From 4d3045acc9adc9126b70e5ca123053218735c1af Mon Sep 17 00:00:00 2001 From: Oscar Levin Date: Wed, 20 Aug 2014 10:50:45 -0600 Subject: [PATCH] Updated chapter files Now individual chapters will compile separately, without messing up the ability of the whole book to use the chapter files as chapters. --- chapter1.tex | 4 -- chapters/AdvancedCounting.pdf | Bin 0 -> 184213 bytes chapters/AdvancedCounting.tex | 9 ++-- chapters/CombinatorialProofs.pdf | Bin 0 -> 170884 bytes chapters/CombinatorialProofs.tex | 8 +-- chapters/Counting.pdf | Bin 0 -> 228342 bytes chapters/Counting.tex | 11 ++-- chapters/GeneratingFunctions.pdf | Bin 0 -> 159021 bytes chapters/GeneratingFunctions.tex | 8 +-- chapters/GraphTheory.pdf | Bin 0 -> 372201 bytes chapters/GraphTheory.tex | 10 ++-- chapters/Induction.pdf | Bin 0 -> 176318 bytes chapters/Induction.tex | 7 +-- chapters/Logic.pdf | Bin 0 -> 149660 bytes chapters/Logic.tex | 7 +-- chapters/NumberTheory.pdf | Bin 0 -> 174466 bytes chapters/NumberTheory.tex | 8 +-- chapters/Quantifiers_Sets.pdf | Bin 0 -> 175011 bytes chapters/Quantifiers_Sets.tex | 10 ++-- chapters/Sequences.pdf | Bin 0 -> 210013 bytes chapters/Sequences.tex | 8 +-- chapters/discrete.sty | 80 ++++++++++++++++++++++++++++++ chapters/images/7bridgescolor.png | Bin 0 -> 198373 bytes 23 files changed, 122 insertions(+), 48 deletions(-) delete mode 100755 chapter1.tex create mode 100644 chapters/AdvancedCounting.pdf create mode 100644 chapters/CombinatorialProofs.pdf create mode 100644 chapters/Counting.pdf create mode 100644 chapters/GeneratingFunctions.pdf create mode 100644 chapters/GraphTheory.pdf create mode 100644 chapters/Induction.pdf create mode 100644 chapters/Logic.pdf create mode 100644 chapters/NumberTheory.pdf create mode 100644 chapters/Quantifiers_Sets.pdf create mode 100644 chapters/Sequences.pdf create mode 100644 chapters/discrete.sty create mode 100644 chapters/images/7bridgescolor.png diff --git a/chapter1.tex b/chapter1.tex deleted file mode 100755 index b8ed30fe3..000000000 --- a/chapter1.tex +++ /dev/null @@ -1,4 +0,0 @@ -% This is chapter1.tex. Some sort of introduction to discrete mathematics, the types of problems, and why teaching it in middle school is awesome. - -\chapter[Introduction]{Why Discrete Mathematics?} - diff --git a/chapters/AdvancedCounting.pdf b/chapters/AdvancedCounting.pdf new file mode 100644 index 0000000000000000000000000000000000000000..294c1f6c7056ff1ccc44246c54c77351494fefc8 GIT binary patch literal 184213 zcmce-V~{ORzQ5buyKURHZQHhO+qSvewr%aU?cKKR?z`tVbIzG_|8wKcxpCswo2trM z->i%kD^@(uCo@Upg+*x?XjvdhW*3K6AzAV1@$C#P@wvGn>7-3;&795g8Cltw@c%j> z=|nB8olP9^=|rs!oK1vHjO>g}AbEKqotzy_3~V6X*RwUG;`ZARdS+^GY)ta1QOePp z(*m{{Gp%7E;w|*+M-TGqms(nE$_d8yFa2^o6AFwUfyagjql{G&s@^IhV^v2~n%*YD zwid$h{1jd#5A#(m8azF9Evki5&?>nl1_;O1HUBqOjiWwDaU{G_&@@s1VNMrT~xckk{(G zqdYm*(DKn(RY%F2QGiPeDuwrLuZV(Orf_79vwZjpwGgtKi9B6;{^))xuJKf;K7<%~ z!>TFwwnQc7eo@4Gv+tJJV}7xUTCnBzrog)BcDN3;N&Fz4e5RL;VJm8I)v$+87%acy z+k@T3R8ALLa~6|pE4&-BM4{M`$%Vp}^(q&C=p&v->n-gFm_y6>PI2=}(I6}JLiV5} zn0Rw{yeP=Co7v`WFC&NBS?cTF(dfHzKN>A)5(B&+@9EXuJadfKIWqVeSY1vmofz$= 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Gxc?t{-Vq!C literal 0 HcmV?d00001 diff --git a/chapters/CombinatorialProofs.tex b/chapters/CombinatorialProofs.tex index 93fba7505..a2778a07d 100644 --- a/chapters/CombinatorialProofs.tex +++ b/chapters/CombinatorialProofs.tex @@ -1,12 +1,12 @@ \documentclass[12pt]{article} -\usepackage{../discrete} +\usepackage{discrete} -\usetikzlibrary{shapes} +\def\thetitle{Combinatorial Proofs} % will be put in the center header on the first page only. +\def\lefthead{Math 228 Notes} % will be put in the left header +\def\righthead{\thetitle} % will be put in the