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Math Mode
LATEX has a special mode for formatting mathematical formulas.In addition to displaying complicated mathematical notations,this mode allows the use of:
• Subscripts and superscripts
• Greek letters and various special symbols
Thus, math mode is also useful for some nonmathematical text:
The CH 3 COOH was irradiated with α -rays while at atemperature of 350 C.
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Types of Math Mode
1. Text math mode (\begin math . . .\end math ): the formulaappears in the middle of running text (e.g. x2 + y2 ).
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 forreference purposes (1):
H : I → πk( GL 2 n ( C )) , H t = 0 11 0
t
· 1 00 B ·
0 11 0
t(1)
Long or tall or important formulae should ordinarily be displayed.
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Using Math Mode
There are several shorthand techniques of using math mode.
• For text math mode, use $. . . $ (recommended) or \( . . . \) .
• For display math mode, use $$ . . . $$ or \[ . . . \] .
It is important to make sure that the way you end math modematches the way you started it. For example,
\begin math math stuff $
will not work.
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Example
For $a\in A = \OO_V,W$, let\[\ord_V(a) = l_A(A/(a)) \]denote the length of $A/(a)$as an A-module: we extend this as\[\ord_V\left(\fracab\right)= \ord_V(a) - \ord_V(b).\] Then,for $r\in R(W_i) $, we constructthe divisor\[\divv(r) = \sum_\substackV\subset W \\ \codim(V) = 1\ord_V(r)[V].\]
For a A = O
V,W , letord V ( a ) = lA( A/ ( a ))
denote the length of A/ ( a ) as an A-module: we extend this as
ord V ab = ord V ( a ) −ord V ( b) .
Then, for r R( W i), we construct thedivisor
div( r ) =
V W codim( V )=1
ord V ( r )[ V ].
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Typing Mathematical Expressions
• Numbers, Roman variable names, and most symbols of basicarithmetic may be typed directly:
I f $a + 2 = 4 + b$ and
$2(3b - a) = 43$,then $b = 47/4$.
If a + 2 = 4 + b and 2(3 b
− 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 .
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Typefaces in Math Mode
Letters typed in math mode are set in an italic type, as isconventional for Roman variables ( x , etc.).
But do not use this as a quick way to italicize ordinary text!Words typed in math mode look reallyfreakin ′ugly (that was$really freakin’ ugly$ ). Use \emph... instead.
If you want to put text inside math mode, you canuse \textyour text here . If that doesn’t work, add\usepackageamsmath before the line \begindocument , or use
\textrmyour text here .
For sin, cos, lim, and other notations written in upright type,use commands \sin , \cos , \lim , and so forth.
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Super- and Subscripts
To get a superscript, use ^text . To get a subscript, use_text .
Both a subscript and a superscript can be placed on the sameexpression.
To get a ′ (prime), use ’ repeated as many times as needed.
Examples:
Command Result Command Resulta^b ab a^b + c ab+ c
a’ a′ a’’’ a′′′a_b ab a_b + c ab+ c
a_0^n+1 an +10 a^n+1_0 an +1
0
x^y^z xyz
a_b_c abc
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Nonmath Uses of Math Mode
Subscripts and superscripts are often useful in chemical formulae
and temperature values.
Text ResultCH$_3$COOH CH 3 COOH
180$^\circ$C 180 C
$^238_92$U 23892 U
Notice that subscripts and superscripts may be attached tonothing (as in $_3$ in the formula for acetic acid above).
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Assignment 1 solution
If $f(\omega) = \omega -e\log\omega$ then $f’(\omega) =1 - e/\omega$ and $e^f(\omega)= \Omega(1)$ in positive $\omega$.
If f ( ω) = ω
−e log ω then f
′( ω) = 1
−e/ω
and ef ( ω) = Ω(1) in positive ω.
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Fractions and Roots
Fraction: use \frac numerator denominator (\frac 35 → 35 ).
(In text math mode, the slashed forms n/d usually look better.)
Square root: use \sqrt · · · (\sqrt 3x + 5 →√ 3 x + 5).
n th power root: use
\sqrt[n]
· · · (
\sqrt[3] x
→ 3√ x ).
