hw1temp_132sp17.tex -...

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\documentclass[notitlepage,11pt]{article} \usepackage{amsmath,amssymb,amscd,mathrsfs,amscd,amsthm} \usepackage{verbatim} \usepackage[pdftex]{graphics,color} \usepackage[nohead,height=9.8in]{geometry} % Page geometry \usepackage{hyperref} % Allows use of hyperlinks within the document \setcounter{secnumdepth}{5} \setcounter{section}{-1} % Theorem-style environments \newtheoremstyle{therm}{6pt}{4pt}{\itshape}{0pt}{\sffamily\bfseries}{.}{ }{} \theoremstyle{therm} \newtheorem{thm}{Theorem}[subsection] \newtheorem{lem}[thm]{Lemma} \newtheorem*{thme}{Theorem} \newtheorem*{core}{Corollary} \newtheorem{prp}[thm]{Proposition} \newtheorem{cor}[thm]{Corollary} \theoremstyle{definition} \newtheorem{dfn}[thm]{Definition} \newtheorem*{clm}{Claim} \newtheorem{rmk}[thm]{Remark} \newtheorem*{ntn}{Notation} \newtheorem{exa}[thm]{Example} \newtheorem{exer}[thm]{Exercise} \newtheorem*{rmke}{Remark} \newtheorem*{qst}{Question} \newenvironment{pff}{{\em Proof:}}{\qed} \numberwithin{equation}{section} % Greek shortcuts \newcommand{\af}{\alpha} \newcommand{\bt}{\beta} \newcommand{\gm}{\gamma} \newcommand{\dt}{\delta} \newcommand{\ep}{\varepsilon} \newcommand{\zt}{\zeta} \newcommand{\et}{\eta} \newcommand{\io}{\iota} \newcommand{\te}{\theta} \newcommand{\ld}{\lambda} \newcommand{\sm}{\sigma} \newcommand{\kp}{\kappa} \newcommand{\ph}{\varphi} \newcommand{\ps}{\psi} \newcommand{\rh}{\rho} \newcommand{\om}{\omega} \newcommand{\ta}{\tau} \newcommand{\Gm}{\Gamma} \newcommand{\Dt}{\Delta} \newcommand{\Et}{\Eta} \newcommand{\Te}{\Theta} \newcommand{\Ld}{\Lambda} \newcommand{\Sm}{\Sigma} \newcommand{\Ph}{\Phi} \newcommand{\Ps}{\Psi} \newcommand{\Om}{\Omega}
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% Blackboard maths symbols \newcommand{\Q}{{\mathbb{Q}}} \newcommand{\Z}{{\mathbb{Z}}} \newcommand{\R}{{\mathbb{R}}} \newcommand{\C}{{\mathbb{C}}} \newcommand{\N}{{\mathbb{N}}} \newcommand{\F}{{\mathbb{F}}} \newcommand{\K}{{\mathbb{K}}} \newcommand{\E}{{\mathbb{E}}} \renewcommand{\H}{{\mathbb{H}}} % Gothic german letters \newcommand{\mfa}{{\mathfrak{a}}} \newcommand{\mfb}{{\mathfrak{b}}} \newcommand{\mfc}{{\mathfrak{c}}} \newcommand{\mfd}{{\mathfrak{d}}} \newcommand{\mfe}{{\mathfrak{e}}} \newcommand{\mff}{{\mathfrak{f}}} \newcommand{\mfg}{{\mathfrak{g}}} \newcommand{\mfh}{{\mathfrak{h}}}
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