Beginner LaTeX Guide

${\LaTeX}$ is an extremely useful typesetting language to learn, especially in a math environment like this. However, the quick instructions Brilliant.org gives just aren't good enough to use for most situations.

This is why I've decided to create a beginner's ${\LaTeX}$ guide. There is a table of contents for easy symbol or format finding. I hope you can refer to this guide later, when writing solutions, problems, or notes.

Note: You can also view Latex codes by hovering over the equation. Read Seeing actual $\LaTeX$ for more details!

To quickly navigate to the part you want via the Table of Contents, press CTRL+F, and type in the section you want (including the tilde's ~ before and after the section).

Table of Contents

~Using LaTeX~

~Text~

~Basic Operations~

~Fractions~

~Sums, Products, Limits, and Integrals~

~Modular Arithmetic~

~Trigonometry~

~Combinatorics~

~Geometry~

~Calculus~

~Parentheses~

~Fitting Parentheses~

~Tables and Arrays~

~Other~

~Using LaTeX~

To use LaTeX, put a backslash and a left parenthesis before the math you want to LaTeXify, and put a backslash and a right parenthesis after the math you want to LaTeXify. For example:

Imgur Imgur

Shows up as $1+2+3=6$

However, if you want your math to be more conspicuous and centered, you can use a backslash then a left bracket, then your math, then a backslash then a right bracket. For example:

Imgur Imgur

Shows up as

$1+2+3=6$

This second option is the display text. A lot of other math operations will look better in this text. To force the first option to also use display text, you can add a \displaystyle at the beginning.

~Text~

To write text in LaTeX use \text{your text here}. This gives $\text{your text here}$

To use bolded text, use \textbf{your text here}. This gives $\textbf{your text here}$

Italicized text is similar: \textit{your text here}. This gives $\textit{your text here}$

~Basic Operations~

"x+y" gives $x+y$

"x-y" gives $x-y$

"x=y" gives $x=y$

"x\times y" gives $x\times y$

"x\cdot y" gives $x\cdot y$

"x\div y" gives $x\div y$

"x\pm y" gives $x\pm y$

"x\mp y" gives $x\mp y$

x^{y} gives $x^{y}$

x_{y} gives $x_{y}$

\sqrt{x} gives $\sqrt{x}$

\sqrt[y]{x} gives $\sqrt[y]{x}$

\log_{a}b gives $\log_{a}b$

\ln a gives $\ln a$ (that's a lowercase "l" in the beginning, not an uppercase "i")

Note that many of you use "*" or "." for multiplying. This shows up as $*$ and $.$ which don't look good. Use $\times$ or $\cdot$ instead.

Also, the brackets in x^{y} or x_{y} may be omitted if the index is a single character. However, if it is more than one character like $x^{10}$ , then brackets are needed or else it will show up as $x^10$ .

~Fractions~

Many people simply put a slash between the numerator and denominator to represent a fraction: $x/y$ . However, there are neater ways in LaTeX.

\frac{x}{y} is the standard way to write fractions: $\frac{x}{y}$

\dfrac{x}{y} gives a bigger clearer version. However, this takes up more vertical space: $\dfrac{x}{y}$ the "d" stands for "display text".

EXTRA

\cfrac{x}{y} is a special type of fraction formatting. This is for continued fractions, hence the "c". typing \cfrac{x}{x+\cfrac{y}{y+\cfrac{z}{2}}} gives $\cfrac{x}{x+\cfrac{y}{y+\cfrac{z}{2}}}$

~Sums, Products, Limits, and Integrals~

These four are in the same group because they format differently than other symbols.

"\sum" gives $\sum$

"\prod" gives $\prod$

"\lim" gives $\lim$

"\int" gives $\int$

We can add the other elements of each thing by using _ and ^:

\sum_{i=0}^n gives $\sum_{i=0}^n$

\prod_{i=0}^n gives $\prod_{i=0}^n$

\lim_{x\rightarrow n} gives $\lim_{x\rightarrow n}$

\int_{a}^{b} gives $\int_a^b$

However, these don't look very good. However, once putting it on display text, either using the brackets or using \displaystyle as said in the beginning of the guide, we can make them look normal.

\displaystyle\sum_{i=0}^n gives $\displaystyle\sum_{i=0}^n$

\displaystyle\prod_{i=0}^n gives $\displaystyle\prod_{i=0}^n$

\displaystyle\lim_{x\rightarrow n} gives $\displaystyle\lim_{x\rightarrow n}$

\displaystyle\int_{a}^{b} gives $\displaystyle\int_{a}^{b}$

~Modular Arithmetic~

"\equiv" gives $\equiv$

\mod{a} gives $\mod{a}$

\pmod{a} gives $\pmod{a}$

\bmod{a} is \mod{a} without the space before it: $a\bmod{b}$ versus $a\mod{b}$

"a\mid b" creates $a\mid b$ , which states that $b$ is divisible by $a$ .

~Trigonometry~

Many of you simply put "sin" and "cos" and be done with it; however, adding a backslash before those two make it look much better.

\sin gives $\sin$ (as opposed to $sin$ )

\cos gives $\cos$ (as opposed to $cos$ )

\tan gives $\tan$

\sec gives $\sec$

\csc gives $\csc$

\cot gives $\cot$

\arcsin gives $\arcsin$

\arccos gives $\arccos$

\arctan gives $\arctan$

Putting a ^{-1} after the trigonometric function designates it as the inverse. For example, \sin^{-1} gives $\sin^{-1}$ .

