fix spacing, add details

ch04.tex

@@ -11,7 +11,7 @@ \chapter{Methods and testing}
 
 \section{Math methods}
 
-In the next two sections, we'll take a break from conditions and logic and discuss other areas of mathematics in Java.
+%In the next two sections, we'll take a break from conditions and logic and discuss other areas of mathematics in Java.
 
 \index{Math class}
 \index{class!Math}
@@ -190,10 +190,13 @@ \section{Defining new methods}
 
 Notice the extra space between the lines.
 If we wanted more space between them, we could invoke the same method repeatedly.
-
-%Or we could write yet another method (named \java{threeLine}) that displays three blank lines:
+Or we could write yet another method (named \java{threeLine}) that displays three blank lines.
 %Pulling together the code from the previous section, the complete program looks like this:
 
+In the following program, \java{main} invokes \java{threeLine}, and \java{threeLine} invokes \java{newLine} three times.
+%Since \java{newLine} has no parameters, it requires no arguments, as shown when it is invoked in \java{main}.
+Because \java{newLine} is in the same class as \java{threeLine}, we don't have to specify the class name like \java{NewLine.newLine()}.
+
 \begin{trinket}{NewLine.java}
 public class NewLine {
 
@@ -215,11 +218,7 @@ \section{Defining new methods}
 }
 \end{trinket}
 
-In this example, \java{main} invokes \java{threeLine}, and \java{threeLine} invokes \java{newLine} three times.
-%Since \java{newLine} has no parameters, it requires no arguments, as shown when it is invoked in \java{main}.
-Because \java{newLine} is in the same class as \java{threeLine}, we don't have to specify the class name like \java{NewLine.newLine()}.
-
-Beginners wonder why it's worth the trouble to write other methods, when they could just do everything in \java{main}.
+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}
@@ -790,6 +789,12 @@ \section{Exercises}
 This exercise reviews the flow of execution through a program with multiple methods.
 Read the following code and answer the questions.
 
+\begin{code}
+public static void main(String[] args) {
+    zippo("rattle", 13);
+}
+\end{code}
+
 \begin{code}
 public static void baffle(String blimp) {
     System.out.println(blimp);
@@ -809,12 +814,6 @@ \section{Exercises}
 }
 \end{code}
 
-\begin{code}
-public static void main(String[] args) {
-    zippo("rattle", 13);
-}
-\end{code}
-
 \begin{enumerate}
 
 \item Write the number {\tt 1} next to the first line of code in this program that will execute.

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{!=} do work with strings -- they just don't do what you expect.
-%We'll explain what they do later; 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}
@@ -388,6 +388,7 @@ \section{Boolean variables}
 
 
 \section{Boolean methods}
+\label{boolmeth}
 
 \index{boolean}
 \index{method!boolean}
@@ -450,7 +451,9 @@ \section{Validating input}
 
 One of the most important tasks in any computer program is to {\bf validate} input from the user.
 People often make mistakes while typing, especially on smartphones, and incorrect inputs may cause your program to fail.
+
 Even worse, someone (i.e., a {\bf hacker}) may intentionally try to break into your system by entering unexpected inputs.
+You should never assume that users will input the right kind of data.
 
 Consider this simple program that prompts the user for a number and computes its logarithm:
 

ch08.tex

@@ -286,9 +286,7 @@ \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.
 
-%TODO reference appendix B instead? or use a different example?
-
-For example, this method (from Appendix~\ref{extras}) determines whether an integer has only one digit.
+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.
 
 \begin{code}