From d6c61d988bfa4255baf9cdae42db59ebee38363f Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Tue, 25 May 2021 17:10:49 +0200 Subject: Added files --- src/Homework1/Homework1.aux | 4 + src/Homework1/Homework1.log | 257 ++++++++++++++++++++++++++++++++++++++++++++ src/Homework1/Homework1.pdf | Bin 0 -> 120157 bytes src/Homework1/Homework1.tex | 143 ++++++++++++++++++++++++ 4 files changed, 404 insertions(+) create mode 100644 src/Homework1/Homework1.aux create mode 100644 src/Homework1/Homework1.log create mode 100644 src/Homework1/Homework1.pdf create mode 100644 src/Homework1/Homework1.tex (limited to 'src/Homework1') diff --git a/src/Homework1/Homework1.aux b/src/Homework1/Homework1.aux new file mode 100644 index 0000000..cde7be1 --- /dev/null +++ b/src/Homework1/Homework1.aux @@ -0,0 +1,4 @@ +\relax +\newlabel{prop:fta}{{1}{1}} +\newlabel{eq:fubini}{{2}{1}} +\gdef \@abspage@last{2} diff --git a/src/Homework1/Homework1.log b/src/Homework1/Homework1.log new file mode 100644 index 0000000..644875f --- /dev/null +++ b/src/Homework1/Homework1.log @@ -0,0 +1,257 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/VoidLinux) (preloaded format=pdflatex 2021.2.3) 1 APR 2021 11:38 +entering extended mode + \write18 enabled. + %&-line parsing enabled. +**homework1.tex +(./homework1.tex +LaTeX2e <2020-10-01> patch level 2 +L3 programming layer <2020-12-03> xparse <2020-03-03> +(/usr/share/texmf-dist/tex/latex/base/article.cls +Document Class: article 2020/04/10 v1.4m Standard LaTeX document class +(/usr/share/texmf-dist/tex/latex/base/size12.clo +File: size12.clo 2020/04/10 v1.4m Standard LaTeX file (size option) +) +\c@part=\count177 +\c@section=\count178 +\c@subsection=\count179 +\c@subsubsection=\count180 +\c@paragraph=\count181 +\c@subparagraph=\count182 +\c@figure=\count183 +\c@table=\count184 +\abovecaptionskip=\skip47 +\belowcaptionskip=\skip48 +\bibindent=\dimen138 +) +(/usr/share/texmf-dist/tex/latex/base/inputenc.sty +Package: inputenc 2020/08/01 v1.3d Input encoding file +\inpenc@prehook=\toks15 +\inpenc@posthook=\toks16 +) +(/usr/share/texmf-dist/tex/latex/amsmath/amsmath.sty +Package: amsmath 2020/09/23 v2.17i AMS math features +\@mathmargin=\skip49 + +For additional information on amsmath, use the `?' option. +(/usr/share/texmf-dist/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 AMS text + +(/usr/share/texmf-dist/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 generic functions +\@emptytoks=\toks17 +\ex@=\dimen139 +)) +(/usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d Bold Symbols +\pmbraise@=\dimen140 +) +(/usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty +Package: amsopn 2016/03/08 v2.02 operator names +) +\inf@bad=\count185 +LaTeX Info: Redefining \frac on input line 234. +\uproot@=\count186 +\leftroot@=\count187 +LaTeX Info: Redefining \overline on input line 399. +\classnum@=\count188 +\DOTSCASE@=\count189 +LaTeX Info: Redefining \ldots on input line 496. +LaTeX Info: Redefining \dots on input line 499. +LaTeX Info: Redefining \cdots on input line 620. +\Mathstrutbox@=\box47 +\strutbox@=\box48 +\big@size=\dimen141 +LaTeX Font Info: Redeclaring font encoding OML on input line 743. +LaTeX Font Info: Redeclaring font encoding OMS on input line 744. +\macc@depth=\count190 +\c@MaxMatrixCols=\count191 +\dotsspace@=\muskip16 +\c@parentequation=\count192 +\dspbrk@lvl=\count193 +\tag@help=\toks18 +\row@=\count194 +\column@=\count195 +\maxfields@=\count196 +\andhelp@=\toks19 +\eqnshift@=\dimen142 +\alignsep@=\dimen143 +\tagshift@=\dimen144 +\tagwidth@=\dimen145 +\totwidth@=\dimen146 +\lineht@=\dimen147 +\@envbody=\toks20 +\multlinegap=\skip50 +\multlinetaggap=\skip51 +\mathdisplay@stack=\toks21 +LaTeX Info: Redefining \[ on input line 2923. +LaTeX Info: Redefining \] on input line 2924. +) +(/usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support +\symAMSa=\mathgroup4 +\symAMSb=\mathgroup5 +LaTeX Font Info: Redeclaring math symbol \hbar on input line 98. +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 106. +) +(/usr/share/texmf-dist/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2013/01/14 v3.01 AMS font symbols +) +(/usr/share/texmf-dist/tex/latex/amscls/amsthm.sty +Package: amsthm 2020/05/29 v2.20.6 +\thm@style=\toks22 +\thm@bodyfont=\toks23 +\thm@headfont=\toks24 +\thm@notefont=\toks25 +\thm@headpunct=\toks26 +\thm@preskip=\skip52 +\thm@postskip=\skip53 +\thm@headsep=\skip54 +\dth@everypar=\toks27 +) +(/usr/share/texmf-dist/tex/latex/geometry/geometry.sty +Package: geometry 2020/01/02 v5.9 Page Geometry + +(/usr/share/texmf-dist/tex/latex/graphics/keyval.sty +Package: keyval 2014/10/28 v1.15 key=value parser (DPC) +\KV@toks@=\toks28 +) +(/usr/share/texmf-dist/tex/generic/iftex/ifvtex.sty +Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. 