mathematics latex guide

7/17/2019 Mathematics Latex Guide

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LTEX and FriendsMathematics

Marc van Dongen

Mathematics

Advanced Mathematics

Acronyms & Abbreviations

About this DocumentLTEX and FriendsMathematics

http://csweb.ucc.ie/~dongen/LAF/LAF.html

M. R. C. van Dongen



http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math ModeSub- and Superscripts

Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions

Sums, Products, and Friends

Existing Functions and

OperatorsIntegration/Dierentiation

Roots

Changing the Style

Symbol Tables



About this Document

AMS -LTEX

AMS -LTEX is a useful platform for typesetting mathematics.

Supported by the American Mathematical Society ().

Provides useful extensions to LTE

X.

The distribution has two main parts:

amscls document class and theorem package.amsmath Extension package.

Makes math writing easier and improves quality.

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Provided Packages

amsmath Environments for displayed equations and more.

amstext A \text command for typesetting text in formula.

amsopn \DeclareMathOperator for “operator names”.

The operators are typeset like \sin and \lim.

amsthm Extensions of \newtheorem command.

Also provides proof environment.

amscd Environment for simple commutative diagrams.

amsfonts Extra fonts including blackboard boldface (A, B, …).

amssymb Lots of extra symbols.

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

LTEX’s Typesetting Modes

text Typeset as basic text.

ordinary math Typeset as math in the running text.display math Typeset as math in display.

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Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Text → $ → Ordinary Math → $ → Text

LTE

X Input

The Binomial Theorem states

$\sumˆn_i=

\binomni aˆi bˆn-i = (a + b)ˆn$.

Substituting $$ for $a$

and $$ for $b$ gives us$\sumˆn_i=

\binomni = ˆn$.

LTEX Output

The Binomial Theorem statesn

i =0 (ni )ai bn−i = (a + b)n.

Substituting 1 for a and 1 for b gives usn

i =0 (ni ) = 2n.

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Superscripts

The superscript operator (ˆ) creates a superscript.

$⟨expr⟩ˆ⟨sup⟩$ makes ⟨sup⟩ a superscript of ⟨expr⟩.

So $xˆ + x + $ gives you x 2 + 2x + 1.Grouping works as usual.

So to typeset e a+b you need braces: $eˆa+b$.

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Subscripts

The subscript operator (_) creates a subscript.

$⟨expr⟩_⟨sub⟩$ makes ⟨sub⟩ a subscript of ⟨expr⟩.

So to get f n+2 = f n+1 + f n you need

$f_n + = f_n + + f_n$.

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Mixing Subscripts and Superscripts

Subscripts and superscripts may be nested and combined.

$⟨expr⟩_⟨sub⟩ˆ⟨sup⟩$ is the same as $⟨expr⟩ˆ⟨sup⟩_⟨sub⟩$.Both give you ⟨expr⟩

⟨sup⟩⟨sub⟩

.

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Avoid Su*scripts

simplicity Keep the number of subscripts and superscripts low:

Simpler notation;

Greater transparency.readability The resulting expression is easier to parse.

spacing Fewer inconsistencies in interline spacing.

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions


Existing Functions andOperators

Integration/Dierentiation

Roots

Changing the Style

Symbol Tables



About this Document

Lower Case Greek Letters: Easy as π

regular \alpha (α), \beta (β ), \gamma (γ ), ….

additional italic \varepsilon (ε), \vartheta (ϑ), \varrho (), ….old number \digamma ().

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Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Lowercase Greek Letters

Standard commands

α \alpha ι \iota τ \tauβ \beta κ \kappa υ \upsilonγ \gamma λ \lambda φ \phiδ \delta µ \mu χ \chi \epsilon ν \nu ρ \rho

ζ \zeta ξ \xi ψ \psiη \eta ø \o σ \sigmaθ \theta π \pi ω \omega

A MS -LTE X provided commands

ε \varepsilon κ \varkappa \varrhoϕ \varphi ϑ \vartheta \varpiς \varsigma

\digamma

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Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Uppercase Greek Letters: Easy as Π

regular \Gamma (Γ), \Delta (∆), \Theta (Θ), ….

italic \varGamma (Γ ), \varDelta (∆), \varTheta (Θ), ….

d d

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Uppercase Greek Letters

Standard commands

Γ \Gamma Ξ \Xi Φ \Phi∆ \Delta Π \Pi Ψ \PsiΘ \Theta Σ \Sigma Ω \Omega

Λ \Lambda Υ \Upsilon

A MS -LTE X provided commands

Γ \varGamma Ξ \varXi Φ \varPhi∆ \varDelta Π \varPi Ψ \varPsiΘ \varTheta Σ \varSigma Ω \varOmega

Λ \varLambda Υ \varUpsilon

LT X d F i d

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode

Sub- and Superscripts

Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Display Math

The amsmath package provides display math environments.

Provides starred and unstarred versions.

Some environments allow alignment in multi-line expressions.The alignment positions are specified with & .Line breaks are specified with \\.

LTEX and Friends

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Starred versus Unstarred Environments

Unstarred versions of the environment produce labels:

Starred versions of the environment do not produce labels:

equation*, align*, ….

Avoid the unstarred version unless text refers to the label.

LTEX and Friends

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

The equation Environment

LTEX Input

The following is the Binomial Theorem:\beginequation

\labeleq:Binomial

\sumˆn_i= \binomniaˆibˆn-i = (a+b)ˆn\,.

\endequation

Substituting $$ for˜$a$ and $$ for˜$b$

in˜(\refeq:Binomial) …

LTEX Output

The following is the Binomial Theorem:

ni =0

n

i

ai bn−i = (a + b)n . (1)

Substituting 1 for a and 1 for b in (1) gives us ni =0 (ni ) = 2n.

