LATEX Math Mode - MIT

1 0 LATEX Math ModeRSI 2007 StaffCONTENTS0 ContentsMath Mode .. 1 Types of Math Mode .. 2 Using Math Mode .. 3 Example .. 4 Typing Mathematical Expressions .. 5 Typefaces in Math Mode .. 6 Super- and Subscripts .. 7 Nonmath Uses of Math Mode .. 8 Variables and Symbols in Math Mode .. 9 Assignment 1 solution .. 10 Fractions and Roots .. 11 Assignment 2 solution .. 12 Common Mathematical Functions .. 13 Common Mathematical Symbols .. 14 Assignment 3 solution .. 15 Bounded Sums and Such .. 16 Sum, Integral, Limit Examples .. 17 Union and Intersection Examples .. 18 Assignment 7 Integrals, roots, exponents .. 19 Assignment 7 solution .. 20 Mathematical fonts .. 21 Assignment 8 solution .. 22 Common Error Messages.

2 23 Common Error Messages .. 24 Common Error Messages .. 25 Common Error Messages .. 26 Math ModeLATEX has a special mode for formatting mathematical addition to displaying complicated mathematical notations,this mode allows the use of: Subscripts and superscripts Greek letters and various special symbolsThus, math mode is also useful for some nonmathematical text:The CH3 COOH was irradiated with -rays while at atemperature of 350 of Math math mode(\begin{math}..\end{math}): the formulaappears in the middle of running text ( +y2). math mode(\begin{displaymath}..\end{displayma th}):the formula is set off on its own line. 0sinxx= special type of this mode isequation mode(\begin{equation}..\end{equation}), in which the formula is numbered forreference purposes (1):H:I k(GL2n(C)), Ht=(0 11 0)t (1 00B) (0 11 0)t(1)Long or tall formulae should ordinarily be Math ModeThere are several shorthand techniques of using math mode.

3 For text math mode, use$..$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 $a\in A = \O_{V,W}$, let$$\ord_V(a) = l_A(A/(a))$$denote the length of \(A/(a)\)as an A-module: we extend this as\[\ord_V\left(\frac{a}{b}\right)= \ord_V(a) - \ord_V(b).\] Then,for \begin{math} r\in R(W_i)\end{math}, we construct thedivisor \begin{displaymath}\div(r) = \sum_{\substack{V\subset W \\ \codim(V) = 1}}\ord_V(r)[V].\end{displaymath}Fora A=OV,W, letordV(a) =lA(A/(a))denote the length ofA/(a) as an A-module: we extend this asordV(ab)= ordV(a) ordV(b).Then, forr R(Wi), we construct thedivisordiv(r) = V Wcodim(V)=1ordV(r)[V].

4 4 Typing Mathematical Expressions Numbers, Roman variable names, and most symbols of basicarithmetic may be typed directly:If $a + 2 = 4 + b$ and$2(3b - a) = 43$,then $b = 47/4$.Ifa+ 2 = 4 +band 2(3b a) = 43,thenb= 47/4. Spaces are generally ignored in math mode:$abc+def$and$a b c + d e f$both makeabc+ in Math ModeLetters 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 lookreallyf reakin ugly(that was$really freakin ugly$). Use\emph{..} sin, cos, lim, and other notations written in upright type,use commands\sin,\cos,\lim, and so and SubscriptsTo get a superscript, use^{text}. To get a subscript, use_{text}.

5 Both a subscript and a superscript can be placed on the get a (prime), use repeated as many times as :CommandResultCommandResulta^{b}aba^{b + c}ab+ca a a a a_{b}aba_{b + c}ab+ca_{0}^{n+1}an+10a^{n+1}_{0}an+10x^ {y^{z}}xyza_{b_{c}}abc7 Nonmath Uses of Math ModeSubscripts and superscripts are often useful in chemical formulaeand temperature $_{3}$COOHCH3 COOH180$^{\circ}$C180 C$^{238}_{92}$U23892 UNotice that subscripts and superscripts may be attached tonothing (as in$_{3}$in the formula for acetic acid above).8 Variables and Symbols in Math ModeGreek letters: for lowercase, use\letternamein math mode($\gamma$ ). Some uppercase letters can be obtained by\Lettername($\Gamma$ ).Assignment 1: yourexamplesdirectory, andtypeset the following sentence into the body of the ( ) = elog thenf ( ) = 1 e/ andef( )= (1)in positive.

