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authorSebastiano Tronto <sebastiano.tronto@gmail.com>2021-05-25 17:10:49 +0200
committerSebastiano Tronto <sebastiano.tronto@gmail.com>2021-05-25 17:10:49 +0200
commitd6c61d988bfa4255baf9cdae42db59ebee38363f (patch)
tree118ff3c2424e735149c145524965a4a337e50beb /src/Lecture1/slides
parent46eef66b1e1571c77dc828d7e950b129b4c8bfd0 (diff)
downloadmathsoftware-d6c61d988bfa4255baf9cdae42db59ebee38363f.tar.gz
mathsoftware-d6c61d988bfa4255baf9cdae42db59ebee38363f.zip
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1\documentclass[11pt]{beamer}
2\usetheme{Madrid}
3\usepackage[utf8]{inputenc}
4\usepackage{amsmath}
5\usepackage{svg}
6
7\usepackage{tikz-cd}
8
9\author[\texttt{sebastiano.tronto@uni.lu}]{Sebastiano Tronto}
10\title{Mathematical Software - Introduction}
11\logo{\includegraphics[scale=0.1]{img/unilu.jpg}}
12%\institute{University of Luxembourg}
13
14\date{2021-02-19}
15
16\begin{document}
17
18\begin{frame}
19 \titlepage
20\end{frame}
21
22\begin{frame}
23 \tableofcontents
24\end{frame}
25
26\section{What?}
27\begin{frame}{What}
28 \begin{columns}
29 \column{0.6\textwidth}
30 \begin{itemize}
31 \item {\bf Latex} for writing scientific text
32 \item {\bf Sage} for computations
33 \end{itemize}
34
35 \column{0.4\textwidth}
36 \includegraphics[scale=0.1]{img/latex.png}
37 \vspace{0.5cm}
38
39 \includesvg[scale=0.215]{img/sage}
40 \end{columns}
41\end{frame}
42
43\subsection{Latex}
44\begin{frame}{Latex}
45 \includegraphics[scale=0.1]{img/latex.png}
46 \begin{itemize}
47 \item A typesetting system, has been around since the 1980s
48 \item Currently the best way to write scientific texts (Math, Physics...)
49 \item Can be used for lecture notes, homework, articles, books, graphics
50 (with TikZ), this presentation...%, shopping list...
51 \item ``What you get is what you \emph{mean}'', rather than what you
52 \emph{see}
53 \end{itemize}
54\end{frame}
55
56\begin{frame}[fragile]{Latex - Example}
57 An equation like this:
58 \begin{align*}
59 e^x =& \sum_{n=0}^{\infty} \frac{x^n}{n!} \\
60 =& 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \cdots
61 \end{align*}
62 is written in LaTeX as:
63 \begin{verbatim}
64 \begin{align*}
65 e^x =& \sum_{n=0}^{\infty} \frac{x^n}{n!} \\
66 =& 1 + x + \frac{x^2}{2} +
67 \frac{x^3}{6} + \cdots
68 \end{align*}
69 \end{verbatim}
70\end{frame}
71
72\subsection{Sage}
73\begin{frame}{Sage}
74 \includesvg[scale=0.215]{img/sage}
75 \begin{itemize}
76 \item Free and open source Mathematical software
77 \item Basically python with a lot of Math libraries
78 \item Builds up on existing software such a Pari/GP, NumPy, R...
79 \item Popular for Computational Algebra (Number Theory, Cryptography...)
80 \end{itemize}
81\end{frame}
82
83\section{When?}
84\begin{frame}{When}
85 \begin{tabular}{r|c|c}
86 %Date & Time & Topics \\
87 %\hline
88 February 19 & \texttt{14:00 - 17:30} & Introduction, LaTeX fundamentals \\
89 \hline
90 March 12 & \texttt{14:00 - 17:30} & More advanced LaTeX topics \\
91 \hline
92 March 26 & \texttt{14:00 - 17:30} & LaTeX: presentations, graphics \\
93 \hline
94 April 2 & \texttt{14:00 - 17:30} & ??? (LaTeX or Sage) \\
95 \hline
96 April 23 & \texttt{14:00 - 17:30} & Sage (???) \\
97 \hline
98 May 7 & \texttt{14:00 - {\bf 18:15}} & Sage (???) \\
99 \hline
100 May 21 & \texttt{14:00 - {\bf 18:15}} & Sage (???)
101 \end{tabular}
102\end{frame}
103
104\section{How?}
105\begin{frame}{How}
106 \begin{itemize}
107 \item \textbf{Remote teaching} at least until April 2 included (probably
108 always).
