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- \documentclass{article}
- \usepackage{titling}
- \pretitle{\begin{center}\huge}
- \posttitle{\par\end{center}\vspace{\baselineskip}}
- \preauthor{\normalfont\normalsize\begin{center}\begin{tabular}[t]{c}}
- \postauthor{\end{tabular}\end{center}\vspace{\baselineskip}}
- \title{\sc MATH 296: Homework 1C}
- \author{\sc Aniruddh Agarwal, Tony Bai, Swaraj Nayegandhi, Omer Siddiqui}
- \date{}
- \usepackage[letterpaper, margin=1in]{geometry}
- \usepackage{enumitem}
- \usepackage{mathrsfs}
- \usepackage{amssymb}
- \usepackage{amsmath}
- \usepackage{amsthm}
- \usepackage[utf8]{inputenc}
- \usepackage[english]{babel}
- \usepackage{fancyhdr}
- \usepackage{extramarks}
- \usepackage{amsfonts}
- \usepackage{tikz}
- \usepackage{verbatim}
- \theoremstyle{definition}
- \newtheorem{definition}{Definition}[section]
- \newtheorem{problem}[]{Problem}
- \newtheorem*{bookprob}{Book Problem}
- \newtheorem{exercise}[]{Exercise}
- \theoremstyle{remark}
- \newtheorem*{remark}{Remark}
- \newtheorem{theorem}{Theorem}[section]
- \newtheorem{corollary}{Corollary}[theorem]
- \theoremstyle{Theorem}
- \newtheorem{lemma}[theorem]{Lemma}
- \usetikzlibrary{automata,positioning}
- \pagestyle{fancy}
- \setlength\parindent{0pt}
- %
- % Various Helper Commands
- %
- % For derivatives
- \newcommand{\deriv}[1]{\frac{\mathrm{d}}{\mathrm{d}x} (#1)}
- % For partial derivatives
- \newcommand{\pderiv}[2]{\frac{\partial}{\partial #1} (#2)}
- % Integral dx
- \newcommand{\dx}{\mathrm{d}x}
- % My sanity is important:
- %%
- %% Sets:
- %%
- \newcommand{\Q}{\mathbb{Q}} % Rationals
- \newcommand{\R}{\mathbb{R}} % Reals
- \newcommand{\N}{\mathbb{N}} % Naturals
- \newcommand{\C}{\mathbb{C}} % Complex
- \newcommand{\Z}{\mathbb{Z}} % Integers
- \renewcommand{\H}{\mathbb{H}} % \sqrt{Upper Half Plane}
- %%
- %% Big words:
- %%
- \renewcommand{\hom}{\text{homomorphism}}
- \newcommand{\hyp}{\text{hyperbolic}}
- \newcommand{\spc}{\text{ }}
- %%
- %% Commands that are too long
- %%
- \renewcommand{\to}{\rightarrow}
- \newcommand{\vphi}{\varphi}
- \newcommand{\veps}{\varepsilon}
- \newcommand{\infsum}[1]{\sum_{#1=1}^\infty}
- \newcommand{\norm}[1]{\left\lVert#1\right\rVert}
- %%
- %% Text for math mode
- %%
- \newcommand{\im}{\text{im}}
- \renewcommand{\ker}{\text{ker}}
- \newcommand{\tand}{\text{and}}
- \newcommand{\st}{\text{such that}}
- % Spacing between problems
- \newcommand{\newprob}{\vspace{0.2in}}
- \begin{document}
- \maketitle
- \setcounter{problem}{124}
- \begin{enumerate}
- \item Is there an analogue of the IVT for integrals?\\
- \textit{This was based on Problem 114(f)}.
- \item Can something be said about the commutativity of $S_n$ in general?\\
- \textit{This was based on Problem 115(a)}.
- \item Can an abelian group have a non-abelian subgroup?\\
- \textit{This was based on Problem 115(a)}.
- \item Is there a group homomorphism between $S_3$ and $\Z /6\Z$?\\
- \textit{This was based on Problem 115(a)}.
- \item Can a countable set have uncountably many subgroups?\\
- \textit{This was based on Problem 115(b)}.
- \item What's an example of a topological space that's not trivial and not Hausdorff?\\
- \textit{This was based on Problem 116(b)}.
- \end{enumerate}
- \end{document}
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