LTEX and Friends

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Splitting a Single Equation

LTEX Input

\beginequation*\beginsplit

a & = b + c + d \\

& \qquad + f + g + h \\& > \,.

\endsplit\endequation*

LTEX Output

a = b + c + d

+ f + g + h

> 0 .

LTEX and Friends

h

http://find/




Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

The align Environment

Use align for equation groups with alignment.

Each row is numbered separately.To turn o numbering of current equation: use \nonumber.

LTEX and Friends

Th E i (O )

http://find/



EMathematics

Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

The align Environment (Output)

L

TEX Output

F (z ) =∞

n=0

f nz n (2)

= z +∞n=2

( f n−1 + f n−2)z n (3)

= z + F (z )/z + F (z )/z 2 (4)

= z /(1−

z −

z 2) .

Here the last equation is obtained from (2), (3), and (4) by transitivityof equality and by solving for F (z ).

LTEX and Friends

Th li E i t (I t)

http://find/



Mathematics

Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

The align Environment (Input)

LTEX Input

\beginalign

\labeleq:one

F ( z ) & = \sumˆ\infty_n= f_n zˆn \\

\labeleq:two

& = z + \sumˆ\infty_n=(f_n-+f_n-) zˆn \\\labeleq:three

& = z + F ( z ) / z + F ( z ) / zˆ \\

\nonumber

& = z / ( - z - zˆ) \,.

\endalign

Here the last equation is obtained from˜(\refeq:one),(\refeq:two), and˜(\refeq:three) by transitivity

of equality and by solving for˜$F ( z )$.

LTEX and Friends

Th li E i t M lti l C l

http://find/



Mathematics

Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

The align Environment: Multiple Columns

LTEX Input

\beginalign

a_ & = b_\,, & b_ & = c_\,, & c_ & = d_\,,\\

a_ & = b_\,, & b_ & = c_\,, & c_ & = d_\,,\\

a_ & = b_\,, & b_ & = c_\,, & c_ & = d_\,.

\endalign

LTEX Output

a0 = b0 , b0 = c 0 , c 0 = d 0 , (5)

a1 = b1 , b1 = c 1 , c 1 = d 1 , (6)

a2 = b2 , b2 = c 2 , c 2 = d 2 . (7)

LTEX and FriendsM h i

http://find/



Mathematics

Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

LTEX Usage

\beginalign*x_ & = \,, \\

x_ & = \,, \\\shortintertextand

x_ & = \,.\endalign*

LTEX Output

x 0 = 0 ,

x 1 = 1 ,

and

x 2 = 2 .

LTEX and FriendsM th tiLow level Alignment Building Blocks

http://find/



Mathematics

Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Low-level Alignment Building Blocks

LTEX Input

\beginequation*I = \left[

\beginaligned

&& && \\

&& && \\

&& &&

\endaligned

\right]\,.

\endequation*

LTEX Output

I =

1 0 0

0 1 0

0 0 1

.

LTEX and FriendsMathematicsThe eqnarray Environment

http://find/



Mathematics

Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

The eqnarray Environment

LTEX also has an eqnarray environment.

For multiple equations with horizontal alignment.In short: Don’t use it!

LTEX and FriendsMathematicsText in Formulae

http://find/



Mathematics

Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Text in Formulae

Sometimes you need plain text in mathematical formulae.

AMS -LTEX provides special-purpose \text command.

LTEX Input

\[ \textfinal grade =

\text\textscca + \times \textexam\,. \]

LTEX Output

final grade = + 5× exam .

LTEX and FriendsMathematicsDelimiters

http://find/



Mathematics

Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Delimiters

Every now and then LTEX needs a bit of help.

For example, $f( ˆˆˆ___ )$ gives

f (2222

222) .

Use \left and \right to scale the size of the parentheses.

Then $f\left(ˆˆˆ___\right)$ gives

f

2222

222 .

LTEX and FriendsMathematicsYer \left Yer \right

http://find/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Yer \left, Yer \right, …

L

TEX Output

n! =

1 if 0 ≤ n ≤ 1 ,

n × (n − 1)! otherwise .

LTEX and FriendsMathematicsYer \left Yer \right

http://find/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Yer \left, Yer \right, …

L

TEX Output

n! =

1 if 0 ≤ n ≤ 1 ,

n × (n − 1)! otherwise .

LTEX Input

\[ n! =

\left\

\beginaligned

& && \textif $ \leq n \leq $\,,

\\ & n \times (n-)! && \textotherwise\,.

\endaligned\right.

\]

LTEX and FriendsMathematicsNested Delimiters

http://find/

http://goback/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Nested Delimiters

Common to use square brackets outside parentheses.

This should work especially well in inline math mode.

LTEX Input

Simplifying

$[ ( a + b )ˆ- ( a - b )ˆ ]ˆ$

gives us $ aˆ bˆ$.

LTEX OutputSimplifying [(a + b)2 − (a− b)2]2 gives us 16a2b2.

LTEX and FriendsMathematicsDelimiters on Dierent Lines

http://find/

http://goback/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Delimiters on Dierent LinesHow Not To …

Don’t Try This at Home

\beginalign*

f & = g\left( ˆˆ

+ …\right.

\\& \qquad \left. + \right)\,.

\endalign*

LTEX Output

f = g

333+ …

+3) .

LTEX and FriendsMathematicsDelimiters on Dierent Lines

http://find/

http://goback/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Delimiters on Dierent LinesThe \vphantom Trick

LTEX Input

\beginalign*

f & = g\left( ˆˆ

+ …\right.

\\& \qquad \left.

+ \vphantomˆˆ

\right)\,.\endalign*

LTE

X Output

f = g

333+ …

+3 .

LTEX and FriendsMathematicsOverloading

http://find/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Overloading

Some symbols are used for dierent purposes: overloading.

For example, | is used as left and right delimiter in |·|.

AMS -LTEX provides new commands for delimiters.Delimiters scale with \left and \right.

LTEX and FriendsMathematicsTypesetting ‘Non-delimiting’ Bars

http://find/

http://goback/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

yp g g

LTEX Input

The even digits are

given by$\\, n \in \mathbbN

\,\vert\, \leq n \leq \,\$.

L

TEX OutputThe even digits are given by 2n ∈ N | 0 ≤ n ≤ 4 .

LTEX and FriendsMathematicsMore Variable-sized Bars

http://find/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

$\left\lvert x \right\rvert$

Absolute-values and similar: |x |.

$\left\lVert x \right\rVert$

Norms: x .

LTEX and FriendsMathematicsEvaluation

http://find/

http://goback/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

LTEX Input

\[\left. f ( x )\right \rvert_x= = \,.

\]

LTEX Output

f (x )x =0

= 0 .


M DKnow thy TEX

http://find/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

y E


Say no to $<,,>$!

LTEX Output

Say no to < 1, 2, 3 >!


M DKnow thy TEX

http://find/

http://goback/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

y E

LTEX Input

Let $F ( z )$ be the ordinary generating function of$\left\langle t_,t_, \ldots \right\rangle$.

Then $z F ( z )$ is the ordinary

generating function of$\left\langle ,t_,t_, \ldots \right\rangle$.

LTE

X Output

Let F (z ) be the ordinary generating function of t 0, t 1, . . .. Then zF (z )is the ordinary generating function of 0, t 0, t 1, . . ..


Marc van DongenFloors and Ceilings

http://find/

http://goback/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

LTEX Input

Let $x$ be any real number.By definition$i \leq \left\lfloor x \right\rfloor

\leq x\leq \left\lceil x \right\rceil

\leq I$for all integers $i$ and $I$ such that$i \leq x \leq I$.

LTEX Output

Let x be any real number. By definition i ≤ x ≤ x ≤ x ≤ I for allintegers i and I such that i ≤ x ≤ I.


Marc van DongenVariable-sized Delimiter Commands

http://find/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Standard \ \ \langle \lceil \lfloor \rangle \rceil \rfloor ↑ \uparrow⇓ \Downarrow \updownarrow ↓ \downarrow

⇑ \Uparrow \Updownarrow ( ([ [ | | ) )] ] \| / /\ \backslash

amsmath

| \lvert | \rvert \lVert \rVert


Marc van DongenFractions

http://find/

http://goback/



Marc van Dongen

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Ordinary fractions are typeset using the command \frac.

To get ⟨num⟩⟨den⟩ you use \frac⟨num⟩⟨den⟩.


Marc van DongenUse Fractions with Discretion

http://find/



g

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Fractions in ordinary math mode may aect the interlinespacing.

Use n/d if n and d are “simple.”If d = 0, consider using d × f = n instead of f = n

d .


Marc van DongenContinued Fractions: amsmath

http://find/



g

Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Continued fractions are typeset with the command \cfrac.

Has optional argument (l or r) for placement of numerator.

LTEX Input

\[ \sqrt - = \cfrac +

\cfrac +\dotsb\,. \]

LTE

X Output

√ 2− 1 =

1

2 + 1

2 + · · ·.


Marc van DongenTypesetting Delimited Sums

http://find/

http://goback/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions



Integration/DierentiationRoots

Changing the Style

Symbol Tables



About this Document

LTEX Input

According to folklore Gauss proved that

\[ \sumˆn_i= i=n(n+)/\,. \]

LTEX Output

According to folklore Gauss proved that

n

i =0

i = n(n + 1)/2 .


Marc van DongenDelimited SumsN i U d L I d Pl

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

Notice Upper and Lower Index Placement

LTEX Input

According to folklore Gauss proved that $\sumˆn_i= i=n(n+)/$.

LTEX OutputAccording to folklore Gauss proved that

ni =0 i = n(n + 1)/2.

LTEX Input

According to folklore Gauss proved that \[\sumˆn_i= i=n(n+)/\,.\]

LTEX OutputAccording to folklore Gauss proved that

ni =0

i = n(n + 1)/2 .


Marc van DongenOverriding the Style for Lower and Upper Limits

http://find/

http://goback/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

LTEX Input

\[ \textstyle\sumˆ\infty_n=

ˆ-n = \,. \]

LTEX Output

∞n=0 2−n = 2 .


Marc van DongenOther Variable-sized Operators

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

Standard \sum

´ \int

\bigcap

\prod¸

\oint

\bigcup

\bigoplus

\bigsqcup

\bigwedge

\bigotimes \coprod \bigvee \bigodot

\biguplus

AMS -LTEX

˜ \iint ˝ \iiint ˇ \iiiint´ · ·· ´ \idotsint


Marc van DongenMulti-Line Limits with the \substack Command

http://find/

http://goback/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode

Sub- and SuperscriptsGreek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

LTEX Input

\[ \sum_\substack\text$i$ odd

\\ \leq i\leq n\binomni

= ˆn -\sum_\substack\text$i$ even

\\\leq i\leq n\binomni\,. \]

LTEX Output

i odd

0≤i ≤n

n

i

= 2n −

i even

0≤i ≤n

n

i

.


Marc van DongenComplex Limits with the subarray Environment

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

LTEX Input

\[ \sum_\beginsubarrayl

i \text odd\\

\leq i \leq n

\endsubarray

\binomni

= ˆn -

\sum_\beginsubarrayc

i \text even\\ \leq i \leq n

\endsubarray\,.

\binomni \]

LTEX Output i odd0≤i ≤n

n

i

= 2

n −i even

0≤i ≤n

n

i

.


Marc van DongenComplex Limits with the subarray Environment

http://find/

http://goback/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

LTEX Input

\[ \sum_\beginsubarrayl

i \text odd\\

\leq i \leq n

\endsubarray

\binomni

= ˆn -

\sum_\beginsubarrayc

i \text even\\ \leq i \leq n

\endsubarray\,.

\binomni \]

LTEX Output i odd0≤i ≤n

n

i

= 2

n −i even

0≤i ≤n

n

i

.


Marc van DongenLog-like Functions

http://find/

http://goback/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

arccos \arccos dim \dim log \log

arcsin \arcsin exp \exp max \maxarctan \arctan gcd \gcd min \minarg \arg hom \hom Pr \Prcos \cos inf \inf sec \sec

cosh \cosh ker \ker sin \sincot \cot lg \lg sinh \sinhcoth \coth lim \lim sup \supcsc \csc liminf \liminf tan \tandeg \deg limsup \limsup tanh \tanh

det \det ln \ln


Marc van DongenSubscripts, Superscripts, and Limit Arguments

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

LTEX Input

\[ \lim_x \to

\fracxˆ

x = \,. \]

LTEX Output

limx →0

x 2

x = 0 .


Marc van DongenMore Overloaded Symbols: mod

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

Command Expression Result

\bmod $\gcd( , ) = \gcd( , \bmod )$ gcd(5, 3) = gcd(3, 5 mod 3)\mod $ \equiv \mod $ 2 ≡ 5 mod 3\pmod $ \equiv \pmod $ 2 ≡ 5 (mod 3)\pod $ \equiv \pod $ 2 ≡ 5 (3)


Marc van DongenIntegration

http://find/

http://goback/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

LTEX Input

\[ \intˆb_a xˆ\,d x

= \left. xˆ \right\rvertˆb_a= bˆ - aˆ\,. \]

LTEX Output

ˆ b

a3x 2 dx = x 3|ba = b3 − a3 .


Marc van DongenMultiple Integral Signs

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Changing the Style

Symbol Tables



About this Document

amsmath

´ \int

˜ \iint˝

\iiintˇ

\iiiint´ · · · ´ \idotsint

esint

´ \int

˜ \iint˝

\iiintopˇ

\iiiintop› \sqint

” \sqiint

\ointctrclockwise ı

\ointclockwise# \landupint

% \landdownint

ffl \fint ¯ \dotsintop¸ \ointop

‚ \oiintop fl

\varointctrclockwiseff

\varointclockwise! \varoiint


Marc van DongenDierentiation

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

Dierentiations are typeset using \frac.

You get dudx with \fracd ud x.

You get d 2udx 2 with \fracdˆ ud xˆ.


Marc van DongenDierentiation

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

L

TEX Input

Let $z = xˆ + x y$, then\[ \frac\partial z

\partial x= x + y\,. \]

LTEX Output

Let z = x 2 + xy, then∂ z ∂ x

= 2x + y .


Marc van DongenRoots

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

LTEX Input

… $\sqrt \approx .$.

LTEX Output

…√

2 ≈ 1.414213562.


Marc van DongenA Root is a RootWould 3

√ by any Other Name Smell as Sweet?

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

LTEX Input

… $\sqrt[] = $.

LTEX Output

… 3√

27 = 3.


Marc van Dongen

M h i

Roots: \leftroot and \uproot

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

L

TEX Input

We all agree that

$\sqrt[\beta]k$is equal to

$\sqrt[\leftroot-\uproot\beta]k$.But why are they different in type?

LTEX Output

We all agree that β√ k is equal to β√ k . But why are they dierent intype?


Marc van Dongen

M th ti

Changing the Type Style

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

$\mathititalic + abcˆ$italic + abc 2.

$\mathrmroman + abcˆ$roman + abc2.

$\mathbfbold + abcˆ$

bold

+ abc2

.$\mathsfsans serif + abcˆ$sansserif + abc2.

$\mathttteletype + abcˆ$teletype + abc.

$\mathcalCALLIGRAPHIC$CALLIGRAPHIC .


Marc van Dongen

Mathematics

Operator Symbols

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

\amalg \diamond \sqcap∗ \ast ÷ \div \sqcup \bigcirc \lhd \star \bigtriangledown∓ \mp × \times

\bigtriangleup \odot \triangleleft

• \bullet

\ominus \triangleright

∩ \cap ⊕ \oplus \unlhd· \cdot \oslash \unrhd \circ ⊗ \otimes \uplus ∩

\cup ± \pm ∨ \vee† \dagger \rhd ∧ \wedge

‡ \ddagger \ \setminus \wr


Marc van Dongen

Mathematics

Relation Symbols

http://find/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

< < = =

≤ \leq

> > \ll \smile≈ \approx | \mid \sqsubseteq \asymp |= \models \sqsubset \bowtie = \neq \sqsupseteq∼= \cong \ni \sqsupset

\dashv /

∈ \notin

⊆ \subseteq

.= \doteq \parallel ⊂ \subset≡ \equiv ⊥ \perp \succeq \frown \preceq \succ≥ \geq ≺ \prec ⊇ \supseteq \gg ∝ \propto ⊃ \supset

∈ \in

\simeq

\vdash

\Join∼ \sim


Marc van Dongen

Mathematics

Additional Relation Symbols

http://find/

http://goback/



Mathematics

AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

\approxeq \eqcirc \succapprox \backepsilon \fallingdotseq \succcurlyeq \backsim \multimap \succsim \backsimeq \pitchfork ∴ \therefore∵ \because \precapprox ≈ \thickapprox \between \preccurlyeq ∼ \thicksim

