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author | Karl Berry <karl@freefriends.org> | 2009-05-25 22:41:12 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2009-05-25 22:41:12 +0000 |
commit | 2872c529ef82241e44a9baee18a056cc5442b68f (patch) | |
tree | d0bc6dffd188f066bb4980d54db89ce07db6c339 /Master/texmf-dist/doc/latex/first-latex-doc/latex-second-e.tex | |
parent | 62ad2c7662f9293b35f3c92c65e4c007c5efe335 (diff) |
new doc first-latex-doc (25may09)
git-svn-id: svn://tug.org/texlive/trunk@13460 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/first-latex-doc/latex-second-e.tex')
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diff --git a/Master/texmf-dist/doc/latex/first-latex-doc/latex-second-e.tex b/Master/texmf-dist/doc/latex/first-latex-doc/latex-second-e.tex new file mode 100644 index 00000000000..2c403261078 --- /dev/null +++ b/Master/texmf-dist/doc/latex/first-latex-doc/latex-second-e.tex @@ -0,0 +1,74 @@ +\documentclass{article} +\usepackage{geometry} +\usepackage{fancyhdr} +\usepackage{amsmath,amsthm,amssymb} +\usepackage{graphicx} +\usepackage{hyperref} +\usepackage{lipsum} + +\title{Test document} +\author{Your name \\ \url{you@example.com}} +\date{2009-Oct-12} +\begin{document} +\maketitle +\tableofcontents +\newpage + +This is some preamble text that you enter +yourself.\footnote{First footnote.}\footnote{Second footnote.} + +\section{Text for the first section} +\lipsum[1] + +\subsection{Text for a subsection of the first section} +\lipsum[2-3] +\label{labelone} + +\subsection{Another subsection of the first section} +\lipsum[4-5] +\label{labeltwo} + +\section{The second section} +\lipsum[6] + +Refer again to \ref{labelone}.\cite{ConcreteMath} +Note also the discussion on page \pageref{labeltwo} + +\subsection{Title of the first subsection of the second section} +\lipsum[7] + +There are $\binom{2n+1}{n}$ sequences with $n$ occurrences of +$-1$ and $n+1$ occurrences of $+1$, and Raney's lemma +tells us that exactly $1/(2n+1)$ of these sequences have all +partial sums positive. + +Elementary calculus suffices to evaluate $C$ if we are clever enough +to look at the double integral +\begin{equation*} + C^2 + =\int_{-\infty}^{+\infty} e^{-x^2} \mathrm{d}x + \int_{-\infty}^{+\infty} e^{-y^2} \mathrm{d}y\;. +\end{equation*} + +Solve the following recurrence for $n,k\geq 0$: +\begin{align*} + Q_{n,0} &= 1 + \quad Q_{0,k} = [k=0]; \\ + Q_{n,k} &= Q_{n-1,k}+Q_{n-1,k-1}+\binom{n}{k}, \quad\text{for $n,k>0$.} +\end{align*} + +Therefore +\begin{equation*} +a\equiv b\pmod{m} +\qquad\Longleftrightarrow\qquad +a\equiv b \pmod{p^{m_p}}\quad\text{for all $p$} +\end{equation*} +if the prime factorization of $m$ is $\prod_p p^{m_p}$. + +\begin{thebibliography}{9} +\bibitem{ConcreteMath} +Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, +\textit{Concrete mathematics}, +Addison-Wesley, Reading, MA, 1995. +\end{thebibliography} +\end{document} |