1.9 LaTeX

1. TeX, LaTeX, and Math Formulas

TeX is a typesetting system created by Donald Knuth; LaTeX builds on top of TeX with a more approachable set of document commands and a package ecosystem. When people say "write formulas or papers with LaTeX", they usually mean writing a LaTeX source file and handing it to some TeX engine to process.

LaTeX's core idea resembles Markdown: the source focuses on "what this is", and the typesetting system decides "how it is displayed". Markdown excels at general technical documents, while LaTeX is especially good at math formulas, cross-references, and long documents with consistent typesetting.

2. Writing Formulas in Markdown

This project already supports LaTeX math formulas. In Markdown or MDX, inline formulas are usually placed within a pair of $, and display formulas within a pair of $$.

2.1 Inline Formulas

The mass-energy equation $E = mc^2$ describes the relationship between mass and energy.

Effect: The mass-energy equation $E = mc^2$ describes the relationship between mass and energy.

An inline formula should be part of a sentence and suits short variables, equations, and symbols. Punctuation before and after formulas still follows the semantics of the surrounding text.

2.2 Display Formulas

$$
f(x) = ax^2 + bx + c
$$

Effect:

A display formula occupies its own line and suits longer derivations or expressions that need emphasis. Support for delimiters may differ across Markdown platforms; check in the target renderer before publishing.

3. Common Math Syntax

LaTeX commands usually start with a backslash \, and curly braces {} delimit command arguments. The braces themselves are usually not displayed; they only tell the command which content belongs to the same group.

3.1 Superscripts, Subscripts, and Grouping

By default, ^ and _ apply only to the single token that follows. To include multiple characters, you must group them with curly braces. For example, x^10 treats 1 as the superscript and leaves 0 on the baseline, while x^{10} means the tenth power.

3.2 Fractions, Radicals, and Parentheses

\frac{a+b}{c+d}
\sqrt{x}
\sqrt[n]{x}
\left( \frac{x+1}{x-1} \right)

Corresponding effect:

\frac{numerator}{denominator} denotes a fraction, and \sqrt[n]{expression} denotes the $n$-th root. \left and \right make brackets automatically resize to fit the content between them.

3.3 Greek Letters and Common Symbols

Command names are case-sensitive: \delta produces $\delta$, while \Delta produces $\Delta$. Not every uppercase Greek letter needs a command; those whose shapes match Latin letters are usually written as ordinary letters.

3.4 Sums, Limits, and Integrals

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

\lim_{x \to 0} \frac{\sin x}{x} = 1

\int_a^b f(x)\,dx

Effect:

Large operators such as \sum, \lim, and \int can take subscripts and superscripts to express ranges. In an integral, \, adds a small space so that the integrand is easier to distinguish from the differential; this is a typesetting convention and does not affect the mathematical meaning.

3.5 Math Fonts and Text

\mathbf{v}
\mathbb{R}
\mathcal{F}
\text{when } x > 0

Effect:

• \mathbf{} is often used for bold Latin letters
• \mathbb{} is often used for number sets, such as the real numbers $\mathbb{R}$
• \mathcal{} is often used for calligraphic uppercase letters
• \text{} inserts ordinary text in math mode

Whether a specific command is available depends on the renderer and the packages. For web formulas, rely on the supported list of KaTeX or MathJax; in a full document, it depends on the packages loaded in the preamble.

4. Multi-line Formulas and Structured Expressions

4.1 Aligned Formulas

To align multiple lines of a derivation by the equals sign, use the aligned environment. & marks the alignment position, and \\ starts a new line:

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

Effect:

4.2 Matrices

A = \begin{bmatrix}
1 & 2 \\
3 & 4
\end{bmatrix}

Effect:

In matrices, & separates columns and \\ separates rows. Common environments include:

4.3 Piecewise Functions

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

Effect:

The cases environment usually puts the expression in the first column and the condition in the second. Ordinary words in conditions should go into \text{} so they are not typeset literally as variables.

5. A Minimal LaTeX Document

Formulas in Markdown only handle mathematical expressions. To produce a PDF with titles, sections, and page layout, you need to write a complete .tex document:

\documentclass{article}

\usepackage{amsmath}
\usepackage{hyperref}

\title{LaTeX Getting Started Example}
\author{Your Name}
\date{\today}

\begin{document}

\maketitle
\tableofcontents

\section{Introduction}
This is the body text. An inline formula is written as $E = mc^2$.

\section{An Equation}
\begin{equation}
  \sum_{i=1}^{n} i = \frac{n(n+1)}{2}
  \label{eq:sum}
\end{equation}

Equation~\ref{eq:sum} gives the sum of the first $n$ positive integers.