109 \item \textbf{Learn by doing} graded homework (4-5 assignments), non-graded
110 exercises, free practice. No final exam.
111 \end{itemize}
112\end{frame}
113
114\end{document}
115
diff --git a/src/Lecture1/slides/1-Introduction.toc b/src/Lecture1/slides/1-Introduction.toc
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1\documentclass[11pt]{beamer}
2\usetheme{Madrid}
3\usepackage[utf8]{inputenc}
4\usepackage{amsmath, amssymb, amsfonts, amsthm}
5\usepackage{xcolor}
6
7\usepackage{tikz-cd}
8
9\author[\texttt{sebastiano.tronto@uni.lu}]{Sebastiano Tronto}
10\title{Latex Fundamentals}
11\logo{\includegraphics[scale=0.1]{img/unilu.jpg}}
12%\institute{University of Luxembourg}
13
14\newcommand{\bs}{\textbackslash}
15
16\date{2021-02-19}
17
18\begin{document}
19
20\begin{frame}
21 \titlepage
22\end{frame}
23
24\begin{frame}{Latex}
25 \begin{enumerate}
26 \item Write code (like HTML, not like Python)
27 \item Compile to get a pdf file
28 \item ???
29 \item Profit
30 \end{enumerate}
31\end{frame}
32
33
34\begin{frame}{Document structure}
35 \includegraphics[scale=0.5]{img/example2-preamble-edited.png}
36\end{frame}
37
38\begin{frame}{Preamble}
39 \begin{itemize}
40 \item Include packages with \texttt{\bs usepackage}
41 \item Define properties of the document (\texttt{\bs documentclass},
42 \texttt{\bs author}, ...)
43 \item Define new commands and environments
44 \end{itemize}
45\end{frame}
46
47\begin{frame}{Text formatting}
48 \begin{center}
49
50 \begin{tabular}{ccc}
51 \texttt{\small \bs textbf\{Hello\}} &
52 \texttt{\small \bs textit\{Hello\}} or \texttt{\small\bs emph\{Hello\}} &
53 \texttt{\small \bs underline\{Hello\}} \\
54 \textbf{Hello} & \textit{Hello} & \underline{Hello}
55 \end{tabular}
56
57 \vspace{0.7cm}
58 \begin{tabular}{ccc}
59 \texttt{\small \{\bs small Hello\}} & \hspace{1cm}
60 \texttt{\small \{\bs Large Hello\}} \hspace{1cm} &
61 \texttt{\small \{\bs huge Hello\}} \\
62 {\small Hello} & {\Large Hello} & {\huge Hello}
63 \end{tabular}
64
65 \end{center}
66\end{frame}
67
68\begin{frame}{Text formatting}
69 Some technicalities:
70 \begin{itemize}
71 \item Blocks are delimited by \{ and \}
72 \item \texttt{\bs textbf\{...\}} etc. are commands with one argument
73 \item \texttt{\bs emph\{...\}} is context-aware (when in doubt use this)
74 \item \texttt{\bs Large} etc. change the text until the end of the block
75 \item Some people use \texttt{\{\bs bf Hello\}}, but it is deprecated
76 \end{itemize}
77\end{frame}
78
79\begin{frame}{Text formatting}
80 \begin{center}
81 \begin{tabular}{lc}
82 \texttt{\{\bs tiny Hello\}} & {\tiny Hello} \\
83 \texttt{\{\bs scriptsize Hello\}} & {\scriptsize Hello} \\
84 \texttt{\{\bs footnotesize Hello\}} & {\footnotesize Hello} \\
85 \texttt{\{\bs normalsize Hello\}} & {\normalsize Hello} \\
86 \texttt{\{\bs large Hello\}} & {\large Hello} \\
87 \texttt{\{\bs Large Hello\}} & {\Large Hello} \\
88 \texttt{\{\bs LARGE Hello\}} & {\LARGE Hello} \\
89 \texttt{\{\bs huge Hello\}} & {\huge Hello} \\
90 \texttt{\{\bs Huge Hello\}} & {\Huge Hello} \\
91 \end{tabular}
92 \end{center}
93\end{frame}
94
95\begin{frame}{Math mode}
96 \texttt{One can write math inline, like
97 {\color{red}\bs(} \bs sum\_i\bs frac\{i\}\{2\} {\color{red}\bs)},
98 or in displaystyle:
99 {\color{red}\bs[} \bs sum\_i\bs frac\{i\}\{2\} {\color{red}\bs]}
100 }
101
102 \vspace{1.5cm}
103 One can write math inline, like \(\sum_i\frac{i}{2}\) or in displaystyle:
104 \[\sum_i\frac{i}{2}\]
105\end{frame}
106
107\begin{frame}{Math mode}
108 \begin{center}
109 For formulas spanning multiple lines you can use:
110
111 \vspace{0.5cm}
112 \texttt{\color{red}\bs begin\{align\} (...) \bs end \{align\}}
113 \begin{align}
114 e^x =& \sum_{n=0}^{\infty} \frac{x^n}{n!} \\
115 =& 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \cdots
116 \end{align}
117 or \texttt{\color{red}\bs begin\{align*\} (...) \bs end\{align*\}} for no
118 numbers.