right header -\usepackage{pgf} -\heading{Math 228}{}{Combinatorial Proofs Notes} diff --git a/chapters/Counting.pdf b/chapters/Counting.pdf new file mode 100644 index 0000000000000000000000000000000000000000..97c650681a08e6b1117f4fa9bcab8552f953f108 GIT binary patch literal 228342 zcmcG#V|3-+_MjWvNyXT)ZKtA&ZQHhO+pgHQZ95g)tQfb>d;WO4``mF)-_gB4t-Z#Y z3*VmSH|Hdk6Beaqq+^94on0JSg<%6Q0Bj8`06aV}^isw)rcP!6CU#a%z+XQYdQo#L 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b/chapters/GeneratingFunctions.tex @@ -1,10 +1,10 @@ \documentclass[12pt]{article} -\usepackage{../discrete} - -\heading{Math 228}{}{Generating Functions Notes} - +\usepackage{discrete} +\def\thetitle{Generating Functions} % will be put in the center header on the first page only. +\def\lefthead{Math 228 Notes} % will be put in the left header +\def\righthead{\thetitle} % will be put in the right header \begin{document} \section{Generating Functions} diff --git a/chapters/GraphTheory.pdf b/chapters/GraphTheory.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e6a03e216cc3037fa154cc087e1c38752d4927fe GIT binary patch literal 372201 zcmeFYdt8iZ_y^2d+d9UISckDJIn^L5#~$mjp-m3krc#3>Q4Jl0(#<-w3aw*^2Az-$ zO6NSuj+SCnRMa#z>11lAQPZ5B=f2-->@WL!|9by^KcAn^+D~bEp8L6u-|zRjo=Iz$ z|6)1I>ZksbUcV7l^`AF>=6L?ro#PiR>d*bv%ilX_$N1USbFIgJ{?niPi;r)RSHO7g zFTPuXyq0@;^0#^Qx3%pb7!=^O#jpRq_o<_b&sJxtYEOqw<4K2pzmw@;~Ky3_`2RVOIv=S4*O4fGIix28dJ*FHcVsZ 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100644 --- a/chapters/Induction.tex +++ b/chapters/Induction.tex @@ -1,9 +1,10 @@ \documentclass[12pt]{article} -\usepackage{../discrete} - -\heading{Math 228}{}{Induction Notes} +\usepackage{discrete} +\def\thetitle{The Principle of Mathematical Induction} % will be put in the center header on the first page only. +\def\lefthead{Math 228 Notes} % will be put in the left header +\def\righthead{Induction} % will be put in the right header \begin{document} diff --git a/chapters/Logic.pdf b/chapters/Logic.pdf new file mode 100644 index 0000000000000000000000000000000000000000..430ad9d576e2b68bf3ee89206509b2cbe8cf303a GIT binary patch literal 149660 zcmce-b9AN8x~Lo5c4lnbwv&!JHafO#TOHfB&5ms+9ostnTYIfN*1mh)ao64BoHPHb zQM2Bv`sN?=d!F~LB2yFdLgCUz)7+Qg02QUI`4J`q@yf6&1CN^eH<^UEZMs~p8 zJ}?a87FJFs4gdymD+4DJQ4=FuV-pyDei%n52NMHp7`L?|oYk0v<{R&x{5pnNp!Ir5 zrTioSV<-QzBpz7$Ae5DWxz?$T>7ugMNEC%$PJ3yAL_>3YDzYXmMx^RcyGQ<}1?EM! z&%@*AB8A@2s{E>A#o+m6EKikcn#tG{4(d_-=4NUKVL%VYKwCRnAP?HZCV#Wkb?V~* 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-\section*{Quantifiers and Sets} +%\section*{Quantifiers and Sets} So far we have seen how statements can be combined with logical symbols. This is helpful when trying to understand a complicated mathematical statement - you can determine under which conditions the complicated statement is true. Additionally, we have been able to analyze the logical form of arguments to decide which arguments are valid and which are not. However, the types of statements we have been able to make so far has be sorely limited. 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a/chapters/Sequences.tex b/chapters/Sequences.tex index d89287bad..a09a8a7c0 100644 --- a/chapters/Sequences.tex +++ b/chapters/Sequences.tex @@ -1,10 +1,10 @@ \documentclass[12pt]{article} -\usepackage{../discrete} - -\heading{Math 228}{}{Sequences Notes} - +\usepackage{discrete} +\def\thetitle{Sequences} % will be put in the center header on the first page only. +\def\lefthead{Math 228 Notes} % will be put in the left header +\def\righthead{\thetitle} % will be put in the right header \begin{document} As the legend goes, there is a monastery in Hanoi with a great hall containing 3 tall pillars. Resting on the first pillar are 64 giant disks (or washers) - all different sizes, stacked from largest to smallest. The monks are charged with the following task: they must move the entire stack of disks to the third pillar. However, due to the size of the disks, the monks cannot move more than one at a time. Each disk must be placed on one of the pillars before the next disk is moved. And because the disks are so heavy and fragile, the monks may never place a larger disk on top of a smaller disk. diff --git a/chapters/discrete.sty b/chapters/discrete.sty new file mode 100644 index 000000000..52a211d12 --- /dev/null +++ b/chapters/discrete.sty @@ -0,0 +1,80 @@ +%%% This is discrete.sty +%%% It is an attempt at designing a package to be used in my discrete course notes. It will load amsmath, amsthm, etc and all the definitions I like. + +\ProvidesPackage{discrete} + +\usepackage{amssymb, amsmath, amsthm, mathrsfs, multicol, graphicx} +\usepackage[top=1in, bottom=1in, left=1in, right=1in]{geometry} +\usepackage{changepage} % for adding extra indents in environments +\usepackage{fancyhdr} +\usepackage{tikz} +\usepackage{framed} +\usepackage{textcomp} +\usepackage{booktabs} +\usepackage{ifthen} +\usepackage{everypage} + +\pagestyle{fancy} + + +\AddEverypageHook{% + \ifthenelse{\value{page}=1}% + {\renewcommand{\headrulewidth}{0.0pt}}% + {\renewcommand{\headrulewidth}{0.4pt}}% +} +%\makeatletter\let\thetitle\@title\makeatother +%headers and footers: +\renewcommand{\headrulewidth}{0.1pt} +%\renewcommand{\chaptermark}[1]{\markboth{#1}{}} +\renewcommand{\sectionmark}[1]{\markright{#1}{}} +\lhead{\ifthenelse{\value{page}=1}{}{\footnotesize \lefthead}} +\chead{\ifthenelse{\value{page}=1}{\textbf{\Large \thetitle}}{}} +\rhead{\ifthenelse{\value{page}=1}{}{\footnotesize \righthead}} +\newcommand{\heading}[3]{\clearpage{\lhead{\footnotesize #1} \chead{\bf #2} \rhead{\footnotesize #3}}} +%\chead{\title} +%\newcommand{\cleanpage}{\cfoot{}} + + + +%new list environments +\newcounter{qcounter} +\newcounter{pcounter} +\newenvironment{questions}{\begin{list}{\arabic{qcounter}.~}{\usecounter{qcounter}}}{\end{list}} +\newcommand{\question}[1]{\item #1} +\newenvironment{parts}{\begin{list}{(\alph{pcounter})~}{\usecounter{pcounter}}}{\end{list}} +\renewcommand{\part}[1]{\item #1} + + +\theoremstyle{plain} +\newtheorem*{theorem}{Theorem} +\newtheorem{problem}{Problem} +\newtheorem*{conjecture}{Conjecture} +%\newtheorem{answer}{Answer} + +\theoremstyle{definition} +\newtheorem{definition}{Definition} +%\newtheorem{example}{Example} +\newtheorem{probfact}{Probability Fact} + +\theoremstyle{remark} +\newtheorem*{remark}{Remark} +%\newtheorem*{solution}{Solution} + +%Create indented ``example'' environment: +\newenvironment{example}{\vskip 2em \begin{adjustwidth}{3em}{3em}{\bf Example}: }{\end{adjustwidth}\vskip 2em} +%Create ``solution'' environment: +\newenvironment{solution}{\vskip 1ex \noindent {\em Solution}:}{} +%Create ``defbox'' environment to highlight important definitions +\newenvironment{defbox}[1]{\vskip 1em \begin{framed}\noindent{\bf #1\\}}{\end{framed}} + +\newcommand{\ex}{\noindent{\bf Ex: }} + + +\renewcommand{\qedsymbol}{\small QED} + + +\input{../macros-discrete} + +\endinput + +%%% End of File. \ No newline at end of file diff --git a/chapters/images/7bridgescolor.png b/chapters/images/7bridgescolor.png new file mode 100644 index 0000000000000000000000000000000000000000..aa5d90bce06ec10b6aafb9b5f94364862127b6fc GIT binary patch literal 198373 zcmeFYcQ~7G`#-KzO9xf0QFPK$tM-VrT2!s7y^B^5qeiR{9ct8StG3Xhi50P8MA24J zl$0REYORonotWX9_w$kWa~!|_e*ZuBaX1L>`?{}lz0UJ>o>$C6L!FZx0vv2?Y$tW^ z-+RQy#(`jCJF0x_DDyY;%!MuHx5Iv#x~9jNSLm@P(ag`spWV0eV`G!L^3T_SpwGYn 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