\Bumpeq \precsim ∝ \varpropto \bumpeq \risingdotseq \Vdash \circeq \shortmid \vDash \curlyeqprec \shortparallel \Vvdash \curlyeqsucc \smallfrown \doteqdot

\smallsmile


Marc van Dongen

Mathematics

Fixed-size Arrows

http://find/

http://goback/



AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

↓ \downarrow ⇓ \Downarrow

↑ \uparrow

⇑ \Uparrow

\updownarrow \Updownarrow← \leftarrow ⇐ \Leftarrow→ \rightarrow ⇒ \Rightarrow←− \longleftarrow ⇐= \Longleftarrow−→ \longrightarrow =⇒ \Longrightarrow

↔ \leftrightarrow ⇔ \Leftrightarrow←→ \longleftrightarrow ⇐⇒ \Longleftrightarrow→ \mapsto ← \hookleftarrow−→ \longmapsto → \hookrightarrow \leftharpoonup \nearrow \leftharpoondown

\searrow

\rightharpoonup \swarrow \rightharpoondown \nwarrow \rightleftharpoons


Marc van Dongen

Mathematics

Extensible Arrows: amsmath

http://find/



AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

e ←− \xleftarrowe

e ←−

o\xleftarrow[o]e

e −→ \xrightarrowe

e −→

o\xrightarrow[o]e

e ←− \underleftarrowe

e −→ \underrightarrowe

←→e \overleftrightarrowe e ←→

\underleftrightarrowe


Marc van Dongen

Mathematics

Extensible Arrows: mathtools (No Option)

http://find/



AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

e −− \xleftrightharpoonse

e −− \xrightleftharpoonse

e − \xleftharpoondowne

e − \xrightharpoondowne

e − \xleftharpoonupe

e − \xrightharpoonupe

e ←→ \xleftrightarrowe

e ⇐⇒ \xLeftrightarrowe

e ←− \xhookleftarrowe e −→ \xhookrightarrowee ⇐= \xLeftarrowe

e =⇒ \xRightarrowe

e −→ \xmapstoe


Marc van Dongen

Mathematics

Extensible Arrows: mathtools (With Option)

http://find/

http://goback/



AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

e −−

o\xleftrightharpoons[o]e

e −−

o\xrightleftharpoons[o]e

e −

o\xleftharpoondown[o]e

e −

o\xrightharpoondown[o]e

e −

o\xleftharpoonup[o]e

e −

o\xrightharpoonup[o]e

e ←→

o

\xleftrightarrow[o]e e

⇐⇒o

\xLeftrightarrow[o]e

e ←−

o\xhookleftarrow[o]e

e −→

o\xhookrightarrow[o]e

e ⇐=

o\xLeftarrow[o]e

e =⇒

o\xRightarrow[o]e

e −→

o\xmapsto[o]e


Marc van Dongen

Mathematics

Miscellaneous Symbols

http://find/

http://goback/



AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

ℵ \aleph \flat ¬ \neg∠ \angle ∀ \forall \Re\ \backslash ¯ h \hbar

√ \surd

⊥ \bot ♥ \heartsuit \top \Box \Im \triangle

♣ \clubsuit ı

\imath ∂ \partial♦ \Diamond ∞ \infty \prime♦ \diamondsuit \jmath \sharp \ell \mho ♠ \spadesuit∅ \emptyset ∇ \nabla ℘ \wp∃ \exists \natural \|


Marc van Dongen

Mathematics

Dotless ı and

http://find/



AMS-LTEX

LTEX’s Math Modes

Ordinary Math Mode


Greek Letters

Display Math Mode

Text in Formulae

Delimiters

Fractions




Roots

Changing the Style

Symbol Tables



About this Document

LTEX Input

Some people write$\hati$ and $\hatj$but $\hat\imath$ and

$\hat\jmath$ is better.

LTEX Output

Some people write i and j but ı andˆ is better.


Marc van Dongen

Mathematics

Functions and Operators

http://find/




Declaring New Operators

Managing Content

Arrays and MatricesAccents and Decorations

Braces

Case-based Definitions

Function Definitions

Theorems

Mathematical Punctuation

Spacing and Linebreaks


About this Document

The amsmath package lets you define your own operators.

Ensures proper typesetting in uniform and consistent style.

Gives full control over positioning of sub- and superscripts.


Marc van Dongen

Mathematics

\DeclareMathOperator

http://find/





Managing Content


Braces



Theorems




About this Document

\DeclareMathOperator⟨command⟩⟨sym⟩

Defines ⟨command⟩ for symbol ⟨sym⟩.

⟨sym⟩ is typeset with proper spacing and uniform style.

L

TEX and FriendsMathematics

Marc van Dongen

Mathematics

Example

LTEX Input

http://find/





Managing Content


Braces



Theorems




About this Document

LTEX Input

\documentclassarticle\usepackageamsmath

\DeclareMathOperator\opop\begindocument

… Note that$ \mathrmop = $

does not look pretty.However, $ \op = $looks good.

\enddocument

LTEX Output

… Note that 1op2 = 3 does not look pretty. However, 1 op 2 = 3looks good.

L


Marc van Dongen

Mathematics

Declaring Your own Operators (Continued)Operators with Limit Positions

http://find/





Managing Content


Braces



Theorems




About this Document

LTEX Input

\DeclareMathOperator*\LimLim

LTEX Input

$\Lim_x \to

\fracxˆx = $.…

LTEX Output

… Limx →0 x 2

x = 0. …

L


Marc van Dongen

Mathematics

COntent Oriented LTEX: the cool Package

http://find/





Managing Content


Braces



Theorems




About this Document

Provides commands for consistently typesetting symbols.

