diff --git a/frontmatter/backcover.pdf b/frontmatter/backcover.pdf new file mode 100644 index 000000000..98bd1b775 Binary files /dev/null and b/frontmatter/backcover.pdf differ diff --git a/frontmatter/backcover.tex b/frontmatter/backcover.tex new file mode 100644 index 000000000..d45d0b9db --- /dev/null +++ b/frontmatter/backcover.tex @@ -0,0 +1,96 @@ +\documentclass{article} + +\usepackage{url} +\usepackage{xcolor} +\usepackage{tikz} +\usepackage{mdframed} + + +\definecolor{bg}{HTML}{7681a9} +\pagecolor{bg} + +\usepackage[T1]{fontenc} +\usepackage{newpxtext} +\usepackage[vvarbb,cmintegrals,cmbraces,bigdelims]{newpxmath} +\usepackage[scr=rsfso]{mathalfa}% \mathscr is fancier than \mathcal +\linespread{1.04} % adds more leading (space between lines) +% quantifiers look strange, so change those back to normal: + \DeclareSymbolFont{mysymbols}{OMS}{cmsy}{b}{n} %note we make the figures bold to better match newpx. Replace the ``b'' with an ``m'' to undo this. + %\SetSymbolFont{mysymbols} {bold}{OMS}{cmsy}{b}{n} + %\DeclareSymbolFont{myoperators} {OT1}{cmr} {m}{n} + %\SetSymbolFont{myoperators}{bold}{OT1}{cmr} {bx}{n} + \DeclareMathSymbol{\forall}{\mathord}{mysymbols}{"38} + \DeclareMathSymbol{\exists}{\mathord}{mysymbols}{"39} + %\DeclareMathSymbol{\pm}{\mathbin}{mysymbols}{"06} + %\DeclareMathSymbol{+}{\mathbin}{myoperators}{"2B} + %\DeclareMathSymbol{-}{\mathbin}{mysymbols}{"00} + %\DeclareMathSymbol{=}{\mathrel}{myoperators}{"3D} + + +\begin{document} +\pagestyle{empty} + +\begin{center} +\begin{tikzpicture}[remember picture, overlay, color=bg!90!black] +\def\r{.55} +\newcommand{\hexbox}[3]{ + \def\x{-cos{30}*\r*#1+cos{30}*#2*\r*2} + \def\y{-\r*#1-sin{30}*\r*#1} + \draw (\x,\y) +(90:\r) -- +(30:\r) -- +(-30:\r) -- +(-90:\r) -- +(-150:\r) -- +(150:\r) -- cycle; + \draw (\x,\y) node{#3}; +} + + +% Pascal's triangle +%put row of 1's down left side: + \foreach \row in {0,...,16} { + \hexbox{\row}{0}{\large 1} + } +%fill in the rest of the triangle: + \foreach \row in {1,...,16} { + \pgfmathsetmacro{\entry}{1}; + \foreach \col in {1,...,\row} { + % iterative formula : val = precval * (row-col+1)/col + % (+ 0.5 to bypass rounding errors) + \pgfmathtruncatemacro{\entry}{\entry*((\row-\col+1)/\col)+0.5}; + \global\let\entry=\entry + \ifnum \entry<100 + \hexbox{\row}{\col}{\large \entry} + \else \ifnum \entry<1000 + \hexbox{\row}{\col}{\entry} + \else \ifnum \entry<10000 + \hexbox{\row}{\col}{\footnotesize \entry} + \else + \hexbox{\row}{\col}{\scriptsize \entry} + \fi + \fi + \fi + } + } +\end{tikzpicture} +\end{center} +~ +\vskip 5em +\noindent This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Norther Colorado. This course serves both as an introduction to topics in discrete math and as the ``introduction to proof'' course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. + +\vskip 2em + +\noindent Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. + +\vskip 2em + +\noindent While there are many fine discrete math textbooks available, this text has the following advantages: +\begin{itemize} +\item[--] It is written to be used in an inquiry rich course. +\item[--] It is written to be used in a course for future math teachers. +\item[--] It is open source, with low cost print editions and free electronic editions. +\end{itemize} + +\vskip 7em +\noindent To download the current version, or for information on obtaining the \LaTeX\ source, visit: \url{http://discretetext.oscarlevin.com/}. + + + +\clearpage + +\end{document} diff --git a/frontmatter/dedication.tex b/frontmatter/dedication.tex new file mode 100644 index 000000000..090407d6a --- /dev/null +++ b/frontmatter/dedication.tex @@ -0,0 +1,11 @@ + +\thispagestyle{empty} + +~ +\vskip 2in + +\begin{flushright} +\emph{\large To Shannon and Madeline} 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