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+ +This is a comment + +\section{Text} + +\textbf{This sentence is in boldface} + +\underline{\textit{italicized} maybe in a sentence \textbf{something}} + +\underline{\textit{one inside the other}} + +\emph{also italicized???} + +This is an important sentence, maybe a quote or something, and this \emph{word} is very important. Let's make this sentence longer than one line. + +{\Huge Large words} + +%\appendix + +\section{Math mode} + +This is an inline formula \( \sum_i \frac{i}{22} \), it appears within the text + +This is a displaystyle formula \[ \sum_{\alpha=0}^{2^{10}} \frac2 \alpha{22} \] it appears on its own line + +How sqrt works: \( \sqrt[\phi]{25} \) + + + +\begin{align} +\label{eq} +e^x &= \left(\sum_{i=0}^\infty \frac{x^i}{i!} \right) = \\ +&= \left( 1 + x + \frac{x^2}2 \right)+ \frac{x^3}{6} + \cdots \nonumber +\end{align} + +\[ + \left\{ x \in \reals \quad \text{such that} \quad \frac{ \sinus(x)}{x^2}>0 \right\}\reals +\] + +\[ \sum_i \] + +The first equation we wrote is \eqref{eq} + +\section{Environments} + +\subsection{Lists} +\label{subsectionLists} + +\begin{itemize} + \item One \textbf{item} + \item Another \(2+2=4\) + \item a third one \[\sum_{i=0}^n\] + \item A sublist: + \begin{itemize} + \item[+] First subitem + \item[+] and so on + \end{itemize} + \item Again in the main list +\end{itemize} + +\begin{enumerate}[label=\Roman*] + \item One + \item Two + \item Actually three + \item Three (or not) +\end{enumerate} + +\subsection*{Tables} + +Let's write a table: + +\vspace{1cm} +\begin{tabular}{r||l|c} +\hline +This is a table & second column & third column \\ +\hline +Things & a & \( 2+2 = 4 \)\\ +\hline +more things & b & c +\end{tabular} + +\vspace{1cm} +\[ + \left(\begin{array}{cc} + \int_0^1 e^x & \frac{2}{25} \\ + 0 & 0 \\ + 1111 & 234\alpha + \end{array}\right) +\] + +\[ + \begin{pmatrix} + \int_0^1 e^x & \frac{2}{25} \\ + 0 & 0 \\ + 1111 & 234\alpha + \end{pmatrix} +\] + +\[ +\begin{pmatrix} +1 & 2\\ +3 & 4 +\end{pmatrix} +\overset{L2\rightarrow L2+L3}\longrightarrow +\begin{pmatrix} +1 & 2\\ +4 & 6 +\end{pmatrix} +\] + +\section{Last section} + +In section \ref{subsectionLists} we saw how to write lists + +\begin{mythm}[Gauss] +The equation \(2+x=4\) is true for \(x=2\). +\end{mythm} + +\begin{prop} +A less important fact +\end{prop} + 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[2][]{Outline0.2}{When?}{}% 4 +\BOOKMARK [2][]{Outline0.3}{How?}{}% 5 diff --git a/src/Lecture1/slides/1-Introduction.pdf b/src/Lecture1/slides/1-Introduction.pdf new file mode 100644 index 0000000..17eaaa8 Binary files /dev/null and b/src/Lecture1/slides/1-Introduction.pdf differ diff --git a/src/Lecture1/slides/1-Introduction.snm b/src/Lecture1/slides/1-Introduction.snm new file mode 100644 index 0000000..e69de29 diff --git a/src/Lecture1/slides/1-Introduction.tex b/src/Lecture1/slides/1-Introduction.tex new file mode 100644 index 0000000..2c8c355 --- /dev/null +++ b/src/Lecture1/slides/1-Introduction.tex @@ -0,0 +1,115 @@ +\documentclass[11pt]{beamer} +\usetheme{Madrid} +\usepackage[utf8]{inputenc} +\usepackage{amsmath} +\usepackage{svg} + +\usepackage{tikz-cd} + +\author[\texttt{sebastiano.tronto@uni.lu}]{Sebastiano Tronto} +\title{Mathematical Software - Introduction} +\logo{\includegraphics[scale=0.1]{img/unilu.jpg}} +%\institute{University of Luxembourg} + +\date{2021-02-19} + +\begin{document} + +\begin{frame} + \titlepage +\end{frame} + +\begin{frame} + \tableofcontents +\end{frame} + +\section{What?