%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Tutorial slides on Python.%% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>% Copyright (c) 2005-2009, Prabhu Ramachandran%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\documentclass[14pt,compress]{beamer}%\documentclass[draft]{beamer}%\documentclass[compress,handout]{beamer}%\usepackage{pgfpages} %\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]% Modified from: generic-ornate-15min-45min.de.tex\mode<presentation>{ \usetheme{Warsaw} \useoutertheme{infolines} \setbeamercovered{transparent}}\usepackage[english]{babel}\usepackage[latin1]{inputenc}%\usepackage{times}\usepackage[T1]{fontenc}% Taken from Fernando's slides.\usepackage{ae,aecompl}\usepackage{mathpazo,courier,euler}\usepackage[scaled=.95]{helvet}\definecolor{darkgreen}{rgb}{0,0.5,0}\usepackage{listings}\lstset{language=Python, basicstyle=\ttfamily\bfseries, commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, showstringspaces=false, keywordstyle=\color{blue}\bfseries}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Macros\setbeamercolor{emphbar}{bg=blue!20, fg=black}\newcommand{\emphbar}[1]{\begin{beamercolorbox}[rounded=true]{emphbar} {#1} \end{beamercolorbox}}\newcounter{time}\setcounter{time}{0}\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}\newcommand{\typ}[1]{\texttt{#1}}\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} }%%% This is from Fernando's setup.% \usepackage{color}% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}% % Use and configure listings package for nicely formatted code% \usepackage{listings}% \lstset{% language=Python,% basicstyle=\small\ttfamily,% commentstyle=\ttfamily\color{blue},% stringstyle=\ttfamily\color{orange},% showstringspaces=false,% breaklines=true,% postbreak = \space\dots% }%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Title page\title[Exercises]{Exercises}\author[FOSSEE] {FOSSEE}\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}\date[] {1 May, 2010\\Day 2, Session 5}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}%\logo{\pgfuseimage{iitmlogo}}%% Delete this, if you do not want the table of contents to pop up at%% the beginning of each subsection:\AtBeginSubsection[]{ \begin{frame}<beamer> \frametitle{Outline} \tableofcontents[currentsection,currentsubsection] \end{frame}}% If you wish to uncover everything in a step-wise fashion, uncomment% the following command: %\beamerdefaultoverlayspecification{<+->}%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DOCUMENT STARTS\begin{document}\begin{frame} \titlepage\end{frame}\begin{frame}{Problem 1.1} The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. For example:\\aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.\\ Write a function that returns the aliquot number of a given number. \end{frame}\begin{frame}{Problem 1.2} Pair of numbers (a, b) is said to be \alert{amicable} if aliquot number of a is b and aliquot number of b is a.\\ Example: \texttt{220, 284}\\ Write a program that prints all four digit amicable pairs.\inctime{20}\end{frame}%% \begin{frame}{Problem 2}%% Given an empty chessboard and one Bishop placed in any s%quare, say (r, c), generate the list of all squares the Bi%shop could move to.%% \end{frame}\begin{frame}[fragile] \frametitle{Problem 2} Given a string of numbers like, ``1, 3-7, 12, 15, 18-21'', produce the following list \\ \begin{lstlisting} [1,3,4,5,6,7,12,15,18,19,20,21] \end{lstlisting}\inctime{10}\end{frame}\begin{frame} \frametitle{Problem 3}Given a list of words, find all the anagrams in the list.Solve the problem without using dictionaries.\end{frame}\begin{frame} \frametitle{Problem 4} Count frequencies of words in a file named 'holmes.txt'.\inctime{25}\end{frame}\begin{frame}[fragile] \frametitle{Problem set 4} Central difference \begin{equation*} \frac{sin(x+h)-sin(x-h)}{2h} \end{equation*} \begin{lstlisting} In []: x = linspace(0, 2*pi, 100) In []: y = sin(x) In []: deltax = x[1] - x[0] \end{lstlisting} \pause \begin{enumerate} \item Given this, get the finite difference of sin in the range 0 to 2*pi \end{enumerate}\end{frame}\begin{frame} \frametitle{Problem Set 5} \begin{itemize} \item[5.1] Write a function that plots any regular n-gon given \typ{n}. \item[5.2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for $k=2.5, 3.5$ and $4$ in the same plot.\end{itemize}\end{frame}\begin{frame}[fragile] \frametitle{Problem Set 5} \begin{columns} \column{0.6\textwidth} \small{ \begin{itemize} \item[3] Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) = kx(1-x)$. Plot the successive iterates of this process as explained below. \end{itemize}} \column{0.35\textwidth} \hspace*{-0.5in} \includegraphics[height=1.6in, interpolate=true]{data/cobweb} \end{columns}\end{frame}\begin{frame} \frametitle{Problem Set 5.3} Plot the cobweb plot as follows: \begin{enumerate} \item Start at $(x_0, 0)$ ($\implies$ i=0) \item Draw a line to $(x_i, f(x_i))$ \item Set $x_{i+1} = f(x_i)$ \item Draw a line to $(x_{i+1}, x_{i+1})$ \item $(i\implies i+1)$ \item Repeat from 2 for as long as you want \end{enumerate}\inctime{20}\end{frame}\end{document}