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%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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\documentclass[12pt]{amsart}
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\usepackage{amssymb, amscd, amsmath, amsthm}
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\newtheorem*{utheorem}{Theorem}
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\newtheorem*{ucorollary}{Corollary}
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}{Lemma}
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\newtheorem*{ulemma}{Lemma}
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\newtheorem{definition}[theorem]{Definition}
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\thispagestyle{empty}
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\begin{document}
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\title{Type your title here}
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\author{Type Your Name Here}
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\maketitle
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Last Wednesday's colloquium was given by Isaac Newton. He talked about integration and gave several applications of integrals to daily life.
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$$\int_0^\infty e^{x^2}dx = \sqrt{\pi}/2 $$
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Blah blah.
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$e^x+\Pi$
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$$\sum_{i=1}^{\infty}\frac{1}{i^2}= \frac{1}{1^2}+\frac{1}{2^2}+\cdots =\frac{6}{\pi^2}.$$
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\begin{definition}
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A definite integral is ...blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah 
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\end{definition}
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The main result concerning integrals that Newton discussed was the Fundamental Theorem of Calculus.
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\begin{theorem}[Fundamental Theorem of Calculus]
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Given any continuous function $f$... blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah 
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\end{theorem}
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A 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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This theorem also applies to... blah blah blah blah blah.
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Newton 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. 
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\end{document}
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