} +\begin{frame}{What} + \begin{columns} + \column{0.6\textwidth} + \begin{itemize} + \item {\bf Latex} for writing scientific text + \item {\bf Sage} for computations + \end{itemize} + + \column{0.4\textwidth} + \includegraphics[scale=0.1]{img/latex.png} + \vspace{0.5cm} + + \includesvg[scale=0.215]{img/sage} + \end{columns} +\end{frame} + +\subsection{Latex} +\begin{frame}{Latex} + \includegraphics[scale=0.1]{img/latex.png} + \begin{itemize} + \item A typesetting system, has been around since the 1980s + \item Currently the best way to write scientific texts (Math, Physics...) + \item Can be used for lecture notes, homework, articles, books, graphics + (with TikZ), this presentation...%, shopping list... + \item ``What you get is what you \emph{mean}'', rather than what you + \emph{see} + \end{itemize} +\end{frame} + +\begin{frame}[fragile]{Latex - Example} + An equation like this: + \begin{align*} + e^x =& \sum_{n=0}^{\infty} \frac{x^n}{n!} \\ + =& 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \cdots + \end{align*} + is written in LaTeX as: + \begin{verbatim} + \begin{align*} + e^x =& \sum_{n=0}^{\infty} \frac{x^n}{n!} \\ + =& 1 + x + \frac{x^2}{2} + + \frac{x^3}{6} + \cdots + \end{align*} + \end{verbatim} +\end{frame} + +\subsection{Sage} +\begin{frame}{Sage} + \includesvg[scale=0.215]{img/sage} + \begin{itemize} + \item Free and open source Mathematical software + \item Basically python with a lot of Math libraries + \item Builds up on existing software such a Pari/GP, NumPy, R... + \item Popular for Computational Algebra (Number Theory, Cryptography...) + \end{itemize} +\end{frame} + +\section{When?} +\begin{frame}{When} + \begin{tabular}{r|c|c} + %Date & Time & Topics \\ + %\hline + February 19 & \texttt{14:00 - 17:30} & Introduction, LaTeX fundamentals \\ + \hline + March 12 & \texttt{14:00 - 17:30} & More advanced LaTeX topics \\ + \hline + March 26 & \texttt{14:00 - 17:30} & LaTeX: presentations, graphics \\ + \hline + April 2 & \texttt{14:00 - 17:30} & ??? (LaTeX or Sage) \\ + \hline + April 23 & \texttt{14:00 - 17:30} & Sage (???) \\ + \hline + May 7 & \texttt{14:00 - {\bf 18:15}} & Sage (???) \\ + \hline + May 21 & \texttt{14:00 - {\bf 18:15}} & Sage (???) + \end{tabular} +\end{frame} + +\section{How?} +\begin{frame}{How} + \begin{itemize} + \item \textbf{Remote teaching} at least until April 2 included (probably + always). + \item \textbf{Learn by doing} graded homework (4-5 assignments), non-graded + exercises, free practice. No final exam. + \end{itemize} +\end{frame} + +\end{document} + diff --git a/src/Lecture1/slides/1-Introduction.toc b/src/Lecture1/slides/1-Introduction.toc new file mode 100644 index 0000000..07181a7 --- /dev/null +++ b/src/Lecture1/slides/1-Introduction.toc @@ -0,0 +1,5 @@ +\beamer@sectionintoc {1}{What?