Provides easy commands for typesetting complex matrices.

Provides commands for consistent typesetting expressions.

Inverse trigonometric functions arcsin x versus sin

−1

x .Derivatives d

dx f versus df dx

.Printing of certain functions and polynomialsIntegrals

´ f dx , versus

´ f dx , versus,

´ dx f , ….

L


Marc van Dongen

Mathematics

Ad d M th ti

Arrays and Matrices: array

LTEX Input

http://find/

http://goback/





Managing Content


Braces



Theorems




About this Document

E p

\[ \left(

\beginarrayc

\left\lvert

\beginarraylrc

x & y & z

\\ a & b & c

\endarray

\right\rvert

\\ \alpha

\\ \beta

\endarray

\right) \]

L

TEX Output x y z

2a 3b 4c

αβ

L


Marc van Dongen

Mathematics

Ad anced Mathematics

Matrices

http://find/

http://goback/





Managing Content


Braces



Theorems



Acronyms &

Abbreviations

About this Document

The amsmath package provides six environments for matrices.

All commands are for display math mode.

Not possible to specify horizontal alignment.

Ten columns by default: alignment to the centre.

pmatrix Parentheses as delimiters: (

1 2 3).bmatrix Square brackets as delimiters: [1 2 3].

Bmatrix Braces as delimiters:

1 2 3

.vmatrix Vertical bars as delimiters: |1 2 3|.Vmatrix Double vertical bars as delimiters: 1 2 3.

matrix No delimiters: 1 2 3.

L


Marc van Dongen

Mathematics


Small Matrices

http://find/

http://goback/





Managing Content


Braces



Theorems



Acronyms &

Abbreviations

About this Document

AMS -LTEX also provides a smallmatrix environment.

Delimiters should be typeset with \bigl and \bigr.

$\bigl[\beginsmallmatrix …\endsmallmatrix

\bigr]$.

L


Marc van Dongen

Mathematics


Small Matrices

http://find/

http://goback/





Managing Content


Braces



Theorems



Acronyms &

Abbreviations

About this Document

LTEX Input

… The linear transformation

$\langle\,x,y\,\rangle

\mapsto

\langle\, x + y , y\,\rangle$

is written as follows:

$\bigl[\beginsmallmatrix

& \\ &\endsmallmatrix\bigr]

\bigl[\beginsmallmatrix

x \\ y

\endsmallmatrix\bigr]$.

LTEX Output… The linear transformation x , y → 2x + y, y is written as follows:

2 10 1

x y

.

L


Marc van Dongen

Mathematics


Accents and Decorations

http://find/





Managing Content


Braces



Theorems



Acronyms &

Abbreviations

About this Document

Fixed-size Decorations

x \dotx x \acutex

x \ddotx x \gravex...x \dddotx x \hatx

....x \ddddotx x \tildex

x \mathringx x \barx

x \checkx x \vecx

x \brevex

Extensible Decorations

←−e \overleftarrowe e \overlinee−→e \overrightarrowe e \widetildee←→e \overleftrightarrowe e \widehate

e ←−

\underleftarrowe e \underbare

e ←→

\underleftrightarrowe e \underlinee

e −→

\underrightarrowe

LTE

X and FriendsMathematics

Marc van Dongen

Mathematics


Braces

http://find/




Managing Content


Braces



Theorems



Acronyms &

Abbreviations

About this Document

o

u \overbraceuˆo

u \overbraceu

o u

\underbraceo_u o \underbraceo

LTE


Marc van Dongen

Mathematics


Braces (Continued)

http://find/




Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

LTEX Input

\[ xˆk =

\underbrace

\times x

\times x \times

\dotsb \times x

_\text$k$˜times

$\times x$ \,. \]

LTEX Output

x k = 1 × x × x × · · · × x k times ×x

.

LTE


Marc van Dongen

Mathematics


Case-based Definitions: Cases

http://find/




Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

LTEX Input

\[ n! = \begincases & \textif $n = $\,; \\

(n-) ! \times n & \textif $n > $\,.\endcases \]

LTEX Output

n! = 1 if n = 0 ;

(n− 1)!× n if n > 0 .

LTE


Marc van Dongen

Mathematics


Case-based Definitions: Iversonians

http://find/




Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

LTEX Input

… We define$n ! = [\,n = \,] +

(n-) ! \times n

\times [\,n > \,]$. …

LTEX Output

… We define n! = [ n = 0 ] + (n− 1)!× n× [ n > 0 ]. …

LTE


Marc van Dongen

Mathematics



LT X I

http://find/




Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

LTEX Input

The successor function,$s \colon \mathbbN

\to \mathbbN$,is defined as follows:

\[ s ( n ) \mapsto n+ \,. \]

LTEX Output

The successor function, s : N→N, is defined as follows:

s(n) → n + 1 .

LTE


Marc van Dongen

Mathematics


Theorems

http://find/




Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

Writing theorems, lemmas, and friends is easy with amsthm.

Package ensures consistent numbering and appearance.

A proof environment;

Styles for theorem-like environments;Commands for defining new theorem-like styles; andCommands for defining new theorem-like environments.

LTE


Marc van Dongen

Mathematics


Theorems: Ingredients

http://find/




Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

LTE

X Output

Theorem 2.1.3 (Fermat’s Last Theorem). Let n be any integer greater than 2, then the equation an + bn = c n has no solutions in positive integersa, b, and c.

heading Describes the rôle of the environment.

Usually, Theorem, Lemma, Definition, ….number Numbers the environment (optional).

body The meat.

name Names it (optional).

