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  1. \documentclass{article}
  2.  
  3. \usepackage{titling}
  4. \pretitle{\begin{center}\huge}
  5. \posttitle{\par\end{center}\vspace{\baselineskip}}
  6. \preauthor{\normalfont\normalsize\begin{center}\begin{tabular}[t]{c}}
  7. \postauthor{\end{tabular}\end{center}\vspace{\baselineskip}}
  8.  
  9. \title{\sc MATH 296: Homework 1C}
  10. \author{\sc Aniruddh Agarwal, Tony Bai, Swaraj Nayegandhi, Omer Siddiqui}
  11. \date{}
  12.  
  13. \usepackage[letterpaper, margin=1in]{geometry}
  14.  
  15. \usepackage{enumitem}
  16. \usepackage{mathrsfs}
  17. \usepackage{amssymb}
  18. \usepackage{amsmath}
  19. \usepackage{amsthm}
  20. \usepackage[utf8]{inputenc}
  21. \usepackage[english]{babel}
  22. \usepackage{fancyhdr}
  23. \usepackage{extramarks}
  24. \usepackage{amsfonts}
  25. \usepackage{tikz}
  26. \usepackage{verbatim}
  27.  
  28. \theoremstyle{definition}
  29. \newtheorem{definition}{Definition}[section]
  30. \newtheorem{problem}[]{Problem}
  31. \newtheorem*{bookprob}{Book Problem}
  32. \newtheorem{exercise}[]{Exercise}
  33. \theoremstyle{remark}
  34. \newtheorem*{remark}{Remark}
  35. \newtheorem{theorem}{Theorem}[section]
  36. \newtheorem{corollary}{Corollary}[theorem]
  37.  
  38. \theoremstyle{Theorem}
  39. \newtheorem{lemma}[theorem]{Lemma}
  40.  
  41.  
  42. \usetikzlibrary{automata,positioning}
  43.  
  44. \pagestyle{fancy}
  45.  
  46. \setlength\parindent{0pt}
  47.  
  48. %
  49. % Various Helper Commands
  50. %
  51.  
  52. % For derivatives
  53. \newcommand{\deriv}[1]{\frac{\mathrm{d}}{\mathrm{d}x} (#1)}
  54.  
  55. % For partial derivatives
  56. \newcommand{\pderiv}[2]{\frac{\partial}{\partial #1} (#2)}
  57.  
  58. % Integral dx
  59. \newcommand{\dx}{\mathrm{d}x}
  60.  
  61. % My sanity is important:
  62.  
  63. %%
  64. %% Sets:
  65. %%
  66. \newcommand{\Q}{\mathbb{Q}} % Rationals
  67. \newcommand{\R}{\mathbb{R}} % Reals
  68. \newcommand{\N}{\mathbb{N}} % Naturals
  69. \newcommand{\C}{\mathbb{C}} % Complex
  70. \newcommand{\Z}{\mathbb{Z}} % Integers
  71. \renewcommand{\H}{\mathbb{H}} % \sqrt{Upper Half Plane}
  72.  
  73. %%
  74. %% Big words:
  75. %%
  76. \renewcommand{\hom}{\text{homomorphism}}
  77. \newcommand{\hyp}{\text{hyperbolic}}
  78. \newcommand{\spc}{\text{ }}
  79.  
  80. %%
  81. %% Commands that are too long
  82. %%
  83. \renewcommand{\to}{\rightarrow}
  84. \newcommand{\vphi}{\varphi}
  85. \newcommand{\veps}{\varepsilon}
  86. \newcommand{\infsum}[1]{\sum_{#1=1}^\infty}
  87. \newcommand{\norm}[1]{\left\lVert#1\right\rVert}
  88.  
  89. %%
  90. %% Text for math mode
  91. %%
  92. \newcommand{\im}{\text{im}}
  93. \renewcommand{\ker}{\text{ker}}
  94. \newcommand{\tand}{\text{and}}
  95. \newcommand{\st}{\text{such that}}
  96.  
  97. % Spacing between problems
  98. \newcommand{\newprob}{\vspace{0.2in}}
  99.  
  100. \begin{document}
  101. \maketitle
  102. \setcounter{problem}{124}
  103.  
  104. \begin{enumerate}
  105. \item Is there an analogue of the IVT for integrals?\\
  106.  \textit{This was based on Problem 114(f)}.
  107. \item Can something be said about the commutativity of $S_n$ in general?\\
  108.  \textit{This was based on Problem 115(a)}.
  109. \item Can an abelian group have a non-abelian subgroup?\\
  110.  \textit{This was based on Problem 115(a)}.
  111. \item Is there a group homomorphism between $S_3$ and $\Z /6\Z$?\\
  112.  \textit{This was based on Problem 115(a)}.
  113. \item Can a countable set have uncountably many subgroups?\\
  114.  \textit{This was based on Problem 115(b)}.
  115. \item What's an example of a topological space that's not trivial and not Hausdorff?\\
  116.  \textit{This was based on Problem 116(b)}.
  117. \end{enumerate}
  118. \end{document}
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