New exercises/problems strucutre

.gitignore

@@ -1,3 +1,6 @@
+# ans/sol'ns temp files
+99anssol/
+
 ## Core latex/pdflatex auxiliary files:
 *.aux
 *.lof

02_linear_algebra.tex

@@ -0,0 +1,89 @@
+%!TEX root = all_exercises.tex
+\beforeFirstExercises{ch2}
+
+exercises (if any) for each section would go here... see sample in ch3
+
+\afterLastExercises{ch2}
+
+
+\setcounter{section}{12}
+\section{Linear Algebra Problem}
+
+\begin{problems}{ch2}
+
+
+	\begin{problem}
+		The expression $\alpha \vu$ for $\alpha \in \R$ and
+		unit vector $\vu \in \R^n$ defines a line of points that may be obtained by varying the
+		value of $\alpha$.
+		Derive an expression for the point $\vy$ that lies on this line that is
+		as close as possible to an arbitrary point $\vx \in \R^n$.
+		This operation of replacing a point by its nearest member within some set
+		is called {\em projection}.
+
+		{\em Exercise contributed by Ian Goodfellow}
+
+		\begin{solution}
+			We begin by defining the distance from $\vy$ to $\vx$.
+			We would like to find the $\vy$ that minimizes this distance:
+			\begin{equation}
+			|| \vx - \vy||^2.
+			\end{equation}
+			Next, we need to enforce the constraint that $\vy$ lies on the line defined by $\alpha \vu$.
+			We can do this simply by defining $\vy$ to be $\alpha \vu$.
+			\begin{equation}
+			|| \vx - \alpha \vu ||^2.
+			\end{equation}
+			Next, we expand the expression:
+			\begin{align}
+			& || \vx - \alpha \vu ||^2 \\
+			=& ( \vx - \alpha \vu )^\top (\vx - \alpha \vu) \\
+			=& \vx^\top \vx - 2 \alpha \vx^\top \vu + \alpha^2 \vu^\top \vu \\
+			=& \vx^\top \vx - 2 \alpha \vx^\top \vu + \alpha^2.
+			\end{align}
+			In the last line,
+			we used the fact that $\vu$ is a unit vector to make the simplification $\vu^\top \vu = 1$.
+
+			We can minimize this distance by taking the derivative with respect to $\alpha$ and setting it to zero:
+			\begin{align}
+			& - 2  \vx^\top \vu + 2 \alpha = 0 \\
+			\Rightarrow & \alpha = \vx\top \vu.
+			\end{align}
+
+			Recalling that $\vy = \alpha \vu$, we can conclude that $\vy = \vx^\top \vu \vu$.
+
+			{\em Solution contributed by Ian Goodfellow}
+		\end{solution}
+	\end{problem}
+
+
+	\begin{problem}
+
+		\begin{hint}
+		\end{hint}
+
+		\begin{answer}\end{answer}
+
+		\begin{solution}
+		\end{solution}
+	\end{problem}
+
+
+
+	\begin{problem}
+
+		\begin{hint}
+		\end{hint}
+
+		\begin{answer}\end{answer}
+
+		\begin{solution}
+		\end{solution}
+	\end{problem}
+
+
+
+
+\end{problems}
+
+

03_prob_and_info_theory.tex

@@ -0,0 +1,95 @@
+%!TEX root = all_exercises.tex
+
+\beforeFirstExercises{ch3}
+\section{Why Probability?}
+
+add exercises here...
+
+\section{Random Variables}
+
+\begin{exercises}{ch3}
+
+	\begin{exercise} 
+		EXRCIS  QUESTION
+
+		\begin{eanswer}EXRCIS  ANS\end{eanswer}
+		\begin{esolution}
+			EXRCIS SOLUTION.
+		\end{esolution}
+	\end{exercise}
+
+
+\end{exercises}
+
+\section{Probability Distributions}
+
+\begin{exercises}{ch3}
+
+	\begin{exercise} 
+		Do the following vectors represent probability distributions?
+		\begin{exparts*}
+			\partsitem	$\left(\tfrac{1}{2}, \tfrac{1}{2}, \tfrac{1}{2} \right)^T$
+			\partsitem	$\left(\tfrac{1}{4}, \tfrac{1}{4}, \tfrac{1}{4}, \tfrac{1}{4} \right)^T$
+			\partsitem	$\left(0.3, 0.3, -0.1, 0.5  \right)^T$
+		\end{exparts*}
+
+		\begin{eanswer}\begin{ansparts*}
+					\partsitem No; weights don't add to one.
+					\partsitem Yes.
+					\partsitem No; contains a negative number.
+					\end{ansparts*}\end{eanswer}
+	\end{exercise}
+
+
+\end{exercises}
+
+
+
+
+
+
+\setcounter{section}{13}
+\section{Structured Probabilistic Models}
+
+add exercises here...
+
+
+\afterLastExercises{ch3}
+
+
+
+\setcounter{section}{14}
+\section{Probability and Information Theory Problems}
+
+\begin{problems}{ch3}
+
+
+	\begin{problem}		\label{problem:geometric_distr_biased_coin_until_heads}
+		You have a biased coin which lands on \texttt{heads} with probability $p$,
+		and consequently lands on \texttt{tails} with probability $(1-p)$.
+		Suppose you want to flip the coin until you get \texttt{heads}.
+		Define the random variable $N$ as the number of tosses required until the first \texttt{heads} outcome.
+		What is the probability mass function $P_N(n)$ for success on the $n$\textsuperscript{th} toss?
+		Confirm that the formula is a valid probability distribution by showing $\sum_{n=1}^\infty P_N(n) = 1$.
+
+		\begin{hint}
+			Find the probabilities for cases $n=1,2,3,\ldots$ and look for a pattern.
+		\end{hint}
+
+		\begin{solution}
+			The biased coin flip is modelled by a random variable $Y$,
+			and different coin flips correspond to random variables $Y_1$, $Y_2$, $Y_3$, \ldots which are independent copies of $Y$.
+			The probability of getting \texttt{heads} on the first flip is $P_N(1)=\textrm{Pr}\!\left( \{ Y_1=\texttt{heads} \} \right)\! =p$.
+			The probability of getting \texttt{heads} on the second flip corresponds
+			to the event $\{Y_1=\texttt{tails}\} \ \texttt{AND} \ \{Y_2=\texttt{heads} \}$.
+			We assumed the coin flips are independent so % the probability of this event is the product
+			$P_N(2)=(1-p)p$.
+			Similarly $P_N(3) = (1-p)^2p$.
+			The general formula is $P_N(n) = (1-p)^{n-1}p$.
+		\end{solution}
+	\end{problem}
+
+
+\end{problems}
+
+

