LATEX Math Mode: A Comprehensive Guide, Slides of Microsoft Word Skills

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LATEX Math Mode

RSI 2007 Staff

Contents

• Math Mode
• Types of Math Mode
• Using Math Mode
• Example
• Typing Mathematical Expressions
• Typefaces in Math Mode
• Super- and Subscripts
• Nonmath Uses of Math Mode
• Variables and Symbols in Math Mode
• Assignment 1 solution
• Fractions and Roots
• Assignment 2 solution
• Common Mathematical Functions
• Common Mathematical Symbols
• Assignment 3 solution
• Bounded Sums and Such
• Sum, Integral, Limit Examples
• Union and Intersection Examples
• Assignment 7—Integrals, roots, exponents
• Assignment 7 solution
• Mathematical fonts
• Assignment 8 solution
• Common Error Messages
• Common Error Messages
• Common Error Messages
• Common Error Messages

Types of Math Mode

1. Text math mode (\begin{math}.. .\end{math}): the formula

appears in the middle of running text (e.g. x^2 + y^2 ).

2. Display math mode (\begin{displaymath}... \end{displaymath}):

the formula is set off on its own line. ∫ (^) ∞ 0

sin x x

π 2

A special type of this mode is equation mode (\begin{equation}

... \end{equation}), in which the formula is numbered for

reference purposes (1):

H : I → πk(GL 2 n(C)), Ht =

( 0 1 1 0

)t ·

( 1 0 0 B

) ·

( 0 1 1 0

)t (1)

Long or tall formulae should ordinarily be displayed.

Using Math Mode

There are several shorthand techniques of using math mode.

• For text math mode, use $... $ or (... ).
• For display math mode, use $$... $$ or [... ].

It is important to make sure that the way you end math mode matches the way you started it. For example,

\begin{math} math stuff $

will not work.

Typing Mathematical Expressions

• Numbers, Roman variable names, and most symbols of basic arithmetic may be typed directly:

If $a + 2 = 4 + b$ and $2(3b - a) = 43$, then $b = 47/4$.

If a + 2 = 4 + b and 2(3b − a) = 43, then b = 47/4.

• Spaces are generally ignored in math mode: $abc+def$ and $a b c + d e f$ both make abc + def.

Typefaces in Math Mode

Letters typed in math mode are set in an italic type, as is conventional for Roman variables (x, etc.).

But do not use this as a quick way to italicize ordinary text! Words typed in math mode look reallyf reakin′ugly (that was $really freakin’ ugly$). Use \emph{...} instead.

For sin, cos, lim, and other notations written in upright type, use commands \sin, \cos, \lim, and so forth.

Nonmath Uses of Math Mode

Subscripts and superscripts are often useful in chemical formulae and temperature values.

Text Result CH$_{3}$COOH CH 3 COOH

180$^{\circ}$C 180 ◦C

$^{238}_{92}$U 23892 U

Notice that subscripts and superscripts may be attached to nothing (as in $_{3}$ in the formula for acetic acid above).

Variables and Symbols in Math Mode

Greek letters: for lowercase, use \lettername in math mode ($\gamma$ → γ). Some uppercase letters can be obtained by \Lettername ($\Gamma$ → Γ).

Assignment 1: Open math.tex in your examples directory, and typeset the following sentence into the body of the document.

If f (ω) = ω−e log ω then f ′(ω) = 1−e/ω and ef^ (ω)^ = Ω(1) in positive ω.

Fractions and Roots

Fraction: use \frac{numerator}{denominator} (\frac{ 3 }{ 5 } → 35 ).

(In text math mode, the slashed forms n/d usually look better.)

Square root: use \sqrt{· · · } (\sqrt{3x + 5} →

3 x + 5).

nth^ power root: use \sqrt[n]{· · · } (\sqrt[3]{x} → 3

x).

Assignment 2: Typeset the equation

1 1 + 3

Note that it is numbered.

Assignment 2 solution

\begin{equation} \frac{1}{1 + \sqrt[3]{2}

• \sqrt[3]{4}} = \sqrt[3]{2} - 1 \end{equation}

1 1 + 3 √ 2 + 3 √ 4 = 3

√ 2 − 1 (3)

Common Mathematical Symbols

Most common mathematical symbols have corresponding commands related to the symbol name or symbol appearance.

Command Result Command Result \in ∈ \nabla ∇ \cap,\cup ∩, ∪ \subset,\supset ⊂, ⊃ \geq,\leq ≥, ≤ \ldots,\cdots... , · · ·

To negate = and ∈, use \neq and \notin. Other symbols can be negated using the \not command: \not\leq →6≤, \not> →6>.

Assignment 3: Typeset the following.

If A, B ⊂ Γ then (Γ − A ∪ B) ⊂ (Γ − A ∩ B).

Assignment 3 solution

If $A,B\subset \Gamma$ then $(\Gamma - A\cup B) \subset (\Gamma - A\cap B)$.

If A, B ⊂ Γ then (Γ − A ∪ B) ⊂ (Γ − A ∩ B).

Sum, Integral, Limit Examples

In text: \sum_{i=1}^{\infty} i^{-2} ∑∞ i=1 i−^2

\int_{3}^{2x} y, dy ∫ (^2) x 3 y dy

\lim_{n \to \infty} \frac{1}{n} limn→∞ (^1) n

In displays:

\sum_{i=1}^{\infty} i^{-2}

∑^ ∞ i=

i−^2

\int_{3}^{2x} y, dy

∫ (^2) x 3

y dy

\lim_{n \to \infty} \frac{1}{n} (^) nlim→∞

n

Union and Intersection Examples

In text:

\bigcap_{i=0}^{\infty} U_i ⋂∞ i=0 Ui \bigcup_{k=3}^{n} {1, 2, \ldots, k} ⋃n k=3{^1 ,^2 ,... , k}

In displays:

\bigcap_{i=0}^{\infty} U_i

⋂^ ∞ i=

Ui

\bigcup_{k=3}^{n} {1, 2, \ldots, k}

⋃^ n k=

{ 1 , 2 ,... , k}

(\bigcup_i U_i) \cup (\bigcup_i V_i) (

⋃ i

Ui) ∪ (

⋃ i

Vi)