}{3}{0}{1} +\beamer@subsectionintoc {1}{1}{Latex}{4}{0}{1} +\beamer@subsectionintoc {1}{2}{Sage}{6}{0}{1} +\beamer@sectionintoc {2}{When?}{7}{0}{2} +\beamer@sectionintoc {3}{How?}{8}{0}{3} diff --git a/src/Lecture1/slides/1-Introduction.vrb b/src/Lecture1/slides/1-Introduction.vrb new file mode 100644 index 0000000..5a53bf5 --- /dev/null +++ b/src/Lecture1/slides/1-Introduction.vrb @@ -0,0 +1,14 @@ +\frametitle{Latex - Example} +An equation like this: + \begin{align*} + e^x =& \sum_{n=0}^{\infty} \frac{x^n}{n!} \\ + =& 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \cdots + \end{align*} + is written in LaTeX as: + \begin{verbatim} + \begin{align*} + e^x =& \sum_{n=0}^{\infty} \frac{x^n}{n!} 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file mode 100644 index 0000000..e69de29 diff --git a/src/Lecture1/slides/2-LatexFundamentals.pdf b/src/Lecture1/slides/2-LatexFundamentals.pdf new file mode 100644 index 0000000..a96f172 Binary files /dev/null and b/src/Lecture1/slides/2-LatexFundamentals.pdf differ diff --git a/src/Lecture1/slides/2-LatexFundamentals.snm b/src/Lecture1/slides/2-LatexFundamentals.snm new file mode 100644 index 0000000..e69de29 diff --git a/src/Lecture1/slides/2-LatexFundamentals.tex b/src/Lecture1/slides/2-LatexFundamentals.tex new file mode 100644 index 0000000..fe2c031 --- /dev/null +++ b/src/Lecture1/slides/2-LatexFundamentals.tex @@ -0,0 +1,340 @@ +\documentclass[11pt]{beamer} +\usetheme{Madrid} +\usepackage[utf8]{inputenc} +\usepackage{amsmath, amssymb, amsfonts, amsthm} +\usepackage{xcolor} + +\usepackage{tikz-cd} + +\author[\texttt{sebastiano.tronto@uni.lu}]{Sebastiano Tronto} +\title{Latex Fundamentals} +\logo{\includegraphics[scale=0.1]{img/unilu.jpg}} +%\institute{University of Luxembourg} + +\newcommand{\bs}{\textbackslash} + +\date{2021-02-19} + +\begin{document} + +\begin{frame} + \titlepage +\end{frame} + +\begin{frame}{Latex} + \begin{enumerate} + \item Write code (like HTML, not like Python) + \item Compile to get a pdf file + \item ??? + \item Profit + \end{enumerate} +\end{frame} + + +\begin{frame}{Document structure} + \includegraphics[scale=0.5]{img/example2-preamble-edited.png} +\end{frame} + +\begin{frame}{Preamble} + \begin{itemize} + \item Include packages with \texttt{\bs usepackage} + \item Define properties of the document (\texttt{\bs documentclass}, + \texttt{\bs author}, ...) + \item Define new commands and environments + \end{itemize} +\end{frame} + +\begin{frame}{Text formatting} + \begin{center} + + \begin{tabular}{ccc} + \texttt{\small \bs textbf\{Hello\}} & + \texttt{\small \bs textit\{Hello\}} or \texttt{\small\bs emph\{Hello\}} & + \texttt{\small \bs underline\{Hello\}} \\ + \textbf{Hello} & \textit{Hello} & \underline{Hello} + \end{tabular} + + \vspace{0.7cm} + \begin{tabular}{ccc} + \texttt{\small \{\bs small Hello\}} & \hspace{1cm} + \texttt{\small \{\bs Large Hello\}} \hspace{1cm} & + \texttt{\small \{\bs huge Hello\}} \\ + {\small Hello} & {\Large Hello} & {\huge Hello} + \end{tabular} + + \end{center} +\end{frame} + +\begin{frame}{Text formatting} + Some technicalities: + \begin{itemize} + \item Blocks are delimited by \{ and \} + \item \texttt{\bs textbf\{...