1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%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}
|