119 \end{center}
120\end{frame}
121
122\begin{frame}{Math mode}
123 \begin{itemize}
124 \item Some people use \texttt{\$2+2=4\$} instead of \texttt{\bs(2+2=4\bs)}
125 \item Some \textbf{evil} people use \texttt{\$\$2+2=4\$\$} instead of
126 \texttt{\bs[2+2=4\bs]} (don't try this at home!)
127 \item For \texttt{align} use \texttt{\bs nonumber} to remove one number
128 and \texttt{\&} to align.
129 \item For example I always use \texttt{\$2+2=4\$} and the \texttt{align*}
130 environment.
131 \end{itemize}
132\end{frame}
133
134\begin{frame}{Math mode}
135 \begin{itemize}
136 \item Simple symbols: letters, numbers, $+,-,=,<,>$...
137 \item Symbols that need a \textbf{command}:
138
139 \vspace{0.6cm}
140 \begin{tabular}{c|c|c|c|c}
141 \texttt{\bs alpha, \bs Phi} & \texttt{\bs times, \bs cdot} &
142 \texttt{\bs sum} & \texttt{\bs leq, \bs geq} & \texttt{\bs infty}\\
143 $\alpha,\Phi$ & $\times,\cdot$ & $\sum$ & $\leq,\geq$ & $\infty$
144 \end{tabular}
145 \vspace{0.6cm}
146 \item Negate symbols with \texttt{\bs not}:
147 \begin{align*}
148 \texttt{x \bs not \bs in A} \qquad\to&\qquad x\not\in A\\
149 \texttt{x \bs not = y}\quad\text{ or }\quad\texttt{x \bs neq y}
150 \qquad\to&\qquad x\neq y\\
151 \end{align*}
152 \end{itemize}
153\end{frame}
154
155\begin{frame}{Math mode}
156 \begin{itemize}
157 \item Some commands take one or more \textbf{arguments} (like
158 \texttt{\bs frac}).
159
160 Anything can be an argument:
161 \begin{align*}
162 \texttt{\bs frac\{1\}\{\bs sum\_\{n\}\}}\qquad\to\qquad
163 \frac{1}{\sum_{n} \sqrt n}
164 \end{align*}
165 \item A few commands take \textbf{options}:
166 \texttt{\bs sqrt[3]\{x\}} $\to\,\sqrt[3]{x}$
167 %\item Most of these commands work only in Math mode
168 \end{itemize}
169\end{frame}
170
171
172\begin{frame}{Math mode}
173 \begin{itemize}
174 \item Every symbol can have a \textbf{subscript} and a \textbf{superscript}
175 \begin{align*}
176 \texttt{x\_0\^{}\{23\}} \qquad \to \qquad x_0^{23}
177 \end{align*}
178 \item Anything can be a sub/superscript:
179 \begin{align*}
180 \texttt{\bs int\_\{\bs phi (y)\}\^{}\{2\^{}\{n\_1\}\}}
181 \qquad \to \qquad \int_{\phi(y)}^{2^{n_1}}
182 \end{align*}
183 \end{itemize}
184\end{frame}
185
186
187\begin{frame}{Math mode}
188 \begin{itemize}
189 \item Adjust parentheses size with \texttt{\bs left(} and
190 \texttt{\bs right)}: \[\left(\frac{x+6}{y-2}\right)\]
191 \item Insert text with \texttt{\bs text} and
192 spaces with \texttt{\bs ,} and \texttt{\bs quad}:
193 \[\text{this symbol}\quad \sum_{n=0}^\infty \frac{x^n}{n!} \quad
194 \text{is in math mode}, this is not text\]
195 \end{itemize}
196\end{frame}
197
198\begin{frame}{Math mode}
199
200 \begin{itemize}
201 \item Fancy letters with \texttt{\bs mathcal},
202 \texttt{\bs mathbb} and \texttt{\bs mathfrak}:
203 \begin{align*}
204 \mathcal{A} \qquad \mathbb R \qquad \mathfrak p
205 \end{align*}
206 \item For custom operators use \texttt{\bs operatorname\{oper\}}:
207 \begin{align*}
208 \operatorname{oper}(x)
209 \end{align*}
210 \item Pro-tip: write \texttt{\bs newcommand\{\bs R\}\{\bs mathbb R\}} and
211 \texttt{\bs DeclareMathOperator\{\bs lcm\}\{lcm\}} in your preamble!
