document}

Display math

Common syntax:

Table 3: Display math syntax

Syntax	Note
\[...\]	Simple unnumbered display
\begin{displaymath}...\end{displaymath}	Same idea, longer form
\begin{equation}...\end{equation}	Numbered equation

If you need references like “Eq. (3)”, use equation.

Symbols and Math Fonts

Greek letters

Greek letters are used everywhere in STEM writing: \(\alpha\), \(\beta\), \(\sigma\), \(\pi\), and so on.

Table 4: Common Greek letters

Command	Output	Command	Output
\alpha	\(\alpha\)	\beta	\(\beta\)
\gamma	\(\gamma\)	\delta	\(\delta\)
\theta	\(\theta\)	\lambda	\(\lambda\)
\sigma	\(\sigma\)	\omega	\(\omega\)
\Gamma	\(\Gamma\)	\Sigma	\(\Sigma\)
\Pi	\(\Pi\)	\Omega	\(\Omega\)

Common operators and relations

Table 5: Operators and relations

Command	Symbol	Command	Symbol	Command	Symbol
\times	\(\times\)	\leq	\(\leq\)	\approx	\(\approx\)
\div	\(\div\)	\geq	\(\geq\)	\equiv	\(\equiv\)
\pm	\(\pm\)	\neq	\(\neq\)	\sim	\(\sim\)
\cdot	\(\cdot\)	\ll	\(\ll\)	\propto	\(\propto\)

Sets and logic

Table 6: Sets and logic symbols

Command	Symbol	Command	Symbol	Command	Symbol
\in	\(\in\)	\cup	\(\cup\)	\forall	\(\forall\)
\notin	\(\notin\)	\cap	\(\cap\)	\exists	\(\exists\)
\subseteq	\(\subseteq\)	\emptyset	\(\emptyset\)	\Rightarrow	\(\Rightarrow\)

Math font commands

Table 7: Common math font commands

Command	Output	Typical use
\mathcal{N}	\(\mathcal{N}\)	Distribution or family notation
\mathbb{R}	\(\mathbb{R}\)	Number sets
\mathbf{v}	\(\mathbf{v}\)	Vectors and matrices
\mathrm{d}	\(\mathrm{d}\)	Differential operator
\boldsymbol{\alpha}	\(\boldsymbol{\alpha}\)	Bold Greek symbols

Note

\mathbb and \mathcal are typically used with amssymb/amsfonts, and \boldsymbol needs amsmath.

Practical Advanced Skills

Fractions and roots

Use \frac{a}{b} for fractions and \sqrt{...} for square roots.

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

\[
\sqrt[3]{8} = 2, \quad \sqrt{\sqrt{x}} = x^{1/4}
\]

Spacing and text in math mode

LaTeX ignores normal spaces in math mode. Use spacing commands when needed:

Table 8: Math spacing commands

Command	Space size	Typical use
\,	thin	before \mathrm{d}x, unit spacing
\:	medium	slightly wider operator spacing
\;	thick	stronger separation
\quad	1em	visible separation
\qquad	2em	larger separation

If you need normal words in formulas, use \text{...}.

\[
f(x) = x^2 \quad \text{where} \quad x \in \mathbb{R}
\]

Brackets and delimiters

Use \left and \right for auto-sized brackets:

\[
\left( \frac{a}{b} + \frac{c}{d} \right)^2
\]

For one-sided delimiters, use an invisible boundary like \left..

Alignment (align)

Use align for multi-line derivations with aligned symbols:

\begin{align}
(a+b)^2 &= a^2 + 2ab + b^2 \\
(a-b)^2 &= a^2 - 2ab + b^2
\end{align}

Use align* when you do not want equation numbers.

Matrices

Table 9: Matrix environments

Environment	Bracket style
matrix	none
pmatrix	( )
bmatrix	[ ]
vmatrix	| |

Piecewise functions

Use cases:

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

Custom operators

For operators like var, cov, rank, define them properly:

\DeclareMathOperator{\var}{var}
\DeclareMathOperator{\cov}{cov}
\DeclareMathOperator*{\argmax}{arg\,max}

This gives better spacing and correct limit placement.

Equation Environments

equation

Use equation for one centered formula with one number:

\begin{equation}
  e^{i\pi} + 1 = 0
\end{equation}

Long equations with split

If one equation is too long, nest split inside equation:

\begin{equation}
\begin{split}
(a+b+c)^2 &= a^2+b^2+c^2 \\
          &\quad + 2ab + 2bc + 2ca
\end{split}
\end{equation}

Multiple centered equations with gather

Use gather when lines are independent and do not need alignment.

Theorem Environments (amsthm)

Numbered theorem environments

Define with \newtheorem:

\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}

Unnumbered environments

Use a star version:

\newtheorem*{remark}{Remark}

Styles

• plain: bold heading + italic body (default)
• definition: bold heading + normal body
• remark: italic heading + normal body

Switch style with \theoremstyle{...} before defining environments.

Proof environment

proof is built in by amsthm and ends with a QED symbol automatically.

Tools for Practice and Conversion

TeXnique: A LaTeX Equation Typesetting Game

TeXnique is better understood as a LaTeX equation typesetting game, not just a syntax reference page. You see a target formula, then try to reproduce it with correct LaTeX commands. That loop trains your reflexes: after enough practice, you start to “see” LaTeX when you look at math.

When I first wrote technical reports, the hardest part was not advanced math ideas. It was small formatting details: where to place & in align, when to use \left...\right, and why two similar fraction commands can produce very different visual results. TeXnique works well as a warm-up space for these details. You can test quickly without rebuilding a full document.

If your goal is to build typing fluency, not just memorize commands, TeXnique is a strong starting point. It reduces friction and lets you focus on mathematical meaning instead of syntax anxiety.

The video below gives a quick overview of how people use it in real practice:

After watching, try a small drill: pick three formulas you often use (for example, one limit, one matrix, and one piecewise function), and retype them until you can do it smoothly. This kind of short repetition creates long-term speed gains.

Mathpix Snip: Convert Formula Images to LaTeX

Mathpix Snip helps you convert formula images into LaTeX quickly. It is especially useful when your source is not editable text: lecture slides, scanned PDFs, whiteboard photos, or handwritten notes.

In one of my own note-cleaning sessions, I had a page full of matrix derivations and conditional expectation expressions. Typing everything manually would take a long time. With Mathpix, I got a usable draft much faster, then spent my time on review instead of raw typing.

That is the key: treat OCR output as a first draft, not a final answer. A practical check sequence is:

1. Similar characters (l, 1, I, O, 0)
2. Superscript/subscript nesting
3. Bracket and delimiter matching

The video below shows the basic Mathpix Snip workflow:

A robust workflow is: convert in batch first, then do a focused manual pass in your LaTeX document to unify style and correctness. In short, TeXnique trains your intuition, and Mathpix saves your input time. Using both gives the best balance of speed and quality.

Exercises

Question 1

Which environment is best for a single equation that needs numbering and cross-reference?

• A. \[...\]
• B. displaymath
• C. equation
• D. math

Answer: C — equation

equation provides an automatic equation number, which is necessary for references like Eq. (1).

Question 2

In the align environment, which symbol marks the alignment point?

• A. \\
• B. &
• C. %
• D. #

Answer: B — &

& marks the alignment anchor (usually before =), while \\ is used for line breaks.

Question 3

If you want to insert normal words such as “if” or “where” inside math mode, what should you use?

• A. \mathrm{}
• B. \operatorname{}
• C. \textbf{}
• D. \text{}

Answer: D — \text{}

\text{} is designed for normal text inside formulas.

Question 4

Write a LaTeX snippet for the following piecewise function:

\[ f(x)= \begin{cases} x^2, & x \ge 0\\ -x^2, & x < 0 \end{cases} \]

\[
f(x)=\begin{cases}
  x^2,  & x \ge 0 \\
 -x^2,  & x < 0
\end{cases}
\]

cases is the standard environment for piecewise definitions.

Question 5

Declare an argmax operator in the preamble and typeset:

\[ \arg\max_{x \in \mathbb{R}} f(x) \]

\usepackage{amsmath}
\DeclareMathOperator*{\argmax}{arg\,max}

\[
\argmax_{x \in \mathbb{R}} f(x)
\]

\DeclareMathOperator* lets limits appear above/below in display mode.

Chapter Summary

In this chapter, you learned the full workflow of LaTeX math typesetting: choosing the right AMS packages, switching between inline and display math, using symbols and math fonts correctly, and handling advanced details like spacing, scalable brackets, alignment, matrices, and piecewise functions.

You also learned how to structure formal mathematical writing with amsthm, including theorem, definition, remark, and proof environments. With these tools, you can produce clear and professional math writing for assignments, reports, and papers.

A good next step is to practice equation labels (\label) and references (\ref) in longer documents.