Open in CoCalc
1%Header LaTeX page
2%Has the following short-hands:
3% intersect, union, results, if and only if, modulo, angle
4% all usual sets
5%
6% page settings
7
8\documentclass[12pt]{article}
9\usepackage{latexsym, amsfonts, graphicx, amsthm}
10
11\setlength{\textheight}{8.75in} \setlength{\textwidth}{6.5in}
14\setlength{\oddsidemargin}{0.0in}
15
17
18\newcommand{\aj}{
19\vskip 24pt
20\flushleft{\copyright \hskip 5pt Andrei Jorza \\
21jorza@fas.harvard.edu \\
222003}}
23
24%Enumeration
25  \def\be{\begin{enumerate}}
26  \def\ee{\end{enumerate}}
27  \def\ii{\item}
28  \def\bi{\begin{itemize}}
29  \def\ei{\end{itemize}}
30
31%Equations and Formatting
32  \def\beqa{\begin{eqnarray*}}
33  \def\eeqa{\end{eqnarray*}}
34  \def\dsp{\displaystyle}
35
36\newcommand{\rez}{\Longrightarrow}
37\newcommand{\N}{\mathbf{N}}
38\newcommand{\Z}{\mathbf{Z}}
39\newcommand{\Q}{\mathbf{Q}}
40\newcommand{\R}{\mathbf{R}}
41\newcommand{\C}{\mathcal{C}}
42\newcommand{\CC}{\mathbf{C}}
43\newcommand{\m}{{\textmd{mod}\,\,}}
44\renewcommand{\a}{\angle}
45\renewcommand{\d}{\Delta}
46\renewcommand{\to}{\longrightarrow}
47\renewcommand{\v}{\emptyset}
48\renewcommand{\i}{\cap}
49\renewcommand{\u}{\cup}
50\newcommand{\intp}[1]{\lfloor {#1} \rfloor}
51\newcommand{\binom}[2]{{{#1} \choose {#2}}}
52\newcommand{\dg}{^{\circ}}
53
54\newcommand{\vv}[1]{{#1}_1,{#1}_2,\ldots ,{#1}_n}
55\newcommand{\vvi}[1]{{#1}_1,{#1}_2,\ldots}
56\newcommand{\vvn}[2]{{#1}_1,{#1}_2,\ldots ,{#1}_{#2}}
57
58\newcommand{\bea}{\begin{eqnarray*}}
59\newcommand{\eea}{\end{eqnarray*}}
60\newcommand{\bean}{\begin{eqnarray}}
61\newcommand{\eean}{\end{eqnarray}}
62
63\def\divides{\ |\ }
64\def\dvd{\divides}
65\def\cis{\hbox{cis }}
66\def\ndvd{\,\not|\ }
67\def\natchp{{\bf N'}}
68\def\proof{\par{\bf Proof: }}
69\def\soln{\par{\bf Solution: }}
70\def\hint{{\bf  Hint: }}
71\def\endpf{\hfill \vrule depth-1pt height7pt width6pt}
72\font\ttl=cmr10 scaled \magstep 3
73\theoremstyle{plain}
74\newtheorem{theorem}{Theorem}[section]
75\newtheorem{proposition}[theorem]{Proposition}
76\newtheorem{conjecture}[theorem]{Conjecture}
77\newtheorem{lemma}[theorem]{Lemma}
78\newtheorem{corollary}[theorem]{Corollary}
79
80\theoremstyle{definition}
81\newtheorem{example}[theorem]{Example}
82\newtheorem{definition}[theorem]{Definition}
83\newtheorem{remark}[theorem]{Remark}
84
85
86\renewcommand{\iff}{\Longleftrightarrow}
87