\sinh gives $\sinh$

\cosh gives $\cosh$

\tanh gives $\tanh$

~Combinatorics~

\binom{x}{y} gives $\binom{x}{y}$

\dbinom{x}{y} gives $\dbinom{x}{y}$

~Geometry~

x^{\circ} gives $x^{\circ}$ the degree symbol

\angle gives $\angle$

\Delta gives $\Delta$ , for example $\Delta ABC$

\triangle also does the job: $\triangle ABC$

\odot gives $\odot$ , for example $\odot O$

AB\parallel CD gives $AB\parallel CD$

AB\perp CD gives $AB\perp CD$

A\cong B gives $A\cong B$

A\sim B gives $A\sim B$

~Calculus~

We've already learned to use $\int$ . However, there is much more to calculus than integrals!

There is no command for the total derivative, so you have to use \text{d} to get around it.

For example, \dfrac{\text{d}}{\text{d}x} gives $\dfrac{\text{d}}{\text{d}x}$

Fortunately, there is a symbol for partial derivatives: \partial gives $\partial$ .

So, \dfrac{\partial}{\partial x} gives $\dfrac{\partial}{\partial x}$

Double or even triple integrals can be condensed into \iint and \iiint, respectively. This gives $\displaystyle\iint$ and $\displaystyle\iiint$ (I am using display text).

EXTRA

Line integrals can be written as \oint: $\displaystyle \oint$ .

~Parentheses~

( and ) are standard for parentheses: $(a+b)$

[ and ] are used for brackets: $[a+b]$

{ and } are used for curly brackets: $\{a+b\}$

\lfloor and \rfloor are used for the floor function: $\lfloor a+b\rfloor$

\lceil and \rceil are used for the ceiling function: $\lceil a+b\rceil$

\langle and \rangle are used for vectors: $\langle a,b\rangle$

The vertical line symbol | (not a capital "i" or a lowercase "l"!) is used for absolute value: $|a+b|$

~Fitting Parentheses~

Suppose you want to write $\left(\dfrac{a}{b}\right)^c$ . When you try, it gives $(\dfrac{a}{b})^c$ . How did I stretch the parentheses to fit?

To stretch the parentheses, use \left before the left parenthesis and \right before the right one, like this: \left( and \right). When put back into the expression, this yields $\left(\dfrac{a}{b}\right)^c$ as desired.

This isn't just for parentheses; you can use them on brackets: $\{\dfrac{a}{b}\}$ changes into $\left\{\dfrac{a}{b}\right\}$

You can also use this technique on things that use only one parenthesis/bracket/etc. However, just putting \left or \right will yield an error. This is because \left and \right come in pairs. In orer to sidestep this, you can put a period after the one that you do not need (i.e \left. or \right.). This way it will not produce an error, and it will stretch the parenthesis to size. For example, this: \left. \dfrac{x^3+2x}{3x^2}\right|_0^3 gives this: $\left. \dfrac{x^3+2x}{3x^2}\right|_a^b$

~Tables and Arrays~~

To make tables and arrays, use \ begin{array}{[modifiers]} ... \ end{array}. (A space is put before "begin" and before "end" to prevent the LaTeX from prematurely rendering. Even though there are no brackets around to make it render, it does so anyways, I don't know why.)

In the modifiers section, you put either l for left, c for center, or r for right, per column. For example, to make an array with 3 columns, all formatted to align along the right edge, you put "rrr" inside the modifier. It would look like this: \ begin{array}{rrr} ... \ end{array}.

To add a vertical line between two columns, put the vertical line symbol | between two modifiers: for example, if you wanted a horizontal line between the first two columns in the previous example, then you would put \ begin{array}{r|rr} ... \ end{array}.

For actual inputting in the array, there are two rules: put a "&" sign to notify to switch to the next column, and put a "\ \" divider (again a space is added in between to prevent it from rendering) to notify to switch to the next row. When building the table, always fill in row by row: in the first row, fill in all the corresponding columns, and then switch to the next row; then continue in this manner. For example, if I wanted to make a $3\times 3$ square with the numbers $1\rightarrow 9$ , I would put: \ begin{array}{lcr}1 & 2 & 3 \ \ 4 & 5 & 6 \ \ 7& 8 & 9 \ end{array}. This produces: $\begin{array}{lcr}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7& 8 & 9 \end{array}$ .

To insert horizontal lines between any two rows, put \hline after the divider that separates the two rows. For example, if I wanted to add horizontal lines and vertical lines in the previous example to look like a tic tac toe board, this would be my code: \ begin{array}{l|c|r}1 & 2 & 3 \ \ \hline 4 & 5 & 6 \ \ \hline 7& 8 & 9 \ end{array} and it will produce: $\begin{array}{l|c|r}1 & 2 & 3 \\ \hline 4 & 5 & 6 \\ \hline 7& 8 & 9 \end{array}$

~Other~

To negate any symbol, put \not before the symbol. For example, "\not =" gives $\not =$

Look here for a big list of symbols.

If you don't know how to do something or see something missing in this guide, please do comment below so I can add it! Together, we can make a great LaTeX guide!

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

$p$	$q$	$p \Rightarrow q$
1	1	1
1	0	1
0	1	0
0	0	1

Beginner LaTeX Guide

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