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homework 1} +\author{Sebastiano Tronto} + +\newtheorem{thm}{Theorem} +\newtheorem{prop}[thm]{Proposition} + +\theoremstyle{definition} +\newtheorem{ex}{Exercise} + +\theoremstyle{definition} +\newtheorem*{remark}{Remark} + +\begin{document} + +\noindent\hrulefill + +\begin{center} +\Huge{\textbf{Mathematical Software - Homework 1}} +\end{center} + +\noindent\hrulefill +\begin{center} +\begin{tabular}{lcr} +\texttt{sebastiano.tronto@uni.lu} & \qquad \qquad \qquad \qquad & +\textbf{Deadline: Sunday, March 28th} +\end{tabular} +\end{center} + +\vspace{1cm} + +\begin{center} + \emph{\large + For each of the following exercises submit a .tex and a .pdf file. + } +\end{center} + +\vspace{1cm} + +\begin{ex} + Write a short Latex document that contains the following theorem-like + environments using the \texttt{\textbackslash newtheorem} command of the + \texttt{amsthm} package (the box around the text is not needed): + \begin{center} + \fbox{\parbox{0.95\textwidth}{ + \begin{prop}[Fundamental Theorem of Algebra] + \label{prop:fta} + Let \(p(x)\) be a non-constant polynomial with coefficients in + $\mathbb C$. Then there is \(z\in\mathbb C\) such that $p(z)=0$. + \end{prop} + + \begin{remark} + Proposition \ref{prop:fta} is not true for polynomials with + coefficients in $\mathbb R$. For example + \begin{align} + p(x) = x^2+1 + \end{align} + does not have real roots. + \end{remark} + + \begin{thm} + If $X$ and $Y$ are $\sigma$-finite measure spaces and $f:X\times Y\to + \mathbb R$ is measurable and such that + \begin{align*} + \int_{X\times Y}|f(x,y)|\mathrm d(x,y) < \infty + \end{align*} + then + \begin{align} + \label{eq:fubini} + \int_X\left(\int_Yf(x,y)\mathrm d y\right)\mathrm d x = + \int_Y\left(\int_Xf(x,y)\mathrm d x\right)\mathrm d y = + \int_{X\times Y} f(x,y)\mathrm d(x,y)\,. + \end{align} + \end{thm} + + \begin{remark} + In practice, equation \eqref{eq:fubini} means that we can switch the + order of integration in a double integral. + \end{remark} + }} + \end{center} + Notice that Propositions, Theorems and some of the equations are numbered, + and some of them are referred to in the Remarks. This numbering should change + accordingly if more numbered Theorems and equations are added before this + part of the text. +\end{ex} + +\vspace{0.8cm} + +\begin{ex} +[This is basically a ``do whatever you want, just do something'' exercise] +Write a Mathematical document in Latex, where ``Mathematical'' means any text +that contains both inline and displaystyle symbols and formulas, and where most +of the sentences contain a Mathematical symbol. +For example, you can submit (part of) your homework or notes for another course +that you are following at the moment. + +You must follow the following rules: +\begin{itemize} + \item Your document must be at least 2 pages long. + \item Use the following in your preamble: + \begin{verbatim} +\documentaclass[12pt,a4paper]{article} +\usepackage[left=2.5cm,right=2.5cm,top=2.5cm,bottom=2.5cm]{geometry} + \end{verbatim} +\end{itemize} +The document itself can be about any area of Mathematics, Physics or similar. +The correctness of the Mathematics itself will not be judged for this course. +\end{ex} + +\section*{Grading} + +This homework assignment is worth 25\% of your final grade. + +\vspace{0.3cm} +\textbf{Exercise 1 (10 points).} +\begin{itemize} + \item A correct use of the \texttt{\textbackslash newtheorem} command is + worth 4 out of 10 points. + \item A correct use of the labelling and reference system is worth 4 points. + \item Reproducing correctly the mathematical formulas is worth 2 points. +\end{itemize} + +\textbf{Exercise 2 (10 points).} +\begin{itemize} + \item A resulting pdf file that looks readable and correct is worth 6 out of + 10 points. + \item The correct use of latex commands and environments is worth 4 out of + 10 points. \emph{Examples of mistakes in this sense: adjusting manually + the size of parenthesis instead of using \texttt{\textbackslash left} + and \texttt{\textbackslash right}; using \texttt{\textbackslash Sigma} + when you actually want to write a sum symbol.} +\end{itemize} + + +\end{document} \ No newline at end of file -- cgit v1.3