Romeo and Juliet
Beamer: source file
PowerShell Scripting
Param
(
[Parameter(Mandatory=$True)][float]$number,
[Parameter(Mandatory=$True)][int]$modulus
)
Function compute
{
Param(
[Parameter(Mandatory=$True)][float]$number,
[Parameter(Mandatory=$True)][int]$modulus
)
$counter = 1
if ($modulus -eq 0) {"error: no solutions"} else {
$mod = if ($modulus -gt 0) {$modulus} else {-1 * $modulus}
$num = if ($number -gt 0) {$number} else {-1 * $number}
while ($counter * $mod -le $num) {$counter++}
$final = $num - (($counter - 1) * $mod) ; if ($final -eq 0) {0}
elseif ($number -gt 0 -and $modulus -gt 0) {$final}
elseif ($number -lt 0 -and $modulus -gt 0) {$mod - $final}
elseif ($number -lt 0 -and $modulus -lt 0) {-1 * $final}
elseif ($number -gt 0 -and $modulus -lt 0) {-1 * ($mod - $final)}
}
compute $number $modulus
Param (
[string]$path = $(Read-Host "The path to the play, please"),
[string]$hero = $(Read-Host "The Name of the hero please"),
[string]$first_key_word = $(Read-Host "The first key-word please"),
[string]$second_key_word = $(Read-Host "The first key-word please. Otherwise hit Enter")
)
$counter = 1
$play = [xml](Get-Content "$path.xml")
$play.play.act | ForEach-Object {$act = $PSItem
foreach ($scene in $act.scene)
{ foreach ($speech in $scene.speech)
{if ($speech.speaker -match $hero `
-and ($speech.line -replace '[,\.-\:]') -match $first_key_word `
-and ($speech.line -replace '[,\.-\:]') -match $second_key_word)
{"`n$counter`n$($act.title)`n$($scene.title)`n$($speech.speaker)`n"
$speech.line ; "`n"
$counter = $counter + 1}}}}
LaTeX (simple)
\documentclass[12pt]{article}
%\usepackage{polski}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{comment}
\usepackage{csquotes}
\usepackage{graphicx} % Required for inserting images
\usepackage{blindtext}
\usepackage{wrapfig}
\usepackage{array}
\newcolumntype{C}[1]{>{\centering\arraybackslash}p{#1}}
\newcolumntype{R}[1]{>{\raggedleft\arraybackslash}p{#1}}
\usepackage{enumerate}
\usepackage{lettrine}
%\usepackage{fontspec}
\title{2025IT}
\author{maarten.wolski }
\date{November 2025}
\begin{document}
\maketitle
\begin{abstract}
\blindtext
\end{abstract}
\section{Introduction}
\lettrine{H}{ow about this?} \blindtext
\blindtext
\begin{wrapfigure}{l}{0.4\textwidth}
\includegraphics[scale=0.3]{DylanRotolo.jpg}
\caption{Very famous photo}
\end{wrapfigure}
\blindtext
\section{Nothing Special}
\blindtext
\begin{figure}
\centering
\includegraphics[scale=0.4]{DylanRotolo.jpg}
\caption{The very old and famous photo}
\end{figure}
\blindtext
\blindtext
\begin{table}[]
\centering
\begin{tabular}{|p{3cm}|C{4cm}|R{3cm}|} \hline
A & B & C \\ \hline
\end{tabular}
\end{table}
\blindtext
\begin{enumerate}[i)]
\item hmmm
\item ammmm
\item ototot
\end{enumerate}
\section{Something Unimportant}
\lettrine{H}{imalaya mountains are really impressive}.
It is a mountain range in Asia separating the plains of the Indian
sub-continent from the Tibetan Plateau.
The range has some of the Earth's highest peaks, including
the highest, Mount Everest.
More than 100 peaks exceeding elevations of 7,200 m (23,600 ft)
above sea level lie in the Himalayas.
\begin{thebibliography}{[99]}
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\bibitem Ktoś, Jakaś książka, 2025
\end{thebibliography}
\end{document}
LaTeX (a bit more complex)
\documentclass{fundam2025}
%\usepackage{polski}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{comment}
\usepackage{csquotes}
\usepackage{graphicx} % Required for inserting images
\usepackage{blindtext}
\usepackage{wrapfig}
\usepackage{array}
\newcolumntype{C}[1]{>{\centering\arraybackslash}p{#1}}
\newcolumntype{R}[1]{>{\raggedleft\arraybackslash}p{#1}}
\usepackage{enumerate}
\usepackage{lettrine}
\usepackage{uncial}
\title{2025IT}
\author{maarten.wolski }
\date{November 2025}
\runninghead{Maarten W.}{Intro to \LaTeX}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\large
%\unclfamily
%\sffamily
\maketitle
\begin{abstract}
\blindtext
\end{abstract}
\section{{\unclfamily Introduction}}
\lettrine{H}{ow about this?} \blindtext \cite{Ganter1989}.