\}} etc. are commands with one argument + \item \texttt{\bs emph\{...\}} is context-aware (when in doubt use this) + \item \texttt{\bs Large} etc. change the text until the end of the block + \item Some people use \texttt{\{\bs bf Hello\}}, but it is deprecated + \end{itemize} +\end{frame} + +\begin{frame}{Text formatting} + \begin{center} + \begin{tabular}{lc} + \texttt{\{\bs tiny Hello\}} & {\tiny Hello} \\ + \texttt{\{\bs scriptsize Hello\}} & {\scriptsize Hello} \\ + \texttt{\{\bs footnotesize Hello\}} & {\footnotesize Hello} \\ + \texttt{\{\bs normalsize Hello\}} & {\normalsize Hello} \\ + \texttt{\{\bs large Hello\}} & {\large Hello} \\ + \texttt{\{\bs Large Hello\}} & {\Large Hello} \\ + \texttt{\{\bs LARGE Hello\}} & {\LARGE Hello} \\ + \texttt{\{\bs huge Hello\}} & {\huge Hello} \\ + \texttt{\{\bs Huge Hello\}} & {\Huge Hello} \\ + \end{tabular} + \end{center} +\end{frame} + +\begin{frame}{Math mode} + \texttt{One can write math inline, like + {\color{red}\bs(} \bs sum\_i\bs frac\{i\}\{2\} {\color{red}\bs)}, + or in displaystyle: + {\color{red}\bs[} \bs sum\_i\bs frac\{i\}\{2\} {\color{red}\bs]} + } + + \vspace{1.5cm} + One can write math inline, like \(\sum_i\frac{i}{2}\) or in displaystyle: + \[\sum_i\frac{i}{2}\] +\end{frame} + +\begin{frame}{Math mode} + \begin{center} + For formulas spanning multiple lines you can use: + + \vspace{0.5cm} + \texttt{\color{red}\bs begin\{align\} (...) \bs end \{align\}} + \begin{align} + e^x =& \sum_{n=0}^{\infty} \frac{x^n}{n!} \\ + =& 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \cdots + \end{align} + or \texttt{\color{red}\bs begin\{align*\} (...) \bs end\{align*\}} for no + numbers. + \end{center} +\end{frame} + +\begin{frame}{Math mode} + \begin{itemize} + \item Some people use \texttt{\$2+2=4\$} instead of \texttt{\bs(2+2=4\bs)} + \item Some \textbf{evil} people use \texttt{\$\$2+2=4\$\$} instead of + \texttt{\bs[2+2=4\bs]} (don't try this at home!) + \item For \texttt{align} use \texttt{\bs nonumber} to remove one number + and \texttt{\&} to align. + \item For example I always use \texttt{\$2+2=4\$} and the \texttt{align*} + environment. + \end{itemize} +\end{frame} + +\begin{frame}{Math mode} + \begin{itemize} + \item Simple symbols: letters, numbers, $+,-,=,<,>$... + \item Symbols that need a \textbf{command}: + + \vspace{0.6cm} + \begin{tabular}{c|c|c|c|c} + \texttt{\bs alpha, \bs Phi} & \texttt{\bs times, \bs cdot} & + \texttt{\bs sum} & \texttt{\bs leq, \bs geq} & \texttt{\bs infty}\\ + $\alpha,\Phi$ & $\times,\cdot$ & $\sum$ & $\leq,\geq$ & $\infty$ + \end{tabular} + \vspace{0.6cm} + \item Negate symbols with \texttt{\bs not}: + \begin{align*} + \texttt{x \bs not \bs in A} \qquad\to&\qquad x\not\in A\\ + \texttt{x \bs not = y}\quad\text{ or }\quad\texttt{x \bs neq y} + \qquad\to&\qquad x\neq y\\ + \end{align*} + \end{itemize} +\end{frame} + +\begin{frame}{Math mode} + \begin{itemize} + \item Some commands take one or more \textbf{arguments} (like + \texttt{\bs frac}). + + Anything can be an argument: + \begin{align*} + \texttt{\bs frac\{1\}\{\bs sum\_\{n\}\}}\qquad\to\qquad + \frac{1}{\sum_{n} \sqrt n} + \end{align*} + \item A few commands take \textbf{options}: + \texttt{\bs