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A quick guide to LATEX , Cheat Sheet of Mathematics

Latex is a mathematical tool to write all equations

Typology: Cheat Sheet

2021/2022

Uploaded on 02/03/2022

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A quick guide to L
A
T
E
X
What is L
A
T
E
X?
L
A
T
E
X(usually pronounced “LAY teck,” sometimes “LAH
teck,” and never “LAY tex”) is a mathematics typesetting
program that is the standard for most professional
mathematics writing. It is based on the typesetting program
T
E
X created by Donald Knuth of Stanford University (his first
version appeared in 1978). Leslie Lamp ort was responsible for
creating L
A
T
E
X a more user friendly version of T
E
X. A team of
L
A
T
E
X programmers created the current version, L
A
T
E
X 2ε.
Math vs. text vs. functions
In properly typeset mathematics variables appear in italics
(e.g., f(x) = x2+ 2x3). The exception to this rule is
predefined functions (e.g., sin(x)). Thus it is important to
always treat text, variables, and functions correctly. See the
difference between xand x, -1 and 1, and sin(x) and sin(x).
There are two ways to present a mathematical expression—
inline or as an equation.
Inline mathematical expressions
Inline expressions occur in the middle of a sentence. To
produce an inline expression, place the math expression
between dollar signs ($). For example, typing
$90^{\circ}$ is the same as $\frac{\pi}{2}$ radians
yields 90is the same as π
2radians.
Equations
Equations are mathematical expressions that are given their
own line and are centered on the page. These are usually used
for important equations that deserve to be showcased on their
own line or for large equations that cannot fit inline. To
produce an inline expression, place the mathematical
expression between the symbols \[ and \]. Typing
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\] yields
x=b±b24ac
2a.
Displaystyle
To get full-sized inline mathematical expressions use
\displaystyle. Use this sparingly. Typing
I want this $\displaystyle \sum_{n=1}^{\infty}
\frac{1}{n}$, not this $\sum_{n=1}^{\infty}
\frac{1}{n}$. yields
I want this
X
n=1
1
n, not this P
n=1
1
n.
Images
You can put images (pdf, png, jpg, or gif) in your document.
They need to be in the same location as your .tex file when
you compile the document. Omit [width=.5in] if you want
the image to be full-sized.
\begin{figure}[ht]
\includegraphics[width=.5in]{imagename.jpg}
\caption{The (optional) caption goes here.}
\end{figure}
Text decorations
Your text can be italics (\textit{italics}), boldface
(\textbf{boldface}), or underlined
(\underline{underlined}).
Your math can contain boldface, R(\mathbf{R}), or
blackboard bold, R(\mathbb{R}). You may want to used these
to express the sets of real numbers (Ror R), integers (Zor Z),
rational numbers (Qor Q), and natural numbers (Nor N).
To have text appear in a math expression use \text.
(0,1]=\{x\in\mathbb{R}:x>0\text{ and }x\le 1\} yields
(0,1] = {xR:x > 0 and x1}. (Without the \text
command it treats “and” as three variables:
(0,1] = {xR:x > 0andx 1}.)
Spaces and new lines
L
A
T
E
X ignores extra spaces and new lines. For example,
This sentence will look
fine after it is compiled.
This sentence will look fine after it is compiled.
Leave one full empty line between two paragraphs. Place \\ at
the end of a line to create a new line (but not create a new
paragraph).
This
compiles
like\\
this.
This compiles
like
this.
Use \noindent to prevent a paragraph from indenting.
Comments
Use %to create a comment. Nothing on the line after the %will
be typeset. $f(x)=\sin(x)$ %this is the sine function
yields f(x) = sin(x)
Delimiters
description command output
parentheses (x) (x)
brackets [x] [x]
curly braces \{x\} {x}
To make your delimiters large enough to fit the content, use
them together with \right and \left. For example,
\left\{\sin\left(\frac{1}{n}\right)\right\}_{n}^
{\infty} produces
sin 1
n
n
.
Curly braces are non-printing characters that are used to
gather text that has more than one character. Observe the
differences between the four expressions x^2,x^{2},x^2t,
x^{2t} when typeset: x2,x2,x2t,x2t.
Lists
You can produce ordered and unordered lists.
description command output
unordered list
\begin{itemize}
\item
Thing 1
\item
Thing 2
\end{itemize}
Thing 1
Thing 2
ordered list
\begin{enumerate}
\item
Thing 1
\item
Thing 2
\end{enumerate}
1. Thing 1
2. Thing 2
Symbols (in math mode)
The basics
description command output
addition ++
subtraction -
plus or minus \pm ±
multiplication (times) \times ×
multiplication (dot) \cdot ·
division symbol \div ÷
division (slash) //
circle plus \oplus
circle times \otimes
equal ==
not equal \ne 6=
less than <<
greater than >>
less than or equal to \le
greater than or equal to \ge
approximately equal to \approx
infinity \infty
dots 1,2,3,\ldots 1,2,3,...
dots 1+2+3+\cdots 1+2+3+···
fraction \frac{a}{b} a
b
square root \sqrt{x} x
nth root \sqrt[n]{x} n
x
exponentiation a^b ab
subscript a_b ab
absolute value |x| |x|
natural log \ln(x) ln(x)
logarithms \log_{a}b logab
exponential function e^x=\exp(x) ex= exp(x)
degree \deg(f) deg(f)
pf2

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Download A quick guide to LATEX and more Cheat Sheet Mathematics in PDF only on Docsity!

A quick guide to LATEX

What is LATEX?

LATEX(usually pronounced “LAY teck,” sometimes “LAH teck,” and never “LAY tex”) is a mathematics typesetting program that is the standard for most professional mathematics writing. It is based on the typesetting program TEX created by Donald Knuth of Stanford University (his first version appeared in 1978). Leslie Lamport was responsible for creating LATEX a more user friendly version of TEX. A team of LATEX programmers created the current version, LATEX 2ε.

Math vs. text vs. functions

In properly typeset mathematics variables appear in italics (e.g., f (x) = x^2 + 2x − 3). The exception to this rule is predefined functions (e.g., sin(x)). Thus it is important to always treat text, variables, and functions correctly. See the difference between x and x, -1 and −1, and sin(x) and sin(x). There are two ways to present a mathematical expression— inline or as an equation.

Inline mathematical expressions

Inline expressions occur in the middle of a sentence. To produce an inline expression, place the math expression between dollar signs ($). For example, typing $90^{\circ}$ is the same as $\frac{\pi}{2}$ radians yields 90◦^ is the same as π 2 radians.

Equations

Equations are mathematical expressions that are given their own line and are centered on the page. These are usually used for important equations that deserve to be showcased on their own line or for large equations that cannot fit inline. To produce an inline expression, place the mathematical expression between the symbols [ and ]. Typing [x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}] yields

x = −b ±

b^2 − 4 ac 2 a

Displaystyle

To get full-sized inline mathematical expressions use \displaystyle. Use this sparingly. Typing I want this $\displaystyle \sum_{n=1}^{\infty} \frac{1}{n}$, not this $\sum_{n=1}^{\infty} \frac{1}{n}$. yields

I want this

∑^ ∞

n=

n

, not this

n= 1 n.

Images

You can put images (pdf, png, jpg, or gif) in your document. They need to be in the same location as your .tex file when you compile the document. Omit [width=.5in] if you want the image to be full-sized. \begin{figure}[ht] \includegraphics[width=.5in]{imagename.jpg} \caption{The (optional) caption goes here.} \end{figure}

Text decorations

Your text can be italics (\textit{italics}), boldface (\textbf{boldface}), or underlined (\underline{underlined}). Your math can contain boldface, R (\mathbf{R}), or blackboard bold, R (\mathbb{R}). You may want to used these to express the sets of real numbers (R or R), integers (Z or Z), rational numbers (Q or Q), and natural numbers (N or N). To have text appear in a math expression use \text. (0,1]={x\in\mathbb{R}:x>0\text{ and }x\le 1} yields (0, 1] = {x ∈ R : x > 0 and x ≤ 1 }. (Without the \text command it treats “and” as three variables: (0, 1] = {x ∈ R : x > 0 andx ≤ 1 }.)

Spaces and new lines

LATEX ignores extra spaces and new lines. For example, This sentence will look fine after it is compiled. This sentence will look fine after it is compiled. Leave one full empty line between two paragraphs. Place \ at the end of a line to create a new line (but not create a new paragraph). This compiles

like\ this. This compiles like this. Use \noindent to prevent a paragraph from indenting.

Comments

Use % to create a comment. Nothing on the line after the % will be typeset. $f(x)=\sin(x)$ %this is the sine function yields f (x) = sin(x)

Delimiters

description command output parentheses (x) (x) brackets [x] [x] curly braces {x} {x} To make your delimiters large enough to fit the content, use them together with \right and \left. For example, \left{\sin\left(\frac{1}{n}\right)\right}_{n}^ {\infty}{ produces sin

n

n

Curly braces are non-printing characters that are used to gather text that has more than one character. Observe the differences between the four expressions x^2, x^{2}, x^2t, x^{2t} when typeset: x^2 , x^2 , x^2 t, x^2 t.