{\unclfamily What the hell?}
{\setlength{\arrayrulewidth}{0.5mm}
\begin{table}
\centering
\begin{tabular}{|p{4cm}|C{3cm}|c|}\hline
\multicolumn{3}{|c|}{Some things you may encouter} \\ \hline \hline
Something strange & Something neutral & Something plain \\ \hline
water \textbf{water} Water water water & water & water \\ \hline
\end{tabular}
\caption{An examplary table}
\label{Thick}
\end{table}
}
\blindtext
\begin{wrapfigure}{l}{0.4\textwidth}
\includegraphics[scale=0.3]{DylanRotolo.jpg}
\caption{Very famous photo}
\end{wrapfigure}
\blindtext \cite{Bonikowski}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Nothing Special}
\blindtext
\begin{table}
\centering
\begin{tabular}{|p{4cm}|C{3cm}|c|}\hline
\multicolumn{3}{|c|}{Some things you may encouter} \\ \hline \hline
Something strange & Something neutral & Something plain \\ \hline
water \textbf{water} Water water water & water & water \\ \hline
\end{tabular}
\caption{An examplary table}
\label{Thin}
\end{table}
\begin{figure}
\centering
\includegraphics[scale=0.4]{DylanRotolo.jpg}
\caption{The very old and famous photo}
\end{figure}
\blindtext
\blindtext \cite{Greco2010}
\begin{wraptable}{r}{0.44\textwidth} \normalsize
\caption{My first stupid table}
\rotatebox{180}{
\begin{tabular}{|p{2cm}|c|p{2cm}|}\hline
\multicolumn{3}{|c|}{Minions and Me} \\ \hline
Maarten is a smart minion & Fred & George is a smart minion \\ \hline
\end{tabular}
}
\end{wraptable}
\blindtext
\begin{table}
\centering
\begin{tabular}{|p{3cm}|C{4cm}|R{3cm}|} \hline
A & B & C \\ \hline
\end{tabular}
\end{table}
\blindtext
\begin{enumerate}[i)]
\item hmmm
\item ammmm
\item ototot
\end{enumerate}
\section{Something Unimportant}
\lettrine{H}{imalaya mountains are really impressive}. It is a mountain range in Asia
separating the plains of the Indian sub-continent from the Tibetan Plateau. The range
has some of the Earth's highest peaks, including the highest, Mount Everest. More
than 100 peaks exceeding elevations of 7,200 m (23,600 ft) above sea level lie in the
Himalayas.
\bibliography{it2025}
\bibliographystyle{apalike}
\end{document}
LaTeX (Advanced: Diagrams)
\documentclass{article}
\usepackage{graphicx} % Required for inserting images
\usepackage{graphics}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{diagrams}
\usepackage{color}
\usepackage{amssymb}
\title{Christmas 2025}
\author{maarten.wolski }
%\date{December 2025}
\begin{document}
\maketitle
\section{Introduction}
\begin{diagram}
& &\bigstar & & \\
& \ldLine(2,2)_{o} &\bigstar & \rdLine(2,2)_{o} & \\
o &\ldLine(2,2)_{o} &\bigstar & \rdLine(2,2)_{o}& o \\
o &\ldLine(2,2)_{o} &\bigstar & \rdLine(2,2)_{o}& o\\
o & \ldLine(2,2)_{o}&\bigstar & \rdLine(2,2)_{o}& o\\
o &\ldLine(2,2)_{o} &\bigstar &\rdLine(2,2)_{o} & o\\
o & &\bigstar & & o\\
& &\bigstar & & \\
& & /\backslash & &\\
\end{diagram}
\begin{tabular}{|p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|}\hline
& & & & \\ \hline
& & & & \\ \hline
& & & & \\ \hline
& & & & \\ \hline
\end{tabular}
\begin{figure}[h]
\begin{diagram}
\textrm{Left side} & & \rTo^{\textrm{\textbf{Christmas Tree}}}_{2025} & & Right \\
\dTo & \rdTo(2,3) \rdTo(4,3) & & \ruTo(4,3) \ruTo(2,3) & \\
& & & & \\
Hell & & Purgatory & & Heaven\\
\end{diagram}
\end{figure}
\begin{diagram}
\textrm{Tree 1} & \rTo^{function} &\textrm{Tree 2} & \rTo_{function} & Tree \\
\dLine & & & \ruTo(4,4) & \\
& & & \\
& & & \\
Roots & & & \\
\end{diagram}
\begin{figure}[h!]
