Problem Set 1 SolutionsECS 20 — Fall 2008Jane P. StudentNovember 6, 2008Problem 1Here you’ll put your solution to problem 1. A most excellent solution to problem 1. Make all ofyour solutions excellent and you will make me happy. Don’t you want me to be happy?Problem 2To turn this file into a dvi file type latex sample.tex. The resulting sample.dvi can be lookedat using a previewer such as xdvi (on UNIX) or yap (on Windows), and it can be printed out fromthose programs. To create a pdf file you can say pdflatex sample.tex.When working under Windows I use MiKTeX, a free distribution of LATEX and associated pro-grams. You can download it from various web sites; just google miktex. After downloading MiKTeXyou can put its directory of executables in your path and use a command prompt (DOS window)to do things, editing your tex-files with a Windows-based version of vi or emacs. Alternatively, getyour LATEX distribution under cygwin.Problem 3One of the most important aspects of LATEX is its math mode. Mathematical symbols should looklike a or X5or or A∗ijor Ctri; never write something like x in ordinary text mode—it looks terrible,and means something different from x. Indeed you should regard x, x, x, X , and X as all distinctthings.Problem 4To produce an offset formula you can write things likenXi=1i =n(n + 1)2∈ O(n2)1Problem 5I won’t suggest that becoming goo d with LATEX is easy; it isn’t. But esse ntially all computerscience researchers use this program nowadays—and lots of other scientists and non-scientists do,too. If you are or want to be a “serious” academic, you should learn to use LATEX. I wouldsay that it is the program of choice even for your essays in English or GE clas se s—it not justfor typesetting technical stuff. There are numerous good books on LATEX. The “classical” one isLaTeX: A Document Preparation System (2nd edition), by Leslie Lamport. A more recent one isGuide to LaTeX (4th edition), by Kopka and Daly.Problem 6I’m afraid that producing drawings for inclusion into LATEX opens up a can of worms (yum). Ipersonally use xfig, Illustrator, or Visio; others use different tools. Regardless, doing beautifuldrawings takes substantial time and care. I suggest that, if you do want to typeset your homeworksolutions, just do any accompanying drawings in pencil or