Assignment 2: Typeset the equation
1
1 + 3
√ 2 + 3
√ 4= 3√ 2
−1 (2)
Note that it is numbered.
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Assignment 2 solution
\beginequation\frac11 + \sqrt[3]2
+ \sqrt[3]4 =\sqrt[3]2 - 1
\endequation
11 + 3√ 2 + 3√ 4 = 3√ 2 −1 (3)
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Common Mathematical Functions
Most common mathematical functions and operators havecorresponding commands which are just names of the functions:
• Summation ( ), product ( ), and integral ( ) signs are givenby \sum, \prod , and \int respectively.
• \lim ,
\log ,
\sin ,
\cos ,
\tan ,
\sec ,
\csc ,
\cot yield proper
formatting of these common functions.
Command Result
\log (3x + 5) log(3 x + 5)
\cos (5x + x^2) cos(5 x + x2 )
\sin^2 (4x + 7) sin 2 (4 x + 7)
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Common Mathematical Symbols
Most common mathematical symbols have correspondingcommands 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 benegated using the \not command: \not \leq →≤, \not> →> .
Assignment 3: Typeset the following.
If A, B Γ then (Γ −A B ) (Γ −A ∩B ).
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Bounded Sums and Such
Sums, products, integrals, and the like often have written upperand lower bounds. These can be indicated using _ for the lowerbound and ^ for the upper bound:
\[ \sum_i = -N^i = N\sum_j \geq 0\frac1i^2 + j^3 \]
i= N
i= −N j ≥0
1i2 + j 3
To best display unions and intersections that are bounded, use
\bigcup and \bigcap instead of \cup and \cap .
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Sum, Integral, Limit Examples
In text:\sum_i=1^\infty i^-2 ∞i=1 i−2
\int_3^2x y\, dy 2 x3 y dy
\lim_n \to \infty \frac1n lim n→∞ 1n
In displays:
\sum_i=1^\infty i^-2∞
i=1i−2
\int_3^2x y\, dy 2x
3 y dy
\lim_n \to \infty \frac1n limn→∞1n
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Union and Intersection Examples
In text:
\bigcap_i=0^\infty U_i
∞i=0 U i
\bigcup_k=3^n \1, 2, \ldots, k\ nk=3 1 , 2 , . . . , k
In displays:
\bigcap_i=0^\infty U_i∞
i=0U i
\bigcup_k=3^n \1, 2, \ldots, k\n
k=31 , 2 , . . . , k
(\bigcup_i U_i) \cup (\bigcup_i V_i) (i
U i) (i
V i)
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Assignment 7—Integrals, roots, exponents
Typeset the following equations:
limmin x,y →∞
x + y
x2
+ y2 = 0 (4)
∞−∞e−x2
dx = √ π (5)
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Mathematical fonts
• Various fonts can be used to create unique mathematical
symbols:Bold \ mathbf x x
Calligraphic \ mathcal A ABlackboard bold \ mathbb Z Z
Script
\ mathscr O O
Assignment 8: Typeset the following equation.
R s I
Note: the “I” is bold.
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Assignment 8 solution
\begindisplaymath
\mathbbR^s \supset \mathbfI\enddisplaymath R s I
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Common Error Messages
! Missing $ inserted.<inserted text>
$l.8
?
You have forgotten to end math mode. The line number afterthe “ l. ” (in this case “8”) is the rst line at which L ATEX hasrealized that you have forgotten to end math mode; it is usually
the end of the paragraph the error is in.
Common cause: Forgetting to put a \ before a %.
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Common Error Messages
! Missing $ inserted.<inserted text>
$l.6 30^
\circ?
You have used a command (in this case ^) which L ATEX knows
belongs only in math mode. The line number given is thelocation of the command in question.
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Common Error Messages
! LaTeX Error: \begindisplaymath on input line 8 ended by\enddocument.
See the LaTeX manual or LaTeX Companion for explanation.Type H <return> for immediate help.
...
l.10 \enddocument
?
You have forgotten to end display math mode. The line numberon which math mode began is listed (in this case, “inputline 8”).
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