\centering
\begin{diagram}
\textrm{Start} & \lTo_{f} & Middle & \rLine & Finish \\
\dTo & \rdTo(2,3) & & \rdTo(2,3) \ruTo(2,3) & \\
& & & & \\
Hell & & \textrm{North Pole} & & Hell \\
\end{diagram}
\end{figure}
\begin{figure}[h]
\centering
\begin{diagram}
Start & \rLine & Middle & \rLine & Finish \\
\dTo & \rdTo(2,3) \rdTo(2,2) \ldTo(2,3) & & \ruTo(2,2) \ruDashto(2,3) & Hi \\
& & Heaven & \ruTo(2,2) & \\
\textrm{Left} & & Hell & & \\
\end{diagram}
\end{figure}
\begin{figure}
\centering
\begin{diagram}
& & & \bigstar & & & \\
& & \ruTo(3,3)^{**} & \dLine & \luLine(3,3)^{**} & & \\
& & \ruLine(3,3)^{**} & & \luLine(3,3)^{**} & & \\
o & & \ruLine(3,3)^{**} & & \luLine(3,3)^{**} & & o \\
o & & \ruLine(3,3)^{**} & & \luLine(3,3)^{**} & & o \\
o & & \ruLine(3,3)^{**} & & \luLine(3,3)^{**} & & o\\
o & & \ruLine(3,3)^{**} & & \luLine(3,3)^{**} & & o \\
o & & \ruLine(3,3)^{**} & & \luLine(3,3)^{**} & & o \\
o & & \ruLine(3,3)^{**} & & \luLine(3,3)^{**} & & o\\
o & & & & & & o\\
o & & & /\backslash & & & o \\
\end{diagram}
\caption{Our Chritmas Tree}
\label{fig:placeholder}
\end{figure}
\begin{figure}[h]
\begin{center}
\begin{diagram}
& & & God & & & \\
& & \ldTo(3,5) & & \rdTo(3,5) & & \\
Revelation & & &\rLine & & & Creation \\
& &\rdLine(2,5) && \ldLine(2,5) & & \\
& & & & & & \\
Human & & &\rTo & & & World \\
& & & & & & \\
& & & Redemption & & & \\
\end{diagram}
\end{center}
\caption{Star of Redemption}
\end{figure}
\begin{figure}[h!]
\begin{diagram}
& & & Top & & &\\
& &\ldTo(3,4) & & \rdTo(3,4) & &\\
LeftTop & & & \rLine & & & RightTop \\
&\rdLine(3,4) & & & &\ldLine(3,4) & \\
Left & & & \rTo & & & Right \\
& & & & & & \\
& & & Bottom & & &\\
\end{diagram}
\end{figure}
\begin{figure}[h]
\begin{diagram}
& & & GOD & & & \\
& &\ldTo(3,5) & &\rdTo(3,5) & & \\
Revelation& & & \rLine & & &Creation\\
& \rdLine(3,5) & & & &\ldLine(3,5) & \\
& & & & & &\\
Human& & & \rTo & & &World\\
& & & & & & \\
& & & Redemption & & &\\
\end{diagram}
\end{figure}
\begin{figure}
\centering
\begin{diagram}
%%%%%%%%%% HEAD
\textrm{\textcolor{blue}{L 3}} & \textrm{\textcolor{blue}{L 2}} & \textrm{\textcolor{blue}{L 1}} & \textrm{\textcolor{red}{C 0}} & \textrm{\textcolor{blue}{R 1}} & \textrm{\textcolor{blue}{R 2}} & \textrm{\textcolor{blue}{R 3}} \\
%%%%%%%%%% 0 ROW
\textrm{leftU 2,6} & 0 & \lDashto & O & \rDotsto & 6 & ~~~~~ \\
%%%%%%%%%% 1 ROW
\textrm{leftU 2,5} & 1 \luDashto(5,3) & \ldTo(3,6) \luDotsto(2,6) \ldTo(2,1) \ldTo~{\textcolor{red}{red}}(2,2) \ldTo(2,3) \ldTo(2,4) & \dLine & \ruDashto(2,6) \rdTo(2,4) \rdTo(2,2) \rdTo(2,1) \rdTo(2,3) \rdTo(2,4) \rdTo(2,5) \rdTo(2,6) \rdDotsto(3,6) & 5 &\\
%%%%%%%%%% 2 ROW
\textrm{\textcolor{red}{leftD 2,2}} & 2 & \luTo(2,5) & O & \ruTo(2,5) & 4 &\\
%%%%%%%%%% 3 ROW
& 3 & \luTo(2,4) & \dLine & \ruTo(2,4) & 3 &\\
%%%%%%%%%% 4 ROW
& 4 & \luTo(2,3) & OO & \ruTo(2,3) \ldDashto(5,3) & 2 &\\
%%%%%%%%%% 5 ROW
& 5 & \luTo(2,2) & OOO & \ruTo(2,2) & 1 & \\
%%%%%%%%%% 6 ROW
\textrm{\textcolor{blue}{leftD 3,6}} & 6 & \luTo(2,1) \lTo & OOOO & \ruTo(2,1) \rTo & 0 & \textrm{\textcolor{blue}{rightD 3,6}} \\
\end{diagram}
\caption{The guide to coordinates}
\end{figure}
\begin{figure}
\centering
\begin{diagram}
& & & \bigstar & & & o \\
& & \ruDashto(3,4) \ldDashto(3,4) & \bigstar & & \ruDashto(6,2) & \bigstar \\
x & & & \bigstar & & \ldDotsto(5,2) & \\
& o & & \bigstar & & & \\
\bigstar & & & \bigstar & & & \\
\end{diagram}
\end{figure}
\section{Powershell}
\begin{verbatim}
Windows PowerShell
Copyright (C) Microsoft Corporation. All rights >>>>> reserved.