\end{document}

A document consists of several parts:

1. \documentclass{article} selects the document class
2. \usepackage{...} loads packages in the preamble
3. \title, \author, and \date define metadata
4. \begin{document} and \end{document} wrap the body
5. \section{...} defines the section structure
6. The equation environment creates a numbered display equation
7. \label and \ref establish stable cross-references

5.1 Chinese Documents

Chinese documents usually use XeLaTeX or LuaLaTeX, with the ctex document class or package handling Chinese typesetting:

\documentclass[UTF8]{ctexart}

\title{Chinese Course Report}
\author{Your Name}
\date{\today}

\begin{document}
\maketitle

\section{Introduction}
This is a Chinese document written with LaTeX.

\end{document}

Whether ctexart is available depends on whether the corresponding package is installed in your TeX distribution. Chinese fonts, school templates, and compilation engines may have additional requirements; follow the course or template instructions first, and do not mix preamble configurations from the web without checking them.

6. Lists, Figures, and Tables

6.1 Lists

\begin{itemize}
  \item First item of an unordered list
  \item Second item of an unordered list
\end{itemize}

\begin{enumerate}
  \item First step of an ordered list
  \item Second step of an ordered list
\end{enumerate}

itemize creates an unordered list and enumerate an ordered list; each item starts with \item. LaTeX handles indentation and numbering, so you do not need to type bullet symbols manually.

6.2 Figures and Floats

\usepackage{graphicx}

\begin{figure}[htbp]
  \centering
  \includegraphics[width=0.7\textwidth]{images/result.png}
  \caption{Experiment Results}
  \label{fig:result}
\end{figure}

figure is a float: LaTeX places the figure by weighing the current position and the remaining space on the page. [htbp] permits trying here, top, bottom, or a float page, but does not guarantee that the figure appears exactly where it is in the source.

6.3 Tables

\begin{table}[htbp]
  \centering
  \caption{Experiment Data}
  \label{tab:data}
  \begin{tabular}{lcr}
    \hline
    Item & Count & Time \\
    \hline
    Plan A & 10 & 1.2 s \\
    Plan B & 10 & 0.8 s \\
    \hline
  \end{tabular}
\end{table}

In tabular, the column format {lcr} means left-aligned, centered, and right-aligned respectively. Like matrices, & separates columns and \\ separates rows. For complex tables, keep the data clear first; do not mimic spreadsheets with many vertical rules and merged cells.

7. Editing and Compilation Workflow

7.1 Online and Local Tools

Online platforms suit beginners and collaboration; local environments suit offline use, automated builds, and large projects. Do not install several distributions and mix them at will, because command paths, package versions, and caches may interfere with each other.

7.2 Compilation Commands

After installing a TeX distribution, you can compile from the terminal:

xelatex main.tex

Documents with tables of contents, cross-references, or bibliographies often need multiple compilation passes. latexmk automatically chooses the rounds to run based on dependencies:

latexmk -xelatex main.tex

A successful compilation usually produces a PDF plus auxiliary files such as .aux, .log, and .toc. Which files should be committed to Git depends on the project convention; usually you keep .tex files, figures, bibliographies, and template sources, and ignore intermediate files that can be regenerated.

8. Common Errors and Troubleshooting

Also check the following paired structures:

• { and }
• \begin{environment} and \end{environment}
• The $ and $ of math mode
• \left and \right

9. More Resources

This section only covers the most common entry-level skills. When you meet a specific need, look up materials by problem:

• LaTeX Project: the official LaTeX project website and introduction materials
• CTAN: the main archive for packages, templates, and documentation
• TeX Live: official TeX Live information
• KaTeX Supported Functions: the command list supported by this project's web formulas

When a course or school provides a template, read the template's README, example files, and compilation instructions first. The template may fix the document class, engine, fonts, bibliography tools, and the submission file structure; general tutorials cannot replace these conventions.

The next section, 1.10 Mermaid, introduces how to use plain text to describe structured charts such as flowcharts and sequence diagrams.

10. TODO Checklist

• Can distinguish a full LaTeX document from math formulas in Markdown
• Can correctly use superscripts, subscripts, fractions, radicals, sums, limits, and integrals
• Understands matrices, piecewise functions, and multi-line formulas aligned by the equals sign
• Understands \documentclass, the preamble, and the document environment
• Can use \label and \ref to create cross-references
• With AI assistance, can choose the correct compilation engine according to the template requirements
• When compilation fails, locates the first error in the log first

11. Questions Worth Thinking About