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89 lines
3.3 KiB
TeX
89 lines
3.3 KiB
TeX
%From M275 "Topology" at SJSU
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\newcommand{\id}{\mathrm{id}}
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\newcommand{\taking}[1]{\xrightarrow{#1}}
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\newcommand{\inv}{^{-1}}
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%From M170 "Introduction to Graph Theory" at SJSU
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\DeclareMathOperator{\diam}{diam}
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\DeclareMathOperator{\ord}{ord}
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\newcommand{\defeq}{\overset{\mathrm{def}}{=}}
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%From the USAMO .tex files
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\newcommand{\ts}{\textsuperscript}
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\newcommand{\dg}{^\circ}
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\newcommand{\ii}{\item}
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% % From Math 55 and Math 145 at Harvard
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% \newenvironment{subproof}[1][Proof]{%
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% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}%
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% {\end{proof}}
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\newcommand{\liff}{\leftrightarrow}
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\newcommand{\lthen}{\rightarrow}
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\newcommand{\opname}{\operatorname}
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\newcommand{\surjto}{\twoheadrightarrow}
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\newcommand{\injto}{\hookrightarrow}
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\newcommand{\On}{\mathrm{On}} % ordinals
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\DeclareMathOperator{\img}{im} % Image
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\DeclareMathOperator{\Img}{Im} % Image
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\DeclareMathOperator{\coker}{coker} % Cokernel
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\DeclareMathOperator{\Coker}{Coker} % Cokernel
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\DeclareMathOperator{\Ker}{Ker} % Kernel
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\DeclareMathOperator{\rank}{rank}
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\DeclareMathOperator{\Spec}{Spec} % spectrum
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\DeclareMathOperator{\Tr}{Tr} % trace
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\DeclareMathOperator{\pr}{pr} % projection
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\DeclareMathOperator{\ext}{ext} % extension
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\DeclareMathOperator{\pred}{pred} % predecessor
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\DeclareMathOperator{\dom}{dom} % domain
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\DeclareMathOperator{\ran}{ran} % range
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\DeclareMathOperator{\Hom}{Hom} % homomorphism
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\DeclareMathOperator{\Mor}{Mor} % morphisms
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\DeclareMathOperator{\End}{End} % endomorphism
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\newcommand{\eps}{\epsilon}
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\newcommand{\veps}{\varepsilon}
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\newcommand{\ol}{\overline}
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\newcommand{\ul}{\underline}
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\newcommand{\wt}{\widetilde}
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\newcommand{\wh}{\widehat}
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\newcommand{\vocab}[1]{\textbf{\color{blue} #1}}
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\providecommand{\half}{\frac{1}{2}}
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\newcommand{\dang}{\measuredangle} %% Directed angle
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\newcommand{\ray}[1]{\overrightarrow{#1}}
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\newcommand{\seg}[1]{\overline{#1}}
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\newcommand{\arc}[1]{\wideparen{#1}}
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\DeclareMathOperator{\cis}{cis}
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\DeclareMathOperator*{\lcm}{lcm}
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\DeclareMathOperator*{\argmin}{arg min}
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\DeclareMathOperator*{\argmax}{arg max}
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\newcommand{\cycsum}{\sum_{\mathrm{cyc}}}
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\newcommand{\symsum}{\sum_{\mathrm{sym}}}
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\newcommand{\cycprod}{\prod_{\mathrm{cyc}}}
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\newcommand{\symprod}{\prod_{\mathrm{sym}}}
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\newcommand{\Qed}{\begin{flushright}\qed\end{flushright}}
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\newcommand{\parinn}{\setlength{\parindent}{1cm}}
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\newcommand{\parinf}{\setlength{\parindent}{0cm}}
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% \newcommand{\norm}{\|\cdot\|}
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\newcommand{\inorm}{\norm_{\infty}}
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\newcommand{\opensets}{\{V_{\alpha}\}_{\alpha\in I}}
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\newcommand{\oset}{V_{\alpha}}
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\newcommand{\opset}[1]{V_{\alpha_{#1}}}
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\newcommand{\lub}{\text{lub}}
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\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}}
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\newcommand{\Del}[3]{\frac{\partial^{#1} #2}{\partial^{#1} #3}}
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\newcommand{\deld}[2]{\dfrac{\partial #1}{\partial #2}}
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\newcommand{\Deld}[3]{\dfrac{\partial^{#1} #2}{\partial^{#1} #3}}
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\newcommand{\lm}{\lambda}
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\newcommand{\uin}{\mathbin{\rotatebox[origin=c]{90}{$\in$}}}
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\newcommand{\usubset}{\mathbin{\rotatebox[origin=c]{90}{$\subset$}}}
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\newcommand{\lt}{\left}
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\newcommand{\rt}{\right}
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\newcommand{\bs}[1]{\boldsymbol{#1}}
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\newcommand{\exs}{\exists}
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\newcommand{\st}{\strut}
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\newcommand{\dps}[1]{\displaystyle{#1}}
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\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} }
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\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed}
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