Try the new cross-platform PowerShell https://aka.ms/pscore6
PS C:\Users\maart> New-Item -ItemType Directory -Path ITOnline2025
Directory: C:\Users\maart
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:01 ITOnline2025
PS C:\Users\maart> Set-Location .\ITOnline2025\
PS C:\Users\maart\ITOnline2025> foreach ($x in 1,2,3)
{New-Item -ItemType Directory -Path "Christmas Tree $x\Santa Claus $x"}
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 1
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:05 Santa Claus 1
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 2
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:05 Santa Claus 2
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 3
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:05 Santa Claus 3
PS C:\Users\maart\ITOnline2025> Get-ChildItem
Directory: C:\Users\maart\ITOnline2025
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:05 Christmas Tree 1
d----- 16/12/2025 13:05 Christmas Tree 2
d----- 16/12/2025 13:05 Christmas Tree 3
PS C:\Users\maart\ITOnline2025> Get-ChildItem '.\Christmas Tree 2\'
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 2
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:05 Santa Claus 2
PS C:\Users\maart\ITOnline2025> Get-ChildItem | ForEach-Object {foreach ($x in 1,2,3)
{New-Item -ItemType Directory -Path $PSItem\"Mikolaj nr $x"}}
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 1
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:08 Mikolaj nr 1
d----- 16/12/2025 13:08 Mikolaj nr 2
d----- 16/12/2025 13:08 Mikolaj nr 3
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 2
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:08 Mikolaj nr 1
d----- 16/12/2025 13:08 Mikolaj nr 2
d----- 16/12/2025 13:08 Mikolaj nr 3
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 3
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:08 Mikolaj nr 1
d----- 16/12/2025 13:08 Mikolaj nr 2
d----- 16/12/2025 13:08 Mikolaj nr 3
PS C:\Users\maart\ITOnline2025> Get-ChildItem | ForEach-Object { foreach
($x in (Get-ChildItem $PSItem)) { if ($x.Name -match "Mikolaj")
{Rename-Item -Path $PSItem\$x -NewName "$($x.Name.Replace('nr','No')) of $PSItem"}}}
PS C:\Users\maart\ITOnline2025> Get-ChildItem | ForEach-Object {Get-ChildItem $PSItem}
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 1
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:08 Mikolaj No 1 of Christmas Tree 1
d----- 16/12/2025 13:08 Mikolaj No 2 of Christmas Tree 1
d----- 16/12/2025 13:08 Mikolaj No 3 of Christmas Tree 1
d----- 16/12/2025 13:05 Santa Claus 1
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 2
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:08 Mikolaj No 1 of Christmas Tree 2
d----- 16/12/2025 13:08 Mikolaj No 2 of Christmas Tree 2
d----- 16/12/2025 13:08 Mikolaj No 3 of Christmas Tree 2
d----- 16/12/2025 13:05 Santa Claus 2
Directory: C:\Users\maart\ITOnline2025\Christmas Tree 3
Mode LastWriteTime Length Name
---- ------------- ------ ----
d----- 16/12/2025 13:08 Mikolaj No 1 of Christmas Tree 3
d----- 16/12/2025 13:08 Mikolaj No 2 of Christmas Tree 3
d----- 16/12/2025 13:08 Mikolaj No 3 of Christmas Tree 3
d----- 16/12/2025 13:05 Santa Claus 3
PS C:\Users\maart\ITOnline2025>
\end{verbatim}
\section{Bash Shell}
\begin{verbatim}
maarten@MaartenYoga:~/OnLineClassIT$ mkdir -p Chirstmas\ Tree\ {1..5}/Santa\ Claus\ {1..3}
maarten@MaartenYoga:~/OnLineClassIT$ ls
Chirstmas Tree 1 Chirstmas Tree 2 Chirstmas Tree 3 Chirstmas Tree 4 Chirstmas Tree 5
maarten@MaartenYoga:~/OnLineClassIT$ ls Chirstmas\ Tree\ 2
Santa Claus 1 Santa Claus 2 Santa Claus 3
maarten@MaartenYoga:~/OnLineClassIT$ ls | xargs -I Item bash -c 'parent="Item" ;
ls "$parent" > "$parent".txt ; while read x ; do old="$x" ;
new="${old/"$old"/"$old of $parent"}" ;
mv "$parent"/"$old" "$parent"/"$new" ; done < "$parent".txt'
maarten@MaartenYoga:~/OnLineClassIT$ ls