212 \end{itemize}
213\end{frame}
214
215\begin{frame}{Math mode}
216 \begin{itemize}
217 \item Wikibooks page on Math mode:
218 {\small\url{https://en.wikibooks.org/wiki/LaTeX/Mathematics}}
219 \item Advanced stuff:
220 {\small\url{https://en.wikibooks.org/wiki/LaTeX/Advanced_Mathematics}}
221 \item List of Mathematical symbols:
222 {\small\url{https://www.caam.rice.edu/~heinken/latex/symbols.pdf}}
223 \end{itemize}
224\end{frame}
225
226\begin{frame}{Environments}
227 \texttt{\color{red}\bs begin\{something\}}
228 Inside an environment
229 \texttt{\color{red}\bs end\{something\}}
230
231 \vspace{0.8cm}
232 \begin{itemize}
233 \item We have seen \texttt{document} and \texttt{align}
234 \item Text and symbols appear differently depending on the environment
235 \item Certain commands are specific to an environment
236 \item You can define new environments
237 \end{itemize}
238\end{frame}
239
240
241\begin{frame}{Environments}
242 Lists: \texttt{\color{red}itemize} and \texttt{\color{red}enumerate}
243
244 \vspace{0.8cm}
245 \begin{columns}
246 \column{0.5\textwidth}
247 \begin{itemize}
248 \item First: \[2+2=4\]
249 \item Second
250 \end{itemize}
251
252 \column{0.5\textwidth}
253 \texttt{\bs begin\{itemize\}}
254
255 \texttt{\qquad \bs item First: \bs[2+2=4\bs]}
256
257 \texttt{\qquad \bs item Second}
258
259 \texttt{\bs end\{itemize\}}
260 \end{columns}
261\end{frame}
262
263\begin{frame}{Environments}
264 Tables: \texttt{tabular} (text) and \texttt{array} (Math mode)
265
266 \vspace{0.8cm}
267 \begin{columns}
268 \column{0.5\textwidth}
269 \begin{tabular}{r|cc}
270 This & is & just \\
271 \hline
272 a & boring & table
273 \end{tabular}
274
275 \column{0.5\textwidth}
276 \texttt{\bs begin\{tabular\}\{r|cc\}}
277
278 \texttt{\qquad This \& is \& just \bs\bs}
279
280 \texttt{\qquad \bs hline}
281
282 \texttt{\qquad a \& boring \& table}
283
284 \texttt{\bs end\{tabular\}}
285 \end{columns}
286
287 \vspace{0.8cm}
288 Matrices: \texttt{array} with parentheses or \texttt{pmatrix}
289\end{frame}
290
291\begin{frame}{Sections}
292 \begin{itemize}
293 \item Use \texttt{\bs section\{Section Name\}} to start a new section
294 \item Also: \texttt{\bs chapter} (book only), \texttt{\bs subsection},
295 \texttt{subsubsection}...
296 \item \texttt{\bs section*\{Name\}} for no number
297 \item Sections after \texttt{\bs appendix} are numbered differently
298 \end{itemize}
299\end{frame}
300
301\begin{frame}{Theorems}
302
303 \begin{itemize}
304 \item In preamble: \texttt{\bs usepackage\{amsthm\}}
305 \item Also in preamble \texttt{\bs newtheorem \{envname\}\{Theorem\}}
306 \item Use \texttt{\bs newtheorem*} for no number
307 \end{itemize}
308\end{frame}
309
310\begin{frame}{Theorems}
311 \begin{columns}
312 \column{0.5\textwidth}
313 \includegraphics[scale=0.3]{img/thm_pre.png}
314
315 \vspace{0.2cm}
316 \vdots
317 \vspace{0.3cm}
318
319 \includegraphics[scale=0.3]{img/thm_tex.png}
320
321 \column{0.5\textwidth}
322 \includegraphics[scale=0.2]{img/thm_pdf.png}
323
324 \vspace{1cm}
325 \end{columns}
326\end{frame}
327
328\begin{frame}{End of the lecture}
329 For next time:
330
331 \vspace{0.8cm}
332 \begin{itemize}
333 \item Install Latex on your PC
334 \item Start writing something in Latex (e.g. homework)
335 \item Email me if you have any question
336 \end{itemize}
337\end{frame}
338
339\end{document}
340
diff --git a/src/Lecture1/slides/2-LatexFundamentals.toc b/src/Lecture1/slides/2-LatexFundamentals.toc
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1\frametitle{Math mode - align and equation}
2\begin{center}
3 For formulas spanning multiple lines you can use:
4 \begin{columns}
5 \column{0.5\textwidth}
6 \texttt{\bs begin\{align\}(...)\bs end \{align\}}
7 \begin{align}
8 \sum_{n=1}^\infty n =& 1+2+3+4+5+\cdots=\\
9 =& -\frac12
10 \end{align}
11 \column{0.5\textwidth}
12 \texttt{\bs begin\{equation\}(...)\bs end \{equation\}}
13 \begin{equation}
14 \sum_{n=1}^\infty n = 1+2+3+4+5+\cdots=\\
15 = -\frac12
16 \end{equation}
17 \end{columns}
18 \end{center}
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@@ -0,0 +1,58 @@
1%% Creator: Inkscape 1.0.1 (unknown), www.inkscape.org
2%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010
3%% Accompanies image file 'sage_svg-tex.pdf' (pdf, eps, ps)
4%%
5%% To include the image in your LaTeX document, write
6%% \input{<filename>.pdf_tex}
7%% instead of
8%% \includegraphics{<filename>.pdf}
9%% To scale the image, write
10%% \def\svgwidth{<desired width>}
11%% \input{<filename>.pdf_tex}
12%% instead of
13%% \includegraphics[width=<desired width>]{<filename>.pdf}
14%%
15%% Images with a different path to the parent latex file can
16%% be accessed with the `import' package (which may need to be
17%% installed) using
18%% \usepackage{import}
19%% in the preamble, and then including the image with
20%% \import{<path to file>}{<filename>.pdf_tex}
21%% Alternatively, one can specify
22%% \graphicspath{{<path to file>/}}
23%%
24%% For more information, please see info/svg-inkscape on CTAN:
25%% http://tug.ctan.org/tex-archive/info/svg-inkscape
26%%
27\begingroup%
28 \makeatletter%
29 \providecommand\color[2][]{%
30 \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}%
31 \renewcommand\color[2][]{}%
32 }%
33 \providecommand\transparent[1]{%
34 \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}%
35 \renewcommand\transparent[1]{}%
36 }%
37 \providecommand\rotatebox[2]{#2}%
38 \newcommand*\fsize{\dimexpr\f@size pt\relax}%
39 \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}%
40 \ifx\svgwidth\undefined%
41 \setlength{\unitlength}{375bp}%
42 \ifx\svgscale\undefined%
43 \relax%
44 \else%
45 \setlength{\unitlength}{\unitlength * \real{\svgscale}}%
46 \fi%
47 \else%
48 \setlength{\unitlength}{\svgwidth}%
49 \fi%
50 \global\let\svgwidth\undefined%
51 \global\let\svgscale\undefined%
52 \makeatother%
53 \begin{picture}(1,0.26172667)%
54 \lineheight{1}%
55 \setlength\tabcolsep{0pt}%
56 \put(0,0){\includegraphics[width=\unitlength,page=1]{sage_svg-tex.pdf}}%
57 \end{picture}%
58\endgroup%

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