6 9 Assignment 1 solutionIf $f(\omega) = \omega -e\log\omega$ then $f (\omega) =1 - e/\omega$ and $e^{f(\omega)}= \Omega(1)$ in positive $\omega$.Iff( ) = elog thenf ( ) = 1 e/ andef( )= (1) in positive .10 Fractions and RootsFraction: use\frac{numerator}{denominator}(\frac{3 }{5} 35).(In text math mode, the slashed formsn/dusually look better.)Square root: use\sqrt{ }(\sqrt{3x + 5} 3x+ 5).nthpower root: use\sqrt[n]{ }(\sqrt[3]{x} 3 x).Assignment 2: Typeset the equation11 +3 2 +3 4=3 2 1(2)Note that it is 2 solution\begin{equation}\frac{1}{1 + \sqrt[3]{2}+ \sqrt[3]{4}} =\sqrt[3]{2} - 1\end{equation}11 +3 2 +3 4=3 2 1 (3)12 Common Mathematical FunctionsMost common mathematical functions and operators havecorresponding commands which are just names of the functions: Summation ( ), product ( ), and integral ( ) signs are givenby\sum,\prod, and\intrespectively.

7 \lim,\log,\sin,\cos,\tan,\sec,\csc,\coty ield properformatting of these common \log (3x + 5)log(3x+ 5)\cos (5x + x^2)cos(5x+x2)\sin^{2} (4x + 7)sin2(4x+ 7)13 Common Mathematical SymbolsMost common mathematical symbols have correspondingcommands related to the symbol name or symbol \in \nabla \cap,\cup , \subset,\supset , \geq,\leq , \ldots,\cdots.. , To negate = and , use\neqand\notin. Other symbols can benegated using the\notcommand:\not\leq 6 ,\not> 6>.Assignment 3: Typeset the , B then ( A B) ( A B).14 Assignment 3 solutionIf $A,B\subset \Gamma$ then$(\Gamma - A\cup B) \subset(\Gamma - A\cap B)$.IfA, B then ( A B) ( A B).15 Bounded Sums and SuchSums, products, integrals, and the like often have written upperand lower bounds.

8 These can be indicated using_for the lowerbound and^for the upper bound:\[ \sum_{i = -N}^{i = N}\sum_{j \geq 0}\frac{1}{i^2 + j^3} \]i=N i= N j 01i2+j3To best display unions and intersections that are bounded, use\bigcupand\bigcapinstead of\cupand\ , Integral, Limit ExamplesIn text:\sum_{i=1}^{\infty} i^{-2} i=1i 2\int_{3}^{2x} y\, dy 2x3y dy\lim_{n \to \infty} \frac{1}{n}limn 1nIn displays:\sum_{i=1}^{\infty} i^{-2} i=1i 2\int_{3}^{2x} y\, dy 2x3y dy\lim_{n \to \infty} \frac{1}{n}limn 1n17 Union and Intersection ExamplesIn text:\bigcap_{i=0}^{\infty} U_i i=0Ui\bigcup_{k=3}^{n} \{1, 2, \ldots, k\} nk=3{1,2, .. , k}In displays:\bigcap_{i=0}^{\infty} U_i i=0Ui\bigcup_{k=3}^{n} \{1, 2, \ldots, k\}n k=3{1,2, .. , k}(\bigcup_i U_i) \cup (\bigcup_i V_i)( iUi) ( iVi)18 Assignment 7 Integrals, roots, exponentsTypeset the following equations:limmin{x,y} x+yx2+y2= 0(4) e x2dx= (5)19 Assignment 7 solution\begin{equation}\lim_{\min\{x,y\ } \to \infty}\frac{x + y}{x^2 + y^2} = 0\end{equation}\begin{equation}\int_{-\i nfty}^{\infty}e^{-x^{2}}dx = \sqrt{\pi}\end{equation}limmin{x,y} x+yx2+y2= 0(5) e x2dx= (6)20 Mathematical fonts Various fonts can be used to create unique mathematicalsymbols:Bold\mathbf{x}xCalli graphic\mathcal{A}ABlackboard bold\mathbb{Z}ZScript\mathscr{O}OAssignm ent 8: Typeset the following INote: the I is 8 solution\begin{displaymath}\mathbb{R}^{s } \supset \mathbf{I}\end{displaymath}Rs I22 Common Error Messages!

9 Missing $ inserted.<inserted text>$ have forgotten to end math mode. The line number afterthe l. (in this case 8 ) is the first line at which LATEX hasrealized that you have forgotten to end math mode; it is usuallythe end of the paragraph the error is cause: Forgetting to put a\before a %.23 Common Error Messages! Missing $ inserted.<inserted text>$ 30^\circ?You have used a command (in this case^) which LATEX knowsbelongs only in math mode. The line number given is thelocation of the command in Error Messages! LATEX Error: \begin{displaymath} on input line 8 ended by\end{document}.See the LATEX manual or LATEX Companion for H <return> for immediate \end{document}?You have forgotten to end display math mode. The line numberon which math mode began is listed (in this case, inputline 8 ).

10 25 Common Error Messages! LATEX Error: \mathbb allowed only in math the LATEX manual or LATEX Companion for H <return> for immediate \mathbb{stuff}?The command in question (in this case\mathbb) is only allowedin math mode and you have tried to use it outside of