Chirstmas Tree 1 Chirstmas Tree 2 Chirstmas Tree 3
Chirstmas Tree 4 Chirstmas Tree 5
Chirstmas Tree 1.txt Chirstmas Tree 2.txt Chirstmas Tree 3.txt
Chirstmas Tree 4.txt Chirstmas Tree 5.txt
maarten@MaartenYoga:~/OnLineClassIT$ ls Chirstmas\ Tree\ 2
Santa Claus 1 of Chirstmas Tree 2 Santa Claus 2 of Chirstmas Tree 2
Santa Claus 3 of Chirstmas Tree 2
maarten@MaartenYoga:~/OnLineClassIT$
maarten@MaartenYoga:~/OnLineClassIT$ ls | xargs -I Item bash -c 'echo Item ; ls -l "Item"'
Chirstmas Tree 1
total 0
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 1 of Chirstmas Tree 1
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 2 of Chirstmas Tree 1
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 3 of Chirstmas Tree 1
Chirstmas Tree 1.txt
-rw-r--r-- 1 maarten maarten 42 Dec 16 12:58 Chirstmas Tree 1.txt
Chirstmas Tree 2
total 0
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 1 of Chirstmas Tree 2
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 2 of Chirstmas Tree 2
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 3 of Chirstmas Tree 2
Chirstmas Tree 2.txt
-rw-r--r-- 1 maarten maarten 42 Dec 16 12:58 Chirstmas Tree 2.txt
Chirstmas Tree 3
total 0
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 1 of Chirstmas Tree 3
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 2 of Chirstmas Tree 3
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 3 of Chirstmas Tree 3
Chirstmas Tree 3.txt
-rw-r--r-- 1 maarten maarten 42 Dec 16 12:58 Chirstmas Tree 3.txt
Chirstmas Tree 4
total 0
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 1 of Chirstmas Tree 4
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 2 of Chirstmas Tree 4
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 3 of Chirstmas Tree 4
Chirstmas Tree 4.txt
-rw-r--r-- 1 maarten maarten 42 Dec 16 12:58 Chirstmas Tree 4.txt
Chirstmas Tree 5
total 0
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 1 of Chirstmas Tree 5
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 2 of Chirstmas Tree 5
drwxr-xr-x 1 maarten maarten 512 Dec 16 12:07 Santa Claus 3 of Chirstmas Tree 5
Chirstmas Tree 5.txt
-rw-r--r-- 1 maarten maarten 42 Dec 16 12:58 Chirstmas Tree 5.txt
maarten@MaartenYoga:~/OnLineClassIT$
\end{verbatim}
The nice feature of Diagrams is this: \begin{diagram}
from~Start & \rTo^{\textbf{Life}}_{\textbf{is sacred}} & to~Finish
\end{diagram}
\end{document}
LaTeX (Beamer Presentations – Simple)
\documentclass{beamer}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{graphicx}
\usepackage{comment}
\definecolor{brightorange}{HTML}{FFA500}
\definecolor{blueme}{HTML}{2A82DA}
\definecolor{greenme}{HTML}{2DDA2A}
\definecolor{orangeme}{HTML}{F77128}
\definecolor{pinkme}{HTML}{F72882}
\definecolor{orangedark}{HTML}{D17B03}
\definecolor{greendark}{HTML}{074203}
\definecolor{yellowme}{HTML}{FFD68D}
\newtheorem{proposition}{Proposition}
\usetheme{Warsaw}
\definecolor{my}{HTML}{444444}
\usecolortheme[named=my]{structure}
\date{}
\title[Writing: How-To]{\textcolor{brightorange}{\textbf{Academic Writing:}}\\ \textcolor{greenme}{\textbf{How-To Knowledge}}}
\author{\textbf{Maarten Wolski \inst{\textcolor{blueme}{1}}} \and \textbf{Joanna Joanna}\inst{\textcolor{pinkme}{2}}}
\institute{$^1$Department of Logic and Cognitive Science\\ Maria
Curie-Skłodowska
University \and $^2$Department of Something Important \\ University of Nowhere
}
\date{}
\begin{document}
%\setbeamercovered{transparent}
\AtBeginSection[]
{
\begin{frame}
\frametitle{Outline}
\tableofcontents[currentsection]
\end{frame}
}
\begin{frame}
\titlepage
\end{frame}
\begin{frame}
Four main qualities of good writing:
\begin{enumerate}
\item \textcolor{blueme}{\textbf{Simplicity}}: makes writing punchy.
\item \textcolor{blueme}{\textbf{Clarity}}: makes it easy to understand.
\item \textcolor{blueme}{\textbf{Elegance}}: makes writing flow well.
\item \textcolor{blueme}{\textbf{Evocativeness}}: makes prose stimulating.
\end{enumerate}
\end{frame}
\section{Simplicity: Case Study}
\end{document}
LaTeX (Beamer Presentations – Advanced)
\documentclass{beamer}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
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\date{}
\title[Metamathematics of Mathematics of Data]{The Mathematics of Metamathematics of Mathematics (of Data)}
\author{\textbf{Marcin Wolski}}
\institute{\textcolor{black}{\textbf{\tiny{Department of Logic and Cognitive Science, Maria
Curie-Skłodowska University, Lublin, Poland}}}}
\date{}
\begin{center}
\begin{minipage}{\textwidth}
%\centering
% \textbf{\textcolor{black}{The Lvov-Warsaw School: Past, Present and Future}}\\
\end{minipage}
%\end{center}
%\begin{center}
\begin{minipage}{\textwidth}
\centering
\begin{tabular}{ccc}
{\includegraphics[scale=.8]{HRb.jpg}} & {\includegraphics[scale=.14]{Rauszerb.png}} & {\includegraphics[scale=.19]{Pawlakb.png}}
\end{tabular}\\
\textbf{\tiny{Helena Rasiowa (1917-1994), Cecylia Rauszer (1942-1994), Zdzis\l{}aw Pawlak (1926-2006)}}
\end{minipage} %\hfill
\end{center}
\begin{document}
\setbeamercovered{transparent}
\AtBeginSection[]
{
\begin{frame}
\frametitle{Outline}
\tableofcontents[currentsection]
\end{frame}
}
\begin{frame}
\vspace{-2.5cm}
\titlepage
\end{frame}
\begin{frame}
\tableofcontents
\end{frame}
\section{Mathematics and Metamathematics of Data}
\subsection{Rough Set Theory}
\begin{frame}
\vspace{-2cm}
\begin{wrapfigure}{l}{4.5cm}
\vspace{-1cm}
\includegraphics[scale=0.35]{RasiowaBook.jpg}
\end{wrapfigure}
\emph{"the book is used for lectures and eagerly read, even by beginners - it does not require the reader to have any special mathematical preparation"}
\end{frame}
\begin{frame}
\begin{figure}[ht!]
\[U = \{apple, grapefruit, kiwi, plum, mango\},\]
\[ Att = \{\textbf{colour},\textbf{firm},\textbf{form}\},\ \ D = \textbf{smooth}\]
%\scalebox{0.88}{
%\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\multicolumn{1}{c}{\textcolor{orangeme}{\textbf{objects}}}& \multicolumn{3}{c}{\textcolor{orangeme}{\textbf{conditional attributes}}} &\multicolumn{1}{c}{\textcolor{orangeme}{\textbf{decision}}} \\ \hline
\textbf{fruit}~ & ~\textbf{colour}~ & ~\textbf{firm}~ & ~\textbf{form}~ & ~\textbf{smooth}~ \\ \hline
~$apple$~ & ~$yellow$~ & ~$no$~ & ~$round$~ & ~$yes$~ \\ \hline
~$grapefruit$~ & $yellow$ & $no$ & $round$ & $no$ \\ \hline
$kiwi$ & $green$ & $no$ & $oval$ & $no$ \\ \hline
$plum$ & $blue$ & $no$ & $oval$ & $yes$ \\ \hline
$mango$ & $green$ & $no$ & $oval$ & $yes$ \\ \hline
\end{tabular}
\caption{A data/decision table of fruits}
%\end{center}
\label{table}
\end{figure}
\end{frame}
\begin{frame}
\begin{definition}[Information System]
A quadruple $\mathcal{I} = (U, Att, Val, f)$ is called an \emph{information
system}, where:
\begin{itemize}
\item $U$ is a nonempty finite set of objects,
\item $Att$ is a nonempty finite set of conditional attributes,
\item $Val = \bigcup_{A\in Att} Val_{A}$, where $Val_{A}$ is the value--domain
of
the attribute $A$,
\item $f:U\times Att \rightarrow Val$ is an information function, such that
for all
$A\in Att$ and $x\in U$ it holds that $f(x,A) \in Val_{A}$.
\end{itemize}
If $f$ is a partial function, then the information system $\mathcal{I}$ is
called
\emph{incomplete}. If the codomain of $f$ is the powerset of $Val$, then the
system is called \emph{multivalued}, \emph{approximate}, or
\emph{nondeterministic}.
\end{definition}
\end{frame}
\begin{frame}
\begin{definition}[Lower and Upper Approximations]
A pair $(U,E)$, where $E$ is an equivalence relation, is called an
\emph{approximation
space}. Define:
\[{L}ow_E(X) = \{x\in U: [x]_E\subseteq X\}, \]
\[{U}pp_E(X) = \{x\in U: [x]_E \cap X \not = \emptyset\}. \]
${L}ow_E(X)$ is called the \emph{lower approximation} of $X$, whereas
${U}pp_E(X)$ is
called the \emph{upper approximation} of $X$.
