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\title{18.118 Decoupling \\
	Lecture template}
\author{Instructor: Larry Guth \\
	Transcribed by   }
\begin{document}
	\maketitle

Here is a template to use for writing up the decoupling notes.  It'll be helpful for me to have them all in a common template so that I can edit them a little.  Maybe at some point I will want to merge them.

If you have particular latex tools that you like to use, you can add them to the preamble.  

It's worth saying a word about pictures.  I draw a lot of pictures in lecture, and I find it difficult to put them in latex.  If you're good at it, then by all means put in pictures.  But here are a couple other thoughts that could make things easier for you.  One thing is that instead of drawing the picture you can often describe it in words.  ``Suppose that $f$ is a tall skinny bump function, which has height about ... on an interval of length ... and decays rapidly off of that interval...''  Another thing is that it's perfectly fine to just draw pictures on a separate sheet of paper, scan them, and then send me the .pdf of the scan.  I'll put it next to .pdf of the lecture notes file.










\end{document}