Lists

You can produce ordered and unordered lists. description command output

unordered list

\begin{itemize} \item Thing 1 \item Thing 2 \end{itemize}

  • Thing 1
  • Thing 2

ordered list

\begin{enumerate} \item Thing 1 \item Thing 2 \end{enumerate}

  1. Thing 1
  2. Thing 2

Symbols (in math mode)

The basics

description command output addition + + subtraction - − plus or minus \pm ± multiplication (times) \times × multiplication (dot) \cdot · division symbol \div ÷ division (slash) / / circle plus \oplus ⊕ circle times \otimes ⊗ equal = = not equal \ne 6 = less than < < greater than > > less than or equal to \le ≤ greater than or equal to \ge ≥ approximately equal to \approx ≈ infinity \infty ∞ dots 1,2,3,\ldots 1 , 2 , 3 ,... dots 1+2+3+\cdots 1 + 2 + 3 + · · · fraction \frac{a}{b} ab square root \sqrt{x}

x nth root \sqrt[n]{x} n

x exponentiation a^b ab subscript a_b ab absolute value |x| |x| natural log \ln(x) ln(x) logarithms \log_{a}b loga b exponential function e^x=\exp(x) ex^ = exp(x) degree \deg(f) deg(f )

Functions

description command output maps to \to → composition \circ ◦ piecewise |x|=

|x| =

x x ≥ 0 −x x < 0

function \begin{cases} x & x\ge 0\ -x & x< \end{cases}

Greek and Hebrew letters

command output command output \alpha α \tau τ \beta β \theta θ \chi χ \upsilon υ \delta δ \xi ξ \epsilon  \zeta ζ \varepsilon ε \Delta ∆ \eta η \Gamma Γ \gamma γ \Lambda Λ \iota ι \Omega Ω \kappa κ \Phi Φ \lambda λ \Pi Π \mu μ \Psi Ψ \nu ν \Sigma Σ \omega ω \Theta Θ \phi φ \Upsilon Υ \varphi ϕ \Xi Ξ \pi π \aleph ℵ \psi ψ \beth i \rho ρ \daleth k \sigma σ \gimel ג

Set theory

description command output set brackets {1,2,3} { 1 , 2 , 3 } element of \in ∈ not an element of \not\in 6 ∈ subset of \subset ⊂ subset of \subseteq ⊆ not a subset of \not\subset 6 ⊂ contains \supset ⊃ contains \supseteq ⊇ union \cup ∪ intersection \cap ∩

big union \bigcup_{n=1}^{10}A_n

⋃^10

n=

An

big intersection \bigcap_{n=1}^{10}A_n

⋂^10

n=

An

empty set \emptyset ∅ power set \mathcal{P} P minimum \min min maximum \max max supremum \sup sup infimum \inf inf limit superior \limsup lim sup limit inferior \liminf lim inf closure \overline{A} A

Calculus

description command output derivative \frac{df}{dx}

df dx derivative \f’ f ′ partial derivative \frac{\partial f} {\partial x}

∂f ∂x integral \int

double integral \iint

triple integral \iiint

limits \lim_{x\to \infty} lim x→∞ summation \sum_{n=1}^{\infty}a_n

∑^ ∞

n=

an

product \prod_{n=1}^{\infty}a_n

∏^ ∞

n=

an

Logic

description command output not \sim ∼ and \land ∧ or \lor ∨ if...then \to → if and only if \leftrightarrow ↔ logical equivalence \equiv ≡ therefore \therefore ∴ there exists \exists ∃ for all \forall ∀ implies \Rightarrow ⇒ equivalent \Leftrightarrow ⇔

Linear algebra

description command output vector \vec{v} ~v vector \mathbf{v} v norm ||\vec{v}|| ||~v||

matrix

\left[ \begin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6\ 7 & 8 & 0 \end{array} \right]

determinant

\left| \begin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 0 \end{array} \right|

determinant \det(A) det(A) trace \operatorname{tr}(A) tr(A) dimension \dim(V) dim(V )

Number theory

description command output divides | | does not divide \not | 6 | div \operatorname{div} div mod \mod mod greatest common divisor \gcd gcd ceiling \lceil x \rceil dxe floor \lfloor x \rfloor bxc

Geometry and trigonometry

description command output angle \angle ABC ∠ABC degree 90^{\circ} 90 ◦ triangle \triangle ABC 4 ABC segment \overline{AB} AB sine \sin sin cosine \cos cos tangent \tan tan cotangent \cot cot secant \sec sec cosecant \csc csc inverse sine \arcsin arcsin inverse cosine \arccos arccos inverse tangent \arctan arctan

Symbols (in text mode) The followign symbols do not have to be surrounded by dollar signs. description command output dollar sign $ $ percent % % ampersand & & pound # # backslash \textbackslash
left quote marks ‘‘ “ right quote marks ’’ ” single left quote ‘ ‘ single right quote ’ ’ hyphen X-ray X-ray en-dash pp. 5--15 pp. 5– em-dash Yes---or no? Yes—or no?

Resources TUG: The TEX Users Group CTAN: The Comprehensive TEX Archive Network Handwriting-to-LATEX sites: Detexify, WebEquation The Comprehensive LATEX Symbol List The Not So Short Introduction to LATEX 2ε Software that generates LATEX code: Mathematica, Maple, GeoGebra LATEX for the Mac: MacTEX LATEX for the PC: TEXnicCenter and MiKTEX LATEX online: ShareLaTeX, Overleaf, Sage LATEX integration with Microsoft Office, Apple iWork, etc: MathType, LATEXiT Dave Richeson, Dickinson College, http://divisbyzero.com/