Captures essence of body.Used to refer to environment by name.


Marc van Dongen

Mathematics


D l i N O t


http://find/




Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

LTE

X Output




body The meat.



LTEX and Friends

Mathematics

Marc van Dongen

Mathematics




http://find/




Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

LTE

X Output




body The meat.



LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



Existing Theorem Styles (Typesetting)

plain Usually associated with: Theorem, Lemma, Corollary,Proposition Conjecture Criterion and Algorithm

http://find/

http://goback/



g p

Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

Proposition, Conjecture, Criterion, and Algorithm.

LTEX OutputTheorem 1.1 (Fermat’s Last Theorem). Let n be any integer greater than 2, then the equation an + bn = c n has no solutions in positive integers a, b, and c.

definition Usually associated with: Definition, Condition, Problem,and Example.

LTEX OutputDefinition 1.2 (Ceiling). The ceiling of real number, r , is the smallest integer, i ,such that r ≤ i .

remark Usually associated with: Remark, Note, Notation, Claim,Summary, Acknowledgement, Case, and Conclusion.

LTEX OutputTip 1.3 (Tip). Don’t do this at home.

LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



Existing Theorem Styles (Numbering)Numbering Depends on Style

http://find/

http://goback/



Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

Numbering may or may not depend on the sectional unit.

independent numbering Theorem 1, Theorem 2, ….dependent numbering Theorem 1.1, Theorem 1.2, ….

Dierent environments may or may not share numbersequences.

with sharing Theorem 1, Lemma 2, Theorem 3, and so on,but not Theorem 2.

without sharing Theorem 1, Lemma 1, Theorem 2, and so on.

LTEX and Friends

Mathematics

Marc van Dongen

Mathematics




http://find/



Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document






LTEX and Friends

Mathematics

Marc van Dongen

Mathematics




http://find/

http://goback/



Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document






LTEX and Friends

Mathematics

Marc van Dongen

Mathematics




http://find/



Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document






LTEX and Friends

Mathematics

Marc van Dongen

Mathematics




http://find/

http://goback/



Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document






LTEX and Friends

Mathematics

Marc van Dongen

Mathematics




http://find/



Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document






LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



M i C t t

Defining New Environments

http://find/

http://goback/



Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

Defining new theorem-like environment styles is done in twostages.

M1 Set the current style;

M2 Define the environments.New environments are typeset in the current style.

LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



Managing Content

Defining the Current Style

http://find/

http://goback/



Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

Defining the current style is done with \theoremstyle.

Command takes the label of the style as its argument.

Initially, the current style is plain.

LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



Managing Content

Defining the Next Environment

http://find/

http://goback/



Managing Content

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

The next environment is defined with \newtheorem.

Environments are typeset according to current style.

Numbering depends on \newtheorem.

LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



Managing Content

Defining Environments Without Option

http://find/

http://goback/



Ma ag g Co te t

Arrays and Matrices


Braces



Theorems



Acronyms &

Abbreviations

About this Document

LTEX Usage

\newtheorem⟨env⟩⟨heading⟩

Defines environment ⟨env⟩ with heading ⟨heading⟩.

Environment is started with new numbering sequence.

LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



Managing Content

Defining Environments With OptionOption as Second Argument

http://find/



g g

Arrays and Matrices


Braces



Theorems



Acronyms &

AbbreviationsAbout this Document

LTEX Usage

\newtheorem⟨env⟩[⟨old⟩]⟨heading⟩

Defines new environment ⟨env⟩ with heading ⟨heading⟩.

New environment shares numbering with ⟨old⟩.

LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



Managing Content

Defining Environments With OptionOption as Last Argument

http://find/



Arrays and Matrices


Braces



Theorems



Acronyms &


LTEX Usage

\newtheorem⟨env⟩⟨heading⟩[⟨unit⟩]

Defines environment ⟨env⟩ with heading ⟨heading⟩.

Here ⟨unit⟩ is the name of a sectional unit.

Starts new numbering sequence that depends on ⟨unit⟩.

LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



Managing Content

Example

LTEX Usage

http://find/

http://goback/



Arrays and Matrices


Braces



Theorems



Acronyms &


\usepackageamsmath\usepackageamsthm

% Current environment style is plain.%% Define environment thm for theorems.\newtheoremthmTheorem

%% Define environment lemma for lemmas.%% Share numbering with thm environment.\newtheoremlemma[thm]Lemma

% Set environment style to definition.

\theoremstyledefinition

%% Define environment def for definitions.%% Share numbering with thm environment.\newtheoremdef[thm]Definition

LTEX and Friends

Mathematics

Marc van Dongen

Mathematics



Managing Content

Defining New Styles

http://find/



Arrays and Matrices


Braces



Theorems




About this Document

\newtheoremstyle defines a new theorem-like style.

Gives you ultimate control.

Usually predefined styles suce.

(plain, definition, and remark.)

LTEX and Friends

MathematicsMarc van Dongen

Mathematics



Managing Content

ProofsLTEX Input

\beginproof[Challenge]

http://find/



Arrays and Matrices


Braces



Theorems




About this Document

\ g p [ g ]

The following proves that$ˆ = ˆ + ˆ$:\[ ˆ = = +

= ˆ + ˆ\,.\qedhere \]

\endproof

LTEX Output

Challenge.The following proves that 32 + 42 = 52:

52 = 25 = 9 + 16 = 32 + 42 .

LTEX and Friends


Mathematics



Managing Content

Dot-like Symbols

http://find/



Arrays and Matrices


Braces



Theorems




About this Document

Low dots $n(n-)\ldots()$: n(n− 1) . . . (1)

Centred dots $x_+\cdots+x_n$: x 1 + · · · + x n

Diagonal dots In arrays and matrices. \ddots: . . .

