diff --git a/book/book.tex b/book/book.tex
index e7d2326..56dfaee 100644
--- a/book/book.tex
+++ b/book/book.tex
@@ -1961,7 +1961,7 @@ \section{Function calls}
 
 \section{Math functions}
 \index{math function}
-\index{function, math}
+\index{function!math}
 
 Python has a math module that provides most of the familiar
 mathematical functions.  A {\bf module} is a file that contains a
@@ -2007,7 +2007,7 @@ \section{Math functions}
 \index{sine function}
 \index{radian}
 \index{trigonometric function}
-\index{function, trigonometric}
+\index{function!trigonometric}
 
 The second example finds the sine of {\tt radians}.  The variable name {\tt radians} is a hint that {\tt sin} and the other trigonometric
 functions ({\tt cos}, {\tt tan}, etc.)  take arguments in radians. To
@@ -2028,7 +2028,7 @@ \section{Math functions}
 
 If you know
 trigonometry, you can check the previous result by comparing it to
-the square root of two divided by two:
+the square root of two, divided by two:
 \index{sqrt function}
 \index{function!sqrt}
 
@@ -2454,8 +2454,8 @@ \section{Stack diagrams}
 \section{Fruitful functions and void functions}
 \index{fruitful function}
 \index{void function}
-\index{function, fruitful}
-\index{function, void} 
+\index{function!fruitful}
+\index{function!void} 
 
 Some of the functions we have used, such as the math functions, return
 results; for lack of a better name, I call them {\bf fruitful
@@ -2522,7 +2522,7 @@ \section{Fruitful functions and void functions}
 
 
 \section{Why functions?}
-\index{function, reasons for}
+\index{function!reasons for}
 
 It may not be clear why it is worth the trouble to divide
 a program into functions.  There are several reasons:
@@ -2990,7 +2990,7 @@ \section{Simple repetition}
 
 \section{Exercises}
 
-The following is a series of exercises using TurtleWorld.  They
+The following is a series of exercises using the {\tt turtle} module.  They
 are meant to be fun, but they have a point, too.  While you are
 working on them, think about what the point is.
 
@@ -4375,7 +4375,7 @@ \section{Exercises}
 
 The following exercises use the {\tt turtle} module, described in
 Chapter~\ref{turtlechap}:
-\index{TurtleWorld}
+\index{turtle module}
 
 \begin{exercise}
 
@@ -4617,7 +4617,7 @@ \section{Incremental development}
 %
 I chose these values so that the horizontal distance is 3 and the
 vertical distance is 4; that way, the result is 5, the hypotenuse 
-of a 3-4-5 triangle. When testing a function, it is
+of a 3-4-5 right triangle. When testing a function, it is
 useful to know the right answer.
 \index{testing!knowing the answer}
 
@@ -7402,7 +7402,7 @@ \section{Lists are mutable}
 
 Figure~\ref{fig.liststate} shows 
 the state diagram for {\tt
-cheeses}, {\tt numbers} and {\tt empty}:
+cheeses}, {\tt numbers} and {\tt empty}.
 \index{state diagram}
 \index{diagram!state}
 
@@ -8472,7 +8472,7 @@ \section{Exercises}
 
 \begin{exercise}
 \index{append method}
-\index{method append}
+\index{method!append}
 \index{list!concatenation}
 \index{concatenation!list}
 
@@ -9696,7 +9696,7 @@ \section{Tuples as return values}
 \index{tuple}
 \index{value!tuple}
 \index{return value!tuple}
-\index{function, tuple as return value}
+\index{function!tuple as return value}
 
 Strictly speaking, a function can only return one value, but
 if the value is a tuple, the effect is the same as returning