\end{definition}
Every (sub)set of
attributes $\mathcal{A} \subseteq Att$ induces an \emph{approximation space},
which is a pair $(U,E_{\mathcal{A}})$, where the
relation
$E_{\mathcal{A}}$ is defined by \[E_{\mathcal{A}} = \{(x,y): f(x,A) = f(y,A)\
\textrm{ for all }\
A\in
\mathcal{A}\}.\]
\end{frame}
\subsection{Formal Concept Analysis}
\begin{frame}
\begin{figure}[ht!]
\[U = \{apple, grapefruit, kiwi, plum, mango\},\]
\[ Att = \{\textbf{yellow}, \textbf{green}, \textbf{blue},\textbf{oval},\textbf{round}, \textbf{smooth}\}\]
\scalebox{0.9}{
%\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\multicolumn{1}{c}{\textcolor{orangeme}{\textbf{objects}}}& \multicolumn{6}{c}{\textcolor{orangeme}{\textbf{properties}}} \\ \hline %&\multicolumn{1}{c}{\textcolor{orangeme}{\textbf{decision}}} \\ \hline
\textbf{fruit}~ & ~\textbf{yellow}~ & ~\textbf{green}~ & ~\textbf{blue}~ & ~\textbf{oval}~ & ~\textbf{round}~ & ~\textbf{smooth}~ \\ \hline
~$apple$~ & \cmark & & & & \cmark & \cmark \\ \hline
~$grapefruit$~ & \cmark & & & & \cmark & \\ \hline
$kiwi$ & & \cmark & & \cmark & & \\ \hline
$plum$ & & & \cmark & \cmark & & \cmark \\ \hline
$mango$ & & \cmark & & \cmark & & \cmark \\ \hline
\end{tabular}
}
\caption{A formal context of fruits}
%\end{center}
\label{table}
\end{figure}
\end{frame}
\begin{frame}
\begin{definition}[Formal Context]
A \emph{formal context} is a triple $(U,Att,R)$, where $U$ is a set of objects,
$Att$ a
set of properties and $R\subseteq U\times Att$ is a binary relation,
where $(x,A)\in R$ reads as \emph{the object $x$ has the property $A$}.
\end{definition}
\begin{definition}[Derivation Operators]
For a formal context $\mathcal{C} = (U,Att,R)$, we define:
\[R'(X) = \{A\in Att:\ (x,A) \in R,\ \textrm{ for all } x \in X\}\]
\[R'(\mathcal{A}) = \{x\in U:\ (x,A) \in R, \textrm{ for all } A\in
\mathcal{A}\},\]
for all $X\subseteq U$ and $\mathcal{A}\subseteq Att$.
\end{definition}
\end{frame}
\subsection{Adjunctions and Toplogy}
\begin{frame}
\begin{definition}[Adjunction/Galois Connection]
\label{d-4e}
Let $\mathcal{U}=(U, \leq)$ and $\mathcal{V}=(V, \preceq)$ be two partially ordered sets (also called posets). If $\pi_{\ast}:U\to V$ and $\pi^{\ast}:V\to U$ are functions satisfying the following requirement:
\begin{center}
\[x\leq\pi^{\ast}(y)\ \textrm{ iff }\ \pi_{\ast}(x)\preceq y,\]
\end{center}
for all $x\in U$ and $y\in V$, then a system $\pi=( \mathcal{U},\pi_{\ast},\pi^{\ast},\mathcal{V})$
is called \emph{adjunction} or \emph{Galois connection}, $\pi_{\ast}$ is called a \emph{left adjoint} of $\pi^{\ast}$, and $\pi^{\ast}$ is called a \emph{right adjoint} of $\pi_{\ast}$.
\end{definition}
\end{frame}
\section{Cecylia Rauszer: Mathematics of Metamathematics}
\subsection{Heyting-Brouwer Algebras}
\begin{frame}
\begin{definition}[Heyting Algebra]
An algebra $(U,\leq,\vee,\wedge,\stackrel{\wedge}{\to},\top,\bot)$ is called \emph{Heyting algebra} iff $(U,\leq,\vee,\wedge,\stackrel{\wedge}{\to},\top,\bot)$ is a bounded distributive lattice and
$\stackrel{\wedge}{\to}$ is a relative pseudo-complement of $x$ to $z$, for $x,y,z \in U$:
%is a relative pseudo-complement of $a$ with respect to $c$, i.e.,
\[ x \wedge y \leq z\ \textrm{ iff }\ y \leq x \stackrel{\wedge}{\to} z,\]
\end{definition}
\begin{definition}[HBA]
\emph{Heyting-Brouwer Algebra} (HBA) $(U,\leq,\vee,\wedge, \stackrel{\wedge}{\to}, \stackrel{\vee}{\to},\top,\bot)$ is a~Heyting algebra
%is a Heyting algebra
$(U,\leq,\vee,\wedge,\stackrel{\wedge}{\to},\top,\bot)$ provided with a \emph{co-implication} $\stackrel{\vee}{\to}$, such that, for $x,y,z \in U $:
\[ x \vee y \geq z\ \textrm{ iff }\ y \geq x \stackrel{\vee}{\to} z,\]
\end{definition}
\end{frame}
\subsection{Heyting-Brouwer Logic}
\begin{frame}
Heyting-Brouwer logic ($HBL$) is defined in the propositional language $\mathcal{L}_{HB}$ whose connectives are:
\[\wedge, \vee, \stackrel{\wedge}{\to}, \stackrel{\vee}{\to}, \top, \bot.\] Axioms of $HBL$ were introduced by C.~Rauszer. Due to the topological settings we use F.~Wolter's version.