sqrt[3]\{x\}} $\to\,\sqrt[3]{x}$ + %\item Most of these commands work only in Math mode + \end{itemize} +\end{frame} + + +\begin{frame}{Math mode} + \begin{itemize} + \item Every symbol can have a \textbf{subscript} and a \textbf{superscript} + \begin{align*} + \texttt{x\_0\^{}\{23\}} \qquad \to \qquad x_0^{23} + \end{align*} + \item Anything can be a sub/superscript: + \begin{align*} + \texttt{\bs int\_\{\bs phi (y)\}\^{}\{2\^{}\{n\_1\}\}} + \qquad \to \qquad \int_{\phi(y)}^{2^{n_1}} + \end{align*} + \end{itemize} +\end{frame} + + +\begin{frame}{Math mode} + \begin{itemize} + \item Adjust parentheses size with \texttt{\bs left(} and + \texttt{\bs right)}: \[\left(\frac{x+6}{y-2}\right)\] + \item Insert text with \texttt{\bs text} and + spaces with \texttt{\bs ,} and \texttt{\bs quad}: + \[\text{this symbol}\quad \sum_{n=0}^\infty \frac{x^n}{n!} \quad + \text{is in math mode}, this is not text\] + \end{itemize} +\end{frame} + +\begin{frame}{Math mode} + + \begin{itemize} + \item Fancy letters with \texttt{\bs mathcal}, + \texttt{\bs mathbb} and \texttt{\bs mathfrak}: + \begin{align*} + \mathcal{A} \qquad \mathbb R \qquad \mathfrak p + \end{align*} + \item For custom operators use \texttt{\bs operatorname\{oper\}}: + \begin{align*} + \operatorname{oper}(x) + \end{align*} + \item Pro-tip: write \texttt{\bs newcommand\{\bs R\}\{\bs mathbb R\}} and + \texttt{\bs DeclareMathOperator\{\bs lcm\}\{lcm\}} in your preamble! + \end{itemize} +\end{frame} + +\begin{frame}{Math mode} + \begin{itemize} + \item Wikibooks page on Math mode: + {\small\url{https://en.wikibooks.org/wiki/LaTeX/Mathematics}} + \item Advanced stuff: + {\small\url{https://en.wikibooks.org/wiki/LaTeX/Advanced_Mathematics}} + \item List of Mathematical symbols: + {\small\url{https://www.caam.rice.edu/~heinken/latex/symbols.pdf}} + \end{itemize} +\end{frame} + +\begin{frame}{Environments} + \texttt{\color{red}\bs begin\{something\}} + Inside an environment + \texttt{\color{red}\bs end\{something\}} + + \vspace{0.8cm} + \begin{itemize} + \item We have seen \texttt{document} and \texttt{align} + \item Text and symbols appear differently depending on the environment + \item Certain commands are specific to an environment + \item You can define new environments + \end{itemize} +\end{frame} + + +\begin{frame}{Environments} + Lists: \texttt{\color{red}itemize} and \texttt{\color{red}enumerate} + + \vspace{0.8cm} + \begin{columns} + \column{0.5\textwidth} + \begin{itemize} + \item First: \[2+2=4\] + \item Second + \end{itemize} + + \column{0.5\textwidth} + \texttt{\bs begin\{itemize\}} + + \texttt{\qquad \bs item First: \bs[2+2=4\bs]} + + \texttt{\qquad \bs item Second} + + \texttt{\bs end\{itemize\}} + \end{columns} +\end{frame} + +\begin{frame}{Environments} + Tables: \texttt{tabular} (text) and \texttt{array} (Math mode) + + \vspace{0.8cm} + \begin{columns} + \column{0.5\textwidth} + \begin{tabular}{r|cc} + This & is & just \\ + \hline + a & boring & table + \end{tabular} + + \column{0.5\textwidth} + \texttt{\bs begin\{tabular\}\{r|cc\}} + + \texttt{\qquad This \& is \& just \bs\bs} + + \texttt{\qquad \bs hline} + + \texttt{\qquad a \& boring \& table} + + \texttt{\bs