LATEX Math for Undergrads Entering \Overline{X+Y} Produces X + Y, and \Widehat{X+Y} Gives X\Widehat+ Y
Total Page：16
File Type：pdf, Size：1020Kb
LATEX Math for Undergrads Entering \overline{x+y} produces x + y, and \widehat{x+y} gives x[+ y. Comment on an expression as Rule One Any mathematics at all, even a single character, here (there is also \overbrace{..}). gets a mathematical setting. Thus, for ``the value of x is 7 '' enter the value of $x$ is $7$. x + y \underbrace{x+y}_{|A|} | {z } Template Your document should contain at least this. jAj \documentclass{article} Dots Use low dots in a list f0; 1; 2;:::g, entered as \usepackage{mathtools,amssymb,amsthm} % imports amsmath \{0,1,2,\,\ldots\}. (If you use \ldots in plain text as \begin{document} with London, Paris, \ldots{}\,. then note the thinspace --document body here-- \end{document} \, before the period.) Use centered dots in a sum or prod- uct 1 + \cdot \cdot + 100, entered as 1+\cdots+100. You can also get Common constructs vertical dots \vdots and diagonal dots \ddots. p p n Roman names Enter , with a backslash, instead x2 x^2 2, 3 \sqrt{2}, \sqrt[n]{3} \tan(x) 2 of tan(x). These get the same treatment. xi;j x_{i,j} 3 , 2=3 \frac{2}{3}, 2/3 sin \sin sinh \sinh arcsin \arcsin Calligraphic letters Use as in $\mathcal{A}$. cos \cos cosh \cosh arccos \arccos ABCDEFGHIJ KLMN OPQRST UVWX YZ tan \tan tanh \tanh arctan \arctan sec \sec coth \coth min \min Get script letters, such as P from $\mathscr{P}$, by csc \csc det \det max \max putting \usepackage{mathrsfs} in the preamble. cot \cot dim \dim inf \inf Greek exp \exp ker \ker sup \sup log \log deg \deg lim inf \liminf \alpha \alpha \xi , \Xi \xi, \Xi ln \ln arg \arg lim sup \limsup \beta \beta o o lg \lg gcd \gcd lim \lim \gamma , \Gamma \gamma, \Gamma \pi , \Pi \pi, \Pi \delta , \Delta \delta, \Delta $ \varpi Other symbols \epsilon \epsilon \rho \rho < < \angle \cdot \cdot " \varepsilon % \varrho \ \leq \leq \measuredangle \pm \pm \zeta \zeta \sigma , \Sigma \sigma, \Sigma ] > > ` \ell \mp \mp \eta \eta & \varsigma \geq \geq k \parallel \times \times \theta \Theta \theta, \Theta \tau \tau 6= \neq 45\circ 45^{\circ} \div \div # \vartheta \upsilon , \Upsilon \upsilon, \Upsilon \ll \ll =\sim \cong \ast \ast \iota \iota \phi , \Phi \phi, \Phi \gg \gg \ncong j \mid \kappa \kappa ' \varphi \ncong \approx \approx \sim \sim \nmid \lambda \Lambda \lambda, \Lambda \chi \chi - \asymp \asymp ' \simeq n! n! \mu \mu , \Psi \psi, \Psi \equiv \equiv \nsim @ \partial \nu \nu !, \Omega \omega, \Omega \nsim \prec \prec \oplus \oplus r \nabla Sets and logic \preceq \preceq \ominus \ominus ~ \hbar \succ \succ \odot \odot \circ \circ [ \cup \mathbb{R} 8 \forall R \succeq \succeq \otimes \otimes p? \star \ \cap Z \mathbb{Z} 9 \exists / \propto \oslash \oslash \surd : \subset \subset Q \mathbb{Q} : \neg = \doteq \upharpoonright \upharpoonright X \checkmark \subseteq \subseteq N \mathbb{N} _ \vee Use a\mid b for the divides relation, a j b, and \supset \supset C \mathbb{C} ^ \wedge a\nmid b for the negation, a b. Also use \mid to \supseteq \supseteq ? \varnothing ` \vdash - 2 \in ; \emptyset j= \models get set builder notation fa 2 S j a is oddg, with 2= \notin @ \aleph n \setminus \{a\in S\mid\text{$a$ is odd}\}. Arrows Negate an operator, as in \not \subset, with \not\subset. Get the set complement Ac with A^{\mathsf{c}} (or A{ with ! \rightarrow, \to 7! \mapsto A^{\complement}, or A with \overline{A}). 9 \nrightarrow \mapsto -! \longmapsto Decorations - ! \longrightarrow \leftarrow ) \Rightarrow $ \leftrightarrow 0 f f’ a_ \dot{a} x~ \tilde{x} ; \nRightarrow # \downarrow f 00 f’’ a\" \ddot{a} x\= \bar{x} =) \Longrightarrow " \uparrow \ast \Sigma \Sigma^{*} x^ \hat{x} ~x \vec{x} \leadsto l \updownarrow If the decorated letter is i or j then some decorations need The right arrows in the first column have matching left \imath or \jmath, as in \vec{\imath}. Some authors use arrows, such as \nleftarrow, and there are some other boldface for vectors: \boldsymbol{x}. matches for down arrows, etc. P3 2 Variable-sized operators The summation j=0 j Displayed equations The equation* environment puts R 3 2 an equation on a separate line. \sum_{j=0}^3 j^2 and the integral x=0 x dx \int_{x=0}^3 x^2\,dx expand when displayed. \begin{equation*} S = k \cdot lg W S=k\cdot\lg W 3 \end{equation*} X Z 3 j2 x2 dx j=0 x=0 You can break into multiple lines. x3 These do the same. sin(x) = x - \begin{multline*} \sin (x)=x-\frac{x^3}{3!} \\ R RRR S 3! \int \iiint \bigcup 5 +\frac{x^5}{5!}-\cdots x \end{multline*} RR \iint H \oint T \bigcap + - \cdot \cdot 5! Fences Align equations using align* () () h i \langle\rangle j j | | \begin{align*} r \cdot D = \rho \nabla\cdot\boldsymbol{D} &= \rho \\ [] [] b c \lfloor\rfloor k k \| \| \nabla\cdot\boldsymbol{B} &= 0 f g \{\} d e \lceil\rceil r \cdot B = 0 \end{align*} Fix the size with \big, \Big, \bigg, or \Bigg. (the left or right side of an alignment can be empty). For n each environment, get a numbered version by dropping the h X k2 i e \Big[\sum_{k=0}^n e^{k^2}\Big] asterisk from the name. k=0 Calculus examples The last three here are display style. To have them grow with the enclosed formula, use \left and \right (although sometimes \big, etc., are necessary). f : R ! R f\colon\mathbb{R}\to\mathbb{R} D i E i; 22 \left\langle i,2^{2^i}\right\rangle 9:8 m=s2 9.8~\text{m}/\text{s}^2 f(x + h) - f(x) Every \left must match a \right and they must end on lim \lim_{h\to 0}\frac{f(x+h)-f(x)}{h} h!0 h the same line in the output. For a one-sided fence, put a Z 2 3 \left. or \right. on the other side. x dx = x =3 + C \int x^2\,dx=x^3/3+C \bigm| d d d df \bigm| r = i + j + k \nabla=\boldsymbol{i}\frac{d}{dx}+ \cdot \cdot \bigm| \left.\frac{df}{dx}\right|_{x_0} dx dx dy dz \bigm|x 0 Discrete mathematics examples There are four Arrays, Matrices Make an array of mathematical text as modulo forms: m mod n is from m\bmod n, and a \equiv b you make a table of plain text. (mod m) is from a\equiv b\pmod m, and a \equiv b mod m 0 $ 0 \begin{array}{rcl} is from a\equiv b\mod m, and a \equiv b (m) is from 1 $ 1 0 &\leftrightarrow &0 \\ 1 &\leftrightarrow &1 \\ a\equiv b\pod m. 2 $ 4 2 &\leftrightarrow &4 \\ For combinations the binomial symbol \bigl( n\bigr) is from . \vdots& &\vdots k . \end{array} \binom{n}{k}. This resizes to be bigger in a display (to require the display version use \dbinom{n}{k} and require Definition by cases is an array with two columns. the inline version with \tbinom{n}{k}). For permutations use nr from n^{\underline{r}} (some ( f_n = authors use P (n; r), or P from {}_nP_r). a if n = 0 \begin{cases} n r fn = a &\text{if $n=0$} \\ Statistics examples r \cdot fn - 1 else r\cdot f_{n-1} &\text{else} \end{cases} 2 p P 2 \sigma = (xi - \mu ) =N \sigma^2=\sqrt{\,\sum (x_i-\mu)^2/N} P A matrix is an array with fences. With a pmatrix environ- E(X) = \muX = (xi - P (xi)) E(X)=\mu_X=\sum (x_i-P(x_i)) ment, you need not specify column alignments. The probability density of the normal distribution \begin{pmatrix} \biggl( \biggr) 2 a b a &b \\ 1 - (x - \mu ) p e 2\sigma 2 c d c &d 2 \end{pmatrix} 2\sigma \pi comes from this. For the determinant use |A| inline and vmatrix in display. p p \frac{1}{sqrt{2\sigma^2\pi}} Spacing in mathematics Improve 2x to 2 x with a \,e^{-\frac{(x-\mu)^2}{2\sigma^2}}!. thin space, as in \sqrt{2}\,x. Slightly wider are \: and \; (the three are in ratio 3 : 4 : 5). Get the improvement of For more See also the Comprehensive LATEX Symbols List n=log n instead of n= log n by using a negative thin space, at mirror.ctan.org/info/symbols/comprehensive and as in n/\!\log n. Bigger spaces are: \quad for ! , and DeTEXify at detexify.kirelabs.org/classify.html. \qquad for ! , which are useful between parts of a display. Get arbitrary space as in \hspace*{0.5cm}. Jim Hefferon, Saint Michael’s College, VT USA 2020-Dec-30.