1%CUT AND PASTE THIS ENTIRE DOCUMENT INTO A BLANK DOCUMENT ON CloudSageMath. Then replace the content (title, name, and so on), with your stuff. If you have problems or errors, let me know!
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3\documentclass[12pt]{amsart}
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5\usepackage{amssymb, amscd, amsmath, amsthm}
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7\newtheorem*{utheorem}{Theorem}
8\newtheorem*{ucorollary}{Corollary}
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12\newtheorem{definition}[theorem]{Definition}
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14\thispagestyle{empty}
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16\begin{document}
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22\maketitle
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24Last Wednesday's colloquium was given by Isaac Newton. He talked about integration and gave several applications of integrals to daily life.
25$$\int_0^\infty e^{x^2}dx = \sqrt{\pi}/2$$
26Blah blah.
27
28$e^x+\Pi$
29
30$$\sum_{i=1}^{\infty}\frac{1}{i^2}= \frac{1}{1^2}+\frac{1}{2^2}+\cdots =\frac{6}{\pi^2}.$$
31
32\begin{definition}
33A definite integral is ...blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah
34\end{definition}
35
36The main result concerning integrals that Newton discussed was the Fundamental Theorem of Calculus.
37
38\begin{theorem}[Fundamental Theorem of Calculus]
39Given any continuous function $f$... blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah
40\end{theorem}
41
42A key example that illustrated this result was... blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah.
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44This theorem also applies to... blah blah blah blah blah.
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47Newton did a great job with his lecture. I understood integrals better than I ever have before. One question I had when I left the lecture was whether his ideas also worked for functions which blah blah blah.
48
49\end{document}
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