Let us define: $\stackrel{\wedge}{\neg} \alpha \stackrel{def}{=} \alpha \stackrel{\wedge}{\to} \bot$, $\stackrel{\vee}{\neg} \alpha \stackrel{def}{=} \alpha \stackrel{\vee}{\to} \top$, and
\[ H = \{ \alpha \stackrel{\wedge}{\to} (\beta \vee (\beta \stackrel{\vee}{\to} \alpha)), (\beta \stackrel{\vee}{\to} \alpha) \stackrel{\wedge}{\to} \stackrel{\vee}{\neg} (\alpha \stackrel{\wedge}{\to} \beta),\]
\[ (\gamma \stackrel{\vee}{\to} (\beta \stackrel{\vee}{\to}\alpha)) \stackrel{\wedge}{\to} ((\alpha \vee \beta) \stackrel{\vee}{\to} \alpha), \stackrel{\wedge}{\neg}(\beta \stackrel{\vee}{\to} \alpha) \stackrel{\wedge}{\to} (\alpha \stackrel{\wedge}{\to} \beta), \stackrel{\wedge}{\neg}(\alpha\stackrel{\vee}{\to} \alpha)\}.\]
The logic $HBL$ is the smallest logic including $INT \cup H$, where $INT$ denotes some axiomatisation of intuitionistic logic, and closed under substitution, \textit{modus ponens}, and
\[ \frac{\alpha}{\stackrel{\wedge}{\neg} \stackrel{\vee}{\neg} \alpha}\ \ .\]
\end{frame}
\subsection{Dominance Rough Sets}
\begin{frame}
\begin{figure}[ht!]
\[U = \{Anne, Bob, Eve, Stephen, Alice\},\]
\[ Att = \{\textbf{science},\textbf{art},\textbf{philosophy}\},\ \ D = \textbf{final score}\]
%\scalebox{0.88}{
%\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\multicolumn{1}{c}{\textcolor{orangeme}{\textbf{objects}}}& \multicolumn{3}{c}{\textcolor{orangeme}{\textbf{conditional attributes}}} &\multicolumn{1}{c}{\textcolor{orangeme}{\textbf{decision}}} \\ \hline
\textbf{student}~ & ~\textbf{science}~ & ~\textbf{art}~ & ~\textbf{philosophy}~ & ~\textbf{final score}~ \\ \hline
~$Anne$~ & ~$4$~ & ~$5$~ & ~$5$~ & ~$5$~ \\ \hline
~$Bob$~ & $3$ & $5$ & $3$ & $4$ \\ \hline
$Eve$ & $4$ & $4$ & $4$ & $4$ \\ \hline
$Stephen$ & $4$ & $5$ & $5$ & $4$ \\ \hline
$Alice$ & $4$ & $5$ & $3$ & $3$ \\ \hline
\end{tabular}
\caption{A data/decision table of students}
%\end{center}
\label{table}
\end{figure}
\end{frame}
\begin{frame}
\begin{figure}
\scalebox{.9}{
\centering
\begin{tabular}{c}\\
\textbf{Classical Rough Set Theory} \\
$\Downarrow$\\
\textbf{Indiscernibility Principle} \\
If $x$ and $y$ are indiscernible with respect to conditional attributes,\\
then $x$ should be classified to the same decision class as $y$.
$ $ \\
$ $\\
$ $\\
\textbf{Dominance-based Rough Sets} \\
Greco, S., Matarazzo, B., Słowiński, R.:\\ Rough sets theory for multi-criteria decision analysis.\\ European Journal of Operational Research, 129, 1 (2001) 1–47\\
$\Downarrow$\\
\textbf{Dominance Principle} \\
If $x$ at least as good as $y$ with respect to conditional attributes ($\boldsymbol{y\leq_D x}$),\\
then $x$ should be classified (with respect to a decision attribute)\\ as least as good as $y$.
\end{tabular}}
%\caption{Principles of interpretation and classification}
\label{Princi}
\end{figure}
\end{frame}
\begin{frame}
{\textbf{\Huge{\textcolor{blueme}{Your} \textcolor{greenme}{Questions},
\textcolor{orangeme}{Comments}, \textcolor{pinkme}{Complaints}, or any Form of
Feedback \textcolor{blueme}{Are Welcome} and Appreciated}}}
\end{frame}
\end{document}
