\usepackage{xcolor}\usepackage{fontspec}\usepackage[sc]{mathpazo}\setmainfont[Ligatures=TeX]{Palatino Linotype}\usepackage{amssymb}\usepackage{amsmath}\usepackage{menukeys}\@ifpackageloaded{hyperref}{}{\usepackage{hyperref}}\definecolor{darkblue}{rgb}{0,0,0.6}\hypersetup{colorlinks=true}\hypersetup{linkcolor=darkblue}\hypersetup{urlcolor=darkblue}\ifx\foobar\undefined \else \newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}%\fi\definecolor{codegray}{gray}{0.9}\newcommand\grid[1]{%\begin{tikzpicture}[baseline=(char.base)] \path[use as bounding box] (0,0) rectangle (1em,1em); \draw[red!50, fill=red!20] (0,0) rectangle (1em,1em); \node[inner sep=1pt,anchor=base west] (char) at (0em,\gridraiseamount) {#1};\end{tikzpicture}}\newcommand\gridraiseamount{0.12em}\makeatletter\newcommand\Grid[1]{% \@tfor\z:=#1\do{\grid{\z}}}\makeatother \makeatletter\def\fnote{\gdef\@thefnmark{}\@footnotetext}\makeatother\newcommand{\HEADER}{{\bf Please submit your solutions to theemail address 7ccsmsen at gmail dot com. Please submit only onehomework per email. Please also submit onlyASCII text or PDFs. Every solution should be preceded by thecorresponding question, like:\begin{center}\begin{tabular}{ll}Q$n$: & \ldots a difficult question from me\ldots\\A: & \ldots an answer from you \ldots\\Q$n+1$ & \ldots another difficult question\ldots\\A: & \ldots another brilliant answer from you\ldots\end{tabular}\end{center}\noindent Solutions will only be accepted until20th December!}\bigskip}\newcommand{\POSTSCRIPT}{{\bf (Optional)} This question is for you to provide regular feedback to me, for example what were the most interesting, least interesting, or confusing parts in this lecture?Is there anything you like to have improved or explained in the handouts?Please feel free to share any other questions or concerns.}