README.md

@@ -1,2 +1,39 @@
 # dlbook_exercises
 Exercises for the Deep Learning textbook at www.deeplearningbook.org
+
+
+Definitions
+-----------
+  - Exercise = easy question with numbering contiguous throughout chapter e.g. E{chapter}.{counter}
+  - Problem = harder end-of-chapter problem 
+
+
+Exercise formatting
+-------------------
+
+  - each exercise section starts an `{exercises}{CHNUM}` where CHNUM is some filename  (e.g. ch2)
+  - each exercise envoronment contains
+    - question text
+    - one or more {hint} environments
+    - an {eanswer} environment (optional)
+    - an {esolution} environment (optional)
+
+
+Problems formatting
+-------------------
+
+  - each problems section starts an `{problems}{CHNUM}` where CHNUM is some filename  (e.g. ch2)
+  - each problem environment contains
+    - question text
+    - one or more {hint} environments
+    - an {answer} environment (optional)
+    - an {solution} environment (optional)
+
+
+
+Credits
+-------
+Ian Goodfellow -- author
+Andrew D. Hwang -- tex macros, via http://www.gutenberg.org/ebooks/33283
+Jim Hefferon -- tex macros, via http://joshua.smcvt.edu/linearalgebra/ 
+Ivan Savov -- copy paste

all_exercises.tex

@@ -0,0 +1,101 @@
+\documentclass[letterpaper,oneside]{book}
+\title{Exercises for the Deep Learning Textbook}
+
+\usepackage{bm}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amsthm}
+
+
+\newif\ifMIT
+%\MITtrue % uncomment to use MIT template
+\MITfalse
+\input{math_commands.tex}
+
+
+\newif\ifSOLSINTHEBACK
+%\SOLSINTHEBACKtrue    % uncomment to for final version (include files in 99ans/ in Answers/Sol'ns Appendix)
+\SOLSINTHEBACKfalse
+\ifSOLSINTHEBACK
+    \usepackage{answers}              %  for solutions in the back
+\else
+    \usepackage[nosolutionfiles]{answers}       % use when proofreading
+\fi
+\input{exercises_commands.tex}
+
+
+
+
+\begin{document}
+\maketitle
+
+
+\part{Applied Math and Machine Learning Basics}
+
+	\setcounter{chapter}{1}
+	\chapter{Linear Algebra}
+	\input{02_linear_algebra.tex}
+
+
+	\chapter{Probability and InformationTheory}
+	\input{03_prob_and_info_theory.tex}
+
+	% continue with other chapters here...
+
+
+
+
+\appendix 
+
+
+
+\ifSOLSINTHEBACK
+
+	\chapter{Answers and solutions}
+
+	\section*{Chapter 2 solutions}
+	\label{sec:chapter2sols}	
+	{ \footnotesize 
+
+		%		\subsection*{Answers to exercises}
+		%		\showExerciseAnswers{ch2}
+		%
+		%		\subsection*{Solutions to selected exercises}
+		%		\showExerciseSolutions{ch2}
+
+		\subsection*{Answers to problems}
+		\showProblemAnswers{ch2}
+
+		\subsection*{Solutions to selected problems}
+		\showProblemSolutions{ch2}
+
+	}
+
+
+	\section*{Chapter 3 solutions}
+	\label{sec:chapter3sols}	
+	{ \footnotesize 
+
+		\subsection*{Answers to exercises}
+		\showExerciseAnswers{ch3}
+
+		\subsection*{Solutions to selected exercises}
+		\showExerciseSolutions{ch3}
+
+		\subsection*{Answers to problems}
+		\showProblemAnswers{ch3}
+
+		\subsection*{Solutions to selected problems}
+		\showProblemSolutions{ch3}
+
+	}
+
+
+
+\else
+	% NO SOLUTIONS IN THE BACK (shown inline for proofreading)
+\fi
+
+
+
+\end{document}