more improvements to flow

Author: ChrisMayfield

ch04.tex

@@ -218,26 +218,6 @@ \section{Defining new methods}
 }
 \end{trinket}
 
-Beginners often wonder why it's worth the trouble to write other methods, when they could just do everything in \java{main}.
-The \java{NewLine} example demonstrates a few reasons:
-
-\begin{itemize}
-
-\item Creating a new method allows you to {\em name a block of statements}, which makes the code easier to read and understand.
-%Methods simplify a program by hiding complex computations behind a single statement, and by using English words in place of arcane code.
-%Which is clearer, \java{newLine} or \java{System.out.println()}?
-
-\item Introducing new methods can {\em make the program shorter} by eliminating repetitive code.
-For example, to display nine consecutive newlines, you could invoke \java{threeLine} three times.
-
-\item A common problem-solving technique is to {\em break problems down} into sub-problems.
-Methods allow you to focus on each sub-problem in isolation, and then compose them into a complete solution.
-
-\end{itemize}
-
-Perhaps most importantly, organizing your code into multiple methods allows you to test individual parts of your program separately.
-It's easier to get a complex program working if you know that each method works correctly.
-
 
 \section{Flow of execution}
 
@@ -266,6 +246,26 @@ \section{Flow of execution}
 %Instead, execution picks up where it left off in the program that invoked \java{main}, which is the Java interpreter.
 %The interpreter takes care of things like deleting windows and general cleanup, and {\em then} the program terminates.
 
+Beginners often wonder why it's worth the trouble to write other methods, when they could just do everything in \java{main}.
+The \java{NewLine} example demonstrates a few reasons:
+
+\begin{itemize}
+
+\item Creating a new method allows you to {\em name a block of statements}, which makes the code easier to read and understand.
+%Methods simplify a program by hiding complex computations behind a single statement, and by using English words in place of arcane code.
+%Which is clearer, \java{newLine} or \java{System.out.println()}?
+
+\item Introducing new methods can {\em make the program shorter} by eliminating repetitive code.
+For example, to display nine consecutive newlines, you could invoke \java{threeLine} three times.
+
+\item A common problem-solving technique is to {\em break problems down} into sub-problems.
+Methods allow you to focus on each sub-problem in isolation, and then compose them into a complete solution.
+
+\end{itemize}
+
+Perhaps most importantly, organizing your code into multiple methods allows you to test individual parts of your program separately.
+It's easier to get a complex program working if you know that each method works correctly.
+
 
 \section{Parameters and arguments}
 

ch05.tex

@@ -47,18 +47,18 @@ \section{Relational operators}
 When comparing values of different numeric types, Java applies the same conversion rules we saw previously with the assignment operator.
 For example, when evaluating the expression \java{5 < 6.0}, Java automatically converts the \java{5} to \java{5.0}.
 
-Most relational operators don't work with strings.
-But confusingly, \java{==} and \java{!=} \emph{seem} to work with strings -- they just don't do what you expect.
-We'll explain what they do later, but in the meantime, don't use them with strings.
-Instead, you should use the \java{equals} method:
-
-\begin{code}
-String fruit1 = "Apple";
-String fruit2 = "Orange";
-System.out.println(fruit1.equals(fruit2));
-\end{code}
-
-The result of \java{fruit1.equals(fruit2)} is the boolean value \java{false}.
+%Most relational operators don't work with strings.
+%But confusingly, \java{==} and \java{!=} \emph{seem} to work with strings -- they just don't do what you expect.
+%We'll explain what they do later, but in the meantime, don't use them with strings.
+%Instead, you should use the \java{equals} method:
+%
+%\begin{code}
+%String fruit1 = "Apple";
+%String fruit2 = "Orange";
+%System.out.println(fruit1.equals(fruit2));
+%\end{code}
+%
+%The result of \java{fruit1.equals(fruit2)} is the boolean value \java{false}.
 
 
 \section{The if-else statement}

ch08.tex

@@ -286,17 +286,20 @@ \section{The leap of faith}
 When you invoke \java{Math.cos} or \java{System.out.println}, you don't examine or think about the implementations of those methods.
 You just assume that they work properly.
 
-For example, this method (from Section~\ref{boolmeth}) determines whether an integer has only one digit.
-Once you convince yourself that this method is correct -- by testing and examination of the code -- you can use the method without ever looking at the implementation again.
+The same is true of other methods.
+For example, consider the method from Section~\ref{boolmeth} that determines whether an integer has only one digit:
 
 \begin{code}
 public static boolean isSingleDigit(int x) {
     return x > -10 && x < 10;
 }
 \end{code}
 
-The same is true of recursive methods.
-When you get to the recursive call, instead of following the flow of execution you should {\em assume} that the recursive invocation works.
+Once you convince yourself that this method is correct -- by examining and testing the code -- you can just use the method without ever looking at the implementation again.
+
+Recursive methods are no different.
+When you get to a recursive call, don't try to follow the flow of execution.
+Instead, you should {\em assume} that the recursive call produces the desired result.
 
 For example, ``Assuming that I can find the factorial of $n-1$, can I compute the factorial of $n$?''
 Yes you can, by multiplying by $n$.
@@ -322,7 +325,7 @@ \section{The leap of faith}
 But that's why it's called the leap of faith!
 
 
-\section{Fibonacci sequence}
+%\section{Fibonacci sequence}
 \label{fibonacci}
 
 \index{fibonacci}
@@ -696,6 +699,15 @@ \section{Exercises}
 \end{exercise}
 
 
+\begin{exercise}  %%V6 Ex6.7
+
+Write a recursive method named \java{oddSum} that takes a positive odd integer \java{n} and returns the sum of odd integers from 1 to n.
+Start with a base case, and use temporary variables to debug your solution.
+You might find it helpful to print the value of \java{n} each time \java{oddSum} is invoked.
+
+\end{exercise}
+
+
 \begin{exercise}  %%V6 Ex6.6
 
 In this exercise, you will use a stack diagram to understand the execution of the following recursive method.
@@ -733,15 +745,6 @@ \section{Exercises}
 \end{exercise}
 
 
-\begin{exercise}  %%V6 Ex6.7
-
-Write a recursive method named \java{oddSum} that takes a positive odd integer \java{n} and returns the sum of odd integers from 1 to n.
-Start with a base case, and use temporary variables to debug your solution.
-You might find it helpful to print the value of \java{n} each time \java{oddSum} is invoked.
-
-\end{exercise}
-
-
 \begin{exercise}  %%V6 Ex6.8
 
 The goal of this exercise is to translate a recursive definition into a Java method.
@@ -805,6 +808,7 @@ \section{Exercises}
 \end{exercise}
 
 
+\newpage
 \begin{exercise}  %%V6 Ex9.4
 
 Create a program called {\tt Recurse.java} and type in the following methods: