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+\documentclass[11pt]{beamer}
+\usetheme{Madrid}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath}
+
+\usepackage{tikz}
+\usetikzlibrary{calc}
+\usepackage{svg}
+
+\author[\texttt{sebastiano.tronto@uni.lu}]{Sebastiano Tronto}
+\title[Python Intro and a bit of Sage]%
+{A Practical Introduction to Python (and a bit of Sage)}
+\logo{\includegraphics[scale=0.1]{img/unilu.jpg}} 
+%\institute{University of Luxembourg} 
+
+\date{2021-04-02} 
+
+\begin{document}
+
+\begin{frame}
+  \titlepage
+\end{frame}
+
+\begin{frame}{Second part - schedule}
+  \begin{tabular}{l|c|c|l}
+    \textbf{Date} & \textbf{Topics} & \textbf{Homework} & \textbf{Deadline}  \\
+    \hline
+    April 2   & Python ``review'', a bit of Sage & (see March 26) & April 18 \\
+    \hline
+    April 23  & Sage: Algebra and Crypto & Homework 3 & May 9                \\
+    \hline
+    May 7     & Sage: Analysis and Statistics  & Homework 4 & May 30         \\
+    \hline
+    May 21    & Fast code, other software  &
+  \end{tabular}
+\end{frame}
+
+
+\begin{frame}{What is programming?}
+  \begin{columns}
+    \column{0.35\textwidth}
+      \includegraphics[scale=0.12]{img/laptop.png}
+    \column{0.1\textwidth}
+      \begin{center}\includegraphics[scale=0.12]{img/equal.png}\end{center}
+    \column{0.35\textwidth}
+      \includegraphics[scale=0.9]{img/calc.jpg}
+  \end{columns}
+  \begin{itemize}
+    \item Software (apps): commands written in a \emph{programming language}
+    \item Programming language: mix of English and symbols
+    \item The code is \emph{compiled} to machine language (C, C++) or\\
+          \emph{interpreted} by some software in the middle (Python)
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Python}
+  \begin{columns}
+    \column{0.7\textwidth}
+      \url{https://www.python.org}
+
+      \vspace{0.3cm}
+      \begin{itemize}
+        \item Interpreted: slower than C, usable interactively
+        \item Simple syntax, easy to learn
+        \item Very popular
+        \item Sage is based on Python
+      \end{itemize}
+    \column{0.25\textwidth}
+      \includegraphics[scale=0.16]{img/python.png}
+  \end{columns}
+\end{frame}
+
+\begin{frame}{The interpreter - Python as a calculator}
+  \begin{center}
+    \includegraphics[scale=0.3]{img/term.png}
+  \end{center}
+\end{frame}
+
+\begin{frame}{The interpreter - Python as a calculator}
+  \url{https://www.python.org/shell}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Each line executed as you enter it, result is printed
+    \item Usual math operations work: try them!
+      \begin{center}
+        \texttt{a+b, a-b, a*b, a/b}\\
+        \texttt{a**b (power), a//b (integer division), a\%b (remainder)}
+      \end{center}
+    \item More math functions:
+      \begin{center} \begin{tabular}{l}
+        \texttt{import math} \\
+        \texttt{math.sqrt(3)}
+      \end{tabular} \end{center}
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Help!}
+  \begin{itemize}
+    \item Type \texttt{help()} for interactive help
+    \item Try \texttt{help("math")} and \texttt{help("import")}
+    \item What does
+      \begin{center} \texttt{from math import *} \end{center}
+    do?
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Variables}
+  \texttt{variable\_name = value \qquad \# This is an assignment}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Save results, use them later
+    \item \texttt{variable\_name}: combination of letters, numbers, underscores
+    \item \texttt{=} always means \emph{assignment}, never \emph{equality}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Types}
+  \texttt{type(variable\_name) \qquad \# Get the type of a variable}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    %\item Tells the computer how to read a variable
+    \item In other languages you must specify the type of a variable
+    \item Python figures out automatically (\emph{dynamic typing})
+    \item Each type allows different operations
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Other types: Boolean and String}
+  \texttt{my\_bool = True}
+
+  \texttt{s1 = "hello!" \qquad \# Same as 'hello!'}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item \texttt{bool}: \texttt{True} or \texttt{False}
+      \begin{itemize}
+        \item Operations on \texttt{bool}:
+              \texttt{and}, \texttt{or}, \texttt{not}
+        \item Operations with boolean result: \texttt{==}, \texttt{!=},
+              \texttt{>}, \texttt{<}, \texttt{>=}, \texttt{<=}
+      \end{itemize}
+    \item \texttt{str}: a string of characters
+      \begin{itemize}
+        \item Useful operations:
+
+          \begin{tabular}{ll}
+            \texttt{len({\bf str})} & \texttt{\# Length, integer value}   \\
+            \texttt{{\bf str} + {\bf str}} & \texttt{\# Concatenation} \\
+            \texttt{{\bf int} * {\bf str}} & \texttt{\# Repetition}
+          \end{tabular}
+      \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Lists and sets}
+  %\texttt{(2.5, True, "hello") \qquad \# Tuple}
+
+  \texttt{[2.5, True, "hello"] \qquad \# List}
+
+  \texttt{\{2.5, True, "hello"\} \qquad \# Set}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    %\item Different collections of objects
+    %\item Tuple: immutable
+    \item Lists: keep order and duplicates
+    \item Sets: disregard order and duplicates, allow set operations
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Lists and sets}
+  Things in common (\emph{\texttt{A} is a list or a set}):
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item \texttt{len(A)}: number of elements (\texttt{\bf int})
+    \item \texttt{x in A}: check if \texttt{x} is in \texttt{A}
+          (\texttt{\bf bool})
+    \item If \texttt{A} contains numbers: \texttt{max(A)}, \texttt{min(A)},
+          \texttt{sum(A)}
+  \end{itemize}
+
+  \vspace{0.3cm}
+  Pass from one type to the other: \texttt{set(A)} and \texttt{list(A)}
+\end{frame}
+
+\begin{frame}{List (and set) comprehension}
+  \texttt{[x**2 {\bf for} x {\bf in} [-1,4,1,0] {\bf if} x < 3]
+          \quad\# Result: [1,1,0]}
+
+  \texttt{\{x**2 {\bf for} x {\bf in} [-1,4,1,0] {\bf if} x < 3\}
+          \quad\# Result: \{0,1\}}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Mathematical way to define lists and sets
+    \item Complete syntax:
+
+          \vspace{0.2cm}
+          \texttt{[f(x,y,\dots) {\bf for} x {\bf in} L {\bf for} y {\bf in} M
+                   \dots \quad {\bf if} cond(x,y,\dots)]}
+
+          \vspace{0.2cm}
+          \begin{itemize}
+            \item Use as many variables \texttt{x, y, \dots} as you want
+            \item \texttt{L, M, \dots} are lists or sets or other collections
+            \item \texttt{f(x,y,\dots)} is any expression depending on the
+                  variables
+            \item \texttt{cond(x,y,\dots)} has Boolean value
+          \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Lists: access elements and sublists}
+  \begin{tabular}{ll}
+    \texttt{A[i]} &
+    \texttt{\# i-th element of A ($i\in \{0,\dots,\texttt{len(A)}-1\}$)} \\
+    \texttt{A[i] = value} & \texttt{\# Change i-th element of A} \\
+    \texttt{A[i:j:k]} & \texttt{\# Sublist from A[i] to A[j] with step k} \\
+    \texttt{A[i:j]} & \texttt{\# Same as A[i:j:1]} \\
+    \texttt{A[i:]} & \texttt{\# Same as A[i:len(A):1]} \\
+    \texttt{A[:j]} & \texttt{\# Same as A[0:j:1]}
+  \end{tabular}
+\end{frame}
+
+\begin{frame}{List operations}
+  \begin{tabular}{ll}
+    \texttt{A.append(x)} & \texttt{\# Append x to A ({\bf change A})} \\
+    \texttt{A.insert(i,x)} &
+    \texttt{\# Insert x in position i ({\bf change A})} \\
+    \texttt{del A[i]} & \texttt{\# Remove i-th element of A ({\bf change A})}\\
+  \end{tabular}
+
+  \vspace{1cm}
+  \begin{tabular}{ll}
+    \texttt{A+B} & \texttt{\# Concatenation of A and B ({\bf list})} \\
+    \texttt{A*n} & \texttt{\# Repetition of A ({\bf list})} \\
+  \end{tabular}
+\end{frame}
+
+\begin{frame}{Set operations}
+  \begin{tabular}{ll}
+    \texttt{A.add(x)} & \texttt{\# Add x to A ({\bf change A})} \\
+    \texttt{A.remove(x)} & \texttt{\# Remove x from A ({\bf change A})}\\
+  \end{tabular}
+
+  \vspace{0.5cm}
+  \begin{tabular}{ll}
+    \texttt{A < B} (or \texttt{A <= B}) &
+    \texttt{\# A contained in (or equal to) B ({\bf bool})} \\
+    \texttt{A > B} (or \texttt{A >= B}) &
+    \texttt{\# A containes (or is equal to) B ({\bf bool})} \\
+  \end{tabular}
+
+  \vspace{0.5cm}
+  \begin{tabular}{ll}
+    \texttt{A | B} & \texttt{\# Union ({\bf set})} \\
+    \texttt{A \& B} & \texttt{\# Intersection ({\bf set})}\\
+    \texttt{A - B} & \texttt{\# Set difference ({\bf set})} \\
+  \end{tabular}
+\end{frame}
+
+\begin{frame}{Writing more complex programs}
+  \begin{center}\includegraphics[scale=0.25]{img/geany.png}\end{center}
+\end{frame}
+
+\begin{frame}{Non-interactive Python}
+  \begin{itemize}
+    \item You can write a file (for example with \url{https://www.geany.org})
+    \item Output results with \texttt{print("string", or, other, values)}
+    \item Get input (\texttt{str}) with \texttt{x = input("Prompt: ")},
+          convert with \texttt{int(x)} or \texttt{float(x)}\dots
+    \item Blocks of code: use \emph{indentation} (see next slides)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]{\texttt{if} statement}
+  \begin{columns}
+    \column{0.45\textwidth}
+      \texttt{{\bf if} \emph{condition}:}
+
+      \texttt{\qquad instruction1}
+      
+      \texttt{\qquad instruction2}
+
+      \texttt{\qquad \dots}
+
+      \texttt{{\bf else}: \# This is optional}
+
+      \texttt{\qquad other inst}
+    \column{0.55\textwidth}
+      \begin{tikzpicture}
+        \tikzstyle{s} = [rectangle, rounded corners, text centered,
+                                                       draw=black, fill=red!30]
+        \tikzstyle{p} = [rectangle, text centered, draw=black, fill=orange!30]
+        \tikzstyle{d} = [rectangle, text centered, draw=black, fill=green!30]
+
+        \node(start)  [s]                     {Start};
+        \node(cond)   [d, below of=start]     {\texttt{\emph{condition}}?};
+        \node(inst1)  [p, right of=cond, xshift=2.7cm] {\texttt{instruction1}};
+        \node(inst2)  [p, below of=inst1]     {\texttt{instruction2}};
+        \node(dots)   [p, below of=inst2]     {\texttt{\dots}};
+        \node(other)  [p, below of=cond, yshift=-0.5cm]  {\texttt{other inst}};
+        \node(end)    [s, below of=other, yshift=-0.5cm] {End};
+
+        \draw[->] (start) -- (cond);
+        \draw[->] (cond) -- node[anchor=south] {\texttt{True}} (inst1);
+        \draw[->] (inst1) -- (inst2);
+        \draw[->] (inst2) -- (dots);
+        \draw[->] (cond) -- node[anchor=east] {\texttt{False}} (other);
+        \draw[->] (dots) |- (end);
+        \draw[->] (other) -- (end);
+      \end{tikzpicture}
+  \end{columns}
+\end{frame}
+
+
+\begin{frame}[fragile]{\texttt{while} loop}
+  \begin{columns}
+    \column{0.45\textwidth}
+      \texttt{{\bf while} \emph{condition}:}
+
+      \texttt{\qquad instruction1}
+      
+      \texttt{\qquad instruction2}
+
+      \texttt{\qquad \dots}
+    \column{0.55\textwidth}
+      \begin{tikzpicture}
+        \tikzstyle{s} = [rectangle, rounded corners, text centered,
+                                                       draw=black, fill=red!30]
+        \tikzstyle{p} = [rectangle, text centered, draw=black, fill=orange!30]
+        \tikzstyle{d} = [rectangle, text centered, draw=black, fill=green!30]
+
+        \node(start)  [s]                     {Start};
+        \node(cond)   [d, below of=start]     {\texttt{\emph{condition}}?};
+        \node(inst1)  [p, right of=cond, xshift=2.7cm] {\texttt{instruction1}};
+        \node(inst2)  [p, below of=inst1]     {\texttt{instruction2}};
+        \node(dots)   [p, below of=inst2]     {\texttt{\dots}};
+        \node(end)    [s, below of=other, yshift=-0.5cm] {End};
+
+        \draw[->] (start) -- (cond);
+        \draw[->] (cond) -- node[anchor=south] {\texttt{True}} (inst1);
+        \draw[->] (inst1) -- (inst2);
+        \draw[->] (inst2) -- (dots);
+        \draw[->] (cond) -- node[anchor=east] {\texttt{False}} (end);
+        \draw[->] (dots) -| ($(cond.south)+(0.4,0)$);
+      \end{tikzpicture}
+  \end{columns}
+\end{frame}
+
+\begin{frame}{\texttt{for} loop}
+  \texttt{{\bf for} i {\bf in} A:}
+
+  \texttt{\qquad instruction1}
+  
+  \texttt{\qquad instruction2}
+
+  \texttt{\qquad \dots}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Repeats instructions as \texttt{i} varies in \texttt{A}
+    \item \texttt{A} can be list, set or other collection
+    \item Example: \texttt{A} can be \texttt{range(\emph{a,b,step})}
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Functions}
+  \texttt{{\bf def} f(x, y, \dots): }
+
+  \texttt{\qquad instruction1}
+  
+  \texttt{\qquad instruction2}
+
+  \texttt{\qquad \dots}
+
+  \texttt{\qquad {\bf return} some\_value}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Useful to divide programs into ``pieces''
+    \item The result of \texttt{f(x,y,\dots)} is given by \texttt{return \dots}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{An example of function (with recursion)}
+  \texttt{def fibonacci(n):}
+
+  \texttt{\qquad if n == 0:}
+
+  \texttt{\qquad \qquad return 0}
+
+  \texttt{\qquad if n == 1:}
+
+  \texttt{\qquad \qquad return 1}
+
+  \texttt{\qquad return fibonacci(n-1) + fibonacci(n-2)}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Elegant, but slow (in this case)
+    \item Can get stuck in infinite loop: when?
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Sage}
+  \begin{center}
+    \includesvg[scale=0.5]{img/sage}
+
+    \url{https://www.sagemath.org}
+  \end{center}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Mathematical software, uses Python as a language
+    \item Use it interactively or with Jupyter notebook
+    \item Try it online: \url{https://sagecell.sagemath.org} or
+          \url{https://cocalc.com/app}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Differences with Python}
+  \begin{tabular}{l|l}
+    \textbf{Python} & \textbf{Sage}                                          \\
+    \texttt{{\color{gray}>>>} {\color{blue}type(5)}} &
+    \texttt{{\color{gray}sage:} {\color{blue}type(5)}}                       \\
+    \texttt{<class 'int'>} & \texttt{<class 'sage.rings.integer.Integer'>}   \\
+    \texttt{{\color{gray}>>>} {\color{blue}5/2}} &
+    \texttt{{\color{gray}sage:} {\color{blue}5/2}}                           \\
+    \texttt{2.5} & \texttt{5/2}                                              \\
+    \texttt{{\color{gray}>>>} {\color{blue}type(5/2)}} &
+    \texttt{{\color{gray}sage:} {\color{blue}type(5/2)}}                     \\
+    \texttt{<class 'float'>} &
+    \texttt{<class 'sage.rings.rational.Rational'>}                          \\
+    \texttt{{\color{gray}>>>} {\color{blue}type(2.5)}} &
+    \texttt{{\color{gray}sage:} {\color{blue}type(2.5)}}                     \\
+    \texttt{<class 'float'>} &
+    \texttt{<class 'sage.rings.real\_mpfr.RealLiteral'>}                     \\
+    \texttt{{\color{gray}>>>} {\color{blue}5**3}} &
+    \texttt{{\color{gray}sage:} {\color{blue}5\^{}3}}                        \\
+    \texttt{125} & \texttt{125}
+  \end{tabular}
+\end{frame}
+
+\begin{frame}{Sage Documentation}
+  \begin{itemize}
+    \item Tutorial (guided examples): type \texttt{tutorial()} or visit
+          \url{https://doc.sagemath.org/html/en/tutorial}
+    \item \texttt{help()}: works as in Python
+    \item Reference manual (detailed technical information):
+          \url{https://doc.sagemath.org/html/en/reference}
+  \end{itemize}
+\end{frame}
+
+
+\end{document}
+