Vertical dots In arrays and matrices. \vdots:...

LTEX and Friends


Mathematics



Managing Content

A d M t i

Pedantic Dots (amsmath)

http://find/

http://goback/



Arrays and Matrices


Braces



Theorems




About this Document

Dots with commas: \dotsc

Dots with binary operators: \dotsb

multiplication dots: \dotsm

Dots with integrals: \dotsiother dots: \dotso

LTEX and Friends


Mathematics



Managing Content

Arrays and Matrices

Example

LTEX Input

http://find/

http://goback/



Arrays and Matrices


Braces



Theorems




About this Document

\ldots Then we have series$A_, A_, \dotsc$,

regional sum

$A_ + A_ + \dotsb$,

orthogonal product

$A_ A_ \dotsm$,

and infinite integral

\[ \int_A_

\!\int_A_\dotsi\,.\]

LTEX Output

…Then we have series A1, A2 , . . . , regional sum A1 + A2 + · · · , orthogonal product A1A2 · · · , andinfinite integral ˆ

A1

ˆ A2

· · · .

LTEX and Friends


Mathematics



Managing Content

Arrays and Matrices

Linebreaks in Ordinary MathNot after Commas

LTEX Usage

for $x = f ( a , b )$, $f ( b , c )$,

http://find/

http://goback/



Arrays and Matrices


Braces



Theorems




About this Document

or˜$f ( b , c )$.


for $x = f ( a , b ) , f ( b , c )$,

or $f ( b , c )$.


Let $x, y$, and $z$ be real numbers.

LTEX Usage

Let $x$, $y$, and $z$ be real numbers.

LTEX and Friends


Mathematics



Managing Content

Arrays and Matrices

Linebreaks in Display Math(Always insert a thin space (\,) before final punctuation symbol.)

Indent line after linebreak by a qquad.

Insert linebreaks before additive operators (+ or −):

http://find/

http://goback/



Arrays and Matrices


Braces



Theorems




About this Document

LTEX Usage

\beginalign*f( x ) & = a + b + c + d \\

& \qquad + e + f + g\,.

\endalign*

Insert linebreak after multiplicative operators (× or /):

LTEX Usage

\beginalign*f ( x ) & = a \times b \times c \times d \times\\

& \qquad e \times f \times g\,.\endalign*

LTEX and Friends


Mathematics



Managing Content

Arrays and Matrices

The breqn Package

http://find/

http://goback/



y


Braces



Theorems




About this Document

Automates some non-trivial linebreaking.

LTEX and Friends


Mathematics



Managing Content

Arrays and Matrices

Conditions

In ordinary math mode put extra space for conditions.

http://find/




Braces



Theorems




About this Document

LTEX Usage

The Fibonacci numbers satisfy$F_n = F_ n - + F_n - $, \ $n \geq $.

Better turn it into a proper sentence.

LTEX Usage

The Fibonacci numbers satisfy$F_n = F_ n - + F_n - $, for˜$n \geq $.

LTEX and Friends


Mathematics



Managing Content

Arrays and Matrices

Conditions

In display math separate formula and conditions using qquad.

http://find/

http://goback/




Braces



Theorems




About this Document

LTEX Usage

\[ zˆ m G ( z ) = \sum_n g_ n - m zˆn\,,\qquad\textinteger $m \geq $\,. \]

LTEX Usage

\[ zˆ m G ( z ) = \sum_n g_ n - m zˆn

\qquad\text(integer $m \geq $)\,. \]

LTEX and Friends


Mathematics



Managing Content

Arrays and Matrices

Physical Units

Physical units should be typeset in roman.

http://find/

http://goback/



Accents and DecorationsBraces



Theorems




About this Document

y yp

Insert thin space between numbers and name of unit.

LTEX Usage

$g = .\,\mathrmm/\mathrmsˆ$

The siunitx package provides support for typesetting units.

Using the package you write \SI.

\metre\per\second\squared.This gives you 9.8 m s−2 as standard, or9.8 m/s2 by setting per=slash with the \sisetup macro.

LTEX and Friends


Mathematics



Managing Content

Arrays and Matrices

Sets

For ordinary sets there is no need for extra spacing.

http://find/






Theorems




About this Document

LTEX Usage

The natural numbers, $\mathbbN$, are defined

$\mathbbN = \ , , , \ldots \$.

For guarded sets you insert extra thin space.

LTEX Usage

The even numbers, $E$, are defined$E = \left\\, n \,:\, n \in \mathbbN \,\right\$.


Marc van Dongen

Mathematics



Managing Content

Arrays and Matrices

Horizontal Spacing Commands

Positive Spacing \hphantom Negative Spacing

http://find/






Theorems




About this Document

Positive Spacing \hphantom Negative Spacing

\, \hphantomM \!

\thinspace M M \negthinspace

\: \hphantomzˆn \negmedspace

\medspace zˆn z n \negthickspace

\;

\thickspace

\quad

\qquad


Marc van Dongen

Mathematics



Managing Content

Arrays and Matrices

Bibliography

http://find/






Theorems




About this Document


Marc van Dongen

Mathematics



About this Document

Acronyms and Abbreviations

American Mathematical Society

Application Programming Interface

http://find/



About this Document

A Programming Language Comprehensive TEX Archive Network

Compact Disk

Frequently Asked Question

Graphical User Interface

Integrated Development Environment International Standard Book Number

Operating System

Système International d’Unités/International System of Units

TE

X Users Group

Uniform Resource Locator

What You See Is What You Get


Marc van Dongen

Mathematics



About this Document

About this Document

http://find/



This document was created with pdflatex.

The LTEX document class is beamer.

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mathematics latex guide

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