end\{tabular\}} + \end{columns} + + \vspace{0.8cm} + Matrices: \texttt{array} with parentheses or \texttt{pmatrix} +\end{frame} + +\begin{frame}{Sections} + \begin{itemize} + \item Use \texttt{\bs section\{Section Name\}} to start a new section + \item Also: \texttt{\bs chapter} (book only), \texttt{\bs subsection}, + \texttt{subsubsection}... + \item \texttt{\bs section*\{Name\}} for no number + \item Sections after \texttt{\bs appendix} are numbered differently + \end{itemize} +\end{frame} + +\begin{frame}{Theorems} + + \begin{itemize} + \item In preamble: \texttt{\bs usepackage\{amsthm\}} + \item Also in preamble \texttt{\bs newtheorem \{envname\}\{Theorem\}} + \item Use \texttt{\bs newtheorem*} for no number + \end{itemize} +\end{frame} + +\begin{frame}{Theorems} + \begin{columns} + \column{0.5\textwidth} + \includegraphics[scale=0.3]{img/thm_pre.png} + + \vspace{0.2cm} + \vdots + \vspace{0.3cm} + + \includegraphics[scale=0.3]{img/thm_tex.png} + + \column{0.5\textwidth} + \includegraphics[scale=0.2]{img/thm_pdf.png} + + \vspace{1cm} + \end{columns} +\end{frame} + +\begin{frame}{End of the lecture} + For next time: + + \vspace{0.8cm} + \begin{itemize} + \item Install Latex on your PC + \item Start writing something in Latex (e.g. homework) + \item Email me if you have any question + \end{itemize} +\end{frame} + +\end{document} + diff --git a/src/Lecture1/slides/2-LatexFundamentals.toc b/src/Lecture1/slides/2-LatexFundamentals.toc new file mode 100644 index 0000000..e69de29 diff --git a/src/Lecture1/slides/2-LatexFundamentals.vrb b/src/Lecture1/slides/2-LatexFundamentals.vrb new file mode 100644 index 0000000..a5775a8 --- /dev/null +++ b/src/Lecture1/slides/2-LatexFundamentals.vrb @@ -0,0 +1,18 @@ +\frametitle{Math mode - align and equation} +\begin{center} + For formulas spanning multiple lines you can use: + \begin{columns} + \column{0.5\textwidth} + \texttt{\bs begin\{align\}(...)\bs end \{align\}} + \begin{align} + \sum_{n=1}^\infty n =& 1+2+3+4+5+\cdots=\\ + =& -\frac12 + \end{align} + \column{0.5\textwidth} + \texttt{\bs begin\{equation\}(...)\bs end \{equation\}} + \begin{equation} + \sum_{n=1}^\infty n = 1+2+3+4+5+\cdots=\\ + = -\frac12 + \end{equation} + \end{columns} + \end{center} diff --git a/src/Lecture1/slides/img/example2-preamble-edited.png b/src/Lecture1/slides/img/example2-preamble-edited.png new file mode 100644 index 0000000..1bce28a Binary files /dev/null and b/src/Lecture1/slides/img/example2-preamble-edited.png differ diff --git a/src/Lecture1/slides/img/example2-preamble.png b/src/Lecture1/slides/img/example2-preamble.png new file mode 100644 index 0000000..e2d7379 Binary files /dev/null and b/src/Lecture1/slides/img/example2-preamble.png differ diff --git a/src/Lecture1/slides/img/latex.png b/src/Lecture1/slides/img/latex.png new file mode 100644 index 0000000..200ec19 Binary files /dev/null and b/src/Lecture1/slides/img/latex.png differ diff --git a/src/Lecture1/slides/img/sage.svg b/src/Lecture1/slides/img/sage.svg new file mode 100644 index 0000000..642e67b --- /dev/null +++ b/src/Lecture1/slides/img/sage.svg @@ -0,0 